Concept Mapping in Teaching Mathematics in

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1. Introduction

It is not easy to motivate pupils and students to indulge in meaningful learning. One of the possibilities is the use of activating and innovative methods of education, which arouse greater interest in pupils and students in the topics covered and facilitate their understanding [1]. It must be pointed out to pupils and students that the information they learn is necessary for everyday life. The role of the teachers in this context is to bring the learners didactic transformations of the mechanical reproductive acquisition of knowledge to the level of acquiring knowledge in a productive way, requiring a certain level of imagination, and creativity, even if the learner has basic knowledge [2]. As Kožuchová and the team of authors [3] state in their publication Curriculum of Primary Education, pupils at the primary level (ISCED 1) should acquire new knowledge and skills especially via their own activities and experiences. They should learn to express the basics of their literacy, including mathematical literacy, as much as possible and communicate it to develop it further [4]. However, teaching mathematics at the primary level is often completed by passively listening to the interpretation of the new curriculum without approaching the practical applicability of the acquired knowledge and skills. Abramovich, Grinshpan, and Milligan [5] in their extensive study describing conceptual approaches to teaching mathematics at all levels of education, state that it is not easy to engage students in the teaching process of mathematics, to arouse in them an internal interest in the subject matter explained, to encourage them to take action and to teach it in the most attractive, engaging way possible, ensuring that a reasonable amount of information is delivered to the learners directly in the classroom.

At present, digital teaching aids with integrated gamification elements and a high degree of interactivity are widely used to increase the effectiveness of teaching various subjects. The concept of digitally-assisted teaching has long been an accepted pedagogical term; however, in primary and secondary education we encounter the phenomenon of digitally supported teaching of languages much more often than the phenomenon of digitally supported teaching of mathematics and sciences. This also says something about the degree of attractiveness of teaching the humanities, and science and technology-related subjects, which are not very popular among the young generation, despite the fact that students are aware of the importance of these subjects in relation to their future profession. This fact is also confirmed by many studies [6,7,8,9,10].

Our research, the results of which are presented in the following, focused on the possibilities of the effective use of author-created experimental teaching materials—digital concept maps supplemented by multimedia teaching resources in teaching mathematics at the primary level of education. The research problem (the purpose of the research survey) was to heighten the prolonged low activity levels of third-grade pupils in the mathematics lessons accompanied by a low interest in the curriculum at the monitored primary school. Based on the findings of various research [11,12,13,14] the authors tried to resolve this problem using digital conceptual maps during the teaching process. Via the digital concept maps used in the process of pedagogical intervention in teaching mathematics, we wanted to point to the potential of increasing the effectiveness of teaching selected topics of mathematics in the third grade of a primary school. Increasing the effectiveness of teaching is primarily associated with the cognitive development of learners, but also at a secondary level with the possibilities of inducing changes in learners’ attitudes and increasing their internal motivation to learn mathematics.

The success or failure of pupils and students at school is determined by a number of factors related to the personality of the learner, but also a number of other external conditions [15,16,17]. As reported by Helus et al. [18] a narrower notion of school success reflects the ideas of what a learner should be, in what direction, and by what means his or her personality should develop. In the context of understanding school success, Helus [19] states that a successful pupil or student is understood as an individual who flawlessly and reliably handles challenging tasks at a high pace. At the same time, however, he adds that the determinants of a learner’s school success cannot be linked solely to his/her marks. In addition to the evaluation of the learner’s performance by the teacher, the determinants influencing a learner’s success or failure include the professional qualification and personality of the teacher, the parents’ education, the socio-economic conditions in which the pupil or student is growing and living, the psychological aspects of his/her personality, attitude to school, learning, the subjects, the pupil or student’s needs and interests and the like ([20,21]). The results of recent studies in this area suggest that school success is an important factor in shaping a student´s future.

Bloom [22] showed that there is a relationship between the motivational aspects of learners and their educational outcomes. In professional publications, Nakonečný [23] and Hvozdík [24] point out that it is possible to find a simple formula expressing the dependence of the learner’s learning performance on two decisive factors, namely ability and motivation (performance = ability × motivation). It is a somewhat simplistic view, but on the other hand, it points to the trend that by inducing appropriate motivation it is possible to significantly influence school success and compensate for the lack of learners’ abilities in the relevant area to a large extent. Simultaneously, this formula draws attention to the fact that even a high level of skills does not in itself guarantee a high learning success for the learner, and similarly, high motivation without adequate skills is not a guarantee of success.

As Jurčo [25] states, the relationship to subjects is actually an expression of attitude and interest in the subject. Regarding the role of gender in learning outcomes, even though the level of intellectual abilities of boys and girls is the same, the difference lies in the structure of the intellect itself [26]. The situation is similar in the area of interests and preferences of various subjects. Research studies in several European countries, as well as the results of the international PISA and TIMSS monitoring, have long confirmed a declining trend in the popularity of mathematics as students grow older [27,28,29,30,31,32]. This is probably closely related to the increasingly abstract nature and complexity of the curriculum in mathematics, which is included in the individual grades of a primary school. This fact is also confirmed by Chvál´s analytical study [33], which draws attention to the significant decline in the popularity of mathematics occurring among pupils and students during their transition to the higher grades of a primary school (transition from ISCED1 to ISCED2). The author team of Federičová and Münich [28] point to a noticeably closer connection between the negative attitudes of boys towards school and their educational results compared to the girls. Pavelková and Hrabal [27] in their study state that Czech students, in addition to considering mathematics to be a very demanding subject, achieve the worst study results of all the classified subjects. This indicates that the popularity of mathematics may be related both to the subjective demands of the subject for students and the actual achievement of students in this subject. Mullis and his colleagues [34] showed from data of the TIMSS 2011 study that there is a clear relationship between the results achieved in the mathematical test and the popularity of the subject. In their research study, Inzlicht and Schmader [35] also confirm that the popularity of a subject with a learner correlates with the achieved learning performance, while this correlation is mediated by motivation.

There are several phenomena related to motivation as an important factor in the educational process, such as whether a student is looking forward to a mathematics lesson, whether s/he enjoys it, or, conversely, perceives it as boring or uninteresting. It is therefore important to take into account other determinants, on basis of which pupils and students build a relationship to education and individual subjects, including mathematics [36]. However, in the present study we do not deal with the determinants of the popularity of mathematics, but with what potential changes in pupils’ attitudes and attitudes to mathematics can be expected due to the application of conceptual mapping in teaching mathematics. However, the primary research question is whether the implementation of concept mapping in the teaching process has an impact on increasing the mathematical performance of pupils in selected thematic units in the mathematics curriculum.

Based on the research activities of available domestic and foreign literary sources [37,38,39,40,41,42,43,44,45,46,47] we may assume that the application of concept mapping at different levels of education may have a positive impact on some aspects of teaching. For example, concept maps allow for a clear structure of the curriculum, help students to better understand the topic, make pupils think about key concepts, relationships, and connections between them, and teach them to distinguish between different levels of generally related phenomena and concepts and, last but not least, discuss, draw, connect, classify knowledge and information, making teaching more interesting and attractive to them [48,49,50].

As part of the solution to this research problem, to obtain relevant research data, we created and designed our own teaching materials (within the FreeMind, Mindomo, and XMind software applications) to support the teaching of selected thematic units in mathematics taught in the third grade of a primary school. The created teaching materials, sets of concept maps supplemented by digital teaching resources, represented intervention elements, the application of which to teaching mathematics should, according to our research assumptions, influence the attitudes of pupils to the subject of mathematics, i.e., to increase motivation and interest in mastering the subject matter of mathematics.

