Mathematical Versus Computational Thinking with a Computer in the Background

Objective: The benefits of computational thinking have become an increasingly acknowledged and popular subject of investigation among researchers. This research aims to gather detail and comprehensive information regarding the learning of computational thinking skills in mathematics at various educational levels through a systematic literature review approach. Methods: With a focus on education level, instructional media, mathematics content, and the components of computational thinking addressed by previous researchers, this paper applied the PRISMA Systematic Review Protocol to offer a comprehensive synthesis of sixteen empirical studies retrieved from the Scopus database on the implementation of computational thinking in mathematics education. Findings: Most research on fostering computational thinking in mathematics education is concentrated at the elementary and junior high school. To optimize the development of computational thinking in mathematics, teachers should be reminded of strategies to support students, particularly through activities involving simulations using various instructional media. Examples of such media include programming platforms, visualization tools, and interactive simulations and games. Number operations and geometry are the mathematical content most widely used for fostering computational thinking. Algorithmic thinking, a crucial component in fostering computational thinking among elementary school students, helps them develop a strong foundation for understanding higher mathematical concepts. Conclusion: A systematic review of computational thinking in learning mathematics at the various education level is conducted in this study. The chosen studies were systematically analyzed for the advancement of computational thinking in learning mathematics to provide new an insight information for educators and stakeholders. Keywords: computational thinking, mathematics, systematic literature review. DOI: http://dx.doi.org/10.23960/jpmipa/v25i1.pp34-52

This research aims to determine the relationship between computational thinking ability and mathematical critical thinking ability of seventh-grade students at SMPN 49 Jakarta. Computational thinking ability is skills or processes in solving problems effectively, while mathematical critical thinking ability is a process of analyzing problems to make an accurate decision. This research used correlation research with research subjects consisting of 14 female students and 16 male students. The instrument in this study is a test in the form of a description, which is measured using indicators. This study used decomposition, pattern recognition, abstraction, and algorithm thinking as indicators of computational thinking ability. This study uses elementary clarification, essential support, inference, advanced clarification, strategy, and tactics as indicators of mathematical critical thinking. The outcome of this research showed a positive correlation between computational thinking ability and students’ mathematical critical thinking ability. The relationship analysis shows a simultaneous and significant relationship between computational thinking and essential mathematical thinking abilities. The correlation test results using Pearson Product Moment obtained a result of 0.897 with a coefficient of determination of 80.5%. The magnitude of the correlation indicates that the two abilities have a solid relationship. If computational thinking ability is high, then mathematical critical thinking ability is also high, and if computational thinking ability is low, then mathematical critical thinking ability is also low.

This study aims to provide an overview of the computational mathematical thinking abilities of male and female students in solving mathematical problems and the aspects (abstraction, decomposition, algorithmic thinking, and generalization) that influence these differences. This study uses a qualitative method with a case study approach in a junior high school in Jakarta for the academic year 2023/2024. The participants in this study are 36 students. Data were collected through written examinations and interviews and analyzed using the triangulation technique. The results of the study showed different patterns of computational thinking skills between male and female students. Male students excel in decomposition and algorithmic thinking but are weak in abstraction and generalization. Female students excel in abstraction and decomposition but are weak in algorithmic thinking and generalization. Both male and female students master the context of decomposition for computational thinking skills but lack mastery in the context of generalization. In conclusion, gender differences influence specific aspects of computational thinking skills, indicating the need for tailored educational strategies to address these differences.

The main objective of this study was to measure the level of computational thinking readiness in prospective first-year mathematics education students. In addition, this study also aims to identify factors that influence their level of readiness towards computational thinking. This research is qualitative and descriptive in nature. This study describes first-year mathematics education students' mathematical computational thinking ability based on the theory of mathematical computational thinking. This study was conducted on first-year mathematics education students in the academic year 2023/2024. There were 16 first-year mathematics education students, all of whom were taken as samples in this study, to obtain more in-depth information about the computational thinking ability of first-year mathematics education students for further research development. The instruments used to collect data on first-year mathematics education students' mathematical computational thinking ability are (1) a mathematical computational thinking ability test and (2) an interview. The data obtained were calculated using statistical tests, and the results will be explained in depth. The mean score of the first-year mathematics education student's computational thinking ability test was 59.68, indicating that students generally have a fairly good level of computational thinking ability.

