Effects of multiple choice options in mathematics learning

Cornelia S. Große 1 *
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1 FB3 Mathematics / Computer Science, University of Bremen, Bremen, Germany
* Corresponding Author
EUR J SCI MATH ED, Volume 5, Issue 2, pp. 165-177.
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In recent years, the ability to use mathematics flexibly in everyday situations is increasingly accentuated, and mathematics education gives more and more attention to problems with realistic contexts. However, it is reported very often that learners have substantial difficulties in connecting mathematics to real situations. In order to solve complex and authentic problems embedded in real situations it is necessary to find translations from verbal descriptions to mathematical notations and to interpret mathematical results with respect to the real situation. In the present work, it was tested experimentally whether translation and interpretation competencies are fostered by presenting multiple choice options from which the learners have to select the correct one. While benefits of translation answer choices emerged, interpretation answer choices did not support learning. However, when the learners were asked to rate how much they liked the problems, opposed results were obtained, indicating that objective learning outcomes and subjective scores did not correspond. Possible reasons for the inconsistent and to some extent unexpected learning outcomes and for the divergence between objective results and subjective statements are discussed.


Große, C. S. (2017). Effects of multiple choice options in mathematics learning. European Journal of Science and Mathematics Education, 5(2), 165-177.


  • Adams, D. M., McLaren, B. M., Durkin, K., Mayer, R. E., Rittle-Johnson, B., Isotani, S., and van Velsen, M. (2014). Using erroneous examples to improve mathematics learning with a web-based tutoring system. Computers in Human Behavior, 36, 401-411. doi: 10.1016/j.chb.2014.03.053
  • Atkinson, R. K., Derry, S. J., Renkl, A., and Wortham, D. (2000). Learning from examples: Instructional principles from the worked examples research. Review of educational research, 70, 181-214.
  • Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84, 191-215.
  • Bandura, A., and Locke, E. A. (2003). Negative self-efficacy and goal effects revisited. Journal of Applied Psychology, 88, 87-99. doi: 10.1037/0021-9010.88.1.87.
  • Blum, W., and Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1, 45-58.
  • Booth, J. L., Lange, K. E., Koedinger, K. R., and Newton, K. J. (2013). Using example problems to improve student learning in algebra: Differentiating between correct and incorrect examples. Learning and Instruction, 25, 24-34. doi: 10.1016/j.learninstruc.2012.11.002.
  • Borromeo Ferri, R. (2009). Zur Entwicklung des Verständnisses von Modellierung bei Studierenden [On the development of students’ understanding of modeling]. In M. Neubrand (Hrsg.), Beiträge zum Mathematikunterricht 2009 (S. 139-142). Münster: WTM.
  • De Kock, W. D., and Harskamp, E. G. (2014). Can teachers in primary education implement a metacognitive computer programme for word problem solving in their mathematics classes? Educational Research and Evaluation, 20, 231-250.
  • Durkin, K., and Rittle-Johnson, B. (2012). The effectiveness of using incorrect examples to support learning about decimal magnitude. Learning and Instruction, 22, 206-214. doi: 10.1016/j.learninstruc.2011.11.001.
  • Galbraith, P. L., and Clatworthy, N. J. (1990). Beyond standard models – Meeting the challenge of modelling. Educational Studies in Mathematics, 21, 137-163.
  • Giannakos, M. N. (2013). Enjoy and learn with educational games: Examining factors affecting learning performance. Computers & Education, 68, 429-439. doi: 10.1016/j.compedu.2013.06.005
  • Greer, B. (1997). Modelling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7, 293-307.
  • Große, C. S. (2014). Learning to solve story problems – supporting transitions between reality and mathematics. European Journal of Psychology of Education, 29, 619–634. doi: 10.1007/s10212-014-0217-6.
  • Große, C. S., and Renkl, A. (2007). Finding and fixing errors in worked examples: Can this foster learning outcomes? Learning and Instruction, 17, 612-634. doi: 10.1016/j.learninstruc.2007.09.008.
  • Heemsoth, T., and Heinze, A. (2014). The impact of incorrect examples on learning fractions: A field experiment with 6th grade students. Instructional Science, 42, 639-657. doi: 10.1007/s11251-013-9302-5.
  • Kalyuga, S. (2008). When less is more in cognitive diagnosis: A rapid online method for diagnosing learner task-specific expertise. Journal of Educational Psychology, 100, 603-612. doi: 10.1037/0022-0663.100.3.603.
  • Kalyuga, S., and Sweller, J. (2004). Measuring knowledge to optimize cognitive load factors during instruction. Journal of Educational Psychology, 96, 558–568. doi: 10.1037/0022-0663.96.3.558.
  • Lave, J., and Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge, UK: Cambridge University Press.
  • McDaniel, M. A., Anderson, J. L., Derbish, M. H., and Morrisette, N. (2007). Testing the testing effect in the classroom. European Journal of Cognitive Psychology, 19, 494-513. doi: 10.1080/09541440701326154.
  • McLaren, B. M., Adams, D., Durkin, K., Goguadze, G., Mayer, R. E., Rittle-Johnson, B., Sosnovsky, S., Isotani, S., and van Velsen, M. (2012). To err is human, to explain and correct is divine: A study of interactive erroneous examples with middle school math students. In 21st Century Learning for 21st Century Skills (pp. 222-235). Berlin: Springer.