2. Methodology

2.1. Concept of Methodological Starting Points

In accordance with the above-mentioned focus of the research investigation and on the basis of the findings presented in the conceptual starting points of the research, the main goal of the research investigation was to verify the following research hypothesis:

Hypothesis.

We assume that teaching supported by innovative teaching aids, such as digital concept maps, contributes to reducing pupils’ negative attitudes towards subjects, specifically the subject of mathematics at the primary level of education (ISCED 1), and these digital teaching aids have a positive impact on the attitude of pupils towards the subject overall.

Verification of the above-mentioned research hypothesis was realized by means of a pedagogical experiment. Within the pedagogical experiment, the possibilities of positively influencing attitudes towards the subject of mathematics were monitored and evaluated, on basis of the use of the teaching aids created for the target group of the 3rd-grade pupils in primary education. At the same time, we monitored and compared the effectiveness of teaching the math curricula in question with and without pedagogical intervention using the digital concept maps we created, supplemented by multimedia teaching resources.

The research took place in the following phases:

Preparation of experimental teaching materials. Construction of a questionnaire designed for the research data collection.
Assessment of the quality of the research tools (reliability/item analysis).
Creation of control and experimental group.
Questionnaire administration.
Realization of the pedagogical experiment.
Questionnaire readministration.
Processing and evaluation of the research data.
Interpretation of research findings.

The first, but logically most important step in achieving the research goal was to create interactive concept maps, which were created by means of the FreeMind, Mindomo, and Xmind software applications, available amongst others. The digital teaching materials thus created are applicable in teaching mathematics in the 3rd grade of primary education as a supporting illustrative material in explaining and fixating the following topics: Propaedeutics of multiplication (to derive and understand the principle of multiplication as a repeated adding of equal parts), Propaedeutics of division (lessons aimed at deriving and understanding the principle of division, as a division of the whole into equal parts), Plane geometric shapes (lessons aimed at consolidating the knowledge of geometry with an emphasis on the geometric shape of the square and rectangle) and Notions of mathematical operations (lessons aimed at consolidating basic mathematical concepts and basic mathematical operations: sum, proportion, difference, and product). The individual parts of digital concept maps supplemented by multimedia teaching resources are designed to be used by pupils as part of their independent work in the classroom or in their home preparation for teaching. In addition, they are designed to diagnose acquired knowledge. The visualization of the processed mathematical concepts and rules plays the main role in the application of the created conceptual maps. Within the pedagogical experiment, we observed the influence of this visualization on the attitudes of the target group of pupils to the subject of mathematics.

The evaluation of the quality of teaching of individual subjects is usually based on the analysis of the content of teaching, the pupils or students’ learning outcomes, and factors influenced by the school that have the potential to interfere with the pupils’ and students’ attitudes to the subject [51]. Therefore, we based the methodology of the evaluation and comparison of the relationship of the pupils involved in our pedagogical experiment on the screening of their attitudes to the following nine factors:

Popularity of the subject;
Interest in the content of the curriculum;
Complexity of the content of the curriculum;
Comprehensibility of the interpretation of the new curriculum;
Usability of knowledge for one’s own future;
Reasons for learning the subject;
Suitability of the specific ways of interpreting the new curriculum;
Sources of concerns related to the subject;
Pupils’ interest in the extracurricular teaching of mathematics.

A self-designed questionnaire was used as a tool to collect the research data, in which the individual items (termed P1 to P9) correspond to the factors mentioned above. Dependence of the obtained research data on the gender factor was not analyzed.

The questionnaire was administrated in printed form in the Slovak language. Simultaneously with the questionnaire development, administration and evaluation rules of the questionnaire survey were elaborated in detail. To solve the research problem, we chose a quantitative method of empirical measurement. It seems that the proposed way, i.e., the print version of the questionnaire, was chosen appropriately, as it did not cause any greater time burden for the pupils, and another benefit of this way of information obtaining was a large amount of research data collected from respondents.

The main goal of the questionnaire was to determine the impact and importance of using digital concept maps within pedagogical intervention, enabling the possibility of inducing positive changes towards mathematics in the given target group of learners, (i.e., pupils of the 3rd grade of a primary school). The questionnaire was administered twice: firstly, as a pretest before the pedagogical experiment (before the concept maps and multimedia teaching materials were introduced into the teaching process) and secondly, as a posttest, after the end of the experiment.

The pedagogical experiment was carried out at a primary school in the region of the city of Nitra (SK) in the school year of 2020/2021. The experimental group (ESC) consisted of 21 pupils (10 boys and 11 girls) and the control group (KSA) consisted of 20 pupils (10 boys and 10 girls) comprised of two 3rd-grade classes in this school. The average age of all respondents involved in the research was 9.4 years.

Knowledge level of the whole research sample (all pupils involved in the experiment, as well as the knowledge level of the pupils within the sub-groups, (i.e., pupils within the experimental ESC group, as well as pupils within the control KSA group) was not of the same level. In our case, however, these differences did not contradict the correctness of the research results, as we did not look at possibilities of influencing education process efficiency (it’s increasing). What we did was look at possibilities of influencing the pupils’ attitudes and approaches to the given topics of mathematics curricula taught in the 3rd grade of primary schools by means of the pedagogical intervention of digital concept maps, developed by us, into the teaching process.

On average, the pupils in the control group had showcased better study results for a long time, higher general learning abilities, and an interest in learning in comparison with the pupils in the experimental group. The pedagogical intervention of the digital concept maps developed by us supplemented by multimedia teaching materials in the teaching process was carried out during the regular mathematics lessons. In order to eliminate the influence of disruptive effects, the lessons, as well as the collection of research data, were carried out in both groups by the class teacher.

2.2. Methodology of Pedagogical Experiment

The pedagogical experiment was based on the intervention of the newly-created experimental teaching materials—digital concept maps, supplemented by multimedia teaching resources in the teaching of selected thematic units within the curriculum of mathematics in the 3rd grade of primary education (Propaedeutics of multiplication, Propaedeutics of division, Plane geometric shapes, Notions of mathematical operations). The teaching process during the pedagogical experiment took place in an experimental and control group.

The educational activity in the experimental group was based on the use of concept maps as an innovative teaching method. Relevant teaching materials were used by the teacher in explaining and fixating the subject matter, but they were also used by the pupils themselves, either as supportive illustrative teaching materials in individual work during the lesson or during homework. In the control group, the interpretation and acquisition of the curriculum took place in a conventional way without the use of the concept maps. The teacher used the teaching aids at his disposal and the lesson was taught as an interview—based on questions. As mentioned above, the cognitive level of the pupils in the experimental and control groups was not the same, which was insignificant from the aspect of the hypothesis verified in the research.

The pupils’ relationship and attitudes to mathematics and the learning of the subject were researched in terms of the nine factors specified in the above using a questionnaire before the start of the experiment (as a pretest) and after it finished (as a posttest).

From the data obtained through the questionnaire administration before and after the pedagogical experiment, changes in pupils´ attitudes towards the subject of mathematics occurred under the influence of the pedagogical intervention of the digital concept maps and multimedia teaching materials were evaluated by the means of mathematical-statistical methods. All obtained data were processed by statistical software, and some auxiliary calculations, data tabulation, and graphical visualizations were processed by other software applications.

A schedule of the carried out pedagogical experiment is presented in Table 1.