The purpose of this study is to select self-regulation and sociality as variables predicting computational thinking skills in order to examine the relationship and influence between them. The subjects of the study were 76 5-year-old infants from kindergartens and daycare centers in Gyeonggi-do Province. The candidates for participation in the study were selected through open recruitment with the cooperation of the institution. The computing power of infants was collected through one-by-one interviews, and the self-regulation and sociality of infants were collected through questionnaires for parents and teachers. In addition, the analysis of the collected data was performed using SPSS WIN 21.0 for descriptive statistics, correlation analysis, and multiple regression analysis. First, self-regulation, sociality, and computational thinking were all above medium value. Second, there was no statistically significant correlation between infant self-regulation and computational thinking, but only mathematical thinking, which was a sub-factor of computational thinking, and it showed no statistically significant influence on computational thinking. Third, there was a statistically significant static correlation between the sociality of infants and computational thinking, and the sociality of infants predicted computational thinking by 21%. In particular, the sociality of infants had been shown to have an impact on logical thinking and mathematical thinking, which were sub-factors of computational thinking. This study serves as a steppingstone for discussion to enhance the computational thinking capabilities of infants by identifying predictors that could explain the computational thinking capabilities of infants.

This chapter analyzes the nature of Computational Thinking (CT) and demonstrates the synergistic relationship between CT and Mathematical Thinking (MT). It cites commonly used definitions of CT and MT and discusses shared problem-solving techniques. The chapter discusses the roles mathematics plays in CT, including how specific mathematical topics interact with specific computing topics, and how mathematical reasoning complements computational reasoning. It explores some principles and practices of CT and performs an analysis of these principles and practices couched in their synergistic relationships to MT. The chapter also discusses a theory of learning for both MT and CT, the application of which suggests directions for pedagogy to enhance the learning of MT and CT concepts.

Mathematical computational thinking skills are essential in mathematics learning, particularly in training systematic problem-solving abilities. However, the limited availability of interactive and effective learning media has remained a significant obstacle to developing these skills. This study aims to develop learning media based on Articulate Storyline 3, which is designed to enhance students' mathematical computational thinking skills. The method employed in this research is Research and Development (R&D) using the ADDIE model, which includes the stages of analysis, design, development, implementation, and evaluation. The subjects of the study were high school students selected through purposive sampling. The research instruments included expert validation questionnaires, user response questionnaires, and tests to assess computational thinking skills. The study results have shown that the developed learning media has achieved a very high level of validity according to evaluations from both material and media experts. Additionally, user responses have demonstrated high satisfaction with the interactivity and ease of media use. Field trials have revealed a significant increase in students' mathematical computational thinking skills after using the learning media. Based on these findings, learning media based on Articulate Storyline 3 has effectively improved mathematical computational thinking skills. These results are expected to contribute positively to more interactive and practical mathematics education innovations.

This study aims to examine the development of Project Based Learning kits using Scratch program to improve students' mathematical computational thinking skills in statistics content. The research method used is Research and Development (R & D) approach which refers to Four-D model: Define, Design, Develop, and Disseminate. In the initial stage, researchers conducted preliminary research through literature studies, school surveys, and draft designs. The study produces Project Based Learning kits using Scratch program consist of student's worksheet, lesson plans, and an instrument of mathematical computational thinking. The design of the model was then revised by the expert trial subject. The subjects of the expert test were mathematics learning experts and several mathematics school teachers. The field Pre-Test and Post-Test were conducted in a Junior High School in Tangerang Selatan on mathematical computational thinking instruments, consisting of four essay test (8 question items). The collected data were analyzed using qualitative and quantitative techniques. In validity aspects, all the three learning kits are valid. From the aspect of effectiveness, the Project Based Learning model intervention can improve students' mathematical computational thinking skills. In terms of practicality, students' responses to the developed worksheets are positive.

The purpose of this study is (1) to describe the characteristics of a good mobile learning application to improve computational thinking and learning independence of high school students. (2) to produce a mobile learning application that is oriented towards computational thinking skills and student learning independence with good quality. The quality of the development results is determined based on Nieveen's criteria, namely valid, practical, and effective. This study is a research and development (R&D) that uses the Borg & Gall development model with 8 development steps, namely preliminary study, planning, initial product development, small group trials, main product revision, limited scale trials, operational product revisions and large-scale trials. The subjects in this study were 36 students from one class at SMA Negeri 1 Gamping, Sleman Regency. The instrument used to measure the validity of the mobile learning application is the expert validation sheet. The instrument to measure the practicality of the mobile learning application is the student response questionnaire. The instrument to measure the effectiveness of the application is the computational thinking test and the student learning independence questionnaire. Validity and practicality data analysis was conducted by converting quantitative data into qualitative form in the form of four standard scale values, while effectiveness data analysis based on test and questionnaire results was conducted using paired sample t-test. The results of the study showed that (1) Mobile learning applications have the characteristics of being easy to apply, flexible to time, lightweight and easy to carry anywhere and also implementing each computational thinking indicator in each stage of the material. (2) The results of expert validation showed that the developed mobile learning application met the valid criteria as seen by the Aiken's validity test score for media experts of 0.83 and 0.68 for material experts. The practicality of the mobile learning application is included in the very good category as seen from the average results with an average percentage of student responses of 87.17%. The effectiveness of the computational thinking test obtained a t-value of 47.22 greater than t (35,0.05) with a score of 1.69, the effectiveness of the learning independence test based on the t test obtained a t-value of 4.85 greater than t (35,0.05) with a score of 1.69. Based on the results obtained, it can be concluded that the developed mobile learning application meets the criteria of validity, practicality and effectiveness.

