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Students’ Mathematical Reasoning and Beliefs in Non-routine Task Solving

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Abstract

Beliefs and problem solving are connected and have been studied in different contexts. One of the common results of previous research is that students tend to prefer algorithmic approaches to mathematical tasks. This study explores Swedish upper secondary school students’ beliefs and reasoning when solving non-routine tasks. The results regarding the beliefs indicated by the students were found deductively and include expectations, motivational beliefs and security. When it comes to reasoning, a variety of approaches were found. Even though the tasks were designed to demand more than imitation of algorithms, students used this method and failed to solve the task.

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References

  • Ball, D. & Bass, H. (2003). Making mathematics reasonable in school. In J. Kilpatrick, W. G. Martin & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 27–44). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Bergqvist, T., Lithner, J., & Sumpter, L. (2008). Upper secondary students' task reasoning. International Journal of Mathematical Education in Science and Technology, 39(1), 1–12.

  • Boaler, J. (1998). Open and closed mathematics: Student experiences and understandings. Journal for Research in Mathematics Education, 29(1), 41–62.

    Article  Google Scholar 

  • Boaler, J., Wiliam, D. & Brown, M. (2000). Students’ experiences of ability grouping—disaffection, polarisation and the construction of failure. British Educational Research Journal, 26(5), 631–648.

    Article  Google Scholar 

  • Boesen, J., Lithner, J. & Palm, T. (2010). The relation between types of assessment tasks and the mathematical reasoning students use. Educational Studies in Mathematics, 75(1), 89–105.

    Article  Google Scholar 

  • Braun, V. & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3, 77–101.

    Article  Google Scholar 

  • Callejo, M. & Vila, A. (2009). Approach to mathematical problem-solving and students’ belief systems. Educational Studies in Mathematics, 72, 111–126.

    Article  Google Scholar 

  • Carlson, M. (1999). The mathematical behavior of six successful mathematics graduate students: Influences leading to mathematical success. Educational Studies in Mathematics, 40(3), 237–258.

    Article  Google Scholar 

  • Cobb, P., Yackel, E. & Wood, T. (1989). Young children’s emotional acts while engaged in mathematical problem solving. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving. A new perspective (pp. 117–148). New York, NY: Springer.

    Chapter  Google Scholar 

  • Dìaz-Obando, E., Plasencia-Cruz, I. & Solano-Alvarado, A. (2003). The impact of beliefs in student’s learning: An investigation with students of two different contexts. International Journal of Mathematical Education in Science and Technology, 34(2), 161.

    Article  Google Scholar 

  • Francisco, J. (2013). The mathematical beliefs and behavior of high school students: Insights from a longitudinal study. Journal of Mathematical Behavior, 32(3), 481–493.

    Article  Google Scholar 

  • Furinghetti, F. & Morselli, F. (2009). Every unsuccessful problem solver is unsuccessful in his or her own way: Affective and cognitive factors in proving. Educational Studies in Mathematics, 70, 71–90.

    Article  Google Scholar 

  • Hannula, M. (2006). Affect in mathematical thinking and learning: Towards integration of emotion, motivation and cognition. In J. Maasz & W. Schloeglmann (Eds.), New mathematics education research and practice (pp. 209–232). Rotterdam, Netherlands: Sense Publishers.

    Google Scholar 

  • Hoyles, C. (1992). Mathematics teaching and mathematics teachers: A meta-case study. For the Learning of Mathematics, 12(3), 32–44.

    Google Scholar 

  • Kloosterman, P. (2002). Beliefs about mathematics and mathematics learning in the secondary school: Measurement and implications for motivation. In G. C. Leder, E. Pehkonen & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 247–269). Dordrecht, Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  • Lerch, C. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 361–372.

    Article  Google Scholar 

  • Lithner, J. (2008). Students’ mathematical reasoning in university textbook exercises. Educational Studies in Mathematics, 52(1), 29–55.

  • Liu, P.-H. (2010). Are beliefs believable? An investigation of college students’ epistemological beliefs and behavior in mathematics. Journal of Mathematical Behavior, 29(2), 86–98.

  • Mercer, J. (2010). Emotional beliefs. International Organization, 64(1), 1–31.

    Article  Google Scholar 

  • Op’ T Eynde, P., De Corte, E. & Verschaffel, L. (2002). Framing students’ mathematics-related beliefs. In G. C. Leder, E. Pehkonen & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 13–37). Dordrecht, Netherlands: Kluwer Academic Publishers.

    Chapter  Google Scholar 

  • Ryan, R. & Deci, E. (2000). Intrinsic and extrinsic motivations: Classic definitions and new directions. Contemporary Educational Psychology, 25(1), 54–67.

    Article  Google Scholar 

  • Schoenfeld, A. (1985). Mathematical problem solving. Orlando, FL: Academic Press.

