Abstract
As block-based programming grows in popularity within education, the integration of its application within teacher education programs needs to be investigated. This article examines block-based programming as a viable tool to teach elementary mathematics conceptually drawing on the connections pre-service teachers made between computational thinking and mathematics. This cross-comparative case study that includes a convergent, mixed-methods design examines how block-based coding and computational thinking for conceptual mathematics (B2C3Math) facilitated ten pre-service teachers’ connections made at a large southeastern US university. Connections between computational thinking and mathematics concepts were investigated while the pre-service teachers’ attitudes towards block-based programming as a conceptual mathematics teaching tool were queried. A focus is not placed on interactive games or simulations made using block-based programming to teach mathematics, but rather on pre-service teachers’ ability to design a lesson teaching mathematics conceptually through the programming process. Descriptive analysis reveals changes in pre-service teachers’ attitudes of the proposed teaching strategy following the implementation of B2C3Math. Pre-service teachers’ reflections and lesson designs provide insight into the quality of the connections made between computational thinking and mathematics for the purpose of conceptual mathematics teaching. Three critical cases are identified to illustrate the spectrum of all ten participants in relation to the major findings. Implications for research and practices using block-based programming for teacher education are discussed.
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Ahmadzadeh, M., Elliman, D., & Higgins, C. (2005). An analysis of patterns of debugging among novice computer science students. ACM SIGCSE Bulletin, 37(3), 84–88.
Bakos, S., & Thibault, M. (2018). Affordances and tensions in teaching both computational thinking and mathematics. In E. Bergqvist, M. Österholm, C. Granberg, & L. Sumpter (Eds.), Proceedings of the 42nd conference of the International Group for the psychology of mathematics education (Vol. 2, pp. 107–114). Umeå: PME.
Ball, D., Hill, H., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(1), 14–17 20–22; 43–46.
Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.
Barr, V., & Stephenson, C. (2011). Bringing computational thinking to K–12: What is involved and what is the role of the computer science education community? ACM Inroads, 2(1), 48–54.
Benedict, A., Holdheide, L., Brownell, M. & Foley, A. (2016). Learning to teach: Practice-based preparation in teacher education. (https://files.eric.ed.gov/fulltext/ED570144.pdf). Accessed 21 Aug 2018.
Bennett, S., Lockyer, L., & Agostinho, S. (2004). Investigating how learning designs can be used as a framework to incorporate learning objects. In R. Atkinson, C. McBeath, D. Donas-Dwyer, & R. Phillips (Eds.), Proceedings of the 21st ASCILITE conference (pp. 116–122). Perth: Australian Society for Computers in Learning in Tertiary Education.
Benton, L., Hoyles, C., Kalas, I., & Noss, R. (2017). Bridging primary programming and mathematics: Some findings of design research in England. Digital Experiences in Mathematics Education, 3(2), 115–138.
Bishop, M., Bhumiratana, B., Crawford, R., & Levitt, K. (2004). How to sanitize data? In Proceedings of the 13th IEEE international workshops on enabling technologies: Infrastructure for collaborative enterprises (pp. 217–222). Los Alamitos: Institute of Electrical and Electronics Engineers Computer Society.
Boaler, J. (2015). Fluency without fear: Research evidence on the best ways to learn math facts. Reflections, 40(2), 7–12.
Bower, M., & Falkner, K. (2015). Computational thinking, the notional machine, pre-service teachers, and research opportunities. In D. D’Souza & K. Falkner (Eds.), Proceedings of the 17th Australasian computing education conference (pp. 37–46). Sydney: Australian Computer Society.
Brennan, K. & Resnick, M. (2012). New frameworks for studying and assessing the development of computational thinking. Paper presented at the annual meeting of the American Educational Research Association (pp. 1–25). Vancouver, BC.
Burke, Q. (2012). The markings of a new pencil: Introducing programming-as-writing in the middle school classroom. Journal of Media Literacy Education, 4(2), 121–135.
Calder, N. (2010). Using Scratch: An integrated problem-solving approach to mathematical thinking. Australian Primary Mathematics Classroom, 15(4), 9–14.
Cameron, L., & Campbell, C. (2013). The case for using learning designs with pre-service teachers. The Australian Journal of Teacher Education, 38(6), 35–46.
