Characteristics of Effective Elementary

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1. Introduction

The aim of mathematics education is multifaceted, reflecting various educational, societal, and personal goals. In general, the development of students’ problem-solving skills, which are necessary for coping with the real world, is the most important goal of mathematics education (OECD, 2023). The overarching goal is to create a mathematically literate population, capable of engaging with the world through a quantitative lens, thus contributing to the personal growth of individuals and the progress of society (Jablonka, 2003; OECD, 2023). To achieve this goal, it is important to focus on the quality of mathematics teaching.

Although teaching is not the only factor that influences students’ learning outcomes, as they are often influenced by socioeconomic factors, quality mathematics education can reduce unequal learning opportunities (Schmidt et al., 2011) if it is based on research-based principles and practices of effective mathematics teaching and learning. These principles and practices provide a comprehensive framework for ensuring that mathematics education is both effective and equitable, fostering not only academic achievement but also a lifelong interest and confidence in mathematics. Several studies elaborate on these principles and practices in detail.

Anthony and Walshaw (2007) conducted a best-evidence synthesis of 660 studies published in New Zealand and similar countries. The aim of this review was to identify and explain the principles that improve mathematics proficiency and reduce inequalities between students of different abilities. The booklet based on the review identified ten principles that can influence student learning (Anthony & Walshaw, 2009). These principles include creating a caring classroom community where students can think independently, ask questions, and take responsibility for their learning. Students are encouraged to learn independently, cooperatively, or through whole-class discussion. Learning mathematics is not seen as merely correcting deficits or filling knowledge gaps but rather as building on what students already know, on their interests and experiences. Common mistakes and misconceptions should not be overlooked as they can contribute to a deeper understanding of mathematical concepts. Working on open-ended problems can stimulate students’ creativity, while math games can improve fluency. Meaningful learning of new concepts or skills involves linking them to other mathematical ideas, different methods of representation, and real-life contexts. Continuous monitoring of student progress and task-oriented feedback are essential to effective math instruction. In elementary mathematics lessons, “students need to be taught how to communicate mathematically, give sound mathematical explanations and justify their solutions” (Anthony & Walshaw, 2009, p. 19). This requires particular attention to the clarity and appropriateness of the language teachers use when explaining mathematical concepts. Effective mathematics teaching is based on the use of appropriate tools, such as representations and manipulatives. Technology plays an important role by providing teachers and students with new ways to explore and represent mathematical concepts. Ultimately, the effectiveness of teaching depends on the teacher’s (pedagogical) content knowledge. Teachers who understand mathematical ideas and know how to teach students can help them develop mathematical understanding.

In the educational context of the United States, the National Council of Teachers of Mathematics (NCTM) first developed standards (NCTM, 2000) and then principles for high-quality mathematics teaching (NCTM, 2014). These principles emphasize high-quality teaching and learning that is accessible to all students, a coherent curriculum, the use of tools and technology to support learning, the integration of assessment into instruction, and teacher professionalism. In terms of effective teaching and learning, the NCTM (2014) identified eight research-based teaching practices. The first emphasizes the alignment of learning objectives to rigorous standards. Students should clearly understand the purpose of the lesson so they can stay motivated and track their own progress. In order to learn mathematics with understanding, students must have the opportunity to solve cognitively demanding tasks. A deeper understanding of mathematical concepts can be promoted by using and linking multiple representations: physical, visual, verbal, contextual, and symbolic. Establishing a culture of discourse that includes whole-class discussion and other forms of communication also improves the quality of mathematics teaching, as do questions that “encourage students to explain and reflect on their thinking” (NCTM, 2014, p. 35). An important element of mathematics instruction is the simultaneous development of conceptual and procedural knowledge. “This approach supports students in developing the ability to understand and explain their use of procedures, to choose flexibly among methods and strategies to solve contextual and mathematical problems, and to produce accurate answers efficiently” (NCTM, 2014, p. 46). To achieve deeper conceptual understanding, it is necessary to support students as they productively struggle with mathematics. To support students’ learning and tailor instruction to their interests and abilities, teachers must continuously and systematically monitor their progress.

As part of a professional development program, Prediger et al. (2022) established five interrelated principles for high-quality mathematics education. The principle of conceptual focus involves learning mathematics with understanding. This means that the development of procedural skills should be based on an understanding of the underlying mathematical concepts. Closely related to conceptual understanding is the principle of cognitive demand, which emphasizes the importance of “higher order mathematical practices such as modeling, arguing, problem solving, generalizing, systematizing, etc.” (p. 7). The next principle consists of two interrelated aspects: student focus and adaptivity. This involves tailoring instruction to students’ interests and individual differences through ongoing formative assessments. The principle of longitudinal coherence is based on the idea of Bruner’s (1977) spiral curriculum, according to which the content of a subject should be organized around interconnected themes that broaden and deepen over time. Finally, encouraging communication between students is crucial for active participation and the articulation of mathematical ideas as it simultaneously fosters the communication skills necessary for mathematical thinking.

The three studies highlight several key principles that are essential for effective mathematics teaching. They emphasize the need for strong conceptual understanding and the development of fluency, both of which can be achieved through cognitively demanding tasks that promote mathematical reasoning. One of the common principles is that students must learn to express mathematical ideas accurately and discuss them with teachers and classmates. It is also important to incorporate different forms of representation and tools, especially modern technologies that can enhance formative assessment. Finally, it emphasizes the need for a coherent spiral curriculum that helps students to continuously broaden and deepen their mathematical understanding.

Recently, several reviews have been published examining different aspects of mathematics education. The systematic review (Schnepel & Aunio, 2022) of 20 studies conducted between 2008 and 2020 aimed to determine the characteristics of effective mathematical interventions for students with intellectual disabilities. Barcelos et al. (2018) conducted a systematic literature review of 42 studies published between 2006 and 2017 that provided evidence of mathematics learning in activities to promote computational thinking skills. The systematic literature review by Svane et al. (2023) analyzed many randomized controlled mathematics interventions published between 2001 and 2021. These interventions were conducted in different educational settings—from early childhood education to high school—and described their main characteristics at each educational level. Putra et al. (2023) analyzed 24 Scopus-indexed articles from 2020 to 2022 that aimed to evaluate the development of students’ mathematical representation skills. The referenced studies did not exclusively target elementary school students, nor did they focus specifically on the characteristics of mathematics instruction in the interventions examined.

There is relatively little research that focuses on elementary school mathematics programs. We found two best-evidence syntheses (Pellegrini et al., 2018; Slavin & Lake, 2008), two meta-analyses (Jacobse & Harskamp, 2011; Pellegrini et al., 2021), and one systematic literature review (Simms et al., 2019). More than 15 years ago, Slavin and Lake (2008) conducted a best-evidence synthesis of 87 studies of elementary school mathematics programs to improve student achievement. The review assessed three main types of interventions: mathematics curricula, computer-assisted instruction (CAI), and instructional process programs. While there is limited evidence for the effectiveness of different mathematics textbooks, moderately positive effects were observed for CAI, and the most significant gains were associated with instructional approaches (e.g., tutoring and cooperative learning).

Ten years later, Pellegrini et al. (2018) conducted a similar study. The study examined 78 high-quality studies, including both randomized and quasi-experimental designs, evaluating 61 programs for grades K–5. The results revealed that the tutoring programs had the greatest positive impact on student outcomes. After tutoring, instructional process programs combined with professional development to help teachers use innovative techniques to organize and manage instruction had the second greatest impact. In contrast, the technology-based interventions, content, and pedagogical professional development had hardly any impact on student outcomes.

Jacobse and Harskamp (2011) conducted a meta-analysis to examine the effects of explicit teaching interventions on the mathematics performance of students in K–6 classes. In particular, the study aimed to determine the overall effects of such interventions and to identify characteristics that moderate these effects, such as teaching methods, duration, and the types of outcome measures used. In addition, the study aimed to investigate the effectiveness of interventions in different mathematical sub-areas. The study examined 40 primary studies published between 2000 and 2010. A total of 69 effect sizes were analyzed, which showed a significant positive average effect (d = 0.58) of these interventions. The study found that there were no significant differences between direct and indirect teaching methods. Domain-specific effects related to different mathematical content areas or subdomains, such as number sense, operations, fractions, measurement, geometry, and word problem solving, can vary across these domains, with certain instructional approaches being more effective in some domains than others. For example, interventions that targeted number sense had a higher average effect size than those that focused on measurement and geometry.

Pellegrini et al. (2021) conducted a meta-analysis of 87 rigorous studies examining 66 elementary school mathematics programs aimed at improving student achievement in grades K–5. The programs were categorized into six groups: tutoring, professional development to improve teachers’ understanding of math content and pedagogy, professional development to improve classroom organization and management, professional development to support the implementation of traditional (non-digital) and digital curricula, and benchmarking to assess student progress. Tutoring programs showed the most significant positive impact (d = 0.20). Professional development programs that focused on the organization and management of instruction (e.g., cooperative learning) also yielded positive results (d = 0.19), while those that focused on teachers’ knowledge of mathematical content and pedagogy and the introduction of new curricula or software, had negligible effects. These studies indicate that strategies focused on engagement, motivation, and personalization produce the best results in elementary school mathematics classrooms, while strategies that focus on textbooks, professional development for mathematics content, and pedagogy have minimal impact on student learning experiences.

In their systematic review, Simms et al. (2019) examined the effectiveness of various instruction-based math interventions in elementary schools. The review included 78 studies covering a wide range of interventions, such as the use of concrete materials, feedback, the use of technology, and different teaching methods. The results suggest that most interventions were effective, although there was considerable variation in the type of intervention, intensity, and quality of the study. Most studies focused on specific outcomes and provided limited evidence on broader pedagogical choices in mathematics education. In addition, this review found no replication studies, which are critical for confirming the reliability of the findings.

Although all the previously mentioned studies aimed to determine the effectiveness of individual elements or the combined effect of elementary mathematics interventions, none of them focused on identifying the presence of specific characteristics of mathematics instruction within the programs analyzed. The researchers broadly defined the main components of the programs without going into detail in describing the interventions. In some cases, these components were predetermined, and the interventions were classified according to the dominant component (Simms et al., 2019). This approach arises from the type of review used in the previous studies, specifically systematic literature reviews, best-evidence syntheses, and meta-analytic studies, but not scoping reviews. While systematic literature reviews, best-evidence syntheses, and meta-analyses aim to answer specific research questions using rigorous methods, scoping reviews are broader in scope and aim to capture the existing literature on a topic (Munn et al., 2018; Sargeant & O’Connor, 2020; Slavin, 1986, 1995). Therefore, we decided to conduct a scoping review to identify the characteristics of teaching that are part of effective mathematics interventions in elementary schools.

Aim and Research Questions

Prediger et al. (2022, p. 2) emphasize that “there is no unique simple way to determine what good teaching is, as instructional quality must be characterized from different perspectives, in particular normative, epistemological, empirical and pragmatic perspectives”. The normative perspective defines what students should learn and how instruction should be conducted. The epistemological perspective is concerned with the core structure and knowledge of mathematics itself. It helps identify the “big ideas” of the subject and the connections between mathematical concepts, ensuring that students experience the authentic essence of mathematics and follow coherent learning pathways. The empirical perspective draws on research evidence and provides data on which teaching methods are effective in improving students’ learning outcomes. Finally, the pragmatic perspective emphasizes practical application in the classroom and acknowledges the challenges teachers face in implementing high-quality instruction. In this review, we focus on the empirical perspective to identify the characteristics of effective interventions in elementary school mathematics education and examine how these characteristics are implemented in classroom practice. To this end, we have posed the following research questions:

RQ1. What are the main characteristics of studies that address effective mathematics interventions in elementary school?

RQ2. What characteristics of mathematics instruction are found in the selected studies?

RQ3. How are the identified characteristics applied in elementary school mathematics teaching?

2. Materials and Methods

To address the research aim and questions posed, we selected a scoping review as a form of knowledge synthesis, which “can clarify key concepts/definitions in the literature and identify key characteristics or factors related to a concept, including those related to methodological research” (Munn et al., 2022, p. 950). In conducting this review, we followed the methodological guidance provided by Peters et al. (2020), which suggests setting the title and research questions, defining inclusion criteria, explaining the search strategy, selecting studies, extracting and analyzing data, and presenting the results.

2.1. Inclusion and Exclusion Criteria

Hadie (2024) points out that inclusion criteria should specify “the types of participants, concepts, contexts, and sources to be considered” (p. 187). In this overview, we focused on elementary school students, which, in many countries, typically includes children aged 7 to 11. However, in some education systems, such as those in the United Kingdom and the Netherlands, elementary school starts earlier, with five-year-old children in first grade. Elementary school can also extend up to the sixth grade, as is the case in Australia, Finland, and the UK, or even up to the eighth grade in the Netherlands, which includes 12-year-old children.

According to Astleitner (2020), educational interventions refer to efforts aimed at overcoming problems in educational contexts and are often integrated into activities such as training, teaching, coaching, or counseling. The focus of this scoping review is on the characteristics of effective interventions in elementary mathematics education. Interventions refer to intentional, targeted efforts designed to improve students’ learning outcomes, conducted in experimental mathematics classrooms. Therefore, all interventions carried out in mathematics classrooms were eligible for inclusion. The effectiveness of these interventions had to be confirmed by the results of the experimental research. In other words, to be included in the review, a positive and statistically significant effect had to be demonstrated. A well-known measure of effect size based on the difference in arithmetic means is Cohen’s d. In this study, Hedges’ g was used, which corresponds to Cohen’s d but with a correction for small sample sizes (Lakens, 2013).

In terms of context, we focused on mathematics interventions delivered in elementary school classrooms, which are typically taught by a single teacher. Elementary school students usually stay in the same classroom with the same group of peers throughout the day. Interventions implemented at preschool, secondary, and higher education levels were excluded. Similarly, we did not include studies conducted in informal or out-of-school contexts (e.g., laboratory), except in cases where math activities were conducted at home but were linked to classroom instruction. Finally, the intervention could have been carried out in any country as long as the research results provided were available in English.

Although a scoping review “can include any literature (e.g., primary studies, systematic reviews, meta-analyses, letters to the editor, guidelines, websites, policy documents)” (Peters et al., 2020, p. 962), we decided to limit the selection to experimental studies that meet a certain level of quality (inclusion criteria no. 4, 5, 6, and 8, as well as the corresponding exclusion criteria). Similar criteria can be found in other studies (Pellegrini et al., 2021; Slavin & Lake, 2008), with the exception of the minimum treatment duration, which was 12 weeks, although we considered the suggestion by Chwo et al. (2018) that eight weeks are enough to avoid the novelty factor (Hawthorne Effect). Finally, all studies in this review were published over a 10-year period (from 2014 to 2023).

2.2. Search Strategy and Selection Studies

To find relevant publications, the first author conducted searches in the following databases: EBSCO, JSTOR, Scopus, ScienceDirect, and Web of Science using the keywords primary, elementary, math*, education, instruction, teaching, lessons, controlled, randomized, trial, experiment, along with the logical operators AND, OR, and NOT. For example, when searching the Web of Science, the following query was used: “ALL = (math* AND (education OR instruction OR teaching) AND (trial OR randomized OR experiment* OR controlled) AND (primary OR elementary)).” To refine the results, we selected the appropriate final publication years, English language, and relevant Web of Science categories (e.g., education, educational research, education scientific disciplines, psychology educational). This search yielded 2130 records, which were exported to an RIS file. Other databases were also searched, and a total of 7019 references were found. To ensure that no studies were overlooked, the first author checked 234 references in Google Scholar and 155 references from two published reviews (Pellegrini et al., 2021; Simms et al., 2019). In the end, 7253 publications were saved using the free application Zotero (Corporation for Digital Scholarship, 2024).

To select the studies, the first and second authors used the online application Rayyan (Ouzzani et al., 2016), which allowed them to identify relevant studies based on titles, abstracts and keywords. This review led to the selection of 423 available reports. In the next stage, the second and third authors reviewed the full papers using inclusion and exclusion criteria (Table 1) and excluded 387 studies. The first author screened 155 references included in the published reviews and excluded 147 articles, mainly based on criteria related to year of publication and negative or statistically non-significant effect sizes. As shown in Figure A1 (Appendix A), this process resulted in 44 reports that met all criteria. Of these 44 reports, 36 were found through database searches, while eight reports were from other reviews (Pellegrini et al., 2021; Simms et al., 2019).

