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Using Habermas’ construct of rationality to analyze students’ computational thinking: The case of series and vector

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Abstract

The aim of this study is to explore the computational thinking (CT) processes of university students with the integration of CAS and ACODESA method within the context of problem-solving. The participants of the study are 22 university students. The embedded design was used in the study. The qualitative data consists of the written products of the students, the Maple files, and the transcriptions of argumentations while the quantitative data consists of the pre and post-test scores of the students in CT practices. The implementation was based on ACODESA method. The pre and post-test scores were compared through the Wilcoxon signed-rank test. It was concluded that ACODESA method had a statistically significant effect on students’ CT performances in the problem-solving process, cognitive processes and transposition. The qualitative data were analyzed within the framework of Habermas' construct of rationality. It was seen that in the series problem, the students showed improvement in constructing factorial concept and exponential expressions with a for loop, defining events and using them as conditionals within the if–then comparison statement. In the vector problem, the students showed improvement in constructing the components of n-dimensional vectors, constructing a for loop to find the angle between these vectors, using the if–then comparison statement to check the equality of the dimensions. The students were able to act more rationally in choosing and using the CT concepts suitable for the purpose and transferring the CT process to the others, thanks to productive argumentations and the semiotic mediational role of the Maple.

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References

  • Adams, D. M., & Hamm, M. E. (1990). Cooperative learning: Critical thinking and collaboration across the curriculum. Thomas.

    Google Scholar 

  • Agbo, F. J., Oyelere, S. S., Suhonen, J., & Laine, T. H. (2021). Co-design of mini games for learning computational thinking in an online environment. Education and Information Technologies, 26(5), 5815–5849.

    Article  Google Scholar 

  • Aho, A. V. (2012). Computation and computational thinking. The Computer Journal, 55(7), 832–835.

    Article  Google Scholar 

  • Aksu, N. & Zengin, Y. (2022). Disclosure of students’ mathematical reasoning through collaborative technology-enhanced learning environment. Education and Information Technologies, 27(2), 1609–1634. https://doi.org/10.1007/s10639-021-10686-x

  • Ardito, G., Mosley, P., & Scollins, L. (2014). We robot: Using robotics to promote collaborative and mathematics learning in amiddle school classroom. Middle Grades Research Journal, 9(3), 73–88.

    Google Scholar 

  • Arvaja, M., Salovaara, H., Häkkinen, P., & Järvelä, S. (2007). Combining individual and group-level perspectives for studying collaborative knowledge construction in context. Learning and Instruction, 17(4), 448–459.

    Article  Google Scholar 

  • Barak, M., & Assal, M. (2018). Robotics and STEM learning: Students’ achievements in assignments according to the P3 task taxonomy-Practice, problem solving, and projects. International Journal of Technology and Design Education, 28(1), 121–144.

    Article  Google Scholar 

  • Benakli, N., Kostadinov, B., Satyanarayana, A., & Singh, S. (2017). Introducing computational thinking through hands-on projects using R with applications to calculus, probability and data analysis. International Journal of Mathematical Education in Science and Technology, 48(3), 393–427.

    Article  Google Scholar 

  • Blum, W., & Leiß, D. (2007). How do students and teachers deal with modeling problems? In C. Haines, W. Blum, P. Galbraith, & S. Khan (Eds.), Mathematical modeling (ICTMA 12): Education, engineering and economics (pp. 222–231). Horwood.

    Google Scholar 

  • Boero, P. (2006). Habermas' theory of rationality as a comprehensive frame for conjecturing and proving in school. In J. Novotná, H. Moraová, M. Krátká & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (pp. 185–192). Prague: PME

  • Boero P., & Morselli, F. (2009). The use of algebraic language in mathematical modelling and proving in the perspektive of Habermas’ theory of rationality. In V. Durand-Guerrier, S. Soury-Lavergne & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (pp. 964–973). Lyon France

  • Boero, P., & Planas, N. (2014). Habermas’ construct of rational behavior in mathematics education: New advances and research questions. In P. Liljedahl, C. Nicol, S. Oesterle & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (pp. 205–235). Vancouver, Canada: PME

  • Boulden, D. C., Rachmatullah, A., Oliver, K. M., & Wiebe, E. (2021). Measuring in-service teacher self-efficacy for teaching computational thinking: Development and validation of the T-STEM CT. Education and Information Technologies, 26(4), 4663–4689.

