1. Introduction
Inquiry-based learning, and consequently inquiry-based teaching, is one of the challenges of recent years in STEM education. One of the privileged areas in which inquiry learning and teaching can be applied is experimental teaching in STEM subjects [1,2,3,4,5]). Inquiry is mainly considered the cornerstone of science education [6,7,8], and inquiry activities and processes provide the context in which students can engage with and understand scientific concepts, acquire knowledge, and apply that knowledge. Inquiry-based teaching supports inquiry-based learning through which students approach and ultimately internalise the way scientific research is conducted. Inquiry-based teaching and learning can be divided into three main categories: guided, structured, and open, based on the level of student and teacher involvement and students’ experience of inquiry-based working methods [7,8,9,10,11,12].
At the dawn of the 21st century, so-called 21st-century skills have become the focus of education reform in many countries. In education, these skills are mainly summarised in the ‘4Cs’: critical thinking and problem-solving, communication, collaboration, creativity and innovation. In February 2018, an article by S. Grover was published entitled “The 5th ‘C’ of 21st Century Skills; Try Computational Thinking (Not Coding)” [13], in which she argues that: “… computational thinking (CT) needs to be …the ‘5th C’ of 21st-century skills—taught to all students”. However, what is CT? There is general confusion among researchers and educational theorists about the definition of CT. However, all agree that key components of CT include abstract thinking, decomposition, synthesis, analysis, generalisation, hierarchy, and algorithmic thinking, among others [14,15,16,17,18,19]. The above data have led several countries to attempt to introduce CT into primary and secondary school curricula. As far as Greece and the new curricula for high school education are concerned [20], CT is envisaged as the second core component, in addition to inquiry learning, which runs cross-cuttingly through all STEM courses.
Several researchers [5,21,22,23,24,25] have highlighted the importance of inquiry-based learning in the development of computational thinking skills through their studies. Strategy development, algorithmic thinking, and problem-solving are critical in inquiry learning processes. Furthermore, as the above researchers argue, computational thinking contributes to a better understanding of STEM courses, and conversely, these courses provide a framework for the development of computational thinking. Indirectly teaching computational thinking through inquiry processes such as projects and problem-solving can enhance learning and improve students’ skills [5,24,26].
There is a consensus in STEM education about the importance of providing students with learning experiences that require developing higher-order cognitive skills. Such learning experiences can occur when digital technology is used in inquiry-based learning, particularly problem-solving. In general, there is a view among many researchers that STEM education is a privileged field for developing students’ CT because, as Li et al. [27] argue, CT is more relevant to specific thinking processes than to programming per se. CT involves searching for appropriate ways of processing information that is progressively improved in terms of efficiency, correctness and elegance. The desired improvement requires using various strategies and skills such as decomposition, analysis, synthesis, practice, prioritisation, algorithmic thinking, abstraction, and modelling. According to Li et al. [27], it is imperative that school curricula and teaching integrate CT into not only computing courses but also other STEM disciplines beyond computing.
Li et al. [27] describe the thinking process integral to inquiry learning. In the context of STEM education, inquiry processes can be introduced in many ways. One of these is using digital technology such as modelling and simulation software, microcosms and virtual laboratories. In the context of inquiry-based learning processes [5,6,28,29] and when teaching STEM courses, one of the ways to promote learning through inquiry and at the same time promote CT skills is to assign students to solve a problem that is first closed and then open, using digital technology. It should be noted that it would be advisable for the problem to be taken from the real world and to be as relevant as possible to the learners’ experience. This inquiry-based learning process is delineated into three primary stages, as outlined in Table 1. The structure of this table is based on the work of Wagh et al. [30], who developed a matrix aligning the elements of inquiry learning with students’ interactions with code. In our adaptation, we created a matrix that maps the inquiry processes to trainees’ actions, highlighting the computational thinking (CT) practices employed during experimental activities or problem-solving tasks using digital media technology (see Table 1).
Educational software, such as simulations, virtual laboratories, microcosmos, and programming environments, can support CT based on inquiry learning [31,32,33]. There are software and virtual laboratories that are commonly used by secondary school teachers worldwide, such as Tracker (physics, mathematics), GeoGebra (mathematics, physics), Chem Collective’s VLab (chemistry), Algodoo (physics), and many more. In light of the above, the question arises as to whether these digital tools are suitable for inquiry-based learning while at the same time promoting the computational thinking skills that are key objectives of the secondary school curricula in STEM subjects in many countries.
Initially, the present study is an attempt to answer the above question, focusing on structuring a set of criteria that should characterise digital media technology in order to be considered suitable for exploratory inquiry-based learning and the promotion of CT skills, with the help of two important publications by Quintana et al. [34] and Reppening et al. [35,36]. The Quintana et al. [34] software evaluation framework is limited to evaluating the ability of software to be used in inquiry processes in STEM education, while the Reppening et al. [36] framework is primarily concerned with evaluating programming environments in terms of their ability to promote students’ computational thinking through their use.
The present study attempts to create a framework for evaluating digital media technology used in STEM courses that simultaneously tests two dimensions of these tools: their ability to support inquiry-based learning and teaching while enhancing computational thinking skills. To this end, we deemed it appropriate to synthesise the thoroughly sound evaluation tools developed by researchers Quintana et al. [34] and Reppening et al. [35,36].
According to the above, we aimed to synthesise and extend these two assessment frameworks to evaluate digital technologies’ ability to support inquiry-based learning and the development of students’ computational thinking. In order to fill the existing gap in the evaluation of digital media technology used in STEM education to simultaneously promote inquiry learning and computational thinking, we considered it beneficial to combine these evaluation frameworks. Indeed, we believe that there is a gap, given the recent notions that computational thinking should be a theme that cuts across all curriculum subjects, and furthermore, the view that STEM subjects are the most appropriate to enhance students’ computational thinking skills. This aim arose in light of the suggestion by many researchers that computational thinking is not an exclusive subject of computer science but that it would be appropriate to teach it as a way of thinking in the context of STEM courses [18,26,27,37].