Table A1 (Appendix B) lists the selected works. For each intervention, in addition to the reference, name, and aim of the program, information on the duration and country of the intervention is included. If the country in which the intervention was conducted participated in the TIMSS study, the average math performance of fourth graders is given in parentheses next to the country name. For India and the Palestinian Territories, only data from the PISA study were available, while Kenya and Malawi did not participate in these international studies. However, the human development index (HDI) values for both countries are below the global average (UNDP, 2024). The last column of Table A1 (Appendix B) contains information about the sample, the type of experimental study (quasi-experiment or randomized controlled trial [RCT]) and the research instrument used (standardized or developed by the researchers). For each study, the measured effect size is compared with the minimum detectable effect size (MDES). It was calculated using a sensitivity power analysis (Bartlett & Charles, 2022; Faul et al., 2007; Perugini et al., 2018) in the program G*Power—Version 3.1.9.7 (Heinrich-Heine-Hochschule Düsseldorf, 2020), which provided us with the effect sizes that would be detectable in each study at a significance level of α = 0.05, with power = 0.80, and taking into account the sample size. The statistical significance of the effect size of the intervention (p) is given in parentheses. All numerical values are rounded to two decimal places. If a study reported multiple effect sizes—e.g., across different years or for different mathematical topics—we combined these into a single effect size. We also calculated combined effect sizes for different characteristics of the studies. The combined effect size $(g_{c o m b i n e d})$ represents a weighted average of the individual effect sizes and is calculated using the following formula:

$g_{combined} = \frac{\sum_{i = 1}^{k} w_{i} d_{i}}{\sum_{i = 1}^{k} w_{i}}$

This formula sums the product of the weight of each study and the effect size and then divides it by the total sum of the weights, where k is the number of groups and $w_{i}$ is the inverse of the variance $v_{i}$ calculated for the effect size $g$ :

$w_{i} = \frac{1}{v_{i}}$

Borenstein et al. (2021) emphasize that the fixed-effect model works under the assumption that the true effect size is identical in each study analyzed. In this approach, the combined effect is considered the best estimate of this common effect size.

2.3. Extracting and Analyzing Data

All references for the included studies were transferred from Zotero to the online application EPPI Reviewer 6 (EPPI Centre, 2024), along with the PDF files of the reports. If an intervention description in a report was brief, and we found a document with a more detailed description, we also included this in the analysis. For example, for the Go Math! and Math in Focus interventions, we found detailed descriptions of these programs (HMH, 2020, 2023) in addition to the research reports (Eddy et al., 2014; Jaciw et al., 2016).

The first and second authors conducted a qualitative analysis of the intervention descriptions using the EPPI Reviewer application to identify the characteristics on which they were based. We did not determine the characteristics in advance but identified and coded them inductively during the analysis. According to Miles et al. (2014), inductive coding refers to codes that gradually emerge during data collection. This type of coding is more exploratory and allows the researcher to uncover certain patterns and characteristics within the data. This approach is in line with the definition of a scoping review, which states that “scoping reviews can clarify key concepts/definitions in the literature and identify key characteristics or factors related to a concept” (Munn et al., 2022). This also supports our aim of identifying the characteristics of effective interventions in elementary school mathematics lessons. The characteristics that we attempted to identify in the descriptions of the interventions served as codes for the qualitative analysis. As inductive coding resulted in 27 characteristics, it was necessary to cluster them. Miles et al. (2014) emphasize that clustering can improve the understanding of a phenomenon by linking codes with similar patterns or meanings. However, the clusters can sometimes overlap and are not always mutually exclusive. Clustering is an attempt to categorize elements that seem to fit together and can also be seen as a way to reach a higher level of abstraction. We called these clusters themes.

3. Results and Discussion

The structure of this chapter is aligned with the research questions. First, we listed the characteristics of the studies included in this review, followed by the characteristics of mathematics teaching found in these studies. Finally, we indicated how these characteristics were applied in elementary school mathematics teaching. The chapter on mathematics teaching is divided into subchapters corresponding to the themes listed in Table 2.

3.1. What Are the Main Characteristics of Studies That Address Effective Mathematics Interventions in Elementary School?

The articles included in the review refer to interventions conducted in various parts of the world (Figure 1). Most interventions were carried out in Europe (18), followed by North America (14), Asia (8), Africa (2), Australia (1), and South America (1). Among individual countries, most studies were conducted in the USA (11), the Netherlands (5), and the UK (3). Two studies each were conducted in Canada, Finland, India, Serbia, and Sweden. One study was conducted in 15 different countries (Figure 1).

Most interventions were carried out in developed countries (32), followed by developing countries (11). Only one study was conducted in the least developed country (Malawi). Based on the results of international assessments such as TIMSS and PISA, most interventions (35) were conducted in countries with above-average performance, while nine were implemented in countries with below-average performance. This group of underperforming countries includes Kenya and Malawi, classified as such based on their HDI scores. In our study, the difference between the average effect sizes of studies conducted in countries with higher educational standards compared to other countries was small (g = 0.31 vs. g = 0.36, respectively). This is not consistent with the assumption that “if education in a particular context is already of a high standard, it may be more difficult to achieve large effect sizes (ceiling effect) than in educational systems with more room for improvement” (Bakker et al., 2019, p. 5). In other words, it can be assumed that even in developed countries, the mathematics performance of elementary school students can be improved. Cheung and Slavin (2016), analyzed 645 studies conducted to determine the effectiveness of programs in reading, mathematics, or science. They found that the instruments developed by the researchers, sample size, and randomized versus quasi-experimental designs had a strong and significant impact on effect sizes. It was found that quasi-experimental studies result in larger effect sizes than RCT designs. Additionally, studies using standardized instruments, especially in combination with a randomized design, on average yield smaller effect sizes than those using researcher-made instruments. Similarly, studies with smaller sample sizes (n < 100) yield 3.5 times larger effect sizes than those with larger samples. A comparison between studies with 250 or more participants and those with smaller samples also shows that with a smaller sample size, nearly twice the effect size can be expected.

In terms of study type, this review included slightly more quasi-experiments (n = 23) than RCTs (n = 21). It was found that the average effect size was larger in quasi-experiments (g = 0.38) than in RCTs (g = 0.29). The difference was even greater between RCT studies that used standardized tests (n = 16) and other studies (n = 28) (g = 0.24 vs. g = 0.43, respectively). In half of the studies (n = 22), standardized instruments were used, measuring an average effect size of 0.25. In the remaining studies (n = 22), researcher-made instruments were used, for which the average effect size was 0.51. It is important to note that 95% of the studies (n = 40) were conducted with a sample size of more than 100 students, while 30 studies (71%) had a sample size greater than 250 students. In those studies, the average effect size was 0.30, while in the remaining 14 studies, an average effect size of 0.58 was found. These results are consistent with other research (Bakker et al., 2019; Cheung & Slavin, 2016; Lipsey et al., 2012), which identified similar ratios of average effect sizes that vary according to study type, measurement instrument, and sample size.

When comparing the measured effect size with the MDES, we found that in 35 (83%) studies, the observed effect size was larger than the effect size calculated based on the sensitivity analysis. This indicates that the effect sizes in these studies were more than sufficient to detect the observed effects. A measured effect size larger than the minimum effect size also has practical significance, suggesting that the effect may not only be statistically significant but also meaningful in practice. In the studies with an effect size above the MDES, the average effect size was 0.37, while it was 0.31 for all studies included in the review.

The interventions were conducted in elementary schools, from 1st to 6th grade (Figure 2). Most interventions were conducted in the second grade (n = 20) and the fewest in the sixth grade (n = 4). The reason why the sixth grade was the least represented can be found in the fact that in most countries, elementary education does not last for six years.

3.2. What Characteristics of Mathematics Instruction Are Found in the Selected Studies?

Based on the qualitative analysis of the descriptions of the interventions included in this review, we identified 27 characteristics of mathematics teaching. In each analyzed intervention, several characteristics were identified. Only one study (Al-Mashaqbeh, 2016) was based on a single characteristic (using technology), while two interventions (Eddy et al., 2014; Jaciw et al., 2016) included all characteristics. We calculated that the analyzed studies had, on average, seven characteristics, which highlights the importance of multi-component interventions in elementary mathematics teaching. This is consistent with other research that also emphasizes the importance of multi-component interventions (Hull et al., 2018; Snilstveit et al., 2015). This differs from the findings of Simms et al. (2019), who, in their systematic review, found that 17 studies were “focused on the delivery context of mathematical instruction”, of which “three studies undertook different pedagogical approaches to delivering mathematical content” (pp. 18–19). The reason for this difference could lie in the way the interventions were categorized. The authors of the systematic review classified studies as “belonging to a subtheme” (p. 12), while we attempted to determine all the characteristics used in the interventions.

Table 2

A list of characteristics identified and categorized in effective interventions for elementary mathematics teaching.

Theme	Characteristic	Characteristic Count	Theme Count
Use of digital technology and non-digital teaching materials	Using digital technology in mathematics learning	21	30
	Teaching materials	12	30
Cognitive engagement, conceptual understanding, and procedural fluency	Reasoning and problem-solving	26	29
	Procedural and conceptual knowledge	15
	Realistic mathematics education	9
Monitoring students’ progress and adaptivity	Feedback and formative assessment	23	29
	Differentiation and individualization	19
	Incremental progression	10
	Using students’ prior knowledge	9
	Scaffolding	7
Active learning and educational games	Active learning	17	26
Active learning and educational games	Educational games	17	26
Social forms of learning	Cooperative learning	17	19
	Frontal instruction	11
	Individual practice	7
Connecting mathematical representations to enable abstract thinking	Manipulatives and visualizations	18	19
	Multiple representations	7
	From concrete to abstract	6
Mathematical communication	Mathematical discussions	11	13
Mathematical communication	Questioning	6	13
Metacognition	Metacognitive strategies	12	13
	Goal setting	6
	Analyzing students’ errors	2
	Critical thinking	2
Curriculum	Integrated curriculum	7	10
	New curriculum	4
	Big ideas	4

We categorized the characteristics into nine themes (Table 2). Unlike the characteristics, which were inductively identified from the descriptions of the interventions, the themes resulted from our effort to connect them into meaningful clusters, while being aware that this could have been carried out differently.

3.3. How Are the Identified Characteristics Applied in Elementary School Mathematics Teaching?

In the final research question, we focused on the ways in which the identified characteristics were implemented in practice. Given the larger number of characteristics, we organized the review according to the nine themes listed in Table 2. The number of studies in which we identified specific themes was usually smaller than the total number of interventions associated with the corresponding characteristics, as multiple characteristics could often be identified within a single study.

3.3.1. Use of Digital Technology and Non-Digital Teaching Materials

The use of digital technology in conjunction with various forms of teaching and learning materials was the most prominent theme in the interventions analyzed (30). This refers to the technology used in 21 studies. Both features were combined with other themes and features. For example, cognitive tasks or visualizations can be included in digital applications as well as in textbooks or workbooks. Although Pellegrini et al. (2018, 2021) found that technology-based interventions had minimal impact on student outcomes, digital technology appears to be more effective when combined with other characteristics of effective mathematics instruction.

The use of digital technology ranges from simple exercises for practicing procedural fluency in addition and subtraction (e.g., Al-Mashaqbeh, 2016; Hassler Hallstedt et al., 2018; Pitchford, 2015) to complex applications for developing advanced skills (e.g., Yeh et al., 2019). Considering the complexity and innovation, the two-player game that includes a teachable agent option should be emphasized (Pareto, 2014). The agent can be taught, or it can learn independently by monitoring the outcomes of the student’s decisions during the game. The questions encourage students to understand the rules and teach the agent to make good decisions. Bakker et al. (2015) emphasize the positive effects of mini-games on the automation of multiplicative operation skills, especially when “mini-games were played at home and debriefed at school” (p. 66). Gamification has been shown to effectively motivate students by providing interactive opportunities that progressively lead students from simpler to more complex mathematical challenges (Christopoulos et al., 2020).

Formative assessment tools such as Snappet (Faber et al., 2017) and adaptive platforms such as IXL Math (Bashkov, 2021) enabled monitoring and formative assessment. This made it possible to adapt the level of difficulty of the tasks and teaching activities to the abilities of the individual students and the class as a whole. For example, the ContectaIdeas platform has an option for an automatic early warning system that recognizes students who are having difficulty solving tasks. Teachers can help these students by assigning them to peers who have proven to be successful. In addition, this system also “detects if there are exercises that are proving difficult for the whole class. Permitting teachers and lab coordinators to freeze the system and explain the necessary concepts” (Araya & Diaz, 2020, p. 4).

However, the use of technology can be challenging at first. Motteram et al. (2016) found that “the main challenges raised by teachers in relation to the use of technology and iPads were in terms of: technological challenges such as internet connection, breaking down, passwords not working; number of iPads per group of learners, limitations of the software; possibly diverting attention away from the quality of reflections” (p. 32).

Previous research on the effectiveness of technology use on mathematics achievement is inconsistent. In meta-analytic studies, Li and Ma (2010) found a mean weighted effect size of 0.28, Cheung and Slavin (2013) determined an effect size of 0.16, Higgins et al. (2019) reported a mean weighted Cohen’s d of 0.68, while Pellegrini et al. (2018, 2021) concluded that technology-based interventions had minimal impact on student outcomes. Based on such results, it is difficult to determine the extent to which technology is effective in mathematics education. Furthermore, it can be assumed that other factors in addition to technology influence the outcomes of mathematics instruction. Li and Ma (2010) found that this applies to the use of technology in special education. They also found that “the method of teaching showed a magnitude of 0.79 SD in favor of using technology in school settings where teachers practiced a constructivist approach to teaching over school settings where teachers practiced a traditional approach to teaching” (p. 230). In our study, technology was combined with other characteristics of effective interventions. It appears that digital technology is more effective when combined with other features of effective mathematics instruction. It is therefore important to ensure that technology is used in elementary mathematics education in a way that also takes into account other features such as (meta)cognitive engagement, conceptual understanding, procedural fluency, and formative assessment.

The introduction of non-digital materials could also contribute to the efficiency of mathematics teaching. This refers to textbooks and workbooks that are aligned with existing (Hall et al., 2022; McNeil et al., 2015) or new curricula (Jaciw et al., 2016; Lindorff et al., 2019). These learning materials contain essential elements of a particular intervention. For example, the Modified Arithmetic Practice intervention workbooks contained primarily mathematical expressions with “operations on the right side of the equal sign (e.g., __ = 4 + 3, 7 = __ + 3, 12 = 8 + 4)” (McNeil et al., 2015, p. 427). Textbooks in programs based on the Singapore approach (Jaciw et al., 2016; Lindorff et al., 2019) encourage students to solve problems in multiple steps and include illustrations showing how to solve them in different ways (HMH, 2023). In addition, several interventions (Have et al., 2018; Piper et al., 2016; Sharma & Singh, 2019) have used teacher guides that aim to inspire or teach teachers how to use learning materials and conduct classroom activities.

In summary, the use of digital technology and non-digital materials in mathematics education offers opportunities to improve teaching practices and enhance student learning. By providing simple tasks with continuous progress monitoring and immediate feedback, students can not only improve their numeracy skills (through practice) but also learn how to solve problems and develop conceptual understanding and metacognitive strategies. Digital tools and non-digital teaching materials can help cater to students’ individual interests and abilities and support teachers in designing effective lessons. However, their effectiveness depends largely on how well they are combined with traditional teaching methods and curriculum objectives.

3.3.2. Cognitive Engagement and Conceptual Understanding

Problem solving is a central component of this theme. According to NCTM (2000, p. 52), “problem solving means engaging in a task for which the solution method is not known in advance”. It is based on non-routine tasks that encourage students to approach them creatively, utilizing higher-order thinking skills (Eddy et al., 2014). Cognitive engagement in mathematics lessons, as detailed in the analyzed interventions, was conducted through various approaches.

In mathematics education, procedural and conceptual knowledge are often linked to ensure that students not only master the ability to perform operations (procedural fluency) but also develop a deep understanding of underlying mathematical concepts (Hakim & Yasmadi, 2021; Rittle-Johnson, 2019). The Math in Focus program encourages students “to gain a deep understanding of concepts through exploration, discussion, and reflection” (HMH, 2020, p. 33). In contrast, the Primary Math and Reading program (Piper et al., 2016) achieves this through teacher modeling of concepts so that students can practice with or without teacher guidance. In the Math Island intervention (Yeh et al., 2019), interactive exercises and videos were used to promote conceptual understanding, while the GO Math! program recommends that “students may use the consumable workbooks to connect vocabulary to concepts as well as write notes regarding new words in places that make sense to them” (Eddy et al., 2014, p. 9).