Computational thinking is increasingly important in the secondary curriculum beyond the computer science classroom, especially in technology heavy STEM fields. We applied the Computational Thinking in Mathematics and Science Taxonomy (Weintrop et al., 2016) to explore how secondary students demonstrated computational thinking in research projects from a month-long STEM enrichment summer program. The preliminary data show that the papers and posters of four students, one from each area of the summer curricula, demonstrate all four of the practices: Data Practices, Modeling and Simulation Practices, Computational Problem Solving Practices, and Systems Thinking Practices. These results indicate that computational thinking provides a useful framework for planning and assessing secondary students’ STEM independent research projects. Key words: computational thinking, research.

Evaluation of creative project production performance in mathematical logic and computational thinking skills among gifted high school students.

Computational thinking is a way of analytic thinking, a general mathematical thinking approach that may be used in solving a problem, a general engineering thinking approach that allows designing and evaluating large and complex systems that exist in the real world, as well as a general scientific thinking approach in understanding computing ability, intelligence, human mind and behavior. With the existence of online games at a time like today, there is a tendency for many students to play online games because it has its own challenges, many of them even spend a lot of money and even forget the time to play online games. there is an urgency to the level of computational thinking of dota two players, so it is necessary to estimate using machine learning techniques to determine the level of computational thinking of dota two game players. The results of this study provide information that in Estimating the Computational Thinking Ability of Dota Dua Game Players Using Machine Learning Techniques using attribute 6 and rapidminer tools version 10 with operators to be used, including retrieval dataset, role set, correlation matrix, selected by weighted, split data, linear regression, apply model and performance. Produces an error accuracy rate in this study, namely, root mean squered error 0.383 +/- 0.000 Squared error 0.146 +/- 0.016 Squared Correlation 1.000, then this value is the best value from several test results. So it can be estimated as follows that the results of the Computational Thinking Ability are good as much as 36 while the Computational Thinking Ability is sufficient as much as 47

Efforts to promote creativity often centre on encouraging people to engage in 'design thinking', 'systems thinking' and 'entrepreneurial thinking'. These different approaches are most often defined, taught and applied in mutual isolation, which has obscured what distinguishes them from each other, what they have in common and how they might be combined. These three approaches are also most often described in isolation from the approaches that characterize other disciplines, all of which are relevant to how problems are identified, framed and solved. These other approaches include 'computational thinking', 'engineering thinking', 'scientific thinking', 'evolutionary thinking', 'mathematical thinking', 'statistical thinking', 'geographical thinking', 'historical thinking', 'anthropological thinking' and many more. Examining these approaches as a set allows each of them to be better understood, and also reveals the connections and contrasts between them. Such comparisons provide the foundation for a more coordinated project to represent how different disciplinary approaches contribute to creative work.

With the increasing advocacy for CT integration in K-12 education, it is important to consider how teacher education programs could better prepare teacher candidates (TCs). At the Faculty of Education at Western University, CT has been included in the curriculum as part of the teacher education program through the course Computational Thinking in Mathematics and Science Education, oriented to Intermediate/Senior (Grades 7 to 12) preservice teachers. In this paper, we describe the case study of the 2017 cohort of the CT course. We aimed to answer the question: What key understandings about CT did teacher candidates develop through their participation in the course? We found that TCs in our course developed a better understanding of: (1) CT connections to the real world, as well as lesson ideas and pedagogical examples to integrate CT in the context of mathematics and science; (2) the different affordances of CT integration; (3) the use of several technologies to implement CT integration; and (4) what CT is, as well as the set of skills that contribute to its development.

This short practitioner report presents information for the planning, teaching and evaluation cycle of a cross curricular Computing, Geography and Mathematics lessons in a 5thgrade classroom. The study focused on both mathematical thinking and Geographical knowledge. The objective of the lesson was to teach children measurement and prediction skills through exploring the Angel Falls, located inside of the Canaima National Park in Venezuela, using the Google expedition application. For the purpose of this study, action research was chosen whereby the findings of this study were used to inform future planning and improve learning. The study found that the students were able to use their logical reasoning to predict the length of many objects including the Angel Falls. The project also found that providing children with real-life learning contexts motivated them to learn and made learning more meaningful. The children were able to transfer and apply their prediction skills during their coding sessions, which highlights the link between mathematical and computational thinking.