Using the software evaluation tool we produced, we attempted to evaluate GeoGebra and Tracker, which are widely used in mathematics and physics in secondary education. In this phase, the researcher interacted with GeoGebra and Tracker software by addressing scenarios or problems derived from curriculum materials, as specified in the physics and mathematics syllabi. The researcher was responsible for implementing these scripts and solving the problems. During this process, comprehensive records were maintained, documenting the actions performed by the researcher in solving each scenario or problem.
Software Evaluation Tool
Over the last twenty years, the use of digital technology, especially in STEM courses, has increased due to the improvement of school infrastructure, the ample supply of digital technology, and the higher level of training of teachers in new technologies [38]. However, what is the purpose of using digital technology? First, it enables teachers to visualise phenomena they could not introduce in the classroom, except through the now-obsolete lecture. Furthermore, as far as the science subjects (physics, chemistry, and biology) are concerned, even phenomena that are relatively easy to study in the science laboratory can be introduced in an even easier and more manageable way through digital technology [38,39,40,41,42,43,44]. A similar phenomenon can be observed in mathematics regarding problem-solving practice, a practice of increasing interest in mathematics education [45,46,47]. In addition, digital technology allows the teacher to involve the learner directly in studying the phenomenon in question. Through the use of appropriate media, learners can interact directly with phenomena, intervene in their evolution, study them at the level of the factors on which they depend, return to earlier stages of their evolution to study them in-depth, intervene in the mechanisms of their evolution, and, most importantly, receive feedback from the medium itself in terms of their actions. In this context, it is now argued that the use of digital technology can promote students’ computational thinking [48,49,50,51] by enhancing key skills that are components of computational thinking, such as analysis, synthesis, abstraction, hierarchy, algorithmic thinking, debugging, and decomposition, as well as problem synthesis, data manipulation, and problem-solving.
One of the key issues is using appropriate digital technology to support the inquiry-based teaching of STEM subjects and to promote basic computational thinking skills in the most appropriate and targeted way. It is necessary to structure a set of criteria by which even a non-specialist in digital technology could judge whether the particular tool he or she uses can best meet the above requirements. Attempts to structure such a set of criteria are rare in the international literature. The literature review found two evaluation frameworks for evaluating digital technology relevant to STEM courses and promoting computational thinking through them. These evaluation frameworks have been concerned either with the ability of the media to support inquiry-based learning [34] or with the ability of programmatic environments to support computational thinking [35,36]. This study aims to synthesise and simultaneously update these evaluation frameworks so that they can simultaneously evaluate digital technology in terms of its ability to support inquiry-based learning on the one hand and promote computational thinking on the other. This objective arose from the fact that, as many researchers argue, STEM courses are a privileged field for potentially enhancing students’ computational thinking and, in addition, for applying the principles of inquiry learning.
The first evaluation framework is found in the research of Quintana et al. [34], which presents a well-structured framework of criteria that must be met to design software that supports inquiry processes in STEM courses. Quintana et al.’s research is based on the theoretical approach of analysing the principles that should underline the software under study and is not simply limited to the observations that can be derived from inductive analysis/investigation of software. Their research has resulted in three main strands that form the framework of the criteria they have structured. According to them, the software should:
Be meaningful to learners.
Enable learners to manage research-related processes in STEM courses.
Enable learners to articulate and reflect.
Each axis is broken down into guidelines composed of specific constructivist/research strategies.
The second evaluation framework is found in the research by Reppening et al. [35,36], according to which the three stages in the process of computational thinking that the computational systems in question should support are as follows:
Problem formulation (abstraction), i.e., making sense of a problem using either spoken/written discourse or visual representations.
The software’s articulation/expression of the solution (automation) is unambiguous.
Executing the solution so that the consequences of the learner’s thinking become apparent and evaluating the solution.
In the article by Reppening et al. [35,36], these stages are detailed by individual processes to be supported by the software.
This paper aims to synthesise the criteria mentioned in the above works to structure a framework of assessment and design criteria for digital technology related to STEM courses and support the promotion of basic components of computational thinking and inquiry-based learning.
In the first step, we aimed to synthesise the principal axes of the evaluation frameworks of Quintana et al. [34] and Reppening et al. [35,36]. After thoroughly exploring the components of these axes, we concluded that the axes set out in the framework of Quintana et al. are of primary importance, as they represent the main aspirations of both software and simulation and programming environments through which computational thinking can be fostered. Figure 1 illustrates the axes of the evaluation framework, divided into primary and secondary axes, and the relationships between them.
The overriding requirement (primary axis A) of software, simulations, and programming environments in the context of STEM education is the ability to generate meaning from their use, especially while using them [34]. The desired outcome for students/users who encounter and use these tools in STEM courses is understanding and internalising the basic skills of scientific inquiry and inquiry-based learning and developing basic computational thinking skills. It is therefore evident that at each step in their use of these computational tools, they should, on the one hand, identify the scientific tools/concepts they are using; for example, why these tools/concepts are used and not some others. On the other hand, they should be able to use these tools/concepts to identify the necessary scientific practices they should use to make sense of their investigation.
A secondary objective (secondary axis I), though not of secondary importance and directly related to primary axis A—especially with regard to developing basic computational thinking skills—is to support students/users in formulating the problem to be investigated [35,36]. Recognising that most computational thinking skills are simultaneously required for the problem-solving process, students/users should be supported by the computational environment in formulating, conceptualising, and defining the problem to be solved. The software or programming environment needs to provide users with appropriate support tools to help them define the problem to be solved, as many problems in STEM have several different aspects that can be distracting for students/users. In addition, the student/user should be supported in transferring the problem to the computational environment to choose those abstractions that will lead to the best possible analysis of the problem into its components and, thus, to the success of its solution.