Fischer et al. (2019) note a common misconception in elementary school mathematics related to students’ interpretation of the equal sign, which is often seen as an operational symbol rather than a relational or equivalence symbol. Together with McNeil et al. (2015), they suggest that positioning operations on the right-hand side of an equation (e.g., ___ = 4 + 3) can help students understand the concept of mathematical equality. This refers to the relational paradigm, where “the solver needs first understand the underlying additive relationship and only then can identify the arithmetical operation required to calculate the unknown element of this relationship” (Polotskaia & Savard, 2018, p. 74). In contrast, the operational paradigm focuses on learning mathematical operations and applying them sequentially to solve word problems. With the aim of building a bridge between the two paradigms, Polotskaia and Savard (2018) propose the equilibrated development approach (EDA) based on the frequent analysis of mathematically incoherent situations (MIS), such as: “Rémi had 11 cinnamon hearts. He ate 6 of them. Now he has 8 cinnamon hearts” (Savard & Polotskaia, 2017, p. 829). In these tasks, students are not required to find the exact answer but recognize possible errors and explain why the scenario is wrong.

To help students achieve deep conceptual understanding and procedural fluency, it is important to use conceptual and procedural variation. Conceptual variation involves examining the core features of a concept from different angles to understand what it includes and what it excludes. Procedural variation, according to HMH (2020), refers to the creation of different problems that students can explore in different ways or to develop connections between different concepts.

The Realistic Mathematics Education (RME) program is an example of embedding problem-solving in real-world contexts. A central concept in RME is mathematization, defined as “an organized learning process in which elements of the real context are transformed into mathematical objects and relations” (Đokić, 2015, p. 109). In mathematization, a distinction is made between horizontal and vertical mathematization. Horizontal mathematization involves transforming real-world scenarios into mathematical abstractions, whereas vertical mathematization refers to advancing within the domain of mathematical objects by applying appropriate concepts and procedures essential for solving problems. To implement this approach, pedagogical practices need to shift towards understanding-based learning, which is particularly important for classroom interactions. The Math in Focus program (HMH, 2020) achieves this by linking mathematical problems to students’ everyday experiences. Similarly, the experimental program by Lazić et al. (2021) engages students by having them measure quantities when baking cookies or use money when buying and selling cookies or toys.

A heuristic approach to problem solving in Math in Focus intervention (Jaciw et al., 2016) draws on Polya’s (1988) four-step method, which includes understanding the problem, planning, implementing the plan, and reflecting. This intervention emphasizes the often neglected first and fourth steps, with students relating a new problem to previously encountered problems in the first step and exploring alternative solutions and evaluating the applicability of the method to other problems in the reflection phase (HMH, 2020). In the Word Problem Enrichment Program (Pongsakdi et al., 2016), the first two of the five problem-solving steps developed by Verschaffel et al. (1999) are used: (a) building a mental representation of the problem, which includes heuristics such as creating schemas or tables, drawing pictures, distinguishing between essential and non-essential data and applying knowledge from the real world, and (b) deciding on a solution method using tools such as flowcharts, pattern recognition, and simplification techniques.

Our analysis of effective mathematics interventions found that students’ cognitive engagement and conceptual understanding can be enhanced by numerous real-world problems placed in context. These problems “are the starting point for the formation of mathematical concepts, not just the fields of application of knowledge” (Đokić, 2015, p. 109). Improving mathematical understanding could be achieved by engaging students in carefully planned learning situations (Lambert et al., 2014) that are designed to promote a deeper understanding of mathematical concepts, such as understanding mathematical equivalence (McNeil et al., 2015). The complexity and difficulty of the problems students face increases over time (HMH, 2020), so continuous monitoring and formative assessment of student progress is necessary “to ensure understanding before moving on to new material” (Solomon et al., 2019, p. 4). Technology could help with this (Copeland et al., 2023). To develop a deep understanding of mathematical ideas, it is crucial to encourage students not to rush with calculations but to focus on understanding the problem before finding an appropriate solution method (Fischer et al., 2019). This can be achieved by teaching students heuristic strategies, such as Polya’s (1988) four-step model. When solving mathematical problems, visual models and manipulatives can help (Hall et al., 2022). To promote conceptual understanding, it is important for students to communicate mathematically with their teachers in interactive, organized classroom situations and with their classmates in small group activities. Finally, the importance of creating a positive atmosphere in the classroom characterized by learning with joy and enthusiasm should be emphasized (Delić-Zimić & Destović, 2019).

As reasoning and problem solving were the most common features in this theme, this is consistent with the findings of other studies that also emphasize the effectiveness of problem-solving-oriented learning (e.g., Myers et al., 2022; Musna et al., 2021). However, the studies included in this review lacked interventions focusing on problem-posing strategies, which have also been shown to be effective (Kul & Çelik, 2020; Zhang et al., 2024), where “students have the opportunity to pose their own mathematical problems” (Cai, 2022, p. 32). This points to a research gap that could be addressed in future studies.

3.3.3. Assess Learning Progress and Adapt Teaching to the Students’ Mathematical Results

This theme includes five supplementary characteristics. By starting with students’ prior knowledge and continuously monitoring their progress while providing high quality and timely feedback, it is possible to effectively scaffold students’ learning and make incremental progress. By integrating these characteristics, teachers can create an effective and student-centered learning environment.

Identifying and using prior knowledge is essential for effective mathematics teaching. This ensures that there is an existing foundation on which new concepts can be introduced, which contributes to deeper and more meaningful learning of mathematics. In Symphony Math intervention, “a student does not move on to the next concept … until she has mastered the current concept. One concept follows logically from the previous concept” (Schwarz, 2019, p. 2). This approach facilitated incremental progress in math instruction, which was further enhanced through scaffolded instruction, adaptive learning systems, mastery-based learning, and regular review. This allowed students to build their understanding step-by-step, as each new concept was based on some prior knowledge. The precise sequencing of tasks, along with tailored feedback and support, allowed them to move on to the next topic when they were ready, thereby deepening their mathematical skills.

Formative assessment is crucial for learning progress. It helps teachers to continuously monitor students’ understanding and improve teaching methods. These include quick checks (HMH, 2023), quizzes (Pitchford, 2015), group discussions (Blanton et al., 2019), and exit tickets (HMH, 2023). All these activities enable the teacher to gather immediate data on student progress and adapt the lessons accordingly. In the digital formative assessment tool Snappet (Faber et al., 2017), students received immediate feedback on their answers, indicating whether they were correct or incorrect. A green curl signified a correct answer, while an incorrect answer was marked with a red cross. Based on these results, the application provided each student with tasks tailored to their performance level. Additionally, teachers could use Snappet to monitor the progress of individual students or the entire class and compare their results with those of other Dutch classes. Teachers could also evaluate individual students’ performance on specific learning objectives relative to their performance on other objectives. In the ISI Math intervention (McDonald Connor et al., 2018), classroom assessment scoring analysis (CASA) was used as a tool to effectively tailor instruction to small groups of learners with varying levels of understanding. Other programs, such as ST Math (Bodner & Coulson, 2021), GO Math! (Eddy et al., 2014), Maths Tablet Intervention (Pitchford, 2015), and Math Island (Yeh et al., 2019) created individualized opportunities for students to learn at their own pace.

Scaffolding was achieved in different ways, including teacher-led/guided discovery (Solomon et al., 2019), the use of hints and clues (de Kock & Harskamp, 2014), working with peers (Pareto, 2014), and the use of technology (Hassler Hallstedt et al., 2018). Formative assessment allowed teachers to tailor support to students’ abilities and interests. For example, the JUMP program allowed “the whole class to work on the same concept simultaneously, while individual students vary widely in terms of where they are in the learning process” (Solomon et al., 2019, p. 4).

The central feature of this theme concerns formative assessment. In a recent systematic review of meta-analytic studies (Sortwell et al., 2024), formative assessment was found to have a positive impact on students’ academic achievement. This is also true for mathematics, although the standardized mean differences (SMD) are not large (SMD = 0.09–0.34). By using formative assessments, teachers can group students according to their specific abilities and give them tasks that are tailored to their performance level. Computerized formative assessments, which have been shown to be effective (Kingston & Nash, 2011; Sortwell et al., 2024), can support this process. In low-resource settings, non-digital alternatives such as quick quizzes, exit tickets, student journals, or structured question-and-answer sessions can be equally effective. Most importantly, clear and immediate feedback helps students to correct mistakes and make consistent progress.

3.3.4. Active Learning and Educational Games

According to Bonwell and Eison (1991, p. 2), active learning refers to “instructional activities involving students in doing things and thinking about what they are doing”. In active learning, students are actively engaged in individual or cooperative activities (Odum et al., 2021) that require higher order thinking (Braun et al., 2017). It is based on socio-constructivist learning theory and is expressed in instructional “practice that engages students in activities such as talking, listening, reading, writing, discussing, reflecting, conjecturing, arguing about the contents, through problem solving, in small groups, involving experimentation, or other activities” (Vale & Barbosa, 2023, p. 574).

In analyzed interventions, active learning was implemented in a variety of ways—from simple exercises aimed at developing fluency and automaticity to more complex strategies such as project-based learning, the 5E model, and the Engage–Learn–Try strategy. Project-based learning involves activities that are interdisciplinary and deal with real-world problems and practical applications. This approach enables students to solve mathematical problems together and finally present their results in the form of “a multimedia presentation, a performance, a written report, a website, or a constructed product” (Delić-Zimić & Destović, 2019). In the Go Math! intervention (Eddy et al., 2014) utilized the 5E model, and the Engage–Learn–Try strategy was included in the Math in Focus intervention (Jaciw et al., 2016). These two complex strategies encourage students to make connections between previous experiences and new tasks, generate ideas and explore possibilities, demonstrate their understanding, apply what they have learned, and assess their understanding, while teachers monitor their progress “to discover which students might need to revisit a concept or skill” (HMH, 2020, p. 39).

Engaging students in physical activities has been the route of active learning in several studies (Have et al., 2018; Magistro et al., 2022; Mullender-Wijnsma et al., 2015; Vazou & Skrade, 2017). According to Mullender-Wijnsma et al. (2015, p. 366), “combining learning activities with physical activity may lead to favorable academic outcomes as well as health improvements”. As an example, Vazou and Skrade (2017) describe the activity “Find your pair”, in which “students are asked to move around the classroom in a movement pattern assigned by the teacher or a student (e.g., skipping), collect a card scattered on the floor which includes either a math problem or the answer to a problem, find the classmate with the matching card (answer or problem, respectively) and continue moving in place as a pair (in a pattern assigned by the teacher or chosen by the students) until the teacher checks all paired cards” (Vazou & Skrade, 2017, p. 5).

In 17 studies, both digital and non-digital games were integrated into mathematics lessons to make learning mathematics interactive, dynamic, and fun. Educational games targeted a range of mathematical skills with varying levels of difficulty, from basic arithmetic and multiplication to higher order topics such as geometry, fractions, and problem-solving. Most digital games included virtual manipulatives and activities that made abstract ideas more tangible. For example, in one of the mini-games (Bakker et al., 2015), students performed multiplication by forming groups of smileys to learn about the commutative property and the distributive strategy. Math Island is “a construction management game in which every student owns a virtual island (a city) and plays the role of mayor. The goal of the game is to build their cities on the islands by learning mathematics” (Yeh et al., 2019, p. 5). In this game, learning is organized in a kind of mathematical knowledge map. Students select the target concepts, and the corresponding content is displayed in their browsers. As students learn math by building their cities, they receive immediate feedback and can track their progress in their personal portfolios. Teachers can then view these portfolios to assess students’ performance and adjust assignments. In addition to digital games, there are also role-playing games with a customer and a shopkeeper in which students handle mathematical units of money while solving real-world problems (Lazić et al., 2021; Sharma & Singh, 2019). The game with teachable agents can be played both competitively and collaboratively (Pareto, 2014). In both types, the goal is always to increase the score. Overall, integrating games into math lessons helps students to improve their skills and increase their problem-solving abilities, making math lessons effective and fun.

The prevalence of active learning strategies in the analyzed interventions aligns with the findings of a previously conducted meta-analysis, which reported an overall effect size of 0.47 when active learning was compared to traditional teaching methods (Freeman et al., 2014). According to Ting et al. (2023), active learning in Asian contexts has an even greater impact on student achievement in STEM subjects (d = 0.66). The authors attribute this to the fact that teaching in Asian contexts is “typically instructor-centered and highly content-oriented, whereby learners are passive recipients of information instead of actively engaged participants in the learning process” (p. 389). Consequently, the introduction of active learning represents a more significant change compared to Western contexts.

To implement active learning in settings less inclined toward this approach, challenges such as the “lack of time to actively involve students in teaching; the amount of content to be covered; lack of resources; lack of instructional materials; lack of administrative support; and that it took too much effort from teachers” (Takele, 2020, p. 12) must be addressed.

Digital tools, such as gamified learning platforms, can facilitate active student learning. However, in environments with limited access to technology, methods such as project-based tasks (Lazić et al., 2021) and hands-on activities can effectively connect mathematical concepts to real-life situations. Even in resource-constrained settings, teachers can design meaningful activities using everyday objects. For instance, buttons or sticks can be used to teach arithmetic, while role-playing games can illustrate concepts like money management in an engaging and relatable way. Embedding math tasks in real-world and culturally relevant contexts further enhances engagement. Tasks related to local markets or common household measurements, for example, highlight the practical relevance of mathematics in students’ daily lives.

This review includes several interventions aimed at improving academic performance through various physical activities. These activities require no special equipment or conditions and can be easily integrated into daily math lessons. They not only enhance students’ performance in mathematics but also “reduce the negative effects of a sedentary lifestyle” (Magistro et al., 2022, p. 8).

3.3.5. Social Forms of Learning

The educational process at school is characterized by different social relationships between the main subjects: the students and the teachers. Bognar and Matijević (2005) state that the social forms of teaching include whole-class teaching, individual learning, and cooperative learning.

Whole-class teaching remains a fundamental approach in mathematics education, especially when introducing new concepts (Magistro et al., 2022), procedures, worked examples (Solomon et al., 2019), or activities (Bakker et al., 2015), as well as when activating prior knowledge (Zahedi et al., 2023). Whole-class teaching can place an explicit emphasis on mathematical language and guide students to use precise terminology when solving problems (Lindorff et al., 2019). The structured nature of whole-class teaching ensures that students are prepared for subsequent individual and group learning activities (Lambert et al., 2014; Schwarz, 2019; Zahedi et al., 2023).

Individual learning is tailored to students’ learning styles and allows them to learn at their own pace. It requires concentration and responsibility but offers students privacy and freedom in completing the task (Babić et al., 2021). Individual learning enables students to develop fluency in completing assignments for both classwork and homework (Eddy et al., 2014). In the Math in Focus program, students were given the opportunity to solve problems on their own and explain their solutions to the teacher and classmates, ultimately applying the knowledge and strategies acquired to new problem situations (HMH, 2017). In the Mathematics and Reasoning program (Worth et al., 2015), students were able to learn independently after teacher-led activities. Independent learning was “supported by online games that the children could access and do individually at school and at home“ (p. 6).

In cooperative learning, groups of students work together, with each member making an individual contribution to completing the task. Cooperative learning in tandem and in small groups was at the forefront of problem-based teaching (Delić-Zimić & Destović, 2019). Students with visible interest participated in problem-solving, asked questions, discussed within their groups, and tried to find a solution as quickly as possible. In contrast to usual cooperative learning based on interdependence and accountability, Kutnick et al. (2017) trained the students in the experimental group beforehand in a relational approach emphasizing trust, safety, and cooperative support. Sharma and Singh (2019) mention several variants of cooperative learning. Cross-over groups are a variation where students start in one group and move to another group after completing tasks to facilitate interaction between students and encourage knowledge sharing between groups. The special characteristic of the buzz group is that the teacher asks a question and, after answering the question, students are asked to help their classmates by explaining the solution, which encourages active learning. If one of the group members acts as a tutor and helps the others to solve problems and clarify doubts, it is a self-help group. In cooperative jigsaw learning, students are given different parts of a task and put the solutions together after they have worked individually.

Previous studies suggest that cooperative learning is more effective than other forms of instruction (Apugliese & Lewis, 2017; Bowen, 2000; Kyndt et al., 2013; Springer et al., 1999). However, the combination of whole-class instruction, cooperative learning, and individual practice appears to provide a robust framework for teaching mathematics in elementary school. Each form plays a complementary role in improving student understanding and achievement. The combination of these approaches creates a dynamic classroom environment in which students not only develop conceptual understanding but also improve their problem-solving skills and their ability to work independently and cooperatively.