    Article  Google Scholar 

  • Bråting, K., & Kilhamn, C. (2021). Exploring the intersection of algebraic and computational thinking. Mathematical Thinking and Learning, 23(2), 170–185.

    Article  Google Scholar 

  • Bråting, K., Kilhamn, C., & Rolandsson, L. (2021). Integrating programming in Swedish school mathematics: Description of a research project. Presented at MADIF12, the twelfth research seminar of the Swedish society for research in mathematics education, Linnaeus University, Vaxjo, Sweden.

  • Brennan, K., & Resnick, M. (2012, April). New frameworks for studying and assessing the development of computational thinking. Paper presented at the 2012 annual meeting of the American Educational Research Association, Vancouver, Canada (pp. 1–25)

  • Chao, P. Y. (2016). Exploring students’ computational practice, design and performance of problem-solving through a visual programming environment. Computers & Education, 95, 202–215. https://doi.org/10.1016/j.compedu.2016.01.010

    Article  Google Scholar 

  • Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155–159. https://doi.org/10.1037/0033-2909.112.1.155

  • Computer Science Teachers Association, & International Society for Technology in Education. (2011). Computational thinking: Leadership toolkit (1st ed.) Retrieved September 4, 2021, from https://www.yumpu.com/en/document/read/43967234/computational-thinking-leadership-toolkit-iste

  • Cramer, J. (2015). Argumentation below expectation: A double-threefold Habermas explanation. In K. Krainer & N. Vondrová (Eds.), Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (pp. 114–120). Prague, Czech Republic: ERME

  • Creswell, J. W. (2012). Educational research planning, conducting and evaluating quantitative and qualitative research(4th ed.). Boston, MA: Pearson Education, Inc

  • Czerkawski, B. C., & Lyman, E. W. (2015). Exploring issues about computational thinking in higher education. TechTrends, 59(2), 57–65. https://doi.org/10.1007/s11528-015-0840-3

    Article  Google Scholar 

  • Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1), 103–131.

    Article  MathSciNet  Google Scholar 

  • Falcade, R., Laborde, C., & Mariotti, M. A. (2007). Approaching functions: Cabri tools as instruments of semiotic mediation. Educational Studies in Mathematics, 66(3), 317–333.

    Article  Google Scholar 

  • Fernández, J. M., Zúñiga, M. E., Rosas, M. V., & Guerrero, R. A. (2018). Experiences in learning problem-solving through computational thinking. Journal of Computer Science and Technology, 18(2), 136–142.

    Article  Google Scholar 

  • Feurzeig, W., Papert, S. A., & Lawler, B. (2011). Programminglanguages as a conceptual framework for teaching mathematics. Interactive Learning Environments, 19(5), 487–501.

    Article  Google Scholar 

  • Field, A. (2009). Discovering statistics using SPSS (3rd edn.). Sage Publications Ltd.

  • Gadanidis, G., Hughes, J., Minniti, L., & White, B. (2017). Computational thinking, grade 1 students and the binomial theorem. Digital Experiences in Mathematics Education, 3(2), 77–96.

    Article  Google Scholar 

  • Gleasman, C., & Kim, C. (2020). Pre-Service Teacher’s Use of Block-Based Programming and Computational Thinking to Teach Elementary Mathematics. Digital Experiences in Mathematics Education, 6(1), 52–90.

    Article  Google Scholar 

  • Habermas, J. (2009). Rationalitäts-und Sprachtheorie. Philosophische Texte: Studienausgabe, Band 2. Suhrkamp.

  • Hitt, F., & Dufour, S. (2021). Introduction to calculus through an open-ended task in the context of speed: representations and actions by students in action. ZDM-Mathematics Education, 53(3), 635–647.