The second axis in the framework for evaluating computing environments for STEM courses, as listed in the study by Quintana et al. [34], concerns the process management mechanisms that the computing environment should provide to the learner/user. These mechanisms should assist the learner/user in constructing a research plan for the problem to be solved. Once the user has passed the stage of formulating and defining the problem, he or she must draw up an action plan to efficiently implement the processes that will clearly express the solution to the problem. In this phase, the user is asked to develop an appropriate strategy to express the solution to the problem as clearly as possible, minimising their involvement in routine tasks that increase the complexity of the solution and are not intended either to solve the problem correctly or to promote the user’s computational thinking. This is where the secondary axis II of supporting the representation of solutions, according to Reppening et al. [35,36], comes in. In the framework we are trying to synthesise, this axis (secondary axis II) is directly related to the mechanisms of process management (primary axis B), and also to the need to produce meaning (primary axis A) as defined by Quintana et al. [34] and as we have analysed when referring to them. Supporting the expression of solutions consists of supporting the learner/user with the appropriate structure of the computing environment, having easy access to the tools needed to work on the problem to be solved, and supporting the writing of the code that the user will be asked to structure in terms of programming environments.
Finally, to achieve the twofold objective of computational environments in STEM education, i.e., the promotion of inquiry-based learning and the cultivation and improvement of computational thinking, it is necessary to support the continuous articulation of the user’s findings and constructs and the reflection on these findings (primary axis C) during the problem-solving process, as well as the execution of the solution and its evaluation (secondary axis III). The mentioned axes C and III are directly related to each other as they both refer to the last stage of the use of the computer system, so the user should now have completed all the necessary steps to arrive at the answers they are looking for, i.e., the solution to the problem. To make this possible, the computer system should provide reminders where needed, guidance and facilitation on the scientific concepts and practices involved in the user’s constructs and findings, and assistance in achieving productive reflection by the user. At the same time, both computer systems and programming systems should allow the user/learner to directly observe the consequences of any intervention in the process of solving the problem, i.e., the use should be supported by direct feedback on the processes followed to solve the problem on the one hand, and to produce meaning through it on the other.
Table 2 below lists the combined guidelines of the above axes [34,35,36] and the strategies that computing systems should follow to align them with the guidelines and axes of the evaluation framework.
2. Methodology
This study seeks to evaluate the effectiveness of a software assessment tool by applying it to two widely used secondary education software programs, GeoGebra and Tracker, in physics and mathematics. GeoGebra is educational software designed to support the teaching and understanding of mathematical and engineering concepts and to aid in solving complex problems. Tracker, conversely, is video analysis and modelling software utilised for addressing engineering challenges found in secondary school physics curricula.
The evaluation process involved using scenarios and problems derived from established mathematics and physics curricula in secondary education. The researchers implemented these scenarios, documenting the participants’ actions as they engaged with the tasks to reach solutions. These actions were then analysed and compared with the criteria set forth by the evaluation tool to assess the software’s capabilities. The results of this evaluation, including detailed findings for both GeoGebra and Tracker, are presented in Appendix A of this study.
In particular, the researcher is a secondary education professor in the field of physics/STEM. Her daily teaching practice involves engaging students in problem-based inquiry, drawing from either the physics curriculum or an interdisciplinary approach that integrates both physics and mathematics, supported by specialised software tools. The lessons take place in the computer lab, where students, working in groups, have access to computers. The lab is also equipped with an interactive whiteboard featuring the software used by the students.
The observations discussed in Appendix A were derived from students’ work on physics and mathematics problems. These students, aged 16 to 18, are high school students from a middle-class suburban area on the outskirts of Athens, the capital of Greece. The study is based on a convenience sample, and the researcher’s recorded observations did not focus on the students themselves or their ability to solve the problems. Instead, the observations centred on the actions they performed while using the software and, more specifically, on whether these actions were supported by the software environment.
The data collection spanned a period of two years, during which the researcher worked with approximately 100 students per year on the same or similar problem sets. Additionally, the researcher independently ran the problems she assigned to her students, supplementing her classroom observations with further detailed notes. These observations were subsequently classified according to thematic axes, guiding principles, and strategic aspects of the software evaluation framework. A comprehensive discussion of these findings, particularly regarding the two evaluated software programs, is provided in Appendix A. The results of these evaluations are presented in Table 3.
3. Results
The results of the evaluation of GeoGebra and Tracker using the evaluation tool are summarised in Table 3. The evaluation tool assessed the software effectively, as evidenced by the processes outlined in Appendix A. It yielded precise results regarding the software’s potential to foster inquiry-based learning and computational thinking. According to this evaluation, GeoGebra is highly effective in supporting students’ abstract thinking in its structure and functionality, reducing complexity, and providing flexible representations. However, it has two significant shortcomings: it does not offer supplementary texts or representations to aid in understanding problems, and it does not support scientific practices. Although the teacher can mitigate these gaps, the software’s inability to support students in writing code is its most notable shortcoming. The evaluation of Tracker software shows that it meets key assessment criteria, effectively supporting abstract thinking, organising information, reducing complexity, and offering flexible representations. However, it needs more support for scientific principles and practices, like GeoGebra.
4. Conclusions
Inquiry-based teaching and learning have been introduced into secondary education in numerous countries for years. However, integrating computational thinking (CT) into the secondary curriculum remains a topic of debate in many countries, whether as a standalone subject, a component of computer science, or a cross-curricular topic. Research indicates that using appropriate software to facilitate inquiry processes through projects or problem-solving in STEM subjects [5,6,27,28] can significantly enhance the development of fundamental CT skills. A key prerequisite is that the digital medium employed must implement as many of the previously synthesised strategies as possible, according to the research of Quintana et al. [34] and Reppening et al. [35,36], to serve the dual purpose of fostering both inquiry-based learning and CT. This study combines and expands two assessment frameworks to evaluate how well digital technologies support inquiry-based learning and the development of students’ CT. GeoGebra and Tracker software, commonly used in secondary math and physics, was assessed using the developed evaluation tool.
