Abstract
The learning of algebraic procedures in middle-school algebra is usually perceived as an algorithmic activity, achieved by performing sequences of short drill-and-practice tasks, which have little to do with conceptual learning or with creative mathematical thinking. The goal of this chapter is to explore possible ways by which all middle-grade students can be encouraged to apply higher-order thinking in the context of tasks that integrate procedural work, conceptual understanding and creative thinking. Each of the five instances presented in this chapter was intended to promote creative thinking in the context of procedural tasks. An a-priori task analysis and data collected in some of our previous studies indicate the presence of many learning competencies and high levels of mathematical creativity in the participating students’ work. Thus, we conclude that certain procedural tasks have a strong potential to promote higher-order, and creative thinking.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arcavi, A. (2005). Developing and using symbol sense in mathematics. For the Learning of Mathematics, 25, 50–55.
Friedlander, A., & Arcavi, A. (2017). Tasks and competencies in the teaching and learning of mathematics. Reston, VA: National Council of Teachers of Mathematics (NCTM).
Friedlander, A., & Arcavi, A. (2012). Practicing algebraic skills: A conceptual approach. Mathematics Teacher, 105(8), 608–614.
Friedlander, A. & Stein, H. (2001). Students’ choice of tools in solving equations in a technological learning environment. In Proceedings of the 25th International Conference for the Psychology of Mathematics Education (Vol. 2, pp. 441–448). Utrecht, Netherlands.
Guilford, J. P. (1967). The nature of human intelligence. New York: McGraw-Hill.
Haspekian, M. (2005). An ‘‘instrumental approach’’ to study the integration of computer tool into mathematics teaching: The case of spreadsheets. International Journal of Computers for Mathematics Learning, 10, 109–141.
Integrated Mathematics, Grades 7–9. (2015). Rehovot, Israel: The Weizmann Institute of Science (in Hebrew).
Kieran, C. (2004). The core of algebra: Reflections on its main activities. In K. Stacey, H. Chick, & M. Kendal (Eds.), The Future of Teaching and Learning of Algebra: 12th ICMI Study (pp. 21–34). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: The state of the art. ZDM Mathematics Education, 45(2), 159–166.
Leikin, R., & Sriraman, B. (Eds.). (2017). Creativity and giftedness. Dordrecht, The Netherlands: Springer.
Mason, J., Graham, A., Pimm, D., & Gowar, N. (1985). Routes to/Roots of Algebra. Milton Keynes, UK: The Open University.
Matz, M. (1982). Towards a process model for high-school algebra errors. In D. Sleeman & S. Brown (Eds.), Intelligent tutoring systems (pp. 25–50). London: Academic Press.
Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91(1), 175–189.
Star, J. R. (2007). Foregrounding procedural knowledge. Journal of Research in Mathematics Education, 38(2), 132–135.
Tabach, M., & Friedlander, A. (2008). Understanding equivalence of algebraic expressions in a spreadsheet-based environment. International Journal of Computers in Mathematics Education, 13(1), 27–46.
Tabach, M., & Friedlander, A. (2013). School mathematics and creativity at the elementary and middle grade level: How are they related? ZDM Mathematics Education, 45(2), 227–238.
Tabach, M., & Friedlander, A. (2017). Algebraic procedures and creative thinking. ZDM Mathematics Education, 49(1), 53–63.
Torrance, E. P. (1974). The torrance tests of creative thinking: Technical-norms manual. Bensenville, IL: Scholastic Testing Services.
Wilson, K., Ainley, J., & Bills, L. (2005). Naming a column on a spreadsheet: Is it more algebraic? In D. Hewitt & A. Noyes (Eds.), Proceedings of the Sixth British Congress of Mathematics Education (pp. 184–191). Warwick, UK
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Tabach, M., Friedlander, A. (2018). Instances of Promoting Creativity with Procedural Tasks. In: Singer, F. (eds) Mathematical Creativity and Mathematical Giftedness. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-73156-8_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-73156-8_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73155-1
Online ISBN: 978-3-319-73156-8
eBook Packages: EducationEducation (R0)