  • Mevarech, Z. R., Terkieltaub, S., Vinberger, T., and Nevet, V. (2010). The effects of meta-cognitive instruction on third and sixth graders solving word problems. ZDM Mathematics Education, 42, 195-203. doi: 10.1007/s11858-010-0244-y.
  • Mwangi, W., and Sweller, J. (1998). Learning to solve compare word problems: The effect of example format and generating self-explanations. Cognition and Instruction, 16, 173-199. doi: 10.1207/s1532690xci1602_2.
  • OECD (2003). The PISA 2003 assessment framework – Mathematics, reading, science and problem solving knowledge and skills. Paris: OECD.
  • Paas, F., Renkl, A., and Sweller, J. (2003). Cognitive load theory and instructional design: Recent developments. Educational Psychologist, 38, 1-4.
  • Palm, T. (2008). Impact of authenticity on sense making in word problem solving. Educational Studies in Mathematics, 67, 37-58. doi: 10.1007/s10649-007-9083-3.
  • Pekrun, R. (2006). The control-value theory of achievement emotions: Assumptions, corollaries, and implications for educational research and practice. Educational psychology review, 18, 315-341. doi: 10.1007/s10648-006-9029-9
  • Powell, S. R. (2011). Solving word problems using schemas: A review of the literature. Learning Disabilities Research & Practice, 26, 94-108.
  • Reinmann, G., and Mandl, H. (2006). Unterrichten und Lernumgebungen gestalten [Teaching and designing learning environments]. In A. Krapp and B. Weidenmann (Hrsg.), Pädagogische Psychologie (pp. 613-658). Weinheim: Beltz PVU.
  • Renkl, A. (1997). Learning from worked-out examples: A study on individual differences. Cognitive Science, 21, 1-29.
  • Renkl, A. (2014). Toward an instructionally oriented theory of example‐based learning. Cognitive Science, 38, 1-37. doi: 10.1111/cogs.12086
  • Renkl, A., Atkinson, R. K., and Große, C. S. (2004). How fading worked solution steps works - A cognitive load perspective. Instructional Science, 32, 59-82.
  • Reusser, K., and Stebler, R. (1997). Every word problem has a solution—the social rationality of mathematical modeling in schools. Learning and Instruction, 7, 309-327.
  • Schukajlow, S., and Blum, W. (2011). Zum Einfluss der Klassengröße auf Modellierungskompetenz, Selbst- und Unterrichtswahrnehmungen von Schülern in selbständigkeitsorientierten Lehr-Lernformen [On the effect of class size on modeling competency and self-reported perceptions of students in self-regulated learning environments]. Journal für Mathematik-Didaktik, 32, 133-151. doi: 10.1007/s13138-011-0025-3.
  • Schukajlow, S., Krug, A., and Rakoczy, K. (2015). Effects of prompting multiple solutions for modelling problems on students’ performance. Educational Studies in Mathematics, 89, 393-417. doi: 10.1007/s10649-015-9608-0
  • Schukajlow, S. and Rakoczy, K. (2016). The power of emotions: Can enjoyment and boredom explain the impact of individual preconditions and teaching methods on interest and performance in mathematics? Learning and Instruction, 44, 117-127.
  • Stark, R., Gruber, H., Renkl, A., and Mandl, H. (2000). Instruktionale Effekte einer kombinierten Lernmethode: Zahlt sich die Kombination von Lösungsbeispielen und Problemlöseaufgaben aus? [Instructional effects of a combined learning method: How effective is the combination of worked examples and problems to-be-solved?]. Zeitschrift für Pädagogische Psychologie, 14, 206-218.
  • Sweller, J. (2010). Element Interactivity and Intrinsic, Extraneous, and Germane Cognitive Load. Educational Psychology Review, 22, 123-138. doi: 10.1007/s10648-010-9128-5.
  • Trafton, J. G., and Reiser, B. J. (1993). The contributions of studying examples and solving problems to skill acquisition. In M. Polson (Ed.), Proceedings of the 15th Annual Conference of the Cognitive Science Society. Hillsdale, NJ: Erlbaum.
  • Van Gog, T., Paas, F., and van Merriënboer, J. J. G. (2004). Process-oriented worked examples: improving transfer performance through enhanced understanding. Instructional Science, 32, 83-98.
  • Van Gog, T., Paas, F., and van Merriënboer, J. J. G. (2006). Effects of process-oriented worked examples on troubleshooting transfer performance. Learning and Instruction, 16, 154-164. doi: 10.1016/j.learninstruc.2006.02.003.
  • Van Gog, T., Paas, F., and van Merriënboer, J. J. G. (2008). Effects of studying sequences of process-oriented and product-oriented worked examples on troubleshooting transfer efficiency. Learning and Instruction, 18, 211-222. doi: 10.1016/j.learninstruc.2007.03.003.
  • Verschaffel, L., De Corte, E., and Borghart, I. (1997). Pre-service teachers’ conceptions and beliefs about the role of real-world knowledge in mathematical modelling of school word problems. Learning and Instruction, 7, 339-359.
  • Verschaffel, L., De Corte, E., and Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems. Learning and Instruction, 4, 273-294.
  • Verschaffel, L., De Corte, E., and Vierstraete, H. (1999). Upper elementary school pupils’ difficulties in modeling and solving nonstandard additive word problems involving ordinal numbers. Journal for Research in Mathematics Education, 30, 265-285.
  • Vye, N. J., Goldman, S. R., Voss, J. F., Hmelo, C., Williams, S., and Cognition and Technology Group at Vanderbilt (1997). Complex mathematical problem solving by individuals and dyads. Cognition and Instruction, 15, 435-484. doi: 10.1207/s1532690xci1504_1.
  • Yerushalmy, M. (1997). Mathematizing verbal descriptions of situations: A language to support modeling. Cognition and Instruction, 15, 207-264. doi: 10.1207/s1532690xci1502_3.
  • Zöttl, L., Ufer, S., and Reiss, K. (2010). Modelling with heuristic worked examples in the KOMMA learning environment. Journal für Mathematik-Didaktik, 31, 143-165. doi: 10.1007/s13138-010-0008-9.