    Article  Google Scholar 

  • Hitt, F., & Gonzalez-Martin, A. (2015). Covariation between variables in a modelling process: The ACODESA (collaborative learning, scientific debate and self-reflexion) method. Educational Studies in Mathematics, 88(2), 201–219.

    Article  Google Scholar 

  • Hitt, F., Saboya, M., & Cortes-Zavala, C. (2017). Rupture or continuity: The arithmetico-algebraic thinking as an alternative in a modelling process in a paper and pencil and technology environment. Educational Studies in Mathematics, 94(1), 97–116.

    Article  Google Scholar 

  • Hoyles, C., & Noss, R. (2015). Revisiting programming to enhance mathematics learning, math + coding symposium. Western University. London, Ontario, Canada: Western University

  • Hussain, S., Lindh, J., & Shukur, G. (2006). The effect of LEGO training on pupils’ school performance in mathematics, problem solving ability and attitude: Swedish data. Journal of Educational Technology and Society, 9(3), 182–194.

    Google Scholar 

  • Kafai, Y. B. (2016). From computational thinking to computational participation in K–12 education. Communications of the ACM, 59(8), 26–27.

    Article  Google Scholar 

  • Kafai, Y. B., & Burke, Q. (2013). Computer programming goes back to school. Phi Delta Kappan, 95(1), 61.

    Article  Google Scholar 

  • Kafai, Y. B., Lee, E., Searle, K., Fields, D., Kaplan, E., & Lui, D. (2014). A crafts-oriented approach to computing in high school: Introducing computational concepts, practices, and perspectives with electronic textiles. ACM Transactions on Computing Education, 14(1), 1–20. https://doi.org/10.1145/2576874

    Article  Google Scholar 

  • Kallia, M., Van Borkulo, S. P., Drijvers, P., Barendsen E., & Tolboom, K. (2021). Characterising Computational Thinking in Mathematics Education: A literature-informed Delphi study. Research in Mathematics Education, pp. Advance online publication. https://doi.org/10.1080/14794802.2020.1852104

  • Kaufmann, O. T., & Stenseth, B. (2020). Programming in mathematics education. International Journal of Mathematical Education in Science and Technology, 52(7), 1029–1048.

    Article  Google Scholar 

  • Leonard, J., Buss, A., Gamboa, R., Mitchell, M., Fashola, O. S., Hubert, T., . . . Almughyirah, S. (2016). Using robotics and game design to enhance children’s self-efficacy, STEM attitudes, and computational thinking skills. Journal of Science Education and Technology, 25(6), 860–876

  • Leontiev, A. (1981). Sign and activity. In J. V. Wertsch (Ed.), The concept of activity theory in soviet psychology (pp. 241–255). M.E. Sharpe.

    Google Scholar 

  • Liu, J., & Wang, L. (2010). Computational Thinking in Discrete Mathematics. IEEE 2nd International Workshop on Education Technology and Computer Science, 1, 413–416.

    Google Scholar 

  • Lindsjørn, Y., Sjøberg, D. I., Dingsøyr, T., Bergersen, G. R., & Dybå, T. (2016). Teamwork quality and project success in software development: A survey of agile development teams. Journal of Systems and Software, 122, 274–286. https://doi.org/10.1016/j.jss.2016.09.028

    Article  Google Scholar 

  • Lockwood, E., & Chenne, A. (2020). Enriching students’ combinatorial reasoning through the use of loops and conditional statements in Python. International Journal of Research in Undergraduate Mathematics Education, 6, 303–346.

    Article  Google Scholar 

  • Lovric, M. (2018). Programming and Mathematics in an Upper-Level University Problem-Solving Course. Primus, 28(7), 683–698.

    Article  Google Scholar 

  • Lye, S. Y., & Koh, J. H. L. (2014). Review on teaching and learning of computational thinking through programming: What is next for K-12? Computers in Human Behavior, 41, 51–61.

