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Beyond additive and multiplicative reasoning abilities: how preference enters the picture

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Abstract

While previous studies mainly focused on children’s additive and multiplicative reasoning abilities, we studied third to sixth graders’ preference for additive or multiplicative relations. This was investigated by means of schematic problems that were open to both types of relations, namely arrow schemes containing three given numbers and a fourth missing one. In study 1, children had to fill out the missing number, while in study 2, children had to indicate all possibly correct answers among a set of given alternatives. Both studies explicitly showed the existence of a preference for additive relations in some children, while others preferred multiplicative relations. Mainly younger children preferred additive relations, whereas mainly children in upper primary education preferred multiplicative relations. Number ratios also impacted children’s preference, especially in fifth grade. Moreover, the results of study 2 provided evidence for the strength of children’s preference and showed that calculation skills do not coincide with preference, and hence, that preference and calculation skills are two distinct child characteristics. The results of both studies using these open problems resembled previous research results using classical multiplicative or additive word problems. This supports the hypothesis that children’s preferred type of relations may be at play in solving classical word problems as well—besides their abilities—and may hence be an additional factor explaining the mistakes that children make in those word problems. This research line thus seems promising for further research as well as educational practice.

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Funding

This study was funded by the research project C16/16/001 “Early development and stimulation of core mathematical competencies” of the Research Fund of the KU Leuven.

Author information

Authors and Affiliations

  1. KU Leuven, Centre for Instructional Psychology and Technology, Dekenstraat 2, Box 3773, 3000, Leuven, Belgium

    Tine Degrande, Lieven Verschaffel & Wim Van Dooren

Authors
  1. Tine Degrande
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  2. Lieven Verschaffel
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  3. Wim Van Dooren
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Corresponding author

Correspondence to Tine Degrande.

Additional information

Tine Degrande. KU Leuven, Centre for Instructional Psychology and Technology, Dekenstraat 2, Box 3773, 3000 Leuven, Belgium. Email: Tine.Degrande@kuleuven.be; Web site of the Centre: https://ppw.kuleuven.be/home/english/research/etrg/CIPT

Current themes of research:

Psychology of mathematics education. Multiplicative reasoning. Additive reasoning. Word problem-solving.

Most relevant publications in the field of Psychology of Education:

Degrande, T., Verschaffel, L., & Van Dooren, W. (2017). Spontaneous focusing on quantitative relations: Towards a characterization. Mathematical Thinking and Learning, 19, 260–275. https://doi.org/10.1080/10986065.2017.1365223.

Degrande T., Verschaffel L., & Van Dooren, W. (2016). Proportional word problem solving through a modeling lens: A half-empty or half-full glass?. In: Felmer P., Pehkonen E., Kilpatrick J. (Eds.), Posing and solving mathematical problems: Advances and new perspectives, (pp. 209–229). Switzerland: Springer International Publishing.

Peeters, D., Degrande, T., Ebersbach, M., Verschaffel, L., & Luwel, K. (2016). Children’s use of number line estimation strategies. European Journal of Psychology of Education, 31, 117–134.

Van Hoof, J., Degrande, T., McMullen, J., Hannula-Sormunen, M., Lehtinen, E., Verschaffel, L., & Van Dooren, W. (2016). The relation between learners’ spontaneous focusing on quantitative relations and their rational number knowledge. Studia Psychologica, 58, 156–170.

Lieven Verschaffel. KU Leuven, Centre for Instructional Psychology and Technology, Dekenstraat 2, Box 3773, 3000 Leuven, Belgium. Email: Lieven.Verschaffel@kuleuven.be; Web site of the Centre: https://ppw.kuleuven.be/home/english/research/etrg/CIPT

Current themes of research:

Early mathematics education. Number sense and estimation. Mental and written arithmetic. Arithmetic word problem solving.

Most relevant publications in the field of Psychology of Education:

De Smedt, B., Torbeyns, J., Stassens, N., Ghesquière, P., & Verschaffel, L. (2010). Frequency, efficiency and flexibility of indirect addition in two learning environments. Learning and Instruction, 20, 205–215.

Dewolf, T., Van Dooren, W., & Verschaffel, L. (2011). Upper elementary school children’s understanding and solution of a quantitative word problem inside and outside the mathematics class. Learning and Instruction, 21, 770–780.

Linsen, S., Verschaffel, L., Reynvoet, B., & De Smedt, B. (2015). The association between numerical magnitude processing and mental versus algorithmic multi-digit subtraction in children. Learning and Instruction, 35, 42–50.

Obersteiner, A., Van Dooren, W., Van Hoof, J., & Verschaffel, L. (2013). The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learning and Instruction, 28, 64–72.

Verschaffel, L., Luwel, K., Torbeyns, J., & Van Dooren, W. (2009). Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education. European Journal of Psychology of Education, 24, 335–359.

Wim Van Dooren. KU Leuven, Centre for Instructional Psychology and Technology, Dekenstraat 2, Box 3773, 3000 Leuven, Belgium. Email: Wim.VanDooren@kuleuven.be; Web site of the Centre: https://ppw.kuleuven.be/home/english/research/etrg/CIPT

Current themes of research:

Mathematics education. Statistical reasoning. Conceptual change. Intuitions and biases in reasoning.

Most relevant publications in the field of Psychology of Education:

Obersteiner, A., Van Dooren, W., Van Hoof, J., & Verschaffel, L. (2013). The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learning and Instruction, 28, 64–72.

Van Dooren, W., De Bock, D., & Verschaffel, L. (2010). From addition to multiplication … and back. The development of students’ additive and multiplicative reasoning skills. Cognition and Instruction, 28, 360–381.

Van Dooren, W., De Bock, D., Hessels, A., Janssens, D., & Verschaffel, L. (2004). Remedying secondary school students’ illusion of linearity: a teaching experiment aiming at conceptual change. Learning and Instruction, 14, 485–501.

Van Hoof, J., Verschaffel, L., & Van Dooren, W. (2015). Inappropriately applying natural number properties in rational number tasks: Characterizing the development of the natural number bias through primary and secondary education. Educational Studies in Mathematics, 90, 39–56.

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Degrande, T., Verschaffel, L. & Van Dooren, W. Beyond additive and multiplicative reasoning abilities: how preference enters the picture. Eur J Psychol Educ 33, 559–576 (2018). https://doi.org/10.1007/s10212-017-0352-y

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  • DOI: https://doi.org/10.1007/s10212-017-0352-y

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