Figure 1 presents an example of a concept map to draw the division principle and Figure 2 presents an example of multimedia teaching materials developed to the digital concept maps—pupils´ activity to multiplication in which pupils learn to multiply by means of addition.

3. Results

The data obtained by administering the questionnaire before and after the pedagogical experiment were processed by mathematical–statistical methods. Based on the results we evaluated the changes in the pupils’ attitudes to the subject of mathematics induced by the influence of pedagogical intervention incorporating the relevant digital concept maps and multimedia teaching materials.

The questionnaire contained nine items in which pupils expressed their views on factors related to mathematics and its teaching. The pupils evaluated mathematics both in terms of their subjective relationship to it (e.g., popularity of the subject, interest and complexity of content, applicability of the subject for their own future) and in terms of their views on learning this subject, (e.g., comprehensibility of new subject matter explained by the teacher, method of interpretation/presentation of the new curriculum by the teacher).

The pupils expressed their agreement or disagreement with the statements/questions expressed in ordinal question numbers 1 to 5 and 9 using a five-point scale [52]. A higher rate of disagreement with the statement/question was expressed by a lower value, total disagreement or rejection being rated as 1. A higher rate of agreement with the statement/question was expressed by a higher value, a full-scale agreement being represented by a 5.

In case of the item P1 (You have different subjects at school. Mathematics would be included in what kind of your subjects) pupils evaluated mathematics more or less as their favorite/disliked subject (5—most favorite, 4—favorite, 3—neither favorite nor disliked, 2—disliked, 1—very much disliked).

In questionnaire item P2 (There is always something interesting to be found in each subject you are learning. You consider mathematics to be a subject) the pupils were asked to evaluate the interesting nature/attractiveness of the subject of mathematics (5—very interesting, 4—interesting, 3—neither interesting nor uninteresting, 2—uninteresting, 1—very much uninteresting).

The third item termed P3 focused on finding out the difficulty of mastering the mathematics curriculum. Based on the statement formulated in this questionnaire item (Whether you are friends with mathematics more or less, do you consider mathematics as a subject), pupils could evaluate the subject of mathematics as 5—very demanding, 4—demanding, 3—neither demanding nor undemanding, 2—undemanding, 1—completely undemanding.

While in the third item the pupils evaluated the difficulty of acquiring mathematics in general, in the fourth P4 item of the questionnaire (During the mathematics class the teacher explains the curriculum. The explanation of the new curriculum) the pupils evaluated to what extent they understand the teacher’s explanation (5—I always understand, 4—I tend to understand, 3—Sometimes I understand but sometimes I do not, 2—I do not understand it very much, 1—I never understand it).

In the fifth questionnaire item P5, (You will learn a lot of new and interesting things in mathematics. Do you think that mathematics is necessary for you as part of a person’s education?) the pupils were asked to express what degree of importance they assign to learning mathematics in a person’s everyday life (5—definitely yes, 4—probably yes, 3—neither yes nor no, 2—probably no, 1—definitely no).

The last ordinal question of the questionnaire was item P9, which examined the pupils’ potential interest, given the opportunity in enrolling in a math class after school. The pupils expressed their opinion using a five-point scale: 5—I’m definitely interested, 4—I’m rather interested, 3—I am neither interested nor uninterested, 2—I’m rather not interested, and 1—I’m definitely not interested.

The other three items of the questionnaire (P6–P8) were closed. In these nominal questionnaire items, the pupils chose one of the answers which corresponded with their viewpoint the most.

In the sixth questionnaire item P6, we looked for the most likely reasons why pupils learn mathematics. The wording of the questionnaire item was the following: Pupils learn individual subjects for various reasons. Why do you usually learn maths? The alternative answers were formulated as follows:

(a). I am interested in mathematics because it helps me to get to know and understand many things;
(b). I am interested in the teaching aids we work with in the mathematics lessons;
(c). I like to solve mathematical problems;
(d). I want to get a good mark;
(e). because the teacher explains it in an interesting way.

The seventh item of the questionnaire (P7) focused on finding out about the ways pupils prefer to be taught a new curriculum. The wording of the item was the following: Pupils prefer different ways of being taught a new curriculum. Which way suits you best? Pupils could choose one answer from the four which most corresponded to their attitude:

(a). When the teacher explains the new curriculum all by himself, without illustrative teaching aids, the interpretation is understandable and clear;
(b). When the teacher explains the new curriculum (subject matter) all by himself, using various teaching aids;
(c). When the teacher involves us—the pupils—in the interpretation of the new curriculum (subject matter);
(d). When the teacher gives us individual tasks and we solve them.

In the eighth item—P8—we wanted to find out what causes pupils to feel fear and anxiety in the mathematics lessons. The wording of the questionnaire was as follows: Some pupils experience fear and anxiety before certain lessons. Do you also fear or dread the maths classes? Why are you afraid? What are you afraid of? Pupils were offered the following possible answers to this question:

(a). I am not afraid or anxious about anything;
(b). Unpreparedness for the lesson (I do not have my homework; I do not have the necessary tools);
(c). Oral examination at the board;
(d). A quick test;
(e). A bad mark.

The reliability of the developed research tool was confirmed by assessing its reliability and identifying suspicious items by a reliability/item analysis. The overall reliability of the questionnaire was calculated using Cronbach’s alpha. The achieved value α = 0.78 confirmed the high internal consistency of the measuring tool used to obtain reliable research data.

The data obtained for each of the questionnaire items within the pretest and posttest were processed depending on the level of the GROUP factor (experimental—ESC, control—KSA). We analyzed the final research data using statistical processing within the Mann–Whitney U test, chi-squared test of independence, Levene non-parametric test, and their graphical visualization. The use of these methods was preceded by the verification of their use, (e.g., verification of the normal distribution of the dependent variable in each group, equality of variances, and expected frequencies for the chi-squared test).

Validity Verification of the Used Statistical Methods

To use the above-mentioned tests following assumptions must be fulfilled:

A. assumptions of the use of simple sort variance analysis

Normal distribution of the depending variable in the particular groups

We checked normality for the depending ordinal variables (1PRE–5PRE, 9PRE, and 1POST–5POST, 9POST) in both research groups of pupils according to the value (category) of the factor GROUP (ESC, KSA). The observed variables do not have a normal distribution.

2.. Assumption of variance equality

Tests of variance equality test the null hypothesis H0:

$H 0 : {σ_{1}}^{2} = \dots = {σ_{i}}^{2}$

Against its alternative H1, that H0 is not valid.

In the case of the variables, 3PRE and 5POST are the tests statistically significant (p < 0.05) (Table 2 and Table 3), which means that the hypothesis on the variance equality is rejected. We can state that in the case of these variables the assumptions were violated.

Due to the violations of the assumptions of the variance analysis validity, the Mann–Whitney U test was used [53].

B. Assumptions of the use of chí-squared test of independence

To analyze multidimensional tables we used chí-squared test of independence. Chí-squared test verifies whether the differences in observed and expected frequencies in pivot table cells are only random (the variables are independent) or statistically significant (the variables are dependent) (1).

(1) $χ^{2} = \sum_{i = 1}^{R} \sum_{j = 1}^{S} \frac{{(a_{i j} - e_{i j})}^{2}}{e_{i j}}$

Chí-squared test of independence is an extension of chí-squared test by a test of fit and i is based on a pivot table of observed frequencies, where the observed frequency a_ij is the frequency of the combination x_i ∧ y_j. The expected frequency of the given pivot table cell is equal to the ratio of the product of the respective observed frequency of the row and column, and the total number of observations.