    Article  Google Scholar 

  • Lyman, F. (1987). Think-Pair-Share: An Ending Teaching Technique. MAA-CIE Cooperative News, 1, 1–2.

    Google Scholar 

  • Maguire, P., Maguire, R., Hyland, P., & Marshall, P. (2014). Enhancing collaborative learning using paired-programming: Who benefits? AISHE-J: The All Ireland Journal of Teaching and Learning in Higher Education, 6(2), 1411–14125.

    Google Scholar 

  • Mariotti, M. A., Durand-Guerrier, V., & Stylianides, G. J. (2018). Argumentation and proof. In T. Dreyfus, M. Artigue, D. Potari, S. Prediger, & K. Ruthven (Eds.), Developing research in mathematics education: Twenty Years of Communication, Cooperation and Collaboration in Europe (pp. 75–89). Routledge.

    Chapter  Google Scholar 

  • McMillan, J., & Schumacher, S. (2010). Research in education: Evidence-based inquiry (7th ed.). Pearson.

    Google Scholar 

  • Moreno León, J., Robles, G., & Román-González, M. (2016). Code to learn: Where does it belong in the K-12 curriculum? Journal of Information Technology Education. Research, 15, 283–303.

    Google Scholar 

  • Morselli, F., & Boero, P. (2009). Proving as a rational behaviour: Habermas’ construct of rationality as a comprehensive frame for research on the teaching and learning of proof. In V. Durand-Guerrier, S. Soury-Lavergne & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (pp. 211–220). Lyon France

  • Morselli, F., & Boero, P. (2011). Using Habermas’ theory of rationality to gain insight into students’ understanding of algebraic language. In J. Cai & E. Knuth (Eds.), Early Algebraization. Advances in Mathematics Education (pp. 453–479). Springer, Berlin, Heidelberg

  • Nardi, A. (Ed.). (1997). Context and consciousness: AT and humancomputer interaction. Cambridge, MA; London: MIT Press

  • Ng, O.-L., & Cui, Z. (2021). Examining primary students’ mathematical problem-solving in a programming context: towards computationally enhanced mathematics education. ZDM- Mathematics Education, 53(4), 847–860.

    Article  Google Scholar 

  • Niemelä, P., Partanen, T., Harsu, M., Leppänen, L., & Ihantola, P. (2017). Computational thinking as an emergent learning trajectory of mathematics. Proceedings of the 17th Koli Calling Conference on Computing Education Research—Koli Calling 17

  • Olteanu, C. (2020). Programming, mathematical reasoning and sense-making. International Journal of Mathematical Education in Science and Technology. Advance online publication. https://doi.org/10.1080/0020739X.2020.1858199

  • Papert, S. A. (1980). Mindstorms: Children, computers, and powerful ideas. Basic Books.

    Google Scholar 

  • Pellas, N., & Vosinakis, S. (2018). The effect of simulation games on learning computer programming: A comparative study on high school students’ learning performance by assessing computational problem-solving strategies. Education and Information Technologies, 23, 2423–2452.

    Article  Google Scholar 

  • Qualls, J. A., & Sherrell, L. B. (2010). Why computational thinking should be integrated into the curriculum. Journal of Computing Sciences in Colleges, 25(5), 66–71.

    Google Scholar 

  • Radford, L. (2008). Theories in mathematics education: A brief inquiry into their conceptual differences. ICMI 11 Survey team 7: The notion and role of theory in mathematics education research. Retrieved August 20, 2021, from http://www.luisradford.ca/pub/31_radfordicmist7_EN.pdf

  • Rasmussen, C., & Keene, K. (2019). Knowing solutions to differential equations with rate of change as a function: Waypoints in the journey. Journal of Mathematical Behavior, 56, 100695.

    Article  Google Scholar 

  • Rich, K. M., Yadav, A., & Larimore, R. A. (2020). Teacher implementation profles for integrating computational thinking into elementary mathematics and science instruction. Education and Information Technologies, 25(4), 3161–3188.