    Google Scholar 

  • Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition and sense-making in mathematics. In D. Grouws (Ed.), Handbook of research in mathematics teaching and learning (pp. 334–370). New York, NY: Macmillan Publishing Company.

    Google Scholar 

  • Sfard, A. & Linchevski, L. (1994). The gains and the pitfalls of reification—the case of algebra. Educational Studies in Mathematics, 26(2–3), 191–228.

    Article  Google Scholar 

  • Sidenvall, J., Lithner, J., & Jäder, J. (2015). Students’ reasoning in mathematics textbook task-solving.  International Journal of Mathematical Education in Science and Technology, 46(4), 533–552.

  • Speer, N. (2005). Issues of methods and theory in the study of mathematics teachers’ professed and attributed beliefs. Educational Studies in Mathematics, 58(3), 361–391.

    Article  Google Scholar 

  • Sumpter, L. (2013). Themes and interplay of beliefs in mathematical reasoning. International Journal of Science and Mathematics Education, 11(5), 1115–1135.

  • Swedish National Agency for Education (2010). Nationellt kursprov i matematik, kurs A, våren 2010, Del I kortsvar [National test in mathematics course a, spring 2010, part i short answers]. Available at http://www.su.se/primgruppen/matematik/kurs-1/tidigare-prov. Swedish.

  • Swedish Schools Inspectorate (2010). Undervisningen i matematik i gymnasieskolan [Mathematics education in upper secondary school] (No. 2010:13). Stockholm, Sweden: Swedish Schools Inspectorate.

  • Yackel, E. & Rasmussen, C. (2002). Beliefs and norms in the mathematics classroom. In G. C. Leder, E. Pehkonen & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 313–330). Dordrecht, Netherlands: Kluwer Academic Publishers.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Education, Health and Social Studies, Dalarna University, SE-791 88, Falun, Sweden

    Jonas Jäder

  2. Department of Social and Welfare Studies, Linköping University, Norrköping, SE-601 74, Sweden

    Jonas Jäder & Johan Sidenvall

  3. School Administration, Municipality of Hudiksvall, SE-824 80, Hudiksvall, Sweden

    Johan Sidenvall

  4. Department of Mathematics and Science Education, Stockholm University, SE-106 91, Stockholm, Sweden

    Lovisa Sumpter

Authors
  1. Jonas Jäder
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  2. Johan Sidenvall
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  3. Lovisa Sumpter
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Corresponding author

Correspondence to Johan Sidenvall.

Appendix

Appendix

Authors’ translation of tasks from Swedish.

1. ‘When using 6 kg of apples Astrid gets 2.8 l of apple juice. How many litres of apple juice will she get using 15 kg of apples, of the same sort?’

2. ‘Which of the following expressions correspond to the perimeter of the figure?

$$ a+b\kern0.75em 2a + 2b\kern0.75em 3a + 2b\kern0.75em 3a + 3b\kern0.5em 4a + 2b $$

Motivate your answer’.

figure a

3. ‘The average age of five employees at a sporting goods store was 24 years. A woman of age 36 years was hired as shop manager. What will be the new average age of the employees at the sporting goods store?’

4. ‘A circular one person American pizza has a diameter of 21 cm. What should the diameter be for the pizza to be a two person pizza?’

Task 1: Swedish National Agency for Education (2005a). Nationellt kursprov i matematik, kurs A, våren 2005 Del I [National test in mathematics Course A Spring 2005 Part I]. Available at http://www.su.se/primgruppen/matematik/kurs-1/tidigare-prov. Swedish.

Task 2: Swedish National Agency for Education (2010). Nationellt kursprov i matematik, kurs A, våren 2010, Del I kortsvar [National test in mathematics Course A, Spring 2010, Part I short answers]. Available at http://www.su.se/primgruppen/matematik/kurs-1/tidigare-prov. Swedish.

Task 3: Swedish National Agency for Education (2005b). Nationellt kursprov i matematik, kurs A, våren 2005 Del II [National test in mathematics Course A Spring 2005 Part II]. Available at http://www.su.se/primgruppen/matematik/kurs-1/tidigare-prov. Swedish.

Task 4: Swedish National Agency for Education (1996). Nationellt kursprov i matematik, kurs A, våren 1996 [National test in mathematics Course A, Spring 1996]. Available at http://www.edusci.umu.se/np/np-b-d/tidigare-prov/. Swedish.

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Jäder, J., Sidenvall, J. & Sumpter, L. Students’ Mathematical Reasoning and Beliefs in Non-routine Task Solving. Int J of Sci and Math Educ 15, 759–776 (2017). https://doi.org/10.1007/s10763-016-9712-3

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  • DOI: https://doi.org/10.1007/s10763-016-9712-3

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