Concerning the GeoGebra software, it is important to highlight that the evaluation results align with the broader findings of Echeverría et al. [52] and S. van Borkulo et al. [53] on this software. Both researchers and the evaluation tool assess GeoGebra as highly effective in supporting students’ abstract thinking in its organisational structure and functionality, reducing overall complexity by relegating complex processes to the background and providing a wide range of adaptable representations. However, the GeoGebra software exhibits two significant deficiencies. Firstly, it does not furnish students or users with auxiliary texts or representations to facilitate understanding, articulation, and reflection on the problem. Secondly, it lacks support in providing information on the scientific features and practices involved. While these gaps can be mitigated by the teacher’s guidance, the most notable shortcoming is the software’s inability to assist learners in writing code when required. A possible recommendation would be to enhance GeoGebra by incorporating live programming capabilities supported by artificial intelligence to enable secondary school students to write code and instantly observe the outcomes.
Similarly, the evaluation of Tracker software revealed that it generally satisfies the key criteria of the assessment tool. It effectively supports abstract thinking, organises information, reduces complexity, and offers diverse, flexible representations. However, like GeoGebra, Tracker must provide users with supporting information on scientific principles and practices. In contrast to GeoGebra, Tracker offers memorable representations and a repository of STEM-related problems, yet it does not permit users to write code to influence the software’s functionality. These observations are corroborated by the research of one of Tracker’s creators [54,55] and by other scholars [56,57].
It would be prudent to apply the criteria framework to evaluate other digital technologies used in STEM education at the secondary level to identify potential shortcomings and reinforce these areas. By doing so, educators and developers can better understand the specific areas where these technologies may need reinforcement. Additionally, it is recommended that in vivo trials be conducted with students engaging in various scenarios using the respective digital technologies. These trials would provide direct insights into how students interact with the technologies, helping to determine whether the tools effectively support inquiry-based learning and CT as outlined in the framework. Moreover, observing students’ problem-solving processes and their ability to apply abstract concepts during these trials would offer critical feedback for improving the design and functionality of the tools. These observations could also highlight how different technologies facilitate or hinder students’ cognitive development in STEM disciplines.
This research study aims to contribute to the more effective design of digital educational environments for STEM subjects, enabling the resolution of both open-ended and closed problems through inquiry processes while simultaneously enhancing computational thinking. We argue that the framework established through its core axes, guiding principles, and the strategies that digital educational environments should serve, must constitute the foundation upon which such software should be designed. Thus, the key evaluation criteria presented in Table 2 can serve as a guide during the design and development phases of educational software intended for STEM education. Furthermore, existing digital media technology could be improved through minor but essential design modifications to satisfy a broader set of criteria outlined in Table 2.
Additionally, for STEM educators, the proposed framework could serve as one of the primary criteria for selecting appropriate digital educational environments for use with their students, ensuring that these environments facilitate inquiry-based teaching and learning while simultaneously promoting students’ computational thinking.
Specifically, as a continuation of this research, further evaluations of digital educational environments could be conducted based on this assessment framework, thereby creating an evaluative ranking of frequently used software in STEM education. The primary classification criterion would be the extent to which these digital environments contribute to the development and support of students’ computational thinking through problem-solving inquiry processes. Such a classification would be particularly valuable to STEM educators when selecting the most suitable digital educational environment, not only to enhance their teaching but, more importantly, to foster essential CT skills in their students.
Finally, since CT is a cognitive skill applicable across all fields, particularly STEM, the established criteria could be used as a standard for designing new digital technologies. These benchmarks would guide the development of tools to improve inquiry-based learning and foster essential CT skills, ensuring that students are better prepared for the demands of modern education and future STEM careers.
Conceptualization, A.B. and K.L.; methodology, A.B.; validation, A.B. and K.L.; formal analysis, A.B., N.T. and G.K.; investigation, A.B. and K.L.; resources, A.B. and K.L.; data curation, A.B., S.P., K.L., G.K. and N.T.; writing—original draft preparation, A.B.; writing—review and editing, A.B., K.L. and S.P.; visualization, A.B.; supervision, A.B. and K.L.; project administration, A.B., N.T., K.L., G.K. and S.P. All authors have read and agreed to the published version of the manuscript.
The original contributions presented in this study are included in the article.
The authors declare no conflict of interest.
Footnotes
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![View Image - Figure 1. Primary and secondary axes of the evaluation framework according to Quintana et al. [34] and Reppening et al. [35,36].](https://media.proquest.com/media/hms/THUM/2/4aozb?_a=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&_s=h%2BASGhSaUHwPY47JQs2x2ui8F%2FE%3D "View Image - Figure 1. Primary and secondary axes of the evaluation framework according to Quintana et al. [34] and Reppening et al. [35,36].")
Enlarge this image.Figure 1. Primary and secondary axes of the evaluation framework according to Quintana et al. [34] and Reppening et al. [35,36].