3.3.6. Connecting Mathematical Representations to Enable Abstract Thinking

This theme encompasses three characteristics: the use of manipulatives and visualization, multiple representations, and progression from the concrete to the abstract. Bartolini and Martignone (2020) define mathematical manipulatives as teaching tools “handled by students in order to explore, acquire, or investigate mathematical concepts or processes and to perform problem-solving activities drawing on perceptual (visual, tactile, or more generally: sensory) evidence” (p. 487). The previous research (Carbonneau et al., 2013; Moyer-Packenham & Westenskow, 2013) has shown that teaching with manipulatives is more effective than any other teaching method, especially when used in line with the findings of cognitive science research (Laski et al., 2015).

Visualizations can contribute to an easier understanding of complex mathematical ideas (Rösken & Rolka, 2006). Their use in mathematics education is recommended based on the results of cognitive research, which indicate that learning is generally more effective through the use of visualizations (Mayer, 2002). This is confirmed by the results of a recent meta-analysis on visualization interventions in mathematics education (Schoenherr et al., 2024), as well as a meta-analytic study on the use of representations in elementary mathematics (Sokolowski, 2018). In general, this topic is quite well researched and suggests that the use of manipulatives and visualizations is an effective approach in mathematics education. This is confirmed by the results of the research included in this review, as this topic was represented in 19 of the 44 selected papers.

The problem with the children and the dogs in the backyard, which together have 30 legs (Solomon et al., 2019), can serve as an example of the use of manipulatives in the interventions analyzed. The task was to find different solutions that fulfill the conditions of the problem. To solve the problem, manipulatives were offered to the students, and they were allowed to present their solutions using words, pictures, and numbers.

McNeil et al. (2015) point out that introducing concrete materials in elementary school mathematics lessons can help students to understand various mathematical concepts. For example, instead of writing a mathematical expression (e.g., 1 + __ = 3) on the board, students’ difficulties in understanding such mathematical equivalence can be overcome by using a scale with the corresponding number of objects on the left and right sides. However, McNeil et al. (2019) are aware that too much focus on concrete materials can make it difficult to learn abstract mathematical concepts. They suggest using them in such a way that they eventually merge into more economical, abstract symbolic representations.

This progression from concrete to symbolic form is based on Bruner’s (1964) theoretical understanding of three types of representation: enactive, iconic, and symbolic representation. Following Piaget’s (2003) theory of cognitive development, he argued that elementary school children, who are largely at the developmental stage of concrete operations, are not yet ready to deal with formal propositions, i.e., to think abstractly. Therefore, it is important that a child learning mathematics has as much sense of abstraction as possible but also a good store of visual images to embody it (Bruner & Kenney, 1965). This theoretical approach was utilized in seven interventions, most notably in the Math in Focus program (Jaciw et al., 2016). In this program, students manipulated various physical objects to explore new concepts and then arrived at abstract symbols or numbers through pictorial representations.

Visualization was achieved in different ways. For example, photos, diagrams, graphic organizers such as mind maps and concept maps, number bonds, number lines, place value charts, fraction models, animated graphic models, etc., were used. In programs based on the Singapore approach (Jaciw et al., 2016; Lindorff et al., 2019), bar models were used as pictorial representations when solving word problems.

The use of multiple representations (e.g., manipulatives, visualizations, words, and mathematical symbols) was found in seven studies. This characteristic, which is an effective practice according to NCTM (2014), is based on Dienes’s principle of perceptual variation: “Small children learn to tell one color from another, one shape from another shape, they learn to recognize boys and such like. This is perceptual discrimination. At a later stage, when they are able to abstract complex concepts, they learn conceptual discrimination. They can learn to tell one abstract structure from another, or tell when they are meeting the same structure dressed up a little differently” (Dienes, 2007, p. 25).

As part of the Inspire Maths program (Lindorff et al., 2019), an increase in the use of different forms of representation was observed among the teachers in the experimental group, which one of them saw as an important change in their own practice: “And, you know, showing it in one way, and just because they can do it in one way doesn’t mean they’ve got the understanding to show it in another, and I find that, that they can show me with the Numicon, but if I challenge them to show me in a different way, you know, they’re kind of maybe thrown a little bit, so, working on that approach is really the main thing that has changed” (Lindorff et al., 2019, p. 18).

The use of manipulatives and visualizations is an important prerequisite for learning mathematics with understanding in elementary school. Digital applications can be used to dynamically illustrate key concepts and visually verify students’ solutions: “Once the student posits their solution and launches the animation, the manipulatives follow rigorous mathematical rules to show why the posited answer did, or did not, solve the math problem” (Bodner & Coulson, 2021, p. 4). In settings with limited access to technology, hands-on alternatives such as physical manipulatives and interactive teaching tools can be equally effective. Low-cost resources such as number lines, fraction tiles, or graphing tools can replicate many of the benefits of digital visualizations, making learning engaging and accessible.

3.3.7. Mathematical Discussions and Questioning

Classroom discussions are an important method for developing mathematical thinking. Kersaint (2015) points out that teachers need to prepare students for meaningful mathematical discussions, especially through an active exchange of ideas with peers. Discussions can be linked to various mathematical tasks and activities, including those carried out with digital tools. For instance, students played mathematical mini-games at home and then discussed what they had learned with their classmates at school (Bakker et al., 2015). They tried to identify effective strategies, which they then tested in the game. In the early algebra intervention by Blanton et al. (2019), discussions were an important aspect of teaching: “Lessons began with a 15-min ‘Jumpstart’ constructed to review previous concepts or prompt students’ thinking about the concept to be addressed in the given lesson. They then transitioned into an investigative activity or set of activities in which students explored the particular lesson focus through small group work. Finally, lessons concluded with a whole-group discussion of students’ findings, followed by a brief ‘Review and Discuss’ that served as a formative assessment“ (p. 13).

Through discussion, students were able to express their thoughts and develop their mathematical ideas. In Go Math! (Eddy et al., 2014; HMH, 2023) and Math in Focus (Jaciw et al., 2016; HMH, 2020), mathematical communication was encouraged in most lessons through a Math Talk Community. In this way, students developed a deeper understanding of mathematical concepts. For a discussion to be effective, it is important that it becomes an integral part of daily instruction, which was the case in the Inspire Maths intervention, as the statement of one teacher shows: “We always start off our maths lesson with a bit of a conversation, or bit of a kind of a challenge thing, then they get to talk to their partners and discuss and give reasons as to how they came to the answer and why, rather than just, yeah, the answer’s twelve, to explain it” (Lindorff et al., 2019, p.17).

By asking effective questions, teachers can gain insight into the way students acquire mathematical concepts and give them the necessary feedback based on this (Othman et al., 2022). Teachers thus use questions to assess and improve students’ thinking and their understanding of important mathematical concepts and relationships. Hall et al. (2022) points out that teachers should encourage students to take responsibility for their own learning and that the use of questioning strategies promotes discourse and creates a safe environment for students. In the Math in Focus program, students are encouraged to explore and solve problems “via effective questioning and demonstrating how mathematics impacts their daily lives—and futures” (HMH, 2020, p. 47). The intervention, based on a Singaporean approach to the teaching and learning of mathematics, describes the development of the practice of questioning in the classroom. Initially, asking questions in class did not play a central role, but by the third quarter of the intervention, “teachers could be heard using more frequent ‘how’ and ‘why’ questions as part of their feedback in response to pupil contributions“ (Lindorff et al., 2019, p. 17), as well as rapid-fire questions to improve fluency. Teachers began to ask questions regularly to prompt students to think and draw conclusions. The questions proved to be particularly important for the teachable agent game (Pareto, 2014), which aimed to improve the learning of basic arithmetic. To motivate students to make predictions and think about numbers and calculations, players were tasked with teaching their agents how to play the game. Considering that this is a very difficult task for elementary school students, a questioning system organized in a progression tree was developed to encourage players to explain their actions and reasoning.

Fostering mathematical discussions begins with creating a classroom environment where students feel comfortable sharing ideas and collaborating. Teachers can support this by asking thought-provoking questions that encourage students to deepen their thinking and explore various approaches to problem-solving. For example, instead of asking for a quick answer, a teacher might ask, “Why do you think this method works?” or “What other strategies could we try to solve this problem?”

Different types of questions can engage students at varying levels of understanding. Open-ended questions such as “What patterns do you notice?” or “How does this relate to what we’ve already learned?” can spark curiosity and creativity. Reflective questions, such as “What might happen if we change this variable?” or “Can you think of a real-world example where this concept applies?” encourage deeper thinking and help students see the connections between mathematical ideas.

Classroom discussions have been shown to be an important aspect of effective interventions in elementary mathematics education, especially when they have become routine in the classroom. Students developed conceptual understanding by sharing their ideas with their classmates. Questions posed by teachers or embedded in digital learning environments motivated students to engage and think strategically.

3.3.8. Metacognition

Metacognition involves maintaining awareness and control over the learning process (Salam et al., 2020). It refers to students’ ability to reflect on their own learning and thinking processes, enabling them to plan their learning processes, monitor their understanding, and evaluate their learning strategies (Bakar & Ismail, 2020). According to a meta-analysis by Sercenia and Prudente (2023), metacognitive strategies not only increase math achievement but also promote cognitive engagement and self-directed learning in students. According to Schraw (1998), metacognition consists of knowledge about cognitive processes and the regulation of cognition. Practices such as goal setting, analyzing student errors, and critical thinking can be associated with regulating cognition (Almeida & Castro, 2023; Jacobs & Paris, 1987; Lucangeli et al., 2019).

Metacognition can be implemented through various instructional practices. A common metacognitive strategy in mathematics education is to encourage “students to reflect on their problem-solving strategies” (Bendixen, 2016, p. 286). In the ReflectED program (Motteram et al., 2016), for example, students are expected to think about what they have learned, reflect on their learning in stages, and discuss how they approach new mathematical tasks. Encouraging students to write about their mathematical thinking is an effective way to promote metacognitive awareness. Keeping journals in mathematics helps students articulate their understanding of concepts and reflect on their problem-solving processes (HMH, 2020). Writing provides students with the opportunity to “reflect on the progress made towards meeting their goal. They wrote one or two sentences that reflected where they were in reaching their goal and what their next steps would be to help them achieve their goal” (Sides & Cuevas, 2020). Peer review is another metacognitive practice used in math teaching, where students are asked to evaluate the work of their classmates (Araya & Diaz, 2020).

The use of technology to implement metacognition in mathematics teaching promotes student engagement and provides tools for reflection and self-regulation. In the interventions analyzed, this was achieved with tools such as Evernote (Motteram et al., 2016), which allowed students to document their learning, reflect on their progress, and set learning goals. Students could write reflections, highlight key points and track their progress over time, which helped them to build confidence and regulate their learning. Math Island (Yeh et al., 2019), a web-based learning platform that combines learning with elements of a construction management game, contributed to students’ metacognition by encouraging them to reflect on their learning progress. Comparing their constructions with the well-developed islands of other students motivated them to engage in self-reflection and put more effort into their learning.

Goal setting can be defined as a metacognitive practice that contributes to self-regulation of the learning process (Toit & Kotze, 2009). In mathematics classes, this often involves setting specific goals for mastering certain skills or solving certain types of problems. Students are then guided to monitor their progress towards these goals through regular self-assessment, reflection, and adaptation of their strategies. In the GO Math! program (HMH, 2023), for example, students are encouraged to assess their progress and reflect on how their goals align with the overarching curricular goals. Sides and Cuevas (2020) conducted the only experiment that focused on goal setting assessment. Third and fourth grade students, with the help of the teacher, set math goals related to multiplication by filling out a form that they then placed in their personal folders. Throughout the week, students took tests to check their progress on the goals they had set. The results were recorded on the chart sheet. “Each Friday during the study, the students completed a reflection on the progress made towards meeting their goal. They wrote one or two sentences that reflected where they were in reaching their goal and what their next steps would be to help them achieve their goal” (Sides & Cuevas, 2020, p. 8). Such an approach proved to be effective in terms of students’ performance in solving multiplication problems, although it did not contribute to their higher motivation and self-efficacy in mathematics.

Dealing with students’ common errors and critical thinking are important characteristics related to metacognition (Lucangeli et al., 2019; Odani & Orongan, 2020); however, they were only mentioned in two interventions (HMH, 2020, 2023). Eddy et al. (2014) found that “Common Errors had the highest reported frequency of ‘never’ being used”, indicating the need to explore these aspects of metacognition in further research.

Integrating metacognitive strategies into mathematics instruction improves student learning. By encouraging reflection, problem solving, and goal setting, teachers can guide their students to deeper understanding and greater academic success. However, this theme still offers much room for future research.

3.3.9. (Integrated) Curriculum

According to the NCTM (2014), curriculum is a fundamental component of an effective mathematics program. Glatthorn at al. (2019, p. 28) define the curriculum as “a set of plans made for guiding learning in the schools, usually represented in retrievable documents of several levels of generality, and the actualization of those plans in the classroom, as experienced by the learners and as recorded by an observer; those experiences take place in a learning environment that also influences what is learned”. A well-developed curriculum specifies what students should learn, the order in which they should learn it, and how their understanding will be assessed. The NCTM (2000, p. 11) emphasizes that the curriculum “must be coherent, focused on important mathematics, and well articulated across the grades”.

Most of the interventions analyzed were based on existing curricula, while only four programs introduced a new curriculum (Hall et al., 2020, 2022; HMH, 2017; Jaciw et al., 2016; Lindorff et al., 2019). In all four curricula, problem-solving was a key element, along with a deep conceptual understanding and knowledge of mathematical processes. The Bridges in Mathematics curriculum (Hall et al., 2020, 2022) places particular emphasis on linguistically, visually, and kinesthetically rich materials for learning mathematics. Go Math! (Eddy et al., 2014) tends to develop deep mathematical understanding through the curriculum, which tends to “articulate learning progressions across grades so that teachers and students recognize the coherence and interconnectedness of topics” (HMH, 2023, p. 17). In two studies, the curriculum was based on the Singapore approach to mathematics (Jaciw et al., 2016; Lindorff et al., 2019). In this approach, students solve problems using the concrete–representational–abstract approach.

The integrated curriculum was prominent in interventions based on combining physical exercises (e.g., walking, running, jumping, skipping rope) with mathematical activities. In the project-based intervention (Lazić et al., 2021), the content of several school subjects (nature and society, literature, and music culture) was “incorporated into mathematics through content aimed at introducing units for measuring time (year, decade, century, millennium), by connecting to a number law, a place number in a number series, representing time units on the timeline (through a series of events in time series), comparisons of multi-digit numbers (through comparisons of years of significant events and years of births and deaths of significant individuals), that is, determining the decade and century of events” (p. 3).

A coherent mathematics curriculum for elementary students requires that mathematical concepts and procedures be connected into big ideas. This characteristic has been emphasized in four interventions (Blanton et al., 2019; Eddy et al., 2014; Jaciw et al., 2016; Schwarz, 2019). Big ideas help to unify the content of a curriculum, while an integrated curriculum applies these unifying concepts across different subject areas, creating a cohesive and meaningful educational experience.

One characteristic of an integrated curriculum, as identified in this review, is its ability to connect mathematical concepts to other disciplines and real-world applications. By situating mathematics instruction in a locally relevant context, teachers can foster greater student engagement. For example, in rural areas, math could be connected to agriculture, while in urban settings, lessons might address public transportation schedules, home energy efficiency, or community resource budgeting. The integrated curriculum also highlights the importance of interdisciplinary connections, enabling students to see how math relates to other subjects. For instance, collaboration between math and science teachers can lead to projects where students calculate the speed of moving objects or graph temperature changes over time, demonstrating the role of math in scientific exploration. Similarly, integrating math with art and design can inspire students to explore symmetry, patterns, and proportions in creative projects, such as designing geometric art or analyzing the mathematical foundations of musical scales.

4. Conclusions

The teaching of elementary mathematics is the starting point for the development of mathematical thinking. Its quality depends on how solid the foundations are for the formation of mathematically literate people. It is crucial to identify what the characteristics of effective elementary mathematics teaching are. For this reason, we conducted a scoping review comprising 44 experimental studies published over a ten-year period (from 2014 to 2023). Based on the qualitative analysis of the description of the interventions, we identified 27 characteristics, which we categorized into nine themes. We found that the analyzed interventions contained at least one and at most 27 features, which corresponds to an average of seven features per intervention. This finding suggests that it is important to use various features of effective elementary school mathematics teaching simultaneously, confirming the findings of previous research (Hull et al., 2018; Mužar Horvat, 2024; Snilstveit et al., 2015).