The only precondition for the use of a chí-squared test (apart from the rules related to the selection of the research sample) is the rule that the expected frequencies are higher than or at most equal to 5 (2).

(2) $e_{i j} = \frac{r_{i} s_{j}}{n} \geq 5$

Significant expected frequencies are not large enough. This assumption of the use of chí-squared test is not fulfilled for any of the variables. That is why the chí-sqaured test results have to be taken with a grain of salt. So, in analyzing these dependencies we, therefore, relied on exploratory techniques (dependence visualizations).

4. Discussion of Research Results

Table 4 contains descriptive statistics (the mean, standard deviation, standard error, and the 95% confidence interval of the mean), the posttest scores for ordinal items 1POST to 5POST and 9POST separately for both groups as well as conclusively for the experimental (ESC) and control group (KSA).

Based on the results of descriptive statistics we identified the zero statistical hypotheses. The zero statistical hypotheses, when monitoring the dependence of pupils’ responses on ordinal items 1POST to 5POST and 9POST in the administered questionnaire (posttest), were formulated so that the responses of the pupils to these questionnaire items do not depend on the GROUP factor. None of the null hypotheses were confirmed because of the final value of p > 0.05, which means that the differences among the responses of the surveyed sample of pupils to the posttest items depending on the GROUP factor were not statistically significant in any case.

As an example of the statistical processing of research data using the Mann–Whitney U test, we present the results of the analysis of the first posttest item (item 1POST), which was used to determine the popularity of mathematics amongst the pupils taking part in the research (groups ESC and KSA). Next, we will focus on the evaluation and overall interpretation of the research results obtained from the other ordinal items of the posttest.

The answers to the first questionnaire item of the posttest (1POST) showed what changes our pedagogical intervention of using conceptual maps and multimedia teaching materials within the selected thematic units Propaedeutics of multiplication, Propaedeutics of division, Planar geometric forms and Concepts of mathematical operations caused in the opinions and attitudes of the pupils of the experimental group (ESC) regarding the popularity of mathematics. The formulation of the null hypothesis tested in the questionnaire item P1 was as follows:

Hypothesis 0.

The respondents’ response to the 1POST posttest item does not depend on the GROUP factor.

Based on the results of the Mann–Whitney U test, p = 0.32 (Table 5), we do not reject the null statistical hypothesis (p > 0.05), i.e., there is no statistically significant difference between the results of the experimental and control groups in the evaluation of the first item of the posttest.

The results of the pupils’ answers to the first item pretest and posttest item are given in the box graphs of Figure 3 and Figure 4. From the graphical visualization of the evaluation of the pupils’ responses to the first pretest item (1PRE) and the first posttest item (1POST) it can be seen that the situation changed only within the experimental group (ESC) to a certain extent. In the case of the 1POST item, the median of the scale (the popularity of mathematics—Mathematics is mine… subject) for the experimental group (ESC) is in the value of 4.5 (a very popular subject) while for the control group (KSA) it is 4 (a popular subject). The quartile range for each group overlaps; the mean 50% of the values for the experimental group (ESC) is in the range of 5 to 4 and for the control group (KSA) in the range of 5 to 3, the maximum value of the scale being 5. Based on the graphical display of the statistical indicators (scale median, quartile, and variation range) of the items 1PRE and 1POST the situation within the control group before and after the pedagogical experiment remained unchanged.

When comparing the results of the evaluation of the first item before (1PRE) and after the pedagogical experiment (1POST) we may conclude with pleasure that there were positive changes in the relationships and attitudes of the pupils of the experimental group (ESC) towards the popularity of mathematics. Moreover, we positively view the fact that the statement formulated in this item in the case of the posttest (1POST) in contrast to the pretest (1PRE) showed a greater homogeneity of responses within the experimental group of pupils (ESC). ESC pupils evaluated the item 1PRE: median 4 on the scale, the mid 50% of the evaluation values are in the range of 5 to 3.5 on the scale from the maximum value of 5). It follows from the above that the pupils of this research group expressed a very positive attitude towards mathematics in their answers. The pupils of the control group (KSA) evaluated the first item of the posttest (1POST) with the same level of positivity to the popularity of mathematics as in the pretest (1PRE).

The above-presented findings confirm the need to pay more attention to the ways in which mathematics is taught at primary schools, rather than to memorizing familiar relationships and lessons. This trend is also pointed out in the works of Gunčaga and Žilková [54], Dofková [55], Suchoradský [56] or Zaldívar-Colado, et al. [57]. Since it has been repeatedly shown, that the more popular the subject of mathematics amongst the pupils is, the better their learning outcomes are, it is logical that teachers will be looking for ways to increase the popularity of this subject [58,59]. Research most often verifies statistically the effectiveness of the innovation of teaching methods towards a more intensive involvement of interactive teaching tools and procedures that encourage pupils’ learning initiative [60].

The results of data analysis obtained for all the six ordinal questionnaire items (P1—popularity of the subject, P2—interesting content of the curriculum, P3—difficulty of the content of the curriculum, P4—comprehensibility of the interpretation of the new curriculum by the teacher, P5—usability of knowledge for one’s own future, P9—pupils’ interest in mathematics as an extracurricular subject) before and after the pedagogical experiment in relation to the GROUP factor were very similar. A positive finding is that within the experimental group of the pupils (ESC) there were slight (but not statistically significant) positive changes in the evaluation of most posttest items compared to the pretest ones. The only exception was the evaluation of the fifth item, which was used to determine the change in pupils’ attitudes to the significance of mathematical knowledge. In the case of this item, the same value of the median of the scale of the answers in the posttest as in the pretest was recorded in the experimental group of pupils (value 5 on the scale: I will definitely use the acquired knowledge of mathematics in everyday life). When evaluating the fifth posttest item (5POST) the pupils maintained the same attitude as they declared in the pretest (5PRE), i.e., they confirmed their unchanged opinion, but simultaneously, they also confirmed a very high degree of significance they attach to the knowledge they acquire studying the subject (Figure 5 and Figure 6). Notably, this posttest item showed the most homogeneous responses from all the six ordinal items (the middle 50% of the experimental group (ESC) pupils’ responses showed a scale of 5—I will definitely use the knowledge of mathematics in everyday life, with the variation range from 5 to 3 from the threshold values of 5 to 1 on the scale).

Through the second item of the posttest (2POST) we tried to find out what changes of opinion compared to the pretest (2PRE) occurred in the pupils of the experimental group (ESC) within the evaluation aspect of the interest of the subject matter taken in mathematics, caused by the pedagogical intervention materials of mind maps and multimedia teaching tools. The graphs presented in Figure 7 and Figure 8 show an increase in the posttest in the median value of the answers of the respondents in the experimental group (ESC) (scale value 5: I consider mathematics very interesting) compared to the pretest by one level scale (scale value 4: mathematics is a subject I consider interesting). The mean 50% of the values for the experimental group (ESC) in the pretest range from 5 (very interesting) to 2 (not interesting) and in the posttest from 5 (very interesting) to 3 (neither interesting nor uninteresting) from the marginal values of 5 (very interesting) to 1 (very uninteresting) on the scale.