Mapping of students’ inquiry processes and actions using CT practices.
| Element of the Inquiry Process | Description of the Inquiry Process | CT Elements in the Inquiry Process (Student Actions) |
|---|---|---|
| Trying to solve a problem (open or closed) | Formulate questions to be answered or hypotheses to be confirmed | Decomposition of the main question/problem and formulation of sub-questions |
| Making sense of exploration | Analyse data and synthesise results to develop claims and formulate evidence-based explanations, observe results, formulate evidence-based claims, and propose theoretical mechanisms or conceptual models to help predict and explain results. | Change variables and re-run process (algorithmic thinking) |
| Engagement within the learning community | Student teamwork | Collaborative exploration |
Guidelines and strategies of the Digital Technology Evaluation Framework according to Quintana et al. [
| AXES | GUIDELINES | STRATEGIES |
|---|---|---|
| Axes A—I | 1. Supporting conceptualisation through verbal and/or visual thinking | 1a. Provide visual memory representations to enhance visual thinking |
| 1b. Provide common STEM problems with short texts or titles | ||
| 2. Support for the transfer of data via explicit abstractions | 2a. Support in the selection of explicit abstractions | |
| 2b. Provide details that the user can focus on and guide the user with feedback | ||
| 3. Use of representations/language to bridge prior knowledge with understanding of the new topic | 3a. Functionality through the visual conceptual organisation | |
| 3b. Descriptions for complex concepts | ||
| 3c. Scientific guidance for the implementation of scientific content | ||
| 4. Organising tools and objects around the meaning and terminology of the scientific object and problem | 4a. Explicit scientific strategies in student-to-tool interactions | |
| 4b. Clear and explicit scientific strategies used by students to construct artefacts | ||
| Axes A—II | 5. Representations that students can explore to reveal important properties of the underlying data | 5a. Representations that can be examined to reveal underlying data properties |
| 5b. Students can explore multiple aspects of the same object or data | ||
| 5c. Flexible representations that students can directly manipulate | ||
| Axes Β—II | 6. Accessible programming environments | 6a. Help with writing the program using visual programming |
| 6b. Focus the programming environment on the meaning of the code and help correct syntax errors | ||
| 7. Minimise complexity | 7a. Reducing the complexity of the computational space in which the investigation takes place through procedures that are invisible to the user. | |
| 7b. Guiding the user, perhaps using AI, to reduce the random complexity that can arise from their choices. | ||
| 8. Provide the necessary structure for complex tasks and functionality | 8a. Limiting complex work by setting proper boundaries for students | |
| 8b. Describe complex operations using ordered and unordered decomposition operations | ||
| 8c. Activity space limitation through the use of functional modes | ||
| 9. Integration of expert guidance on scientific practices | 9a. Integrate expert guidance to clarify the characteristics of scientific practice | |
| 9b. Integrate expert guidance to highlight the rationale for scientific practices | ||
| 10. Automatic handling of unattractive routine work | 10a. Automation of non-obvious parts of tasks to reduce cognitive demands | |
| 10b. Facilitate the organisation of work products | ||
| 10c. Facilitate navigation between tools and activities | ||
| Axes C—III | 11. Support for debugging and modification of misconceptions in programming environments | 11a. Reminders and guidance for code debugging |
| 11b. Live programming capability | ||
| 12. Enable users to see the impact of any change immediately | 12a. Guidance on how to run the application/program immediately after changing | |
| 12b. Helping to focus on and evaluate the differences in results after each change | ||
| 13. Facilitate ongoing articulation and reflection during research | 13a. Reminders and guidance to facilitate production planning | |
| 13b. Reminders and guidance to facilitate productive monitoring | ||
| 13c. Reminders and guidance to facilitate articulation and reflection during the meaning-making process | ||
| 13d. Identifying the scientific characteristics of scientific practices and products |
Strategies fulfilled (✓) or not fulfilled (⨯) by GeoGebra 5 and Tracker 6.1.3 software.
| Strategies | GeoGebra | Tracker |
|---|---|---|
| 1a. Provide visual memory representations to enhance visual thinking | ⨯ | ✓ |
| 1b. Provide common STEM problems with short texts or titles | ⨯ | ✓ |
| 2a. Support in the selection of explicit abstractions | ✓ | ✓ |
| 2b. Provide details that the user can focus on and guide the user with feedback | ✓ | ✓ |
| 3a. Functionality through the visual conceptual organisation | ✓ | ⨯ |
| 3b. Descriptions for complex concepts | ⨯ | ⨯ |
| 3c. Scientific guidance for the implementation of scientific content | ⨯ | ⨯ |
| 4a. Explicit scientific strategies in student-to-tool interactions | ✓ | ✓ |
| 4b. Clear and explicit scientific strategies used by students to construct artefacts | ✓ | ✓ |
| 5a. Representations that can be examined to reveal underlying data properties | ✓ | ✓ |
| 5b. Students can explore multiple aspects of the same object or data | ✓ | ✓ |
| 5c. Flexible representations that students can directly manipulate. | ✓ | ✓ |
| 6a. Help with writing the program using visual programming | ⨯ | ⨯ |
| 6b. Focus the programming environment on the meaning of the code and help correct syntax errors | ⨯ | ⨯ |
| 7a. Reducing the complexity of the computational space in which the investigation takes place through procedures that are invisible to the user. | ✓ | ✓ |
| 7b. Guiding the user, perhaps using AI, to reduce the random complexity that can arise from their choices. | ⨯ | ⨯ |
| 8a. Limiting complex work by setting functional boundaries for students | ✓ | ✓ |
| 8b. Describe complex operations using ordered and unordered decomposition operations | ✓ | ✓ |
| 8c. Activity space limitation through the use of functional modes | ✓ | ✓ |
| 9a. Integrate expert guidance to clarify the characteristics of scientific practice | ⨯ | ⨯ |
| 9b. Integrate expert guidance to highlight the rationale for scientific practices | ⨯ | ⨯ |
| 10a. Automation of non-obvious parts of tasks to reduce cognitive demands | ✓ | ✓ |
| 10b. Facilitate the organisation of work products | ✓ | ✓ |
| 10c. Facilitate navigation between tools and activities | ✓ | ✓ |
| 11a. Reminders and guidance for code debugging | ⨯ | ⨯ |
| 11b. Live programming capability | ⨯ | ⨯ |
| 12a. Guidance on how to run the application/program immediately after changing | ⨯ | ⨯ |
| 12b. Helping to focus on and evaluate the differences in results after each change | ⨯ | ⨯ |
| 13a. Reminders and guidance to facilitate production planning | ⨯ | ⨯ |
| 13b. Reminders and guidance to facilitate productive monitoring | ⨯ | ⨯ |
| 13c. Reminders and guidance to facilitate articulation and reflection during the meaning-making process | ⨯ | ⨯ |
| 13d. Identifying the scientific characteristics of scientific practices and products | ⨯ | ⨯ |
Appendix A
Appendix A.1. GeoGebra Evaluation
GeoGebra is a dynamic mathematics software that combines geometry, algebra, and calculus. It was developed by Markus Hohenwarter [
The next step is to evaluate the specific educational software according to our defined criteria.