The studies included in this review also confirm the findings of previous studies that the type of experimental research, the research instrument, and the sample size influence the power effect (Bakker et al., 2019; Cheung & Slavin, 2016; Lipsey et al., 2012). In this study, we found a slightly higher average effect for quasi-experimental research than for RCTs. The difference was particularly pronounced when the outcomes of interventions were measured with research instruments compared to standardized tests (g = 0.51 and g = 0.25, respectively). Furthermore, studies with sample sizes of fewer than 250 students reported an average effect size of 0.58, compared to 0.30 for studies with larger samples. On the other hand, the difference between the average achievement effect in studies conducted in developed countries and in studies conducted in other countries suggests that the performance of elementary school students in mathematics can be improved in all countries.

Among the interventions analyzed, problem-solving (n = 26), feedback, and formative assessment (n = 23) were the most common characteristics, as was the use of technology (n = 21). The themes that included these characteristics were also present in most of the studies. It can be concluded that for effective elementary school mathematics instruction, it is important to promote students’ cognitive engagement, conceptual understanding, and procedural fluency through problem-solving, active learning, and games, while monitoring students’ progress to ensure the adaptability of instruction. This requires the use of digital technology or non-digital teaching materials. A dynamic shift between whole-class instruction, cooperative and individual learning, the use of manipulatives, and visualizations that lead to abstract thinking can also contribute to the effectiveness of elementary school mathematics instruction. Mathematical communication, metacognition, and curriculum change were less frequently used themes in the interventions analyzed. This primarily relates to critical thinking and “helping students realize that confusion and errors are a natural part of learning, by facilitating discussions on mistakes, misconceptions, and struggles” (NCTM, 2014, p. 52). Exploring these features and themes could be a challenge for future research.

Teaching mathematics is a complex and challenging process that requires the consideration of various factors that can contribute to its effectiveness. This review provides an overview of the characteristics and themes that have been researched over the past decade regarding effective interventions for elementary school mathematics teaching. The findings from this review can help math teachers in designing their lessons. Professional development leaders and researchers can find the key elements for planning their programs and interventions. Finally, the overview of the key findings discussed in this paper can help education policymakers in shaping educational change.

5. Limitations

As we have limited the selection of studies to a period of ten years, it is possible that we have omitted important works published outside this period. These omitted studies could contribute to a more precise determination of the representation of certain features and to answering the research question of how they were used in elementary school mathematics lessons. Nevertheless, we chose to adhere to these limitations for two reasons: First, we obtained 44 methodologically rigorous experiments that indicate with high reliability effective interventions in elementary school mathematics and the corresponding characteristics on which they are based. Second, we found several studies towards the end of this review and found that their inclusion did not help to find new characteristics or provide new information that could extend the understanding of these characteristics. This suggests that the categories were saturated (Creswell, 2013) and that we had sufficient data to draw conclusions. To identify the characteristics of instruction present in effective elementary mathematics education interventions, we selected a scoping review as the appropriate methodological approach (Munn et al., 2022). Additionally, determining which specific combinations of characteristics are most effective would be interesting but falls outside the scope of this review. However, this could serve as a research focus for a future meta-analytic study.

Author Contributions

Conceptualization, B.B. and S.M.H.; methodology, B.B. and S.M.H.; software, B.B. and L.J.M.; validation, B.B., S.M.H. and L.J.M.; formal analysis, B.B. and S.M.H.; investigation, B.B.; resources, B.B, S.M.H. and L.J.M.; data curation, B.B.; writing—original draft preparation, B.B.; writing—review and editing, B.B., S.M.H. and L.J.M.; visualization, B.B.; supervision, B.B.; project administration, B.B.; funding acquisition, B.B., S.M.H. and L.J.M. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors on request.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. Geographical distribution of included studies.

Figure 2. Number of studies conducted in the first through sixth grades of elementary school.

Table 1

Criteria for the inclusion and exclusion of studies.

Inclusion Criteria	Exclusion Criteria
1. The study involves elementary school students from 1st to 5th grade, including 6th grade if it is part of elementary school.	1. The study involves preschool children, secondary school students, or college students.
2. Experimental research focuses on improving students’ outcomes in elementary mathematics.	2. Experiments without a control group, non-experimental research, or studies that do not focus on students’ mathematical performance.
3. The mathematical intervention program conducted in experimental classrooms is described in detail.	3. Insufficient information about the mathematics intervention program, the intervention had nothing to do with elementary mathematics teaching, or it was conducted out of classroom context (e.g., in laboratory).
4. At least two primary school teachers were involved in conducting the lessons and 30 students took part in the intervention and control group.	4. There is only one elementary school teacher in the experimental and control groups, or the lessons are conducted by researchers or individuals associated with the research.5. There is no control group in which the lessons are conducted as usual.6. The student sample is smaller than 30 in one or both groups.
5. The study includes quantitative results of the pupils’ mathematical performance from pretests (where the difference between the control and the experimental group is not greater than 25% of the standard deviation) and posttests, from which the effect size can be calculated or has already been calculated.	7. The research includes only qualitative data or quantitative data from which the effect size cannot be calculated.8. A pretest was not performed.9. The difference between the control and the experimental group at baseline is greater than 25% of the standard deviation.
6. Performance was measured using a general mathematics test that was fair to both the experimental and control groups.	10. The instrument does not measure general mathematical performance, or it is biased toward the intervention group.
7. The study showed a positive and statistically significant (p ≤ 0.05) effect size.	11. There is no positive effect size, or it is not statistically significant (p > 0.05).
8. Interventions lasted at least 8 weeks.	12. Interventions lasted less than 8 weeks.
9. The research was published between 2014 and 2023.	13. The research was published before 2014 or after 2023.
10. The study must be available in English, regardless of the country in which it was conducted.	14. The research is not written in English.

Appendix A

Figure A1. Studies selection process.

Appendix B

Table A1

List of studies included in the review.

(References) Intervention Title (Duration), Country (TIMSS or PISA Results ¹)	Research Aim	SampleType of Study, Type of Measurement InstrumentComparison of Hedges’ g and MDES ² (Significance)
(Al-Mashaqbeh, 2016)IPad in Elementary School Math (3 months), Jordan (420)	The aim of this study was to investigate the impact of traditional teaching methods compared to the use of iPads for teaching mathematics in first grade.	1st grade (42E, 42C)quasi-experiment, researcher-made0.56 * > 0.55 (p = 0.01)
(Araya & Diaz, 2020)Government Elementary Math Exercises Online (12 weeks), Chile (441)	The aim of the study was to evaluate the effectiveness of an online math platform for primary school pupils developed by the Chilean Ministry of Education.	4th grade (659E, 538C)RCT, standardized0.13 < 0.14 (p < 0.04)
(Bakker et al., 2015)Mathematics Mini Games (2 years), the Netherlands (538)	This study investigated the effects of solving multiplication problems in online mini-games on the mathematical results of elementary school students.	2nd and 3rd grade (78E, 327C)RCT, researcher-made0.22 < 0.31(p < 0.05)
(Blanton et al., 2019)Early Algebra Learning Progression (6 months), the USA (535)	The aim was to investigate the effectiveness of an early algebra intervention with a heterogeneous student population.	3rd grade (1637E, 1448C)RCT, researcher-madecorrectness: 0.80 > 0.09 (p < 0.01)
(Bodner & Coulson, 2021)ST Math (34 weeks), the USA (535)	The study was designed to provide empirical evidence of the effectiveness of the ST Math add-on software, in which students solve problems presented in a fun way and use virtual manipulatives.	4th grade (2255E, 2395C)5th grade (2226E, 2437C)RCT, standardized4th grade: 0.06 < 0.07 (p < 0.00)5th grade: 0.10 > 0.07 (p < 0.00)
(Brezovszky et al., 2019)Number Navigation Game (10 weeks), Finland (532)	The study tested the effectiveness of a game-based learning environment to strengthen the adaptive numerical knowledge of elementary school students.	4th, 5th, and 6th grade (642E, 526C)RCT, researcher-madecorrect solutions, multi-op. solutions, and arithmetic fluency: 0.16 * > 0.15 (p < 0.05)
(Christopoulos et al., 2020)Exercise-based Learning Environment Eduten Playground (8 weeks), the United Arab Emirates (544)	The aim of the study was to investigate the extent to which curriculum-driven learning software improves students’ mathematical mastery and numeracy skills compared to the traditional didactic approach.	3rd grade (65E, 70C)quasi-experiment, researcher-made0.40 * < 0.43 (p = 0.02)
(Copeland et al., 2023; An et al., 2022; Bashkov, 2021)IXL Math (14 or 15 weeks), the USA (535)	The aim of the study was to determine the effects of the adaptive learning platform IXL Math on students’ mathematical performance.	grades 3–5 (263E, 282C)RCT, standardized0.13 < 0.21 (p = 0.01)
(de Kock & Harskamp, 2014)A Metacognitive Computer Programme for Word Problem Solving (10 weeks), the Netherlands (538)	Investigating the effectiveness of a metacognitive computer program designed to help students in the problem-solving process by visualizing clues in the form of a staircase.	5th grade (280E, 110C)quasi-experiment, researcher-madeanalyzing word problems: 0.26 * < 0.28 (p = 0.02),solving word problems: 0.29 * > 0.28 (p < 0.01)
(Delić-Zimić & Destović, 2019)Mathematical Modeling (18 weeks), Bosnia and Herzegovina (452)	The aim was to apply mathematical modeling in problem-based teaching and to demystify its role and importance in improving the educational effect.	4th grade (52E, 214C)quasi-experiment, researcher-made0.55 * > 0.39 (p < 0.01)
(Đokić, 2015)Realistic Mathematics Education (3 months), Serbia (508)	The aim was to test whether an innovative textbook based on Realistic Mathematics Education has a positive impact on students’ performance in geometry.	4th grade, (73E, 75C)RCT, researcher-made0.88 * > 0.41 (p < 0.01)
(Eddy et al., 2014; HMH, 2023)GO Math! (2 years), the USA (535)	The study evaluated the impact of GO Math! program, which is based on the common core state standards for mathematics, on student achievement.	grade 1–3 (1382E, 978C)RCT, standardized0.50 > 0.10 (p < 0.01)
(Erol & Batdal Karaduman, 2018)Brain Based Learning (3 months), Turkey (523)	The aim was to investigate the effects of brain-based learning activities on the mathematical success of fourth graders.	4th grade (46E, 45C)quasi-experiment, researcher-made0.86 * > 0.53 (p < 0.01)
(Faber et al., 2017)A Digital Formative Assessment Tool: Snappet (5 months), the Netherlands (538)	The aim of the study was to investigate the effect of the digital tool Snappet, which enables formative feedback, on students’ mathematical performance.	3rd grade (822E, 986C)RCT, standardized0.43 * > 0.12 (p < 0.01)
(Fischer et al., 2019)Arithmetic Comprehension at Elementary School—ACE (1 year), France (485)	The aim of the study was to investigate the development of young students’ understanding of the mathematical concept of equality.	2nd grade (1140E, 1155C)quasi-experiment, researcher-made0.56 * > 0.10 (p = 0.00)
(Hall et al., 2020, 2022)Bridges in Mathematics (6 months), the USA (535)	The goal was to investigate the effectiveness of the student-centered and standards-based Bridges in Mathematics curriculum.	5th grade (1,839E, 3,354C)quasi-experiment,standardized0.25 > 0.07 (p = 0.00)
(Hassler Hallstedt et al., 2018)Mathematics Tablet Intervention for Low Performing Second Graders (20 weeks), Sweden (521)	The aim was to determine the effectiveness of a tablet intervention in improving the mathematical skills of students who initially showed a lower level of performance in mathematics.	2nd grade (151E, 130C)RCT, standardizedaddition 0–12, subtraction 0–12, subtraction 0–18: 0.56 * > 0.30 (p = 0.00)
(Have et al., 2018)Physical Activity Improves Children’s Math Achievement (9 months), Denmark (525)	The aim of the study was to find out how the integration of physical activity into mathematics lessons can influence educational outcomes.	1st grade (268E, 182C)RCT, standardized0.38 > 0.24 (p = 0.01)
(Jaciw et al., 2016; HMH, 2017, 2020)Math in Focus (1 year), the USA (535)	The study evaluated the effectiveness of the Math in Focus program based on the teaching methods used in Singapore.	grade 3–5 (744E, 702C)RCT, standardized0.15 > 0.13 (p = 0.05)
(Kutnick et al., 2017)Relation-Based Group Work Approach (7 months),Hong Kong—China (602)	This study examined whether the relational approach to group work, which focused on developing social relationships, communication, and cooperative problem solving, can improve students’ mathematical performance.	3rd grade (319E, 185C)quasi-experiment, researcher-made0.20 < 0.23 (p = 0.00)
(Lambert et al., 2014)Accelerated Math (1 year), the USA (535)	The aim was to evaluate the impact of a technology-based learning progress monitoring tool on student outcomes.	grade 2–5 (356E, 340C)RCT, standardized0.47 * > 0.19 (p < 0.05)
(Lazić et al., 2021)Project Based Learning (3 months), Serbia (508)	The aim was to investigate the effectiveness of project-based learning in elementary school mathematics lessons.	3rd grade (77E, 70K)quasi-experiment, researcher-made1.04 * > 0.41 (p = 0.00)
(Lindorff et al., 2019)Inspire Maths (1 year), the UK (556)	The aim was to investigate the use of a mathematics textbook based on the Singapore elementary school teaching approach.	1st grade (249E, 281C)RCT, standardized0.42 > 0.22 (p < 0.05).
(Lowrie et al., 2017)Visuospatial reasoning (10 weeks), Australia (516)	The aim was to evaluate the effects of a visuospatial intervention program on students’ mathematical performance.	6th grade (120E, 66C)quasi-experiment, researcher-made0.40 > 0.38 (p < 0.02)
(Magistro et al., 2022)Physically Active Mathematics Lessons (2 years), Italy (515)	The aim was to investigate how the inclusion of physical activities in mathematics lessons affects students’ mathematical performance and gross motor skill development.	1st and 2nd grade (36E, 46C)quasi-experiment, standardizedarithmetic: 0.90 > 0.56 (p = 0.00)
(McDonald Connor et al., 2018), Individualizing student instruction in mathematics (ISI-Math) (6 months), the USA (535)	The aim was to investigate whether individualized mathematics lessons are more effective than non-individualized lessons.	2nd grade (209E, 161C)RCT, standardizedmath fluency: 0.60 > 0.26 (p = 0.00)KeyMath: 0.41 > 0.26 (p = 0.00)
(McNeil et al., 2015)Modified Arithmetic Practice (12 weeks), the USA (535)	The aim was to investigate whether a modified version of arithmetic practice and workbooks can improve students’ understanding of mathematical equations.	2nd grade (83E, 83C)quasi-experiment, researcher-made0.37 < 0.39 (p = 0.00)
(Motteram et al., 2016)ReflectED Programme (28 weeks), the UK (556)	The aim was to evaluate the impact of the ReflectED metacognitive skills program on students’ academic outcomes in mathematics.	5th grade (839E, 731C)RCT, standardized0.30 > 0.13 (p = 0.05)
(Mullender-Wijnsma et al., 2015)Fit and Academically Proficient at School (2 years), the Netherlands (538)	The aim was to evaluate the effectiveness of integrating physical activity into mathematics education.	2nd and 3rd grade (249E, 250C)RCT, standardizedmathematics speed test: 0.51 * > 0.33 (p = 0.00)general mathematics: 0.42 * > 0.22 (p = 0.00)
(Murtagh et al., 2022)Playfulmaths! (6 months), Palestinian Authority (366*)	The aim was to investigate the relationship between learning through play and students’ performance in mathematics.	grade 1–4 (415E, 444C)quasi-experiment, researcher-made0.09 * < 0.17 (p = 0.00)
(Pareto, 2014)The Teachable Agent Game (3 months), Sweden (521)	The study investigated how the interactive learning platform with a teachable agent can influence conceptual understanding and reasoning in mathematics.	grade 2–6 (154E, 129C)quasi-experiment, researcher-made0.34 * > 0.30 (p = 0.00)
(Piper et al., 2016)Primary Math and Reading (PRIMR) Initiative (1 year), Kenya (NA)	The goal was to determine the impact of the PRIMR program, which provides students with learning materials and helps teachers with professional development, on students’ mathematical performance.	1st and 2nd grade (3097E, 1166C)RCT, standardized/procedural index:1st grade: 0.20 > 0.09 (p = 0.03) 2nd grade: 0.37 > 0.09 (p = 0.00)conceptual index in 2nd grade: 0.33 > 0.09 (p < 0.01)
(Pitchford, 2015)Maths Tablet Intervention (8 weeks), Malawi (NA)	The study investigated the impact of using tablets to improve students’ performance in mathematics.	grade 1–3 (104E, 100C)RCT, researcher-made0.32 < 0.35 (p < 0.05)
(Polotskaia & Savard, 2018; Savard & Polotskaia, 2017)Equilibrated Development Approach (3 years), Canada (512)	The aim was to investigate the effectiveness of the relational approach in solving additive word problems.	2nd grade (216E, 196C)quasi-experiment, researcher-made0.44 > 0.25 (p = 0.05)
(Pongsakdi et al., 2016)Word Problem Enrichment Program (WPE) (2 months), Finland (532)	The study investigated whether teacher-created word problems can help “improve student mathematical modeling and problem-solving skills” (p. 23)	4th and 6th grade (97E, 70C)quasi-experiment, researcher-madeword problem solving: 0.55 * > 0.39 (p = 0.00)application word problem: 0.28 * < 0.39 (p < 0.05)
(Schwarz, 2019)Symphony Math (1 year), the USA (535)	The aim was to determine the effectiveness of the intervention based on the web-enabled Symphony Math application.	grade 1–4 (579E, 624C)quasi-experiment, standardized0.42 * > 0.14 (p = 0.00)
(Sharma & Singh, 2019)Interweaving Mathematics Pedagogy and Contents of Teaching (IMPACT) (6 months), India (337*)	The aim was to investigate the effectiveness of the IMPACT program using the mathematics toolkit.	2nd grade (125E, 125C)quasi-experiment, researcher-made1.27 * > 0.32 (p = 0.00)
(Sides & Cuevas, 2020)Student Goal Setting (8 weeks), the USA (535)	The aim of the study was to investigate whether setting goals can motivate students to learn and improve their self-efficacy and performance in mathematics.	3rd and 4th grade (37E, 33C)quasi-experiment, researcher-made1.59 * > 0.60 (p = 0.00)
(Solomon et al., 2019)JUMP Math program (6 months), Canada (512)	The aim of the study was to determine whether the JUMP Math program, which is based on findings documented in the scientific literature, leads to students’ better performance in mathematics.	2nd grade (350E, 204C)5th grade (348 E, 244C)RCT, standardized2nd grade: 0.26 > 0.22 (p < 0.01), 5th grade: 0.22 > 0.21 (p = 0.04)
(Vazou & Skrade, 2017)Move for Thought (8 weeks), the USA (535)	The aim was to investigate whether integrating physical activity into mathematics lessons would improve students’ mathematical performance.	4th and 5th grade (107E, 118C)quasi-experiment, standardized0.55 * > 0.33 (p = 0.00)
(Veldhuis & van den Heuvel-Panhuizen, 2020)Classroom Assessment Techniques (CATs) (6 months), the Netherlands (538)	The aim was to investigate the effects of teachers’ assessment methods in the classroom on students’ performance in mathematics.	3rd grade (207E, 99C)RCT, standardized0.13 < 0.30 (p = 0.04)
(Worth et al., 2015)Mathematics and Reasoning (10 to 12 weeks), the UK (556)	The aim was to determine the effectiveness of the intervention aimed at developing children’s understanding of the logical principles of mathematics.	2nd grade (517E, 848C)RCT, standardized0.20 > 0.14 (p = 0.05)
(Yeh et al., 2019)Math Island (2 years), Taiwan (599)	The aim was to investigate the effects of the online game Math Island on students’ mathematical performance.	2nd and 3rd grade (209E, 125C)quasi-experiment, standardized0.48 * > 0.28 (p < 0.05)
(Zahedi et al., 2023)Blended Learning (3 years)India (337 *)	The aim of the study was to evaluate blended learning in mathematics education using a platform for adaptive digital online content.	2nd grade, (108E, 113C)quasi-experiment, researcher-made0.34 = 0.34, (p < 0.05)