One of the basic preconditions for the success and effectiveness of education is proper motivation. If the teacher arouses the pupil’s interest in learning, this interest motivates the pupil to take initiative and be more active. The conscious acquisition of knowledge and skills then becomes the goal and motive of the pupil’s activities. Our experience confirms that knowledge gained this way is deeper and more lasting. Arousing the pupils’ interest in the subject of mathematics does not only mean teaching the pure curriculum but also conveying it to pupils in an interesting and engaging way. The effort of teachers is to keep the pupils’ attention on the subject being studied as much as possible during the whole lesson and initiate pupils to take an active approach to learning. The teacher adapts motivation not only to the goal of the lesson but also to the content and tries to choose appropriate methods and forms of work. Concept maps are a suitable means to maintain the pupils’ interest in solving practical mathematical problems, as mathematical problems can be easily inserted via links into the concept map, and when opened pupils can work directly on the interactive whiteboard. During the lesson, the pupils are very happy to work with the interactive whiteboard or interactive display installed in the school classroom. Therefore, we consider these didactic tools highly effective in applying concept maps to teaching mathematics.

In the third questionnaire item, we tried to find out how the pupils evaluate the difficulty of the subject. Although there were no statistically significant differences among the pretest (Figure 9) and posttest (Figure 10) responses between the experimental and control groups, there were multiple but not statistically significant changes in the experimental group of pupils (ESC). On the graphs of the evaluation of the third posttest item, we can see (Figure 10) that the answers of the pupils of the experimental group were rather positive, while the middle 50% of answers are in the range of 3 (I consider mathematics to be a subject neither difficult nor undemanding) to 1.5 (1—completely undemanding; 2—undemanding) from the maximum value of 5 on the scale (very demanding). The median of the scale for the experimental group (ESC) reached the value of 2 (I consider mathematics a less demanding subject) and for the control group (KSA) the value 3 (neither demanding nor undemanding). The quartile range of the posttest scale overlaps for both groups of students (KSA, ESC) (Figure 10). Based on the quartile range of answers achieved by the pupils of the experimental group (ESC) in the posttest, it is evident that these respondents in the choice of the answer also marked the possibility compared to the pretest and thus declared that mathematics is considered a very demanding subject (scale value 5).

We agree with the statement of Gunčaga and Žilková [54] who claim that one of the ways which lead to reducing the complexity of learning in the educational content of the subject of mathematics is to increase clarity and practical activities in teaching mathematics. At the same time, however, we are aware that the inclusion of these activities in teaching is time-consuming for teachers, especially with regard to their preparation.

In the fourth questionnaire item, the pupils commented on the extent to which they understood the teacher’s explanation of the new subject matter in the mathematics lessons. On the graphs in Figure 11 and Figure 12, we may see that the pupils in the experimental group (ESC) showed more or less the same attitude also in the posttest (Figure 12) as they declared in the pretest (Figure 11). From the results of the answers of the pupils of the experimental group (ESC) to the fourth posttest item (4POST) it is visible (In the mathematics class, the teacher explains the subject. Sometimes I … understand it), which means that the pupils declared a basically neutral attitude, the middle 50% of the values ranging from 5 (I always understand) to 3 (sometimes I understand, sometimes I don’t) of the 5 (I always understand) threshold to 1 (I don’t understand). The pupils in the control group exhibited almost identical results in the pre and posttest. The change occurred only in the value of the median of the scale, which paradoxically decreased from value 4 (I understand the teaching of the new curriculum in the mathematics lesson) to value 3 (sometimes I understand, sometimes I do not understand the interpretation of the new curriculum in the mathematics lesson).

The results presented in the experiment indicate that the pedagogical intervention of concept mapping in teaching mathematics in the experimental group did not make it easier for pupils to understand the interpretation of the new curriculum, as expected. Of course, this result can be greatly influenced by the short-term use of digital concept maps and multimedia learning materials. On the other hand, the results of the research confirm that the use of concept maps has weakened the previously neutral or rather negative attitude of pupils towards mathematics. After the pedagogical intervention of experimental digital concept maps, the pupils’ relationship to the curriculum taught in mathematics was no longer so neutral or rather negative as before. At this point, we must point out that changing the views and attitudes of individuals is very challenging and requires a longer period of time. In the case of the implementation of our pedagogical experiment, we could influence the attitudes of pupils only for 2 months (the duration of the experiment). On the other hand, the results that manifested themselves in such a short time are all the more significant, i.e., that even during such a short period of time we managed to achieve certain positive changes in the attitudes of pupils.

The ninth questionnaire item identified the potential interest of pupils in enrolling in a mathematics class after school (as a means of motivating pupils and arousing their interest in mathematics) if there was such an opportunity at school. From the graphical evaluation of the answers (Figure 13 and Figure 14) recorded for this item (If there were a possibility, I would enroll in a mathematics class after school), it can be seen that the pupils of the control group in the posttest (9POST) maintained the same attitude as declared in the pretest (9PRE). In both cases, the median of the scale for the control group was 3 (I am neither interested nor uninterested), with the middle 50% of the response values ranging from 4 (I am rather interested) to 1 (I am definitely not interested) of the maximum value of 5 (I’m definitely interested). Based on the results of the posttest visualized in Figure 6 it can be seen that the answers of the pupils of the experimental group in comparison with their answers presented before the pedagogical experiment (pretest) were rather positive, as the middle 50% of answers ranging from 5 (I’m definitely interested) to 2.5 (scale value 3: I am neither interested nor uninterested, scale value 2: I am rather not interested). After-school mathematics clubs provide pupils with space to realize their creative ideas and obtain answers to the questions that interest them in this subject. In a non-traditional, this attractive form of acquiring mathematical knowledge creates space for building the pupils’ relationship to mathematics and last, but not least, contributes to the vocational training of pupils at lower levels of education, as mathematical knowledge and skills are the basis of preparation for work in various professions.

In the nominal questionnaire items P6–P8 the pupils chose one from four given possibilities of the alternative answers, which best corresponded to their attitude:

The aim of the sixth questionnaire item (Pupils learn individual subjects for various reasons. What is the reason why you usually learn mathematics?) was to find out the most common reasons that encourage pupils to learn mathematics.
The seventh questionnaire item (Pupils prefer different ways of being taught the new curriculum/mathematics subject matter. Which way suits you best?) tried to find out what way of teaching suits the pupils the best.
The eighth questionnaire item focused on identifying the factors that made pupils nervous and stressed out before the math classes (Some pupils experience fear and anxiety before certain lessons. Do you also fear or dread the maths classes? Why are you afraid? What are you afraid of?).

There were no statistically significant differences in responses between the experimental and control groups of the pupils in any of the three nominal posttest items (Table 6).

From Table 6 one can see that the relationship between the evaluation of each of the three nominal posttest items and pupils’ belonging to one or the another one of the two groups (ESC, KSA) is not statistically significant (p > 0.05). This means that evaluation of the sixth (6POST), seventh (7POST), and eighth posttest item (8POST) does not depend on the GROUP factor. The contingency coefficient value of 0.16 for 6POST × GROUP, 0.55 for 7POST × GROUP, and 0.53 for 8POST × GROUP is statistically insignificant in all three cases based on the results of Pearson’s chi-squared test. The results of the chi-squared test of the sixth, seventh, and eighth pretest items are, respectively, visualized by interaction graphs presented in Figure 15, Figure 16 and Figure 17. Results of the chi-squared test of the sixth, seventh, and eighth posttest items are visualized by interaction graphs presented, respectively, in Figure 18, Figure 19 and Figure 20. All six interaction graphs confirm the results of Pearson’s chi-squared test, the response curves of pupils´ responses within the pretest and posttest in both groups copy each other.