Appendix A.1.1. Axes A—I (Guidelines 1, 2, 3, 4)
As mentioned above, the software aims to support the user in formulating a problem and, at the same time, to produce meaning during this process. The present software does not allow the user to structure the problem freely within the software. On the contrary, its use presupposes the existence of a given problem. Of course, this problem can be of an open type, as defined in the teaching of mathematics and physics. Open problems can be solved in several ways, even with many solutions. Open-ended mathematics or physics problems invest in the benefits of the inquiry processes students follow as they wrestle with the problem and search for solutions. In this way, students can master and gain a deeper understanding of the knowledge they are building [
Therefore, if the student/user is given an open-ended problem to solve via the GeoGebra software, then this software will support the user in selecting apparent abstractions with details on which the user can focus where and when needed (strategies 2a and 2b). For example, in the problem shown in the adjacent figure (
Enlarge this image.Figure A2. Algebra image for the horizontal shooting problem (from GeoGebra software).
Concerning strategy 3a, it should be noted that the GeoGebra software is characterised by a high level of functionality, with a perfect visual organisation of the sections and the different representations of the software, which helps the student/user to work continuously on the problem to be solved. It is a particularly ergonomic interface, as pointed out by Echeverría et al. [
On the other hand, one of the disadvantages of GeoGebra is that the descriptions of complex concepts provided by the software could be better, as is the scientific guidance for applying scientific content (strategies 3b and 3c). This is where the teacher’s support is essential to ensure that the student gains the maximum benefit from using the software, both in terms of understanding the subject matter taught and the process of developing computational thinking skills.
As seen in
Enlarge this image.Figure A3. The GeoGebra graphics window for the horizontal shot problem (image from GeoGebra software).
Appendix A.1.2. Axes A—II (Guideline 5)
We could characterise the GeoGebra software as satisfactory in terms of the possibility for the student/user to explore multiple representations of the same data through its different fields. For example, the solution to a mathematical system can be solved within the software either algebraically or graphically (
Enlarge this image.Figure A4. Solving the system algebraically (left) or graphically (right) (image from GeoGebra software).
Of course, the representational possibilities offered by the software could be more extensive, which is to be expected since the present software has been designed as purely mathematical software, even though it can easily be used in engineering problems. For example, the previous solution of a 2 × 2 system could involve finding the position and meeting time of two bodies performing a smooth linear motion on the same line, given the necessary constraints. The representations are limited to algebra, graphics, or field geometry (strategy 5a). However, these representations are quickly inspected by the student/user within the software, allowing the student/user to explore the problem in at least two ways: algebraically and graphically. In addition, these representations are highly malleable and relatively easy to manipulate. Of course, whether or not these representations are malleable depends on the choices made by the student/user during the problem definition phase. For example, suppose the problem is to investigate the conditions under which an intersecting line is transformed into a tangent to the graph of a secondary function, like the average and momentary speed of a moving body. In that case, the student/user is asked to define two moving points of the function through which the line passes and then move from the intersecting line to the tangent by moving these points on the function’s graph (
Enlarge this image.Figure A5. Intercept (left) and tangent (right) of a function for introducing the differential concept (image from GeoGebra software).
Appendix A.1.3. Axes B—II (Guidelines 6, 7, 8, 9, 10)
The GeoGebra software allows users to program by supporting two programming languages, GGBScript and JavaScript. Although GGBScript can be easier than JavaScript, writing a piece of code when the software’s needs require it is difficult for the student/user. This means that guideline 6 needs to be met, as there is no assistance in writing the code (strategies 6a and 6b).
The apparent complexity of the GeoGebra software in the software user interface is reduced to the maximum extent possible. Numerous procedures necessary for the different requirements that may exist during the solution of a problem are performed invisibly without creating additional difficulties for the student/user when attempting to solve a problem with the software. For example, a function’s roots, maxima and minima can appear in the graphical representation of the function (
The GeoGebra software also allows the student/user to describe the complex tasks required to solve the problem with ordered or unordered decomposition tasks that the user has to define, thus activating the skills of analysis, decomposition, subtraction and synthesis (strategy 8b). The following figure shows the calculation of the average and instantaneous speed between time differences in the time-displacement graph of a moving object. The student/user has defined two moving points on the graph x = f(t) and the corresponding line, as well as a dynamic text box where the average speed is calculated each time as the slope of the line. In the case of the tangent, the instantaneous velocity, the student/user is asked to work out how to calculate the slope using the possibilities offered by the software and basic computational thinking skills (
Enlarge this image.Figure A7. Calculation of average and instantaneous velocity (image from GeoGebra software).
On the other hand, during the student/user’s actions to address the problem to be solved, complex situations often arise where the software does not provide any support or assistance (strategy 7b). At these stages, the teacher’s assistance is needed to help the student/user solve problems of unwanted complexity. The same problem is presented in guideline 9 (strategies 9a and 9b). The GeoGebra software needs to contain built-in guidance on the scientific concepts used. Its use requires either the student/user’s knowledge of the scientific concepts being worked on or the active support of the teacher by teaching these concepts beforehand or by supporting and guiding the student/user during the problem-solving phase. Which of the two strategies the teacher chooses depends on the problem to be solved that he/she has set for his/her students.