* If the value of Hedges’s g is not given in the paper, it was calculated using the available results with online calculators (Lenhard & Lenhard, 2022; Wilson, 2023). ¹ TIMSS 2019 or PISA* 2022 average mathematics achievement. If a country did not participate in the TIMSS study, the PISA results were listed. In the case of India, 2009 PISA results were listed for the state of Tamil Nadu. ² The minimum detectable effect size (MDES) was calculated using G*Power version 3.1.9.7 (Heinrich-Heine-Hochschule Düsseldorf, 2020) based on sensitivity analysis, which can be used to evaluate published research. It answers the question “What effect size was a study able to detect with a power of 1 − β = 0.80 given its sample size and α as specified by the author? In other words, what is the minimum effect size to which the test was sufficiently sensitive?” (Faul et al., 2009, p. 1149). A one-sided test for the difference between two independent means was used.

References

Al-Mashaqbeh, I. IPad in elementary school math learning setting. International Journal of Emerging Technologies in Learning; 2016; 11, 2 pp. 48-52. [DOI: https://dx.doi.org/10.3991/ijet.v11i02.5053]

Almeida, L. M. W. D.; Castro, É. M. V. d. Metacognitive strategies in mathematical modelling activities: Structuring an identification instrument. Journal of Research in Mathematics Education; 2023; 12, 3 3. [DOI: https://dx.doi.org/10.17583/redimat.12926]

An, X.; Schonberg, C.; Bashkov, B. M. IXL implementation fidelity and usage recommendations. Online submission; 2022; Available online: https://eric.ed.gov/?id=ED629011 (accessed on 8 January 2025).

Anthony, G.; Walshaw, M. Effective pedagogy in mathematics/Pàngarau best evidence synthesis iteration [BES]. New Zealand Ministry of Education; 2007; Available online: https://thehub.sia.govt.nz/assets/documents/42433_BES_Maths07_Complete_0.pdf (accessed on 8 January 2025).

Anthony, G.; Walshaw, M. Effective pedagogy in mathematics. UNESCO International Bureau of Education; 2009; Available online: https://eric.ed.gov/?id=ED540738 (accessed on 8 January 2025).

Apugliese, A.; Lewis, S. E. Impact of instructional decisions on the effectiveness of cooperative learning in chemistry through meta-analysis. Chemistry Education Research and Practice; 2017; 18, 1 pp. 271-278. [DOI: https://dx.doi.org/10.1039/C6RP00195E]

Araya, R.; Diaz, K. Implementing government elementary math exercises online: Positive effects found in RCT under social turmoil in Chile. Education Sciences; 2020; 10, 9 9. [DOI: https://dx.doi.org/10.3390/educsci10090244]

Astleitner, H. Foreword. Intervention research in educational practice alternative theoretical frameworks and application problems; Astleitner, H. Waxmann: 2020; pp. 7-16. [DOI: https://dx.doi.org/10.31244/9783830991977]

Babić, T.; Kolar, L.; Miličević, M. Individual, cooperative and collaborative learning and students’ perceptions of their impact on their own study performance. 2021 44th International Convention on Information, Communication and Electronic Technology (MIPRO); Opatija, Croatia, 27 September–1 October; 2021; pp. 864-869. [DOI: https://dx.doi.org/10.23919/MIPRO52101.2021.9596728]

Bakar, M. A. A.; Ismail, N. Metacognitive learning strategies in mathematics classroom intervention: A review of implementation and operational design aspect. International Electronic Journal of Mathematics Education; 2020; 15, 1 5937. [DOI: https://dx.doi.org/10.29333/iejme/5937]

Bakker, A.; Cai, J.; English, L.; Kaiser, G.; Mesa, V.; Van Dooren, W. Beyond small, medium, or large: Points of consideration when interpreting effect sizes. Educational Studies in Mathematics; 2019; 102, 1 pp. 1-8. [DOI: https://dx.doi.org/10.1007/s10649-019-09908-4]

Bakker, M.; Van Den Heuvel-Panhuizen, M.; Robitzsch, A. Effects of playing mathematics computer games on primary school students’ multiplicative reasoning ability. Contemporary Educational Psychology; 2015; 40, pp. 55-71. [DOI: https://dx.doi.org/10.1016/j.cedpsych.2014.09.001]

Barcelos, T.; Muñoz-Soto, R.; Villarroel, R.; Merino, E.; Silveira, I. Mathematics learning through computational thinking activities: A systematic literature review. JUCS—Journal of Universal Computer Science; 2018; 24, 7 pp. 815-845. [DOI: https://dx.doi.org/10.3217/jucs-024-07-0815]

Bartlett, J.; Charles, S. Power to the people: A Beginner’s tutorial to power analysis using jamovi. Meta-Psychology; 2022; 6, 3078. [DOI: https://dx.doi.org/10.15626/MP.2021.3078]

Bartolini, M. G.; Martignone, F. Lerman, S. Manipulatives in mathematics education. Encyclopedia of mathematics education; Springer International Publishing: 2020; pp. 487-494. [DOI: https://dx.doi.org/10.1007/978-3-030-15789-0_93]

Bashkov, B. M. Assessing the impact of IXL Math over three years: A quasi-experimental study. IXL Learning; 2021; Available online: https://eric.ed.gov/?id=ED628125 (accessed on 8 January 2025).

Bendixen, L. D. Greene, J. A.; Sandoval, W. A.; Bråten, I. Teaching for epistemic change in elementary classrooms. Handbook of epistemic cognition; Routledge: 2016; pp. 281-299.

Blanton, M.; Stroud, R.; Stephens, A.; Gardiner, A.; Stylianou, D.; Knuth, E.; Isler-Baykal, I.; Strachota, S. Does early algebra matter? The effectiveness of an early algebra intervention in grades 3 to 5. American Educational Research Journal; 2019; 56, 5 pp. 1930-1972. [DOI: https://dx.doi.org/10.3102/0002831219832301]

Bodner, M.; Coulson, A. Randomized trial of elementary school ST Math software intervention reveals significant efficacy. MIND Research Institute; 2021; Available online: https://eric.ed.gov/?id=ED616922 (accessed on 8 January 2025).

Bognar, L.; Matijević, M. Didaktika [Didactics]; Školska knjiga: 2005.

Bonwell, C. C.; Eison, J. A. Active learning: Creating excitement in the classroom (No. 1; ASHE-ERIC higher education reports). The George Washington University, School of Education and Human Development; 1991; Available online: https://eric.ed.gov/?id=ED336049 (accessed on 8 January 2025).

Borenstein, M.; Hedges, L. V.; Higgins, J. P. T.; Rothstein, H. R. Introduction to meta-analysis; 2nd ed. Wiley: 2021.

Bowen, C. W. A quantitative literature review of cooperative learning effects on high school and college chemistry achievement. Journal of Chemical Education; 2000; 77, 1 116. [DOI: https://dx.doi.org/10.1021/ed077p116]

Braun, B.; Bremser, P.; Duval, A. M.; Lockwood, E.; White, D. What does active learning mean for mathematicians?. Notices of the American Mathematical Society; 2017; 64, 2 pp. 124-129. [DOI: https://dx.doi.org/10.1090/noti1472]

Brezovszky, B.; McMullen, J.; Veermans, K.; Hannula-Sormunen, M. M.; Rodríguez-Aflecht, G.; Pongsakdi, N.; Laakkonen, E.; Lehtinen, E. Effects of a mathematics game-based learning environment on primary school students’ adaptive number knowledge. Computers & Education; 2019; 128, pp. 63-74. [DOI: https://dx.doi.org/10.1016/j.compedu.2018.09.011]

Bruner, J. S. The course of cognitive growth. American Psychologist; 1964; 19, 1 pp. 1-15. [DOI: https://dx.doi.org/10.1037/h0044160]

Bruner, J. S. The process of education; Harvard University Press: 1977.

Bruner, J. S.; Kenney, H. J. Representation and mathematics learning. Monographs of the Society for Research in Child Development; 1965; 30, 1 pp. 50-59. [DOI: https://dx.doi.org/10.2307/1165708]

Cai, J. What research says about teaching mathematics through problem posing. Éducation et Didactique; 2022; 16, 16. [DOI: https://dx.doi.org/10.4000/educationdidactique.10642]

Carbonneau, K. J.; Marley, S. C.; Selig, J. P. A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology; 2013; 105, 2 pp. 380-400. [DOI: https://dx.doi.org/10.1037/a0031084]

Cheung, A. C. K.; Slavin, R. E. The effectiveness of educational technology applications for enhancing mathematics achievement in K-12 classrooms: A meta-analysis. Educational Research Review; 2013; 9, pp. 88-113. [DOI: https://dx.doi.org/10.1016/j.edurev.2013.01.001]

Cheung, A. C. K.; Slavin, R. E. How methodological features affect effect sizes in education. Educational Researcher; 2016; 45, 5 pp. 283-292. [DOI: https://dx.doi.org/10.3102/0013189X16656615]

Christopoulos, A.; Kajasilta, H.; Salakoski, T.; Laakso, M. -J. Limits and virtues of educational technology in elementary school mathematics. Journal of Educational Technology Systems; 2020; 49, 1 pp. 59-81. [DOI: https://dx.doi.org/10.1177/0047239520908838]

Chwo, G. S. M.; Marek, M. W.; Wu, W. -C. V. Meta-analysis of MALL research and design. System; 2018; 74, pp. 62-72. [DOI: https://dx.doi.org/10.1016/j.system.2018.02.009]

Copeland, S.; Cook, M.; Grant, A.; Ross, S. Randomized-control efficacy study of IXL math in holland public schools. Center for Research and Reform in Education; 2023; Available online: https://jscholarship.library.jhu.edu/handle/1774.2/69038 (accessed on 8 January 2025).

Corporation for Digital Scholarship,. Zotero (Version 7.0.10) [Computer software]; 2024; Available online: https://www.zotero.org/ (accessed on 8 January 2025).

Creswell, J. W. Qualitative inquiry and research design: Choosing among five approaches; 3rd ed. SAGE: 2013.

de Kock, W.; Harskamp, E. Can teachers in primary education implement a metacognitive computer programme for word problem solving in their mathematics classes?. Educational Research and Evaluation; 2014; 20, 3 pp. 231-250. [DOI: https://dx.doi.org/10.1080/13803611.2014.901921]

Delić-Zimić, A.; Destović, F. Avdaković, S. Mathematical modeling and statistical representation of experimental access. Advanced technologies, systems, and applications III: Proceedings of the international Symposium on innovative and interdisciplinary applications of advanced technologies (IAT); Springer: 2019; Vol. 1, pp. 36-48. [DOI: https://dx.doi.org/10.1007/978-3-030-02574-8_4]

Dienes, Z. P. Sriraman, B. Some thoughts on the dynamics of learning mathematics. Zoltan Paul Dienes and the dynamics of mathematical learning; University of Montana Press: 2007; pp. 1-118. Available online: https://www.zoltandienes.com/wp-content/uploads/2018/08/ZPD_and_Dynamics_of_Math_Learning-Monograph2_2007.pdf (accessed on 8 January 2025).

Đokić, O. J. The effects of RME and innovative textbook model on 4th grade pupils’ reasoning in geometry. Proceedings: Developing mathematical language and reasoning; Charles University, Faculty of Education: Novotná, J.; Moraová, H. 2015; pp. 107-117. Available online: https://www.semt.cz/proceedings/semt-15.pdf#page=108 (accessed on 8 January 2025).

Eddy, R. M.; Hankel, N.; Goldman, A.; Murphy, K. Houghton mifflin harcourt GO math! Efficacy study year two final report. Cobblestone Applied Research & Evaluation, Inc; 2014; Available online: https://s3.amazonaws.com/prod-hmhco-vmg-craftcms-public/research/HMH_GoMath_RCT_1_3_Final_Report_2014.pdf (accessed on 8 January 2025).

Erol, M.; Batdal Karaduman, G. The effect of activities congruent with brain based learning model on students’ mathematical achievement. NeuroQuantology; 2018; 16, 5 pp. 13-22. [DOI: https://dx.doi.org/10.14704/nq.2018.16.5.1342]

Evidence for PolicyPractice Information (EPPI) Centre. EPPI-reviewer (Version 6.15.5.0); [Online app]; 2024; Available online: https://eppi.ioe.ac.uk/cms/Default.aspx?alias=eppi.ioe.ac.uk/cms/er4 (accessed on 8 January 2025).