Cobb, P., Wood, T., & Yackel, E. (1990). Classrooms as learning environments for teachers and researchers. In R. Davis, C. Maher, & N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics (pp. 125–146). Reston: National Council of Teachers of Mathematics.
Costa, A., & Kallick, B. (2008). Learning and leading with habits of mind: 16 essential characteristics for success. Alexandria: Association for Supervision and Curriculum Development.
Creswell, J. (2013). Qualitative inquiry and research design: Choosing among five approaches (3rd ed.). Los Angeles: Sage Publications.
Creswell, J. (2015). A concise introduction to mixed methods research. Thousand Oaks: Sage Publications.
Engage NY (2012). Pedagogical shifts demanded by the Common Core State Standards. (https://www.engageny.org/resource/common-core-shifts). Accessed 14 Oct 2018.
Fereday, J., & Muir-Cochrane, E. (2006). Demonstrating rigor using thematic analysis: A hybrid approach of inductive and deductive coding and theme development. International Journal of Qualitative Methods, 5(1), 80–92.
Fessakis, G., Gouli, E., & Mavroudi, E. (2013). Problem solving by 5–6 years old kindergarten children in a computer programming environment: A case study. Computers & Education, 63, 87–97.
Francis, K., & Davis, B. (2018). Coding robots as a source of instantiations for arithmetic. Digital Experiences in Mathematics Education, 4(2–3), 71–86.
Gadanidis, G. (2017). Five affordances of computational thinking to support elementary mathematics education. Journal of Computers in Mathematics and Science Teaching, 36(2), 143–151.
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.
Gleasman, C. & Kim, C. (2018). Use of block-based coding in teaching conceptual mathematics. Paper presented at Association for Educational Communications and Technology Conference. Kansas City, MO.
Greene, J. (2007). Mixed methods in social inquiry. San Francisco: Jossey-Bass.
Georgia Department of Education. (2016). Georgia standards of excellence. Retrieved September 5, 2017, from https://www.georgiastandards.org/Georgia-Standards/Documents/Grade-K-5-Mathematics-Standards.pdf. Accessed 5 Sept 2017.
Grover, S., & Basu, S. (2017). Measuring student learning in introductory block-based programming. In M. Caspersen, S. Edwards, T. Barnes, & D. Garcia (Eds.), Proceedings of the 2017 ACM SIGCSE technical symposium on computer science education (pp. 267–272). New York: Association for Computing Machinery Press.
Hambrusch, S., Hoffmann, C., Korb, J., Haugan, M., & Hosking, A. (2009). A multidisciplinary approach towards computational thinking for science majors. ACM SIGCSE Bulletin, 41(1), 183.
Harel, I. (1990). Children as software designers: A constructionist approach for learning mathematics. Journal of Mathematical Behavior, 9(1), 3–93.
Hohensee, C. (2014). Backward transfer: An investigation of the influence of quadratic functions instruction on students’ prior ways of reasoning about linear functions. Mathematical Thinking and Learning, 16(2), 135–174.
K12CS (2016). K–12 computer science framework. (http://www.k12cs.org). Accessed 14 Oct 2018.
Kim, C., Kim, M., Lee, C., Spector, M., & DeMeester, K. (2013). Teacher beliefs and technology integration. Teaching and Teacher Education, 29, 76–85.
Kim, C., Kim, D., Yuan, J., Hill, R., Doshi, P., & Thai, C. (2015). Robotics to promote elementary education pre-service teachers’ STEM engagement, learning, and teaching. Computers & Education, 91, 14–31.
Kim, E., Oliver, J. & Jackson, D. (2016). Connecting the imperatives of STEM, NGSS, deep learning and assessment: A conceptual paper. Paper presented at the National Association for Research in Science Teaching. Baltimore, MD.
Kim, C., Yuan, J., Vasconcelos, L., Shin, M., & Hill, R. (2018). Debugging during block-based programming. Instructional Science, 46(5), 767–787.
Lewandowski, G., Bouvier, D., McCartney, R., Sanders, K., & Simon, B. (2007). Commonsense computing (episode 3): Concurrency and concert tickets. In Proceedings of the third international workshop on computing education research (pp. 133–144). New York: Association for Computing Machinery Press.
Ma, L. (2010). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah: Lawrence Erlbaum Associates.