Guideline 10 is directly related to the complexity mentioned above and is met to a significant extent by the GeoGebra software. The software performs many tasks invisibly and automatically, thus reducing the cognitive demands on students/users. For example, suppose the problem to be solved is to investigate the existence of some basic factoring rules by discovering a pattern in the first derivative of a set of functions (
At the same time, the multiple fields provided by the software to the user are easy to use and help to organise and check the student/user’s output, either by displaying them simultaneously in the interface, especially in the online version of the software, or by displaying them in separate windows in the desktop version (strategies 10b and 10c).
Appendix A.1.4. Axes C—III (Guidelines 11, 12, 13)
Guidelines 11 and 12 refer to programming environments. Therefore, evaluating their application in the GeoGebra software is impossible. As already mentioned, it is possible to write code in this software, but this is on a small scale, and it cannot offer anything to the student/user in terms of learning a STEM subject and cultivating computational thinking skills.
Finally, regarding the continuous articulation and reflection on the products of the student/user’s work while working on the problem to be solved, as set out in guideline 13 (strategies 13a, 13b, 13c and 13d), we should note that the GeoGebra software does not provide these options. Nevertheless, the continuous articulation of the problem and the reflection on the data generated by the software, following the actions of the user, are part of the inquiry process that the student/user must follow in order to successfully model the problem to be solved and lead to the answering of any questions and/or the discovery of new data related to the problem. More specifically, by introducing the problem elements into the algebraic domain, the student/user must cultivate data analysis, subtraction, and synthesis skills to model and ultimately visualise the problem in the graphical domain. Thinking abstractly, the student/user should mathematise the problem, often taken from everyday life, identify the variables, and define them as such through the software. They should also observe the existence of patterns, if any, and identify and interpret the variations observed in each case in the graphical domain. Ultimately, making sense as the student/user attempts to model and solve a problem with GeoGebra is a dynamic process of constant user interaction with the software.
Appendix A.2. Tracker Evaluation
Tracker is a free video analysis and modelling tool based on the Open Source Physics (OSP) Java framework. It was developed by Douglas Brown, Robert Hanson, and Wolfgang Christian for use in physics education. Video modelling with Tracker combines video with computer modelling (
Tracker software is used worldwide to teach mechanics, kinematics, and more. Tracker can be used to study spectroscopic images and diffraction phenomena. The Tracker software also has several applications in secondary biology relating to images taken using a microscope. Particularly in the study and teaching of engineering phenomena, using the Tracker software is a dynamic process with direct user involvement at all stages of the study. It is a process that can significantly promote the computational thinking skills of the user through the actions that the user is required to perform to succeed in the study and, ultimately, to solve a problem.
Appendix A.2.1. Axes A—I (Guidelines 1, 2, 3, 4)
It is software that helps the user to formulate the problem by allowing them to upload videos that they can find in the relevant library/repository of the software, or even videos that they have produced, in an attempt to define a problem to be solved in the context of the subject that they are studying (strategy 1b). In this way, the teacher or student can, for example, find a free fall video or make their own. Thus, we first conceptualise the problem to be solved by visualising it (strategy 1a). This process helps the user to clarify precisely what they want to study. After a thorough study of the video, it even allows them to define new features of the phenomenon that they might have missed and could study.
In the second step, the software supports the necessary abstractions (strategy 2a) that need to be made in order to monitor the motion and record key quantities that could help to study the phenomenon. For example, suppose the task is to study the motion of a ball, laboratory vehicle, or even an actual vehicle. In that case, the user should use the software to record the position of the moving body at any given time. Since the body has non-zero dimensions, he is asked to think abstractly and, with the help of the software, to define a point on the moving body whose position the software monitors during the video. If the moving body turns during its movement, the user has to choose a suitable point of the body to follow its movement so that the software “sees” it during the whole movement (strategy 2b). For example, consider a yellow tennis ball with black writing on its surface. In this case, after watching the video, the user should set the reference point to, for example, the yellow surface of the ball that is visible throughout the video. In addition, depending on the movement that the user wishes to study with the help of the video, he/she should choose a coordinate system for tracking it. The software allows the user to define the coordinate system, e.g., Cartesian or polar coordinates, that they wish to use or that are imposed by the requirements of their study concerning the motion they are studying. Finally, for the measurements to be reliable, the software assists the user in selecting the appropriate scale, which is defined by the user using the tools provided by the software.
All of the above features can certainly promote computational thinking skills, such as abstraction, analysis, synthesis, and modelling (strategies 1a, 1b, 2a and 2b), provided that the student is given an open-ended problem where he or she is asked to work within the software and edit the video, either alone or in a group. However, even the problems where the video is initially edited by the teacher, while not providing the above opportunities for students to develop computational thinking skills, provide similar opportunities at later stages, as discussed below.
Enlarge this image.Figure A9. Tracking, axes, and scale calibration in a video recording of a bouncing cart (image from Tracker software).
Regarding the ability of the software to provide descriptions of complex concepts and scientific guidance for applying scientific content (strategies 3b and 3c), it should be stressed that the software could be faster, but this is not a disadvantage. The software aims not to teach new concepts directly but to enable students to investigate the phenomena previously taught in class and to confirm the validity of the relevant theory. In addition, the Tracker software allows students to solve new open problems related to these phenomena, activating prior knowledge and computational thinking skills in the way described above.
Finally, for strategies 4a and 4b, which concern the organisation of tools and objects around the meaning and terminology of the scientific object and the problem, it should be stressed that part of this organisation is already prepared by the software itself, from the moment the user selects an axis system and calibrates it. The software measures position coordinates, velocities, momentums, and kinetic energies. The rest of the organisation, however, is left to the user to structure according to the requirements of the problem to be solved using the tools provided by the software.
For example, when a student studies the free fall of a ball by modelling a video, he is asked to define the quantities he is interested in studying (
Enlarge this image.Figure A10. Parameter and data function input window (image from the Tracker software).