Faber, J. M.; Luyten, H.; Visscher, A. J. The effects of a digital formative assessment tool on mathematics achievement and student motivation: Results of a randomized experiment. Computers & Education; 2017; 106, pp. 83-96. [DOI: https://dx.doi.org/10.1016/j.compedu.2016.12.001]

Faul, F.; Erdfelder, E.; Buchner, A.; Lang, A. -G. Statistical power analyses using G*Power 3.1: Tests for correlation and regression analyses. Behavior Research Methods; 2009; 41, 4 pp. 1149-1160. [DOI: https://dx.doi.org/10.3758/BRM.41.4.1149]

Faul, F.; Erdfelder, E.; Lang, A. -G.; Buchner, A. GPower 3: A flexible statistical power analysis program for the social, Behavioral and Biomedical sciences, Beh. Behavior Research Methods; 2007; 39, 2 pp. 175-191. [DOI: https://dx.doi.org/10.3758/BF03193146]

Fischer, J. -P.; Sander, E.; Sensevy, G.; Vilette, B.; Richard, J. -F. Can young students understand the mathematical concept of equality? A whole-year arithmetic teaching experiment in second grade. European Journal of Psychology of Education; 2019; 34, 2 pp. 439-456. [DOI: https://dx.doi.org/10.1007/s10212-018-0384-y]

Freeman, S.; Eddy, S. L.; McDonough, M.; Smith, M. K.; Okoroafor, N.; Jordt, H.; Wenderoth, M. P. Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences; 2014; 111, 23 pp. 8410-8415. [DOI: https://dx.doi.org/10.1073/pnas.1319030111] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/24821756]

Glatthorn, A. A.; Boschee, F. A.; Whitehead, B. M.; Boschee, B. F. Curriculum leadership: Strategies for development and implementation; 5th ed. SAGE: 2019.

Hadie, S. N. H. ABC of a scoping review: A simplified JBI scoping review guideline. Education in Medicine Journal; 2024; 16, 2 pp. 185-197. [DOI: https://dx.doi.org/10.21315/eimj2024.16.2.14]

Hakim, L.; Yasmadi, B. Conceptual and procedural knowledge in mathematics education. Design Engineering; 2021; 9, pp. 1271-1280.

Hall, G. J.; Schaefer, P.; Hedges, T.; Grodsky, E. Examining Bridges in Mathematics and differential effects among English language learners. Madison Education Partnership; 2020; Available online: https://mep.wceruw.org/documents/MEP-MEMO-Bridges.pdf (accessed on 8 January 2025).

Hall, G. J.; Schaefer, P.; Hedges, T.; Grodsky, E. Examining bridges in mathematics and differential effects among english language learners. School Psychology Review; 2022; 51, 4 pp. 392-405. Available online: https://www.tandfonline.com/doi/full/10.1080/2372966X.2020.1871304 (accessed on 8 January 2025).

Hassler Hallstedt, M.; Klingberg, T.; Ghaderi, A. Short and long-term effects of a mathematics tablet intervention for low performing second graders. Journal of Educational Psychology; 2018; 110, 8 pp. 1127-1148. [DOI: https://dx.doi.org/10.1037/edu0000264]

Have, M.; Nielsen, J. H.; Ernst, M. T.; Gejl, A. K.; Fredens, K.; Grøntved, A.; Kristensen, P. L. Classroom-based physical activity improves children’s math achievement—A randomized controlled trial. PLoS ONE; 2018; 13, 12 e0208787. [DOI: https://dx.doi.org/10.1371/journal.pone.0208787] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/30557397]

Heinrich-Heine-Hochschule Düsseldorf. G*Power: Statistical power analyses for Mac and Windows (Version 3.1.9.7) [Computer software]; Available online: https://www.psychologie.hhu.de/arbeitsgruppen/allgemeine-psychologie-und-arbeitspsychologie/gpower (accessed on 8 January 2025).2020; February 21

Higgins, K.; Huscroft-D’Angelo, J.; Crawford, L. Effects of technology in mathematics on achievement, motivation, and attitude: A meta-analysis. Journal of Educational Computing Research; 2019; 57, 2 pp. 283-319. [DOI: https://dx.doi.org/10.1177/0735633117748416]

Houghton Mifflin Harcourt (HMH). Math in focus: Elementary grades efficacy study (No. 526);Educational Research Institute of America; 2017; Available online: https://s3.amazonaws.com/prod-hmhco-vmg-craftcms-public/research/HMH_Math_in_Focus_RM_3-5_2017SY_Update.pdf (accessed on 8 January 2025).

Houghton Mifflin Harcourt (HMH). Math in focus: Singapore math by marshall cavendish: Evidence base; 2020; Available online: https://s3.amazonaws.com/prod-hmhco-vmg-craftcms-public/research/Math-In-Focus-2020-Foundations-Paper-LR.pdf (accessed on 8 January 2025).

Houghton Mifflin Harcourt (HMH). Go Math!: Research evidence base; 2023; Available online: https://s3.amazonaws.com/prod-hmhco-vmg-craftcms-public/documents/HMH-Go-Math-Evidence-Base-Final.pdf (accessed on 8 January 2025).

Hull, D. M.; Hinerman, K. M.; Ferguson, S. L.; Chen, Q.; Näslund-Hadley, E. I. Teacher-led math inquiry: A cluster randomized trial in Belize. Educational Evaluation and Policy Analysis; 2018; 40, 3 pp. 336-358. [DOI: https://dx.doi.org/10.3102/0162373718768430]

Jablonka, E. Mathematical Literacy. Second international handbook of mathematics education; Bishop, A. J.; Clements, M. A.; Keitel, C.; Kilpatrick, J.; Leung, F. K. S. Springer: 2003; pp. 75-102. [DOI: https://dx.doi.org/10.1007/978-94-010-0273-8_4]

Jaciw, A. P.; Hegseth, W. M.; Lin, L.; Toby, M.; Newman, D.; Ma, B.; Zacamy, J. Assessing impacts of Math in Focus, a “Singapore Math” program. Journal of Research on Educational Effectiveness; 2016; 9, 4 pp. 473-502. [DOI: https://dx.doi.org/10.1080/19345747.2016.1164777]

Jacobs, J. E.; Paris, S. G. Children’s metacognition about reading: Issues in definition, measurement, and instruction. Educational Psychologist; 1987; 22, 3–4 pp. 255-278. [DOI: https://dx.doi.org/10.1080/00461520.1987.9653052]

Jacobse, A. E.; Harskamp, E. G. A meta-analysis of the effects of instructional interventions on students’ mathematics achievement. GION, Gronings Instituut voor Onderzoek van Onderwijs, Opvoeding en Ontwikkeling, Rijksuniversiteit Groningen; 2011; Available online: https://hdl.handle.net/11370/1a0ea36d-3ca3-4639-9bb4-6fa220e50f38 (accessed on 8 January 2025).

Kersaint, G. Orchestrating mathematical discourse to enhance student learning: Creating successful classroom environments where every student participates in rigorous discussions. Curriculum Associates; 2015; Available online: https://www.curriculumassociates.com/programs/i-ready-learning/classroom-math/orchestrating-mathematical-discourse-whitepaper (accessed on 8 January 2025).

Kingston, N.; Nash, B. Formative assessment: A meta-analysis and a call for research. Educational Measurement: Issues and Practice; 2011; 30, 4 pp. 28-37. [DOI: https://dx.doi.org/10.1111/j.1745-3992.2011.00220.x]

Kul, Ü.; Çelik, S. A meta-analysis of the impact of problem posing strategies on students’ learning of mathematics. Revista Romaneasca Pentru Educatie Multidimensionala; 2020; 12, 3 3. [DOI: https://dx.doi.org/10.18662/rrem/12.3/325]

Kutnick, P.; Fung, D.; Mok, I.; Leung, F.; Li, J.; Lee, B.; Lai, V. Implementing effective group work for mathematical achievement in primary school classrooms in Hong Kong. International Journal of Science and Mathematics Education; 2017; 15, 5 pp. 957-978. [DOI: https://dx.doi.org/10.1007/s10763-016-9729-7]

Kyndt, E.; Raes, E.; Lismont, B.; Timmers, F.; Cascallar, E.; Dochy, F. A meta-analysis of the effects of face-to-face cooperative learning. Do recent studies falsify or verify earlier findings?. Educational Research Review; 2013; 10, pp. 133-149. [DOI: https://dx.doi.org/10.1016/j.edurev.2013.02.002]

Lakens, D. Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology; 2013; 4, 00863. [DOI: https://dx.doi.org/10.3389/fpsyg.2013.00863] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/24324449]

Lambert, R.; Algozzine, B.; Gee, J. M. Effects of progress monitoring on math performance of at-risk students. Journal of Education, Society and Behavioural Science; 2014; 4, pp. 527-540. [DOI: https://dx.doi.org/10.9734/BJESBS/2014/7259] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/25435303]

Laski, E. V.; Jor’dan, J. R.; Daoust, C.; Murray, A. K. What makes mathematics manipulatives effective? Lessons from cognitive science and montessori education. SAGE Open; 2015; 5, 2 2158244015589588. [DOI: https://dx.doi.org/10.1177/2158244015589588]

Lazić, B. D.; Knezević, J. B.; Maričić, S. M. The influence of project-based learning on student achievement in elementary mathematics education. South African Journal of Education; 2021; 41, 3 1849. [DOI: https://dx.doi.org/10.15700/saje.v41n3a1909]

Lenhard, W.; Lenhard, A. Computation of effect sizes [Online app]; 2022; Available online: https://doi.org/10.13140/RG.2.2.17823.92329 (accessed on 29 December 2024).

Li, Q.; Ma, X. A meta-analysis of the effects of computer technology on school students’ mathematics learning. Educational Psychology Review; 2010; 22, 3 pp. 215-243. [DOI: https://dx.doi.org/10.1007/s10648-010-9125-8]

Lindorff, A. M.; Hall, J.; Sammons, P. Investigating a Singapore-based mathematics textbook and teaching approach in classrooms in England. Frontiers in Education; 2019; 4, 00037. [DOI: https://dx.doi.org/10.3389/feduc.2019.00037]

Lipsey, M. W.; Puzio, K.; Yun, C.; Hebert, M. A.; Steinka-Fry, K.; Cole, M. W.; Roberts, M.; Anthony, K. S.; Busick, M. D. Translating the statistical representation of the effects of education interventions into more readily interpretable forms (No. NCSER 2013-3000). National Center for Special Education Research, Institute of Education Sciences, U.S. Department of Education; 2012; Available online: https://ies.ed.gov/ncser/pubs/20133000/pdf/20133000.pdf (accessed on 8 January 2025).

Lowrie, T.; Logan, T.; Ramful, A. Visuospatial training improves elementary students’ mathematics performance. British Journal of Educational Psychology; 2017; 87, 2 pp. 170-186. [DOI: https://dx.doi.org/10.1111/bjep.12142]

Lucangeli, D.; Fastame, M. C.; Pedron, M.; Porru, A.; Duca, V.; Hitchcott, P. K.; Penna, M. P. Metacognition and errors: The impact of self-regulatory trainings in children with specific learning disabilities. ZDM; 2019; 51, 4 pp. 577-585. [DOI: https://dx.doi.org/10.1007/s11858-019-01044-w]

Magistro, D.; Cooper, S. B.; Carlevaro, F.; Marchetti, I.; Magno, F.; Bardaglio, G.; Musella, G. Two years of physically active mathematics lessons enhance cognitive function and gross motor skills in primary school children. Psychology of Sport and Exercise; 2022; 63, 102254. [DOI: https://dx.doi.org/10.1016/j.psychsport.2022.102254]

Mayer, R. E. Cognitive theory and the design of multimedia instruction: An example of the two-way street between cognition and instruction. New Directions for Teaching and Learning; 2002; 2002, 89 pp. 55-71. [DOI: https://dx.doi.org/10.1002/tl.47]

McDonald Connor, C.; Mazzocco, M. M. M.; Kurz, T.; Crowe, E. C.; Tighe, E. L.; Wood, T. S.; Morrison, F. J. Using assessment to individualize early mathematics instruction. Journal of School Psychology; 2018; 66, pp. 97-113. [DOI: https://dx.doi.org/10.1016/j.jsp.2017.04.005] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/29499792]

McNeil, N. M.; Fyfe, E. R.; Dunwiddie, A. E. Arithmetic practice can be modified to promote understanding of mathematical equivalence. Journal of Educational Psychology; 2015; 107, 2 pp. 423-436. [DOI: https://dx.doi.org/10.1037/a0037687]

McNeil, N. M.; Hornburg, C. B.; Brletic-Shipley, H.; Matthews, J. M. Improving children’s understanding of mathematical equivalence via an intervention that goes beyond nontraditional arithmetic practice. Journal of Educational Psychology; 2019; 111, 6 pp. 1023-1044. [DOI: https://dx.doi.org/10.1037/edu0000337]

Miles, M. B.; Huberman, A. M.; Saldaña, J. Qualitative data analysis: A methods sourcebook; 3rd ed. SAGE: 2014.

Motteram, G.; Choudry, S.; Kalambouka, A.; Hutcheson, G.; Barton, H. ReflectED: Evaluation report and executive summary. Education Endowment Foundation; 2016; Available online: https://eric.ed.gov/?id=ED581262 (accessed on 8 January 2025).

Moyer-Packenham, P. S.; Westenskow, A. Effects of virtual manipulatives on student achievement and mathematics learning. International Journal of Virtual and Personal Learning Environments (IJVPLE); 2013; 4, 3 pp. 35-50. [DOI: https://dx.doi.org/10.4018/jvple.2013070103]

Mullender-Wijnsma, M. J.; Hartman, E.; de Greeff, J. W.; Bosker, R. J.; Doolaard, S.; Visscher, C. Improving academic performance of school-age children by physical activity in the classroom: 1-year program evaluation. Journal of School Health; 2015; 85, 6 pp. 365-371. [DOI: https://dx.doi.org/10.1111/josh.12259]

Munn, Z.; Peters, M. D. J.; Stern, C.; Tufanaru, C.; McArthur, A.; Aromataris, E. Systematic review or scoping review? Guidance for authors when choosing between a systematic or scoping review approach. BMC Medical Research Methodology; 2018; 18, 1 143. [DOI: https://dx.doi.org/10.1186/s12874-018-0611-x]

Munn, Z.; Pollock, D.; Khalil, H.; Alexander, L.; Mclnerney, P.; Godfrey, C. M.; Peters, M.; Tricco, A. C. What are scoping reviews? Providing a formal definition of scoping reviews as a type of evidence synthesis. JBI Evidence Synthesis; 2022; 20, 4 pp. 950-952. [DOI: https://dx.doi.org/10.11124/JBIES-21-00483] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/35249995]

Murtagh, E.; Sawalma, J.; Martin, R. Playful maths! The influence of play-based learning on academic performance of Palestinian primary school children. Educational Research for Policy and Practice; 2022; 21, 3 pp. 407-426. [DOI: https://dx.doi.org/10.1007/s10671-022-09312-5]

Musna, R. R.; Juandi, D.; Jupri, A. A meta-analysis study of the effect of Problem-Based Learning model on students’ mathematical problem solving skills. Journal of Physics: Conference Series; 2021; 1882, 1 012090. [DOI: https://dx.doi.org/10.1088/1742-6596/1882/1/012090]

Mužar Horvat, S. Značajke učinkovite početne nastave matematike: Sustavni pregled literature [Features of effective elementary mathematics instruction: A systematic literature review]. Marsonia: Časopis za društvena i humanistička istraživanja; 2024; 3, 1 pp. 55-68.

Myers, J. A.; Witzel, B. S.; Powell, S. R.; Li, H.; Pigott, T. D.; Xin, Y. P.; Hughes, E. M. A meta-analysis of mathematics word-problem solving interventions for elementary students who evidence mathematics difficulties. Review of Educational Research; 2022; 92, 5 pp. 695-742. [DOI: https://dx.doi.org/10.3102/00346543211070049]

National Council of Teachers of Mathematics (NCTM). Principles and standards for school mathematics; National Council of Teachers of Mathematics: 2000.

National Council of Teachers of Mathematics (NCTM). Principles to actions: Ensuring mathematical success for all; National Council of Teachers of Mathematics: 2014.

Odani, A. O.; Orongan, R. C. Critical thinking, mathematical dispositions, and metacognitive awareness of students: A causal model on performance. International Journal of Science and Research; 2020; 10, 7 pp. 698-709. [DOI: https://dx.doi.org/10.21275/SR21707180858]

Odum, M.; Meaney, K. S.; Knudson, D. V. Active learning classroom design and student engagement: An exploratory study. Journal of Learning Spaces; 2021; 10, 1 pp. 27-41. Available online: https://libjournal.uncg.edu/jls/article/view/2102 (accessed on 8 January 2025).