    Article  Google Scholar 

  • Rodríguez-Martínez, J. A., González-Calero, J. A., & Sáez-López, J. M. (2020). Computational thinking and mathematics using Scratch: An experiment with sixth-grade students. Interactive Learning Environments, 28(3), 316–327.

    Article  Google Scholar 

  • Roman-Gonzalez, M., Perez-Gonzalez, J.-C., & Jimenez-Fernandez, C. (2017). Which cognitive abilities underlie computational thinking? Criterion validity of the Computational Thinking Test. Computers in Human Behavior, 72, 678–691.

    Article  Google Scholar 

  • Sanford, J. F., & Naidu, J. T. (2016). Computational thinking concepts for grade school. Contemporary Issues in Education Research (CIER), 9(1), 23–32.

    Article  Google Scholar 

  • Shaffer, D. W. (2012). Models of situated action: Computer games and the problem of transfer. In C. Steinkuehler, K. Squire, & S. Barab (Eds.), Games learning, and society: Learning and meaning in the digital age (pp. 403–433). Cambridge, UK: Cambridge University Press. https://doi.org/10.1017/CBO9781139031127.028

  • Serrano-Cámara, L. M., Paredes-Velasco, M., Alcover, C. M., & Velazquez-Iturbide, J. Á. (2014). An evaluation of students’ motivation in computer-supported collaborative learning of programming concepts. Computers in Human Behavior, 31, 499–508. https://doi.org/10.1016/j.chb.2013.04.030

    Article  Google Scholar 

  • Sinclair, N., & Patterson, M. (2018). The Dynamic Geometrisation of Computer Programming. Mathematical Thinking and Learning, 20(1), 54–74.

    Article  Google Scholar 

  • Slavin, R. E. (1988). Cooperative learning and student achievement. Educational Leadership, 46(2), 31–33.

    Google Scholar 

  • Stephan, M., & Rasmussen, C. (2002). Classroom mathematical practices in differential equations. Journal of Mathematical Behavior, 21, 459–490.

    Article  Google Scholar 

  • Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory (2nd ed.). Sage.

    Google Scholar 

  • Strijbos, J., & Fischer, F. (2007). Methodological Challenges for Collaborative Learning Research, 17(4), 389–464.

    Google Scholar 

  • Strijbos, J.-W., Martens, R. L., Jochems, W. M. G., & Broers, N. J. (2004). The effect of functional roles on group efficiency: Using multilevel modeling and content analysis to investigate computersupported collaboration in small groups. Small Group Research, 35(2), 195–229.

    Article  Google Scholar 

  • Taylor, M., Harlow, A., & Forret, M. (2010). Using a computer programming environment and an interactive whiteboard to investigate some mathematical thinking. Procedia - Social and Behavioral Sciences, 8, 561–570.

    Article  Google Scholar 

  • Thomas, G. B., Weir, M. D., & Hass, J. R. (2010). Thomas Calculus (12th ed.). Pearson Education Inc.

    Google Scholar 

  • Thompson, P. (2002). Some remarks on conventions and representations. In F. Hitt (Ed.), Mathematics Visualisation and Representations (pp. 199–206). Mexico: PME-NA and Cinvestav-IPN

  • Uzumcu, O., & Bay, E. (2021). The effect of computational thinking skill program design developed according to interest driven creator theory on prospective teachers. Education and Information Technologies, 26, 565–583.

    Article  Google Scholar 

  • Voogt, J., Fisser, P., Good, J., Mishra, P., & Yadav, A. (2015). Computational thinking in compulsory education: Towards an agenda for research and practice. Education and Information Technologies, 20(4), 715–728.

    Article  Google Scholar 

  • Voskoglou, M., & Buckley, S. (2012). Problem solving and computational thinking in a learning environment. Egyptian Computer Science Journal, 36(4), 28–46.

    Google Scholar 

  • Wang, X.-M., & Hwang, G.-J. (2017). A problem posing-based practicing strategy for facilitating students’ computer programming skills in the team-based learning mode. Educational Technology Research and Development, 65(6), 1655–1671.