Appendix A.2.2. Axes A—II (Guideline 5)
The Tracker software fulfils strategies 5a, 5b, and 5c to a very satisfactory degree. The representations provided by the software can be considered particularly flexible (strategy 5c) since it allows the user to trace the movement (trajectory marking) in any part of the video that interests him, to trace the centre of mass in problems involving body systems and to study the movement of the centre of mass. However, it also offers the possibility of displaying a stroboscopic image of the movements in the video. This image is particularly useful in the study of body impacts. In addition, the representations provided can be considered flexible, multiple, and also with the possibility of controlling them (strategies 5a, 5b, and 5c), since the user is provided with the possibility of creating graphs of different quantities and using them to determine the dependence or not of the quantities and the nature of this dependence. For example, when studying free fall, students have been taught and intuitively understand that it is an accelerated motion. The software allows students to establish and ultimately prove that it is a straight line, smoothly accelerating motion. One qualitative way is by tracing the body’s trajectory, where, by noting the successive positions of the moving body, frame by frame, the student finds that in equal periods, the body travels longer and longer distances. Another way is to look at the velocity vectors in each video frame, where the student will see that these vectors become larger and larger as the body descends. Another way is to examine the vertical velocity versus time matrix, where an increase in the vertical velocity measure is evident. Finally, it is possible to use the software to draw a graph of vertical speed versus time, from which the software, using statistical analysis, gives the user the function that relates the two physical quantities. In this way, the user can confirm the time–velocity relationship known from theory.
Of course, it should be stressed that all the above representations are not provided a priori to the user. However, it is up to the user to choose the appropriate representation depending on the problem to be solved. For example, suppose the user is asked to compute the displacement of a car seen moving in a video or the vertical displacement of the Falcon 9 rocket until its crash during its landing in 2016 (video available in the Tracker library,
Appendix A.2.3. Axes B—II (Guidelines 6, 7, 8, 9, 10)
The Tracker software is not a programming environment and, therefore, cannot be evaluated at the level of guideline 6, as it is exclusively concerned with this type of environment.
Guideline 7 on minimising software complexity has been met to a large extent. The user is not involved in the complex procedures for calculating the velocities and accelerations of the moving bodies under investigation, which are performed in the background (strategies 7a and 10a) using the method of least differences between the positions of the moving bodies and the time instants. The software also allows the user to fill any gaps in the measurement file. This is done using a simple command that leads to linear correlation procedures of the existing values in the background (strategies 7a and 10a) to find and fill in the values relating to intermediate positions of the trajectory. This procedure is particularly useful in cases where the user wishes to process and visualise data from an external source, such as an Excel file (
In this case, the student can study and visualise a move for which there is no video, such as a Formula 1 Grand Prix move for which there is a speed file. There are many such videos on YouTube. After recording the speed values of the car for each moment in an Excel file, the user can give this file to the Tracker, model the movement and study it. The student can do the same with an Excel file containing measurements from an actual experiment. In this way, they can model the data they have and visualise it by creating a simulation of the real-world motion, thus gaining the ability to make comparisons. The above process requires various computational thinking skills, the most important being the user’s recognition that accurate modelling/simulation in a 100 fps (frames per second) video requires a time step in the measurements of 0.01 s. In such cases, it is not uncommon to have missing values, which, as explained, the user can generate following a command in the software that runs in the background.
The above shows that the software provides the necessary structure for complex tasks like the previous one. At the same time, it is highly functional (strategies 8a, 8b, 8c, 10b, and 10c), which is reinforced by the fact that in the initial window, the user can, if he/she chooses, simultaneously have an image of the video, the table of values, and the graphical representations, or focus on what he/she is interested in at any given time (
Finally, regarding guideline 9 on integrating expert guidance on scientific practices, the software must guide the scientific practices used. With relevant prior knowledge of physics, the user is invited to work with the software on open or closed engineering problems at an inquiry level, with or without the teacher’s guidance. The more the teacher intervenes, the less the students’ computational thinking skills are activated and vice versa. It is therefore necessary to find the necessary balance between teacher intervention and student self-direction to activate and cultivate students’ computational thinking skills as much as possible without getting them ’lost’ in identifying software functions.
Appendix A.2.4. Axes C—III (Guidelines 11, 12, 13)
Guidelines 11 and 12 relate to programming environments; therefore, we cannot comment on them concerning the Tracker software. It should be mentioned that Tracker, like most software, provides help to the user for all its functions. This helps students when asked to tackle an open engineering problem without particular guidance from the teacher. The help provided is always clear and to the point. In addition, the Tracker allows the user to take introductory notes on the problem bodies being studied and save them for later use when and if they need to refer to them. It is also possible to save the entire experiment so that it can be continued and/or developed at a later stage and, of course, to access the results at any time.
Finally, guideline 13 on continuous articulation and reflection on the problem that users are asked to solve should be stressed that this process is not included in the software but is part of the inquiry process that students are asked to follow to model and study the problem. The key components of computational thinking that students should activate to successfully study the phenomenon and answer any question posed to them are the productive planning of the modelling, the productive monitoring of it and, finally, the production of meaning through this process. Of course, the software helps in this direction with its multiple and malleable representations. It allows students to focus on a different phenomenon feature each time, either through the video itself, the data table or the graphs. However, the students decide where to focus, whether to define new quantities to study or new graphs, and whether they have correctly traced, calibrated, and used axes. Moreover, therein lies the potential for students’ computational thinking skills to emerge and be cultivated through the software while simultaneously exploring engineering issues.
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Details
; Tselios, Nikolaos 1
; Kaliampos, George 1
; Lavidas, Konstantinos 1
; Papadakis, Stamatios 2
1 Department of Educational Science and Early Childhood Education, University of Patras, 26504 Patras, Greece;
2 Department of Preschool Education, University of Crete, 74100 Rethymno, Greece