The relative numbers of the individual alternative responses recorded under items P6–P8 in the pretests and posttests (separately for the experimental and control group) are presented by means of the interaction graphs in Figure 15, Figure 16, Figure 17, Figure 18, Figure 19 and Figure 20.

As for the sixth pretest questionnaire item, it is clear from the graph in Figure 15 that the rankings from the most frequent to the less frequent choices by the control and experimental groups of pupils essentially mirror each other. The most frequently chosen answer by the respondents in the experimental (ESC) and control group (KSA) was answer a—I am interested in mathematics because it helps me to get to know and understand many things (ESC—30.0%, KSA—33.3%). In the control group, answer d—I want to get a good mark, was equally frequent (33.3%).

Although the difference in the evaluation of the sixth posttest questionnaire item between the experimental and control groups of pupils (ESC, KSA) is not statistically significant, the order of the answers from the most frequent to the least frequent one in both groups of respondents is not the same. Regarding the specific results of the posttest (Figure 18), in the experimental group of pupils (ESC) the most frequent answer was option c—I like to solve mathematical problems, chosen by 25% of the respondents. Answer a—mathematics interests me and helps me to get to know and understand many things, answer d—to get a good mark and answer e—because the teacher explains it interestingly was chosen by 20% of the pupils, respectively. In the experimental group, answer e was chosen by four pupils. If we compare the posttest with the results of the pretest (answer—e was chosen by two pupils in the experimental group), we may observe a slightly positive change in the rise of the absolute number of this option amongst the pupils in the experimental group.

We believe that the positive change observed in the posttest amongst the pupils of the experimental group was caused by the influence of the pedagogical intervention of digital concept maps and the incorporation of multimedia teaching aids into teaching. This assumption of ours is based on the results of various studies, e.g., Vaníček [61], Uhlířová [46] or Hollenstein, Thurnheer, and Vogt [62], who proved a significant educational contribution of the application of concept maps into teaching mathematics at the first stage of primary school. We must understand that the level of improvement will naturally be individual and depend on the specific choice of the thematic unit to which the teacher plans to apply it. In addition, these teaching aids are used to facilitate the demonstration of relationships between concepts. They also contribute to the development of pupils’ and students’ critical and analytical thinking [63,64,65]. The findings of several studies [66,67,68] confirm that the main advantage of digital concept maps is the creation of a stimulating learning environment that attracts pupils and students; hence, we may be talking about their great motivational potential.

In the control group of the pupils (KSA) the most frequently chosen answer in the sixth questionnaire item in the posttest (38%) was the answer a—I am interested in mathematics because it helps me to get to know and understand many things (Figure 18). This result confirms the pupils’ higher level of general intelligence in this group, which is also documented by the fact that the control group (KSA) of students shows better study results on average, has higher general study prerequisites and abilities, and interest in learning compared to the pupils of the experimental group (ESC). One-third of the pupils (33%) chose answer b as the reason that most often encourages them to learn mathematics—I am interested in the teaching aids we work with in the mathematics lessons. We recorded this second, most common choice of answer in the control group of pupils (KSA), despite the fact that the interpretation of the curriculum in this group took place in a conventional way and the teacher used the teaching aids he had at his disposal.

The results of the statistical analysis of the answers to the seventh questionnaire item obtained before the pedagogical experiment (Figure 16) show that the pupils in both groups are most comfortable when the teacher explains the new curriculum (subject matter) all by himself, using various teaching aids (answer b). The order of the answers determined by their descending number in the control and experimental group of pupils is the same, namely b–c–a–d, which does not match the results recorded in both groups of the respondents (ESC, KSA) in the posttest (Figure 19).

According to the results of the posttest represented in Figure 19, the greatest divergence in the frequency of the answers between the two groups of respondents (ESC, KSA) occurred at the answer c—the teacher involves us—the pupils—in the interpretation of the new curriculum (subject matter). From the values of the relative numbers, it is clear that this method of interpreting the new curriculum in the mathematics class is preferred by 47.6% of the pupils in the control group and (only) 30% of the pupils in the experimental group. The order of the alternative answers of the control group of pupils determined by their descending number is c–b–a–d (Figure 19). Due to the results of the pretest, the order of the pupils’ answers in the posttest differs only in the first two positions, in the opposite order of answers b and c. In most cases, up to 47.6% of pupils in the control group are satisfied when the teacher involves us—the pupils—in the interpretation of the new curriculum (subject matter) (choice of the answer c). The second most common choice was answer b, according to which the teacher explains the new curriculum (subject matter) all by himself, using various teaching aids. This method is preferred by 28.6% of the pupils surveyed. None of the pupils in the control group chose answer d—the teacher gives us individual tasks and we solve them in the posttest.

An interesting situation arose in the answers to the seventh posttest item. In the posttest, the respondents of the experimental group chose three answers as their most preferred way of learning the new mathematics curriculum, namely answer a—the teacher explains the new curriculum (subject matter) all by himself, without illustrative teaching aids, the interpretation is understandable and clear, answer b—the teacher explains the new curriculum (subject matter all by himself, using various teaching aids, and answer c—the teacher involves us—the pupils—in the interpretation of the new curriculum (Figure 19). In all three cases, the same relative response rate of 30% was recorded. We believe that the pupils who agree that the most appropriate way to interpret the new curriculum in mathematics is when the teacher explains the new curriculum (subject matter) all by himself, without illustrative teaching aids, the interpretation being understandable and clear (choice of answer a) actually declare their satisfaction with learning in a non-creative manner during which nothing else except for the passive mechanical recording of the comments during the interpretation of the new curriculum is required of them. In this context, we agree with the statement published in the proposed Concept to Improve Mathematical Education at Primary and Secondary Schools in the Slovak Republic [69] (National Institute for Education, 2019) that the prevalence of such mathematics teaching, in which learners (pupils and students) are mostly passive recipients of information, can discourage them from learning mathematics.

The results recorded may be considered surprising, or rather unexpected. We expected larger relative numbers of pupils in the experimental group to prefer the teacher involving pupils in the interpretation of the new curriculum (choice c) or prefer the way of explaining the new curriculum (subject matter) accompanied by the use of various teaching aids (answer b). These expectations of ours were related to the fact that during the teaching of the relevant thematic units (Propaedeutics of multiplication, Propaedeutics of division, Planar geometric formations, and Concepts of mathematical operations) concept mapping was applied in the experimental group of pupils, associated with the use of attractive digital teaching aids supporting pupils’ learning activity. It is therefore questionable whether this intervention approach in mediating the new curriculum has left a corresponding positive response in the pupils. It is also questionable whether the pupils interviewed have a well-used way of explaining the new curriculum, in which their teacher leads them to a proactive mathematical approach. However, the presented findings correspond with the repeated findings of the State School Inspectorate ([70,71]), namely that in the first four grades of a primary school the teaching of the new curriculum is based on pure explanation by the teacher and pupils are mostly just passive recipients of a wide range of information, which we do not consider adequate in relation to quality assurance in education. According to the study of Analysis of Findings on the State of Education in Slovakia [72], the solution to this situation may be the application of alternative teaching procedures to replace the usual ones, in which it is necessary to emphasize the attractiveness of both the method of presentation and its content, (e.g., to replace or at least supplement the lengthy theory by solving interesting practical tasks and activities).