Maloney, J., Resnick, M., Rusk, N., Silverman, B., & Eastmond, E. (2010). The Scratch programming language and environment. ACM Transactions on Computing Education, 10(4), 1–15.
National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
NCTM. (2014). Principles to actions: Ensuring mathematical success for all. Reston: National Council of Teachers of Mathematics.
NGSC. (2013). Next generation science standards: For states, by states. Washington, DC: National Academics Press.
Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers. Dordrecht: Kluwer Academic Publishers.
Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books.
Patton, M. (2015). Qualitative research and evaluation methods (4th ed.). Thousand Oaks: Sage Publications.
Pea, R., & Kurland, D. (1984). On the cognitive effects of learning computer programming. New Ideas in Psychology, 2(2), 137–168.
Rayner, V., Pitsolantis, N., & Osana, H. (2009). Mathematics anxiety in preservice teachers: Its relationship to their conceptual and procedural knowledge of fractions. Mathematics Education Research Journal, 21(3), 60–85.
Resnick, M. (1999). Decentralized modeling and decentralized thinking. In W. Feurzeig & N. Roberts (Eds.), Modeling and simulation in science and mathematics education (pp. 114–137). New York: Springer-Verlag.
Rittle-Johnson, B., Schneider, M., & Star, J. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27(4), 587–597.
Ruona, W. (2005). Analyzing qualitative data. In R. Swanson & E. Holton (Eds.), Research in organizations: Foundations and methods of inquiry (pp. 233–263). San Francisco: Berrett-Koehler.
Schanzer, E. (2015). Algebraic functions, computer programming, and the challenge of transfer. Unpublished Ph.D. dissertation. Cambridge: Harvard University (https://dash.harvard.edu/handle/1/16461037). Accessed 2 Dec 2018.
Stake, R. (1995). The art of case study research. Thousand Oaks: Sage Publications.
Stohlmann, M., Moore, T., Cramer, K., & Maiorca, C. (2015). Changing pre-service elementary teachers’ beliefs about mathematical knowledge. Mathematics Teacher Education and Development, 16(2), 4–24.
Thanheiser, E., Browning, C., Moss, M., Watanabe, T. & Garza-Kling, G. (2010). Developing mathematical content knowledge for teaching elementary school mathematics. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1. (http://www.k-12prep.math.ttu.edu/journal/1.contentknowledge/thanheiser01/article.pdf). Accessed 2 Dec 2018.
Tømte, C., Enochsson, A., Buskqvist, U., & Kårstein, A. (2015). Educating online student teachers to master professional digital competence: The TPACK-framework goes online. Computers & Education, 84, 26–35.
Tondeur, J., van Braak, J., Sang, G., Voogt, J., Fisser, P., & Ottenbreit-Leftwich, A. (2012). Preparing pre-service teachers to integrate technology in classroom practice: A synthesis of qualitative evidence. Computers & Education, 59(1), 134–144.
van Boxtel, J. (2016). Reason: A self-instruction strategy for twice-exceptional learners struggling with common-core mathematics. Teaching Exceptional Children, 49(1), 66–73.
White, B., & Frederiksen, J. (1998). Inquiry, modeling, and meta-cognition: Making science accessible to all students. Cognition and Instruction, 16(1), 3–118.
Wing, J. (2006). Computational thinking. Communications of the ACM, 49(3), 33–35.
Yadav, A., Zhou, N., Mayfield, C., Hambrusch, S., & Korb, J. (2011). Introducing computational thinking in education courses. In Proceedings of the 42nd ACM technical symposium on computer science education (pp. 465–470). New York: Association for Computing Machinery Press.
Yin, R. (2002). Case study research: Design and methods. Thousand Oaks: Sage Publications.
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This research is partially supported by grant 1712286 from the National Science Foundation (USA) to PI ChanMin Kim. Any opinions, findings, or conclusions are those of the authors and do not necessarily represent official positions of NSF.
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Gleasman, C., Kim, C. Pre-Service Teacher’s Use of Block-Based Programming and Computational Thinking to Teach Elementary Mathematics. Digit Exp Math Educ 6, 52–90 (2020). https://doi.org/10.1007/s40751-019-00056-1
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DOI: https://doi.org/10.1007/s40751-019-00056-1