OECD. PISA 2022 assessment and analytical framework; PISA, OECD Publishing: 2023; [DOI: https://dx.doi.org/10.1787/dfe0bf9c-en]

Othman, R.; Shahrill, M.; Mohd Roslan, R.; Nurhasanah, F.; Zakir, N.; Asamoah, D. The questioning techniques of primary school mathematics teachers in their journey to incorporate dialogic teaching. Southeast Asian Mathematics Education Journal; 2022; 12, 2 pp. 125-148. [DOI: https://dx.doi.org/10.46517/seamej.v12i2.198]

Ouzzani, M.; Hammady, H.; Fedorowicz, Z.; Elmagarmid, A. Rayyan—A web and mobile app for systematic reviews. Systematic Reviews; 2016; 5, 1 210. [DOI: https://dx.doi.org/10.1186/s13643-016-0384-4] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/27919275]

Pareto, L. A teachable agent game engaging primary school children to learn arithmetic concepts and reasoning. International Journal of Artificial Intelligence in Education; 2014; 24, 3 pp. 251-283. [DOI: https://dx.doi.org/10.1007/s40593-014-0018-8]

Pellegrini, M.; Lake, C.; Inns, A.; Slavin, R. E. Effective programs in elementary mathematics: A best-evidence synthesis [Best Evidence Encyclopedia]. Johns Hopkins University School of Education’s Center for Research and Reform in Education (CRRE); 2018; Available online: http://173.213.237.113/word/elem_math_Oct_8_2018.pdf (accessed on 8 January 2025).

Pellegrini, M.; Lake, C.; Neitzel, A.; Slavin, R. E. Effective programs in elementary mathematics: A meta-analysis. AERA Open; 2021; 7, 2332858420986211. [DOI: https://dx.doi.org/10.1177/2332858420986211]

Perugini, M.; Gallucci, M.; Costantini, G. A practical primer to power analysis for simple experimental designs. International Review of Social Psychology; 2018; 31, 1 20. [DOI: https://dx.doi.org/10.5334/irsp.181]

Peters, M. D. J.; Marnie, C.; Tricco, A. C.; Pollock, D.; Munn, Z.; Alexander, L.; McInerney, P.; Godfrey, C. M.; Khalil, H. Updated methodological guidance for the conduct of scoping reviews. JBI Evidence Synthesis; 2020; 18, 10 2119. [DOI: https://dx.doi.org/10.11124/JBIES-20-00167] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/33038124]

Piaget, J. Piercy, M.; Berlyne, D. E. The psychology of intelligence; Routledge: 2003.

Piper, B.; Ralaingita, W.; Akach, L.; King, S. Improving procedural and conceptual mathematics outcomes: Evidence from a randomised controlled trial in Kenya. Journal of Development Effectiveness; 2016; 8, 3 pp. 404-422. [DOI: https://dx.doi.org/10.1080/19439342.2016.1149502]

Pitchford, N. J. Development of early mathematical skills with a tablet intervention: A randomized control trial in Malawi. Frontiers in Psychology; 2015; 6, 485. [DOI: https://dx.doi.org/10.3389/fpsyg.2015.00485] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/25954236]

Polotskaia, E.; Savard, A. Using the relational paradigm: Effects on pupils’ reasoning in solving additive word problems. Research in Mathematics Education; 2018; 20, 1 pp. 70-90. [DOI: https://dx.doi.org/10.1080/14794802.2018.1442740]

Polya, G. How to solve it: A new aspect of mathematical method; 2nd ed. Princeton University Press: 1988.

Pongsakdi, N.; Laine, T.; Veermans, K.; Hannula-Sormunen, M. M.; Lehtinen, E. Improving word problem performance in elementary school students by enriching word problems used in mathematics teaching. Nordic Studies in Mathematics Education; 2016; 21, 2 pp. 23-44. [DOI: https://dx.doi.org/10.7146/nomad.v21i2.148723]

Prediger, S.; Götze, D.; Holzäpfel, L.; Rösken-Winter, B.; Selter, C. Five principles for high-quality mathematics teaching: Combining normative, epistemological, empirical, and pragmatic perspectives for specifying the content of professional development. Frontiers in Education; 2022; 7, 969212. [DOI: https://dx.doi.org/10.3389/feduc.2022.969212]

Putra, R. W. Y.; Sunyono, S.; Haenilah, E. Y.; Hariri, H.; Sutiarso, S.; Nurhanurawati, N.; Supriadi, N. Systematic literature review on the recent three-year trend mathematical representation ability in scopus database. Infinity Journal; 2023; 12, 2 pp. 243-260. [DOI: https://dx.doi.org/10.22460/infinity.v12i2.p243-260]

Rittle-Johnson, B. Dunlosky, J.; Rawson, K. A. Iterative development of conceptual and procedural knowledge in mathematics learning and instruction. The Cambridge handbook of cognition and education; Cambridge University Press: 2019; pp. 124-147. [DOI: https://dx.doi.org/10.1017/9781108235631.007]

Rösken, B.; Rolka, K. A picture is worth a 1000 words—The role of visualization in mathematics learning. Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education; Charles University in Prague, Faculty of Education: 2006; Vol. 4, pp. 457-464.

Salam, M.; Misu, L.; Rahim, U.; Hindaryatiningsih, N.; Ghani, A. Strategies of metacognition based on behavioural learning to improve metacognition awareness and mathematics ability of students. International Journal of Instruction; 2020; 13, 2 pp. 61-72. [DOI: https://dx.doi.org/10.29333/iji.2020.1325a]

Sargeant, J. M.; O’Connor, A. M. Scoping reviews, systematic reviews, and meta-analysis: Applications in veterinary medicine. Frontiers in Veterinary Science; 2020; 7, 00011. [DOI: https://dx.doi.org/10.3389/fvets.2020.00011] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/32047759]

Savard, A.; Polotskaia, E. Who’s wrong? Tasks fostering understanding of mathematical relationships in word problems in elementary students. ZDM; 2017; 49, 6 pp. 823-833. [DOI: https://dx.doi.org/10.1007/s11858-017-0865-5]

Schmidt, W. H.; Cogan, L. S.; McKnight, C. C. Equality of educational opportunity: Myth or reality in U.S. schooling?. American Educator; 2011; 34, 4 pp. 12-19. Available online: https://eric.ed.gov/?id=EJ909927 (accessed on 8 January 2025).

Schnepel, S.; Aunio, P. A systematic review of mathematics interventions for primary school students with intellectual disabilities. European Journal of Special Needs Education; 2022; 37, 4 pp. 663-678. [DOI: https://dx.doi.org/10.1080/08856257.2021.1943268]

Schoenherr, J.; Strohmaier, A. R.; Schukajlow, S. Learning with visualizations helps: A meta-analysis of visualization interventions in mathematics education. Educational Research Review; 2024; 45, 100639. [DOI: https://dx.doi.org/10.1016/j.edurev.2024.100639]

Schraw, G. Promoting general metacognitive awareness. Instructional Science; 1998; 26, 1 pp. 113-125. [DOI: https://dx.doi.org/10.1023/A:1003044231033]

Schwarz, P. Raising the bar district-wide using Symphony Math. Symphony Learning; 2019; Available online: https://content.symphonylearning.com/assets/web/SLC_Graves_2020_02_27.pdf (accessed on 8 January 2025).

Sercenia, J. C.; Prudente, M. S. Effectiveness of the metacognitive-based pedagogical intervention on mathematics achievement: A meta-analysis. International Journal of Instruction; 2023; 16, 4 pp. 561-578. [DOI: https://dx.doi.org/10.29333/iji.2023.16432a]

Sharma, A.; Singh, S. IMPACT: Interweaving mathematics pedagogy and content of teaching-at elementary level. International Journal of Advance and Innovative Research; 2019; 5, 4 pp. 13-25.

Sides, J. D.; Cuevas, J. A. Effect of goal setting for motivation, self-efficacy, and performance in elementary mathematics. International Journal of Instruction; 2020; 13, 4 pp. 1-16. [DOI: https://dx.doi.org/10.29333/iji.2020.1341a]

Simms, V.; McKeaveney, C.; Sloan, S.; Gilmore, C. Interventions to improve mathematical achievement in primary school-aged children. Nuffield Foundation; 2019; Available online: https://pure.ulster.ac.uk/ws/portalfiles/portal/76895050/Math_interventions.pdf (accessed on 8 January 2025).

Slavin, R. E. Best-evidence synthesis: An alternative to meta-analytic and traditional reviews. Educational Researcher; 1986; 15, 9 pp. 5-11. [DOI: https://dx.doi.org/10.3102/0013189X015009005]

Slavin, R. E. Best evidence synthesis: An intelligent alternative to meta-analysis. Journal of Clinical Epidemiology; 1995; 48, 1 pp. 9-18. [DOI: https://dx.doi.org/10.1016/0895-4356(94)00097-A] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/7853053]

Slavin, R. E.; Lake, C. Effective programs in elementary mathematics: A best-evidence synthesis. Review of Educational Research; 2008; 78, 3 pp. 427-515. [DOI: https://dx.doi.org/10.3102/0034654308317473]

Snilstveit, B.; Stevenson, J.; Menon, R.; Phillips, D.; Gallagher, E.; Geleen, M.; Stamp, M.; Jobse, H.; Schmidt, T.; Jimenez, E. The impact of education programmes on learning and school participation in low-and middle-income countries; International Initiative for Impact Evaluation (3ie): 2015; [DOI: https://dx.doi.org/10.23846/SRS007]

Sokolowski, A. The effects of using representations in elementary mathematics: Meta-analysis of research. The International Academic Forum (IAFOR); 2018; 6, 3 pp. 129-152. [DOI: https://dx.doi.org/10.22492/ije.6.3.08]

Solomon, T.; Dupuis, A.; O’Hara, A.; Hockenberry, M. -N.; Lam, J.; Goco, G.; Ferguson, B.; Tannock, R. A cluster-randomized controlled trial of the effectiveness of the JUMP math program of math instruction for improving elementary math achievement. PLoS ONE; 2019; 14, 10 e0223049. [DOI: https://dx.doi.org/10.1371/journal.pone.0223049]

Sortwell, A.; Trimble, K.; Ferraz, R.; Geelan, D. R.; Hine, G.; Ramirez-Campillo, R.; Carter-Thuiller, B.; Gkintoni, E.; Xuan, Q. A systematic review of meta-analyses on the impact of formative assessment on K-12 students’ learning: Toward sustainable quality education. Sustainability; 2024; 16, 17 7826. [DOI: https://dx.doi.org/10.3390/su16177826]

Springer, L.; Stanne, M. E.; Donovan, S. S. Effects of small-group learning on undergraduates in science, mathematics, engineering, and technology: A meta-analysis. Review of Educational Research; 1999; 69, 1 pp. 21-51. [DOI: https://dx.doi.org/10.3102/00346543069001021]

Svane, R. P.; Willemsen, M. M.; Bleses, D.; Krøjgaard, P.; Verner, M.; Nielsen, H. S. A systematic literature review of math interventions across educational settings from early childhood education to high school. Frontiers in Education; 2023; 8, 1229849. [DOI: https://dx.doi.org/10.3389/feduc.2023.1229849]

Takele, M. H. Implementation of active learning methods in mathematics classes of Woliso town primary schools, Ethiopia. International Journal of Science and Technology Education Research; 2020; 11, 1 pp. 1-13.

Ting, F. S. T.; Shroff, R. H.; Lam, W. H.; Garcia, R. C. C.; Chan, C. L.; Tsang, W. K.; Ezeamuzie, N. O. A meta-analysis of studies on the effects of active learning on Asian students’ performance in science, technology, engineering and mathematics (STEM) subjects. The Asia-Pacific Education Researcher; 2023; 32, 3 pp. 379-400. [DOI: https://dx.doi.org/10.1007/s40299-022-00661-6]

Toit, S. d.; Kotze, G. Metacognitive strategies in the teaching and learning of mathematics. Pythagoras; 2009; 70, pp. 57-67. [DOI: https://dx.doi.org/10.4102/pythagoras.v0i70.39]

United Nations Development Programme (UNDP),. Breaking the gridlock: Reimagining cooperation in a polarized world; 2024; Available online: https://hdr.undp.org/system/files/documents/global-report-document/hdr2023-24reporten.pdf (accessed on 8 January 2025).

Vale, I.; Barbosa, A. Active learning strategies for an effective mathematics teaching and learning. European Journal of Science and Mathematics Education; 2023; 11, 3 pp. 573-588. [DOI: https://dx.doi.org/10.30935/scimath/13135]

Vazou, S.; Skrade, M. A. B. Intervention integrating physical activity with math: Math performance, perceived competence, and need satisfaction†. International Journal of Sport and Exercise Psychology; 2017; 15, 5 pp. 508-522. [DOI: https://dx.doi.org/10.1080/1612197X.2016.1164226]

Veldhuis, M.; van den Heuvel-Panhuizen, M. Supporting primary school teachers’ classroom assessment in mathematics education: Effects on student achievement. Mathematics Education Research Journal; 2020; 32, 3 pp. 449-471. [DOI: https://dx.doi.org/10.1007/s13394-019-00270-5]

Verschaffel, L.; De Corte, E.; Lasure, S.; Van Vaerenbergh, G.; Bogaerts, H.; Ratinckx, E. Learning to solve mathematical application problems: A design experiment with fifth graders. Mathematical Thinking and Learning; 1999; 1, 3 pp. 195-229. [DOI: https://dx.doi.org/10.1207/s15327833mtl0103_2]

Wilson, B. D. Practical meta-analysis effect size calculator (Version 2023.11.27) [Online app]. Campbell Collaboration; 2023; Available online: https://www.campbellcollaboration.org/calculator/ (accessed on 8 January 2025).

Worth, J.; Sizmur, J.; Ager, R.; Styles, B. Improving numeracy and literacy: Evaluation report and executive summary. Education Endowment Foundation; 2015; Available online: https://eric.ed.gov/?id=ED581142 (accessed on 8 January 2025).

Yeh, C.; Cheng, H.; Chen, Z.; Liao, C.; Chan, T. Enhancing achievement and interest in mathematics learning through Math-Island. Research and Practice in Technology Enhanced Learning; 2019; 14, 1 5. [DOI: https://dx.doi.org/10.1186/s41039-019-0100-9]

Zahedi, S.; Bryant, C.; Iyer, A.; Jaffer, R. The use of blended learning to promote learner-centered pedagogy in elementary math classrooms. Educational Research for Policy and Practice; 2023; 22, 3 pp. 389-408. [DOI: https://dx.doi.org/10.1007/s10671-023-09346-3]

Zhang, L.; Stylianides, G. J.; Stylianides, A. J. Enhancing mathematical problem posing competence: A meta-analysis of intervention studies. International Journal of STEM Education; 2024; 11, 1 48. [DOI: https://dx.doi.org/10.1186/s40594-024-00507-1]

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Abstract

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Considering that the teaching of mathematics in elementary school is an important prerequisite for the development of mathematically literate citizens, it is essential to identify what makes it effective. The aim of this study is to determine the characteristics of effective interventions in elementary school mathematics education. To this end, a scoping review was conducted that included 44 experimental studies published between 2014 and 2023. Through a qualitative analysis of the intervention descriptions, we identified 27 characteristics, which were categorized into nine thematic units. We found that, on average, seven characteristics were used per intervention. The results of this study suggest that effective elementary school mathematics instruction should foster students’ conceptual understanding and procedural fluency through problem-solving, active learning, and mathematical games. This can be achieved through a dynamic alternation of whole-class instruction and cooperative and individual learning with the use of manipulatives and visualizations to reach the level of abstraction. Considering that the analyzed interventions rarely addressed students’ common errors and critical thinking, future research could focus on these aspects in elementary school mathematics education.

Details

Title

Characteristics of Effective Elementary Mathematics Instruction: A Scoping Review of Experimental Studies

Author

Bognar, Branko¹

; Horvat, Sanela Mužar²

; Matić, Ljerka Jukić³

¹ Department of Pedagogy, Faculty of Humanities and Social Sciences, University J. J. Strossmayer of Osijek, 31000 Osijek, Croatia
² Department of Social Sciences and Humanities, University of Slavonski Brod, 35000 Slavonski Brod, Croatia; [email protected]
³ School of Applied Mathematics and Informatics, University J. J. Strossmayer of Osijek, 31000 Osijek, Croatia; [email protected]

First page

Publication year

2025

Publication date

2025

Publisher

MDPI AG

e-ISSN

22277102

Source type

Scholarly Journal

Language of publication

English

DOI

https://doi.org/10.3390/educsci15010076

ProQuest document ID

3159411284