The results of the eighth item of the questionnaire, in which we wanted to identify the most frequent sources of fear, are graphically presented in Figure 17 and Figure 20. According to Průcha, Walterová, and Mareš [73], one of the factors influencing the pupils’ relationship to mathematics is the fear caused by the school environment, which may be related to concerns about the teacher, his/her teaching style, the complexity of the curriculum, or concerns about oral testing.

As it can be seen from the graphs presented in Figure 17, in the experimental group of the respondents (ESC) the most frequent answer in the pretest was option a—I am not afraid or anxious about anything, which was chosen by 45% of the respondents. Most pupils, namely 33.3%, in the control group (KSA) opted for answer b –unpreparedness for the lesson (I do not have my homework, I do not have the necessary tools). It can be seen from the graphic visualization of the results that in the experimental and control groups of the pupils the order of frequency of the answers in the first two and the last position differ. The order of the answers of the pupils of the control group was b–a–c–d–e, in descending order, and the order of the frequency of the answers of the pupils in the experimental group is a–e–c–d–b. When choosing answers b—unpreparedness for the lesson (I do not have my homework, I do not have the necessary tools), and d—a quick test, the same value of its number was recorded in the experimental group of pupils, namely 2 (Figure 17). It is also worth noting that the fear of math lessons from getting a bad mark (answer e) was chosen by only one pupil in the control group out of the total number of 21 respondents, which we perceive as positive information.

The results recorded in the posttest were significantly different for both groups compared to the pretest results (Figure 20). The most frequent answer of the respondents of the experimental (ESC) and control group (KSA) to the question of what causes them to fear and dread mathematics was answer a—I am not afraid or anxious about anything. In the case of the experimental group, 40% of the pupils chose this answer, while, in the case of the control group it was 47.6%. From the graph in Figure 20 presenting the posttest results, it is clear that the order from the most frequent choice to the less frequent ones in the experimental group of pupils (a–e–c–d–b) essentially coincides with the order recorded in the pretest (Figure 17). The pupils often relate their negative feelings about mathematics to the fear of getting a bad mark (answer e), which may be due to their excessive attachment to marks, in many cases not corresponding to their knowledge. This concern was confirmed by 20% of the interviewed pupils in the experimental group.

Although the results of our research do not directly confirm this (see the evaluation of items 3PRE and 3POST), the most common cause of concern or outright fear of mathematics is its complexity. Pupils are afraid of misunderstanding the challenging curriculum and the consequences in the form of getting bad marks. It is the acquisition of the best possible mark that is often the dominant if not the only motivation of the pupils to learn. However, school success has two sides: an objective one, which is characterized by meeting the prescribed standards and requirements declared in the curricular documents, and a subjective one, related to the fact that the pupil feels the success and satisfaction of the activity. Given this fact, the teacher should evaluate the pupils´ performance in an individual way, comparing the level and results of their previous and current work, leading to the pupils’ partial school achievements and progress to be the best.

In the case of the control group, the choice from the most frequent response to the least frequent one obtained within the eighth item of the posttest is in the following order: a–b–c–e–d. It is worth noting that between the first and the second most frequently chosen answer, it is possible to observe a more significant drop in the frequency of opting for this answer in both the experimental and control groups (Figure 20). On the graphical visualization of the control group pupils’ answers, it can be seen that the biggest concerns about math lessons are related to the pupils’ concerns about their oral examination at the board (answer c) and their unpreparedness for the lesson, e.g., in the form of failing to do homework or failing to bring along the necessary teaching aids (choice b).

Fear of the mathematics lessons (not only) caused by the school environment can have a motivating effect to some extent. For example, a pupil’s fear of written assignments works well as a motivating factor for his/her thorough home preparation for the lesson, which, in this case, is called active fear. On the other hand, if a pupil’s fear of testing on the blackboard is too great, the pupil may perform worse due to nervousness, which may be reflected in his/her lower school success. It has been shown (and our research confirms this) that some individuals perceive school examinations at the board as complicated, stressful situations where a pupil or student may be exposed to the unpleasant feeling of embarrassment. On the other hand, some pupils and students pass the exam on the board without any emotion; for others, it may be a challenge to prove they have nailed it. The results of the pupils’ answers obtained within the evaluation of the mentioned determinant of teaching mathematics coincide, in many respects, with the results of the research findings of Vondrová, Rendl, and the team of authors [74] who carried out their research in the first four grades of a primary school.

Despite the fact, that the results of the presented research study cannot be generalized due to the scope of the research sample, we consider them to be beneficial and inspiring for mathematics teachers working at the primary level of education (ISCED 1).

5. Conclusions

The results of the pedagogical experiment did not confirm the validity of the established hypothesis, whereby we assumed that teaching supported by innovative teaching aids such as concept maps contributes to reducing pupils’ negative attitudes towards subjects, specifically the subject of mathematics at the primary level (ISCED 1). Due to the pedagogical intervention of concept mapping in the teaching of selected topics belonging to the mathematics curriculum of the third grade in a primary school, no statistically significant changes occurred in the pupils’ attitudes to the observed factors of mathematics, which were the popularity of mathematics, interest in this subject, curriculum and understanding of the interpretation of the subject matter, the usability of the acquired knowledge and skills, fear and apprehension of mathematics as a subject. We put the reason down mainly to the fact that the concept maps were a completely new didactic method during the implementation of the pedagogical experiment in the target group of pupils, which they had not yet encountered in any other subject. Since the pupils had encountered digital concept maps for the first time, we assume that especially in this age group of pupils, a longer period of time is needed to understand the essence of concept mapping. We believe that the more frequent use of this innovative method in the teaching process will make concept maps more comprehensible for pupils and make it easier for them to understand the often complex abstract mathematical relationships and contexts. The validity of this assumption is confirmed by the fact that despite the short duration of the use of concept maps in teaching within the pedagogical intervention, several positive (but not statistically significant) changes took place in the pupil’s approach and attitudes to teaching mathematics. Overall, it may be stated that the experimental verification of the impact of pedagogical intervention using digital concept maps to influence pupils’ attitudes to the acquisition of mathematical knowledge has delivered various findings into primary education, which may be considered beneficial and inspiring for the development of the area of branch didactics of mathematics.

Author Contributions

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

Acknowledgments

The authors of the paper wish to acknowledge the valuable contributions and support of the partners of the Faculty of Education, Comenius University in Bratislava, the Faculty of Education, Constantine the Philosopher University in Nitra, and DTI University in Dubnica nad Váhom.

Conflicts of Interest

The authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Tables

View Image - Figure 1. Concept map-drawing principle of division. Legend: Delenie-Division; 16 rozdelíme na 4 časti-we break into 4 parts; zapisujeme-we take in writing; počítame–we calculate; odčítali sme 4 – krát-we subtracted 4 times; výsledok-result; delenec-divident; deliteľ-divisor; podiel-quotient; 16 lienok rozdeľujeme na 4 časti-we separate 16 ladybirds into 4 parts (groups); 12 lienok-12 ladybirds; 4 lienky-4 ladybirds.

Figure 1. Concept map-drawing principle of division. Legend: Delenie-Division; 16 rozdelíme na 4 časti-we break into 4 parts; zapisujeme-we take in writing; počítame–we calculate; odčítali sme 4 – krát-we subtracted 4 times; výsledok-result; delenec-divident; deliteľ-divisor; podiel-quotient; 16 lienok rozdeľujeme na 4 časti-we separate 16 ladybirds into 4 parts (groups); 12 lienok-12 ladybirds; 4 lienky-4 ladybirds.