    Article  Google Scholar 

  • Weintrop, D., Beheshti, E., Horn, M., Orton, K., Jona, K., Trouille, L., & Wilensky, U. (2016). Defining computational thinking for mathematics and science classrooms. Journal of Science Education and Technology, 25(1), 127–147.

    Article  Google Scholar 

  • Wing, J. (2006). Computational thinking. Communications of the ACM, 49(3), 33–35.

    Article  Google Scholar 

  • Wing, J. (2008). Computational thinking and thinking about computing. Philosophical Transactions of the Royal Society a: Mathematical, Physical and Engineering Sciences, 366(1881), 3717–3725.

    Article  MathSciNet  MATH  Google Scholar 

  • Wing, J. (2010). Research notebook: Computational thinking—What and why? The Link Magazine. Retrieved August 12, 2021, from https://www.cs.cmu.edu/link/research-notebook-computational-thinking-what-and-why

  • Wu, B., Hu, Y., Ruis, A. R., & Wang, M. (2019). Analysing computational thinking in collaborative programming: A quantitative ethnography approach. Journal of Computer Assisted Learning, 35, 421–434.

    Article  Google Scholar 

  • Zengin, Y. (2017). Investigating the use of the Khan Academy and mathematics software with a flipped classroom approach in mathematics teaching. Educational Technology & Society, 20(2), 89–100.

    Google Scholar 

  • Zengin, Y. (2018). Examination of the constructed dynamic bridge between the concepts of differential and derivative with the integration of GeoGebra and the ACODESA method. Educational Studies in Mathematics, 99(3), 311–333. https://doi.org/10.1007/s10649-018-9832-5

    Article  Google Scholar 

  • Zengin, Y. (2021). Students’ understanding of parametric equations in a collaborative technology-enhanced learning environment. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2021.1966848

  • Zengin, Y. (2022). Construction of proof of the Fundamental Theorem of Calculus using dynamic mathematics software in the calculus classroom. Education and Information Technologies, 27(2), 2331–2366. https://doi.org/10.1007/s10639-021-10666-1.

    Article  Google Scholar 

  • Zhong, B., Wang, Q., Chen, J., & Li, Y. (2017). Investigating the period of switching roles in pair programming in a primary school. Journal of Educational Technology & Society, 20(3), 220–233.

    Google Scholar 

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  1. Department of Mathematics and Science Education, Faculty of Education, Hacettepe University, Beytepe, 06800, Ankara, Turkey

    Selin Urhan

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Appendix 1

Appendix 1

  1. 1.

    The standard deviation of the elements in a list of \(L=\{{a}_{i}|i=\mathrm{1,2},...n,{a}_{i}\in {\mathbb{R}}\}\) with \(n\) elements is found using the following formula:

$$SD=\sqrt{\frac{\sum_{i=1}^{n}{{(a}_{i}-arithmetic\:mean)}^{2}}{n}}$$

Based on this information, construct the procedure that finds the standard deviation of the list \(L\) whose elements are entered from the keyboard.

  1. 2.

    \(n\) numbers will be entered from the keyboard. Construct a procedure that finds the largest of the numbers that were entered (“sort” command will not be used).

  2. 3.

    For a natural number \(n<1000\) entered from the keyboard, construct a procedure that finds numbers between \(100\) and \(n\) that are equal to the sum of the cubes of their digits.

  3. 4.

    A natural number \(n\) is requested from the user. Construct a procedure that finds the number of prime numbers between \(2\) and \(n\)(“isprime” and “prime” commands will not be used).

  4. 5.

    Construct a procedure that calculates the area of the region between two curves bounded by the lines \(x=a\) and \(x=b\) (The parameters of your procedure will be the functions \(f(x)\) and \(g(x)\) and the numbers \(a\) and \(b\)).

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Urhan, S. Using Habermas’ construct of rationality to analyze students’ computational thinking: The case of series and vector. Educ Inf Technol 27, 10869–10948 (2022). https://doi.org/10.1007/s10639-022-11002-x

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