# The Spreadsheet Affordances in Solving Complex Word Problems

• Susana Carreira
• Sandra Nobre
Chapter
Part of the ICME-13 Monographs book series (ICME13Mo)

## Abstract

This chapter focuses on the affordances of the spreadsheet in solving a complex word problem in light of the multiple conceptual models that students produce in their approaches to the solution with the digital medium. The empirical study carried out examines, through a qualitative analysis, a set of resolutions produced by a class of 8th grade students to a word problem involving multiple variables and conditions. The aim is to appreciate how the way in which the students take advantage of the spreadsheet can be related to their approaches to a problem that is algebraically translated into a system of simultaneous equations. We found that the spreadsheet offered students diverse ways of formulating relational conditions in solving a problem for which they had not yet learned the formal algebraic method. The affordances of the spreadsheet were fundamental for the success of the students in solving the problem. It provided them a representational medium for capturing the structure of the situation and it suggested ways of conceptually modelling the several conditions presented. In particular, the spreadsheet opened up opportunities for assigning meaning to and expressing the multiple conditions (equations and inequalities) that structure the problem.

## Keywords

Problem solving Spreadsheet Affordances Conceptual models Algebraic thinking

## References

1. Abramovich, S. (1998). Manipulative and numerical spreadsheet templates for the study of discrete structures. International Journal of Mathematical Education in Science and Technology, 29, 233–252.
2. Ainley, J., Bills, L., & Wilson, K. (2004). Constructing meanings and utilities within algebraic tasks. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th PME Conference (Vol. 2, pp. 1–8). Bergen, Norway: PME.Google Scholar
3. Bell, A. (1996). Problem-solving approaches to algebra: Two aspects. In N. Berdnarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 167–185). Dordrecht: Kluwer.
4. Blanton, M., & Kaput, J. (2005). Journal for Research in Mathematics Education, 36(5), 412–446.Google Scholar
5. Calder, N. (2010). Affordances of spreadsheets in mathematical investigation: Potentialities for learning. Spreadsheets in Education (eJSiE), 3(3), Article 4 (Online Journal).Google Scholar
6. Carreira, S., Jones, K., Amado, N., Jacinto, H., & Nobre, S. (2016). Youngsters solving mathematical problems with technology: The results and implications of the problem@Web project. New York, NY: Springer.
7. Dettori, G., Garuti, R., & Lemut, E. (2001). From arithmetic to algebraic thinking by using a spreadsheet. In R. Sutherland, T. Rojano, A, Bishop, & R. Lins (Eds), Perspectives on school algebra (pp. 191–208). Dordrecht: Kluwer.Google Scholar
8. Friedlander, A. (1998). An EXCELlent bridge to algebra. Mathematics Teacher, 91(50), 382–383.Google Scholar
9. Gibson, J. (1986). The ecological approach to visual perception. New York: Lawrence Erlbaum.Google Scholar
10. Haspekian, M. (2005). An ‘instrumental approach’ to study the integration of a computer tool into mathematics teaching: The case of spreadsheets. International Journal of Computers for Mathematical Learning, 10(2), 109–141.
11. Hegedus, S. (2013). Young children investigating advanced mathematical concepts with haptic technologies: Future design perspectives. The Mathematics Enthusiast, 10(1 & 2), 87–108.Google Scholar
12. Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65–97). New York, NY: Macmillan.Google Scholar
13. Johanning, D. (2004). Supporting the development of algebraic thinking in middle school: a closer look at students’ informal strategies. Journal of Mathematical Behavior, 23, 371–388.
14. Kaput, J. (1999). Teaching and learning a new algebra with understanding. In E. Fennema & T. A. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133–155). Mahwah, NJ: Lawrence Erlbaum.Google Scholar
15. Kieran, C. (1996). The changing face of school algebra. In C. Alsina, J. M. Alvares, B. Hodgson, C. Laborde, & A. Pérez (Eds.), International congress on mathematical education 8: Selected lectures (pp. 271–290). Seville: SAEM Thales.Google Scholar
16. Kieran, C. (2006). Research on the learning and teaching of algebra. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 11–50). Rotherham: Sense.Google Scholar
17. Kieran, C., & Yerushalmy, M. (2004). Research on the role of technological environments in algebra learning and teaching. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra: The 12th ICMI study (pp. 95–152). Dordrecht, The Netherlands: Kluwer.Google Scholar
18. Koedinger, K. R., Alibali, M. W., & Nathan, M. J. (2008). Trade-offs between grounded and abstract representations: Evidence from algebra problem solving. Cognitive Science, 32, 366–397.
19. Lesh, R., Behr, M., & Post, T. (1987). Rational number relations and proportions. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 41–58). Hillsdale, NJ: Erlbaum Associates.Google Scholar
20. Mason, J. (2008). Making use of children’s powers to produce algebraic thinking. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 57–94). New York: Erlbaum.Google Scholar
21. Moreno-Armella, L., & Hegedus, S. (2009). Co-action with digital technologies. ZDM—International Journal on Mathematics Education, 41, 505–519.
22. Moreno-Armella, L., Hegedus, S., & Kaput, J. (2008). From static to dynamic mathematics: Historical and representational perspectives. Educational Studies in Mathematics, 68, 99–111.
23. NCTM. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.Google Scholar
24. Nobre, S. (2016). O desenvolvimento do pensamento algébrico: Uma experiência de ensino com alunos do 9.º ano (Unpublished Doctoral Thesis). Lisboa: Universidade de Lisboa. Available at http://hdl.handle.net/10451/25071.
25. Rojano, T. (1996). Developing algebraic aspects of problem solving within a spreadsheet environment. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 137–146). Dordrecht: Kluwer.
26. Rojano, T. (2002). Mathematics learning in the junior secondary school: Students’ access to significant mathematical ideas. In L. English, M. B. Bussi, G. A. Jones, R. A. Lesh, & D. Tirosh (Eds.), Handbook of international research in mathematics education (Vol. 1, pp. 143–161). Mahwah, NJ: Lawrence Erlbaum.Google Scholar
27. Schoenfeld, A. (2008). Early algebra as mathematical sense making. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 479–510). New York: Lawrence Erlbaum.Google Scholar
28. Slavitt, D. (1999). The role of operation sense in transitions from arithmetic to algebra thought. Educational Studies in Mathematics, 37, 251–274.
29. Stacey, K., & MacGregor, M. (2000). Learning the algebraic method of solving problems. Journal of Mathematical Behavior, 18(2), 149–167.
30. Wagner, S. (1983). What are these things called variables? Mathematics Teacher, 76, 474–479.Google Scholar
31. Wilson, K. (2007). Naming a column on a spreadsheet. Research in Mathematics Education, 8, 117–132.
32. Windsor, W. (2010). Algebraic thinking: A problem solving approach. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education (Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia) (pp. 665–672). Freemantle, Australia: MERGA.Google Scholar
33. Yerushalmy, M. (2006). Slower algebra students meet faster tools: Solving algebra word problems with graphing software. Journal for Research in Mathematics Education, 37, 356–387.Google Scholar
34. Zazkis, R., & Liljedahl, P. (2004). Understanding primes: The role of representation. Journal for Research in Mathematics Education, 35(3), 164–186.

© Springer Nature Switzerland AG 2019

## Authors and Affiliations

• 1
• 2
Email author
• Susana Carreira
• 1
• 2
• Sandra Nobre
• 2
• 3