Figure 2. ActivInspire activity inserted via a link in the concept map—multiples of numbers Calculate.

Figure 3. Box graphs of the first item of the pretest-1PRE.

Figure 4. Box graphs of the first item of the posttest-1POST.

Figure 5. The box graph of the fifth item of the pretest-5PRE.

Figure 6. The box graph of the fifth item of the posttest-5POST.

Figure 7. The box graph of the second item of the pretest-2PRE.

Figure 8. The box graph of the second item of the posttest-2POST.

Figure 9. The box graph of the third item of the pretest-3PRE.

Figure 10. The box graph of the third item of the posttest-3POST.

Figure 11. The box graph of the fourth item of the pretest-4PRE.

Figure 12. The box graph of the fourth item of the posttest-4POST.

Figure 13. The box graph of the ninth item of the pretest-9PRE.

Figure 14. The box graph of the ninth item of the posttest-9POST.

Figure 15. Interaction graph of the sixth item of the pretest-6PRE.

Figure 16. Interaction graph of the seventh item of the pretest-7PRE.

Figure 17. Interaction graph of the eighth item of the pretest-8PRE.

Figure 18. Interaction graph of the sixth item of the posttest-6POST.

Figure 19. Interaction graph of the seventh item of the posttest-7POST.

Figure 20. Interaction graph of the eighth item of the posttest-8POST.

Table 1

Pedagogical experiment schedule.

Groups within the Pedagogical Experiment	Pretest	Kind of the Pedagogical Intervention	Posttest
ESC (Experimental group)	Q1	VPM	Q1
KSA (Control group)	Q1	KKV, KTU	Q1

Legend: KKV—traditional teaching; VPM = intervention of concept maps in teaching; KTU = use of classical textbooks in teaching; Q1—administration of the same questionnaire used firstly as pretest and secondly as posttest.

Table 2

Levene nonparametric test for the pretest.

	MS—Effect	MS—Error	F-Statistic	p-Value
1PRE	1.58101	0.507387	3.115985	0.085357
2PRE	0.048646	0.374569	0.129873	0.720509
3PRE	2.356183	0.340679	6.916132	0.012163
4PRE	0.102997	0.118963	0.865795	0.357846
5PRE	0.301045	0.123993	2.427928	0.127269
9PRE	0.101813	0.638528	0.159449	0.691843

Table 3

Levene nonparametric test for the posttest.

	MS—Effect	MS—Error	F-Statistic	p-Value
1POST	0.477879	0.377277	1.26665	0.267274
2POST	0.080362	0.185407	0.43344	0.514174
3POST	0.070328	0.317079	0.2218	0.640297
4POST	0.54887	0.1402	3.91492	0.054953
5POST	1.850305	0.10609	17.44094	0.000161
9POST	0.002178	0.465589	0.00468	0.945823

Table 4

The descriptive characteristics and confidence intervals of the posttest.

	Factor level	N	1POST Mean	1POST St Dev.	1POST St.Error	1POST −95.00%	1POST +95.00%
Total		41	4.073171	1.08144	0.168893	3.731826	4.414515
Group	KSA	21	3.904762	1.135991	0.247894	3.387665	4.421859
Group	ESC	20	4.25	1.019546	0.227977	3.772838	47.27162
	Factor level	N	2POST Mean	2POST St dev.	2POST St.error	2POST −95.00%	2POST +95.00%
Total		41	4.195122	0.781649	0.122073	3.948403	4.441841
Group	KSA	21	4	0.774597	0.169031	3.647408	4.352592
Group	ESC	20	4.4	0.753937	0.168585	4.047147	4.752853
	Factor level	N	3POST Mean	3POST St dev.	3POST St.error	3POST −95.00%	3POST +95.00%
Total		41	2.365854	1.066679	0.166587	2.029168	2.702539
Group	KSA	21	2.333333	0.966092	0.210819	1.893574	2.773093
Group	ESC	20	2.4	1.187656	0.265568	1.84416	2.95584
	Factor level	N	4POST Mean	4POST St dev.	4POST St.error	4POST −95.00%	4POST +95.00%
Total		41	3.585366	0.865321	0.13514	3.312237	3.858495
Group	KSA	21	3.52381	0.749603	0.163577	3.182594	3.865025
Group	ESC	20	3.65	0.988087	0.220943	3.187561	4.112439
	Factor level	N	5POST Mean	5POST St dev.	5POST St.error	5POST −95.00%	5POST +95.00%
Total		41	4.878049	0.457991	0.071526	4.733489	5.022609
Group	KSA	21	5	0	0	5	5
Group	ESC	20	4.75	0.638666	0.14281	4.451095	5.048905
	Factor level	N	9POST Mean	9POST St dev.	9POST St.error	9POST −95.00%	9POST +95.00%
Total		41	2.878049	1.469611	0.229515	2.414182	3.341915
Group	KSA	21	2.47619	1.364516	0.297762	1.85507	3.097311
Group	ESC	20	3.3	1.49032	0.333246	2.602509	3.997491

Table 5

Mann–Whitney U test for item 1POST.

	Rank Sum—KSA	Rank Sum—ESC	U	Z	p-Value
1POST	402	459	171	–1.00416	0.315303

Table 6

Results of the chí-squared test of the independence of the questionnaire nominal items according to the GROUP factor.

ITEM/FACTOR	Pearson’s chi-Squared Test
ITEM/FACTOR	chi-Square	df	p-Value
6POST (5)/GROUP (2)	6.623995	4	0.15714
7POST (4)/GROUP (2)	3.068344	4	0.54645
8POST (5)/GROUP (2)	3.152088	4	0.53270

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The paper deals with the application of concept mapping in teaching mathematics at the primary level of education (ISCED 1), as well as the experimental verification of its qualitative contribution to the process of education. The authors present results obtained in a sample survey aimed at monitoring possibilities of influencing pupils’ relationship to teaching and mastery of mathematics using digital concept maps within the process of pedagogical intervention. The authors tested the degree to which digital concept maps influence changes in the pupils’ opinions and attitudes to mathematics (subject popularity, interest in the subject, easiness of understanding, fear and apprehension of mathematics) while explaining and fixating the curriculum of selected mathematics topics in the third grade of a primary school. The results of the experiment did not confirm that teaching supported by concept maps contributes to reducing pupils’ negative attitudes towards subjects, particularly in mathematics at the primary level (ISCED 1). Due to the pedagogical intervention of concept mapping, no statistically significant changes occurred in the pupils’ attitudes to the observed factors of mathematics. However, the authors have come up with research findings that may be notable in the field of branch didactics of mathematics and digital technologies.

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Title

Concept Mapping in Teaching Mathematics in Slovakia: Pedagogical Experiment Results

Author

Záhorec, Ján¹

; Hašková, Alena²

; Hrmo, Roman³

¹ Faculty of Education, Comenius University in Bratislava, 813 34 Bratislava, Slovakia
² Faculty of Education, Constantine the Philosopher University in Nitra, 949 01 Nitra, Slovakia; [email protected]
³ DTI University, 018 41 Dubnica nad Váhom, Slovakia; [email protected]

First page

1965

Publication year

2022

Publication date

2022

Publisher

MDPI AG

e-ISSN

22277390

Source type

Scholarly Journal

Language of publication

English

DOI

https://doi.org/10.3390/math10121965

ProQuest document ID

2679780221

Concept Mapping in Teaching Mathematics in Slovakia: Pedagogical Experiment Results

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