doi:

DOI: 10.3724/SP.J.1041.2017.00745

Acta Psychologica Sinica (心理学报) 2017/49:6 PP.745-758

The overuse of proportional reasoning and its cognitive mechanism: A developmental negative priming study


Abstract:
The overuse of proportional reasoning refers to a phenomenon that students improperly use proportional reasoning to solve non-proportional problems (e.g., addition problems in the present study). No research to date has directly illuminated the cognitive mechanism of the phenomenon since it is widely found in different countries and different ages. Therefore, we aimed to explore the potential cognitive mechanism in the current study from a new perspective based on the Inhibitory Control Model. The model suggests that solving a problem successfully not only requires the grasp of the underlying logic but also the inhibition of the misleading strategies. Accordingly, we proposed a hypothesis that the failure to inhibit the improper proportional thinking rather than the failure to grasp the additive logic would lead to students' overuse of proportional reasoning since they may have already mastered additive thinking.

Key words:proportional reasoning,inhibitory control,negative priming,missing-value word problem,mathematics cognition

ReleaseDate:2017-08-10 07:39:28



Babai, R., Shalev, E., & Stavy, R. (2015). A warning intervention improves students' ability to overcome intuitive interference. ZDM, 47, 735-745.

Borst, G., Poirel, N., Pineau, A., Cassotti, M., & Houdé, O. (2013). Inhibitory control efficiency in a Piaget-like class-inclusion task in school-age children and adults:A developmental negative priming study. Developmental Psychology, 49, 1366-1374.

De Bock, D., van Dooren, W., Janssens, D., & Verschaffel, L. (2002). Improper use of linear reasoning:An in-depth study of the nature and the irresistibility of secondary school students' errors. Educational Studies in Mathematics, 50, 311-334.

De Bock, D., van Dooren, W., Janssens, D., & Verschaffel, L. (2007). The illusion of linearity:From analysis to improvement. US:Springer.

De Neys, W., Lubin, A., & Houdé, O. (2014). The smart nonconserver:Preschoolers detect their number conservation errors. Child Development Research, 2014, Article ID 768186.

De Neys, W., Moyens, E., & Vansteenwegen, D. (2010). Feeling we're biased:Autonomic arousal and reasoning conflict. Cognitive, Affective, & Behavioral Neuroscience, 10, 208-216.

Diamond, A. (2013). Executive functions. Annual Review of Psychology, 64, 135-168.

Fernández, C., Llinares, S., van Dooren, W., De Bock, D., & Verschaffel, L. (2011). Effect of number structure and nature of quantities on secondary school students' proportional reasoning. Studia Psychologica, 53, 69-81.

Fernández, C., Llinares, S., van Dooren, W., De Bock, D., & Verschaffel, L. (2012). The development of students' use of additive and proportional methods along primary and secondary school. European Journal of Psychology of Education, 27, 421-438.

Frings, C., Feix, S., Röthig, U., Brüser, C., & Junge, M. (2007). Children do show negative priming:Further evidence for early development of an intact selective control mechanism. Dvelopmental Psychology, 43, 1269-1273.

Fu, X. C., & Li, X. D. (2015). Intuitive rules in school mathematical comparison tasks. Education Research Monthly, (2), 106-111.

[付馨晨, 李晓东. (2015). 中小学数学比较任务中的直觉法则研究与展望. 教育学术月刊, (2), 106-111.]

Fu, X. C., & Li, X. D. (2017). Cognitive Inhibition:A new perspective on problem solving. Journal of Psyhological Science, 40(1), 58-63.

[付馨晨, 李晓东. (2017). 认知抑制——问题解决研究的新视角. 心理科学, 40(1), 58-63]

Gillard, E., Van Dooren, W., Schaeken, W., & Verschaffel, L. (2009). Dual processes in the psychology of mathematics education and cognitive psychology. Human Development, 52(2), 95-108.

Gogtay, N., Giedd, J. N., Lusk, L., Hayashi, K. M., Greenstein, D., Vaituzis, A. C., … Thompson, P. M. (2004). Dynamic mapping of human cortical development during childhood through early adulthood. Proceedings of the National Academy of Sciences of the United States of America, 101, 8174-8179.

Houdé, O. (2007). First insights on "neuropedagogy of reasoning". Thinking & Reasoning, 13, 81-89.

Houdé, O., Pineau, A., Leroux, G., Poirel, N., Perchey, G., Lanoë, C., … Mazoyer, B. (2011). Functional magnetic resonance imaging study of Piaget's conservation-of-number task in preschool and school-age children:A neo-Piagetian approach. Journal of Experimental Child Psychology, 110, 332-346.

Houdé, O., & Borst, G. (2014). Measuring inhibitory control in children and adults:Brain imaging and mental chronometry. Frontiers in Psychology, 5, 616.

Houdé, O., & Borst, G. (2015). Evidence for an inhibitory-control theory of the reasoning brain. Frontiers in Human Neuroscience 9, 148.

Jiang, R. H., Li, X. D., Fernández, C., & Fu, X. C. (in press). Students' performance on missing-value word problems:A cross-national developmental study. European Journal of Psychology of Education, doi:10.1007/s10212-016-0322-9

Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In M. Behr & J. Hiebert (Eds.), Number concepts and operations in the middle grades (vol. 2, pp. 93-118). Reston:National Council of Teachers of Mathematics.

Li, X. D., Jiang, R. H., & Qian, Y. J. (2014). 5~8 greaders' overuse of proportionality on missing-value problems. Journal of Mathematics Education, 23(6), 73-77.

[李晓东, 江荣焕, 钱玉娟. (2014). 中小学生对比例推理的过度使用. 数学教育学报, 23(6), 73-77.]

Li, X. D., Xu, W., & Li, N. Y. (2012). The negative priming effect in Piaget-like tasks in the "Infra-logic" domain. Journal of Psychological Science, 35(2), 358-363.

[李晓东, 徐雯, 李娜燕. (2012). 潜逻辑运算类皮亚杰守恒任务中的负启动效应. 心理科学, 35(2), 358-363.]

Lubin, A., Houdé, O., & de Neys, W. (2015). Evidence for children's error sensitivity during arithmetic word problem solving. Learning and Instruction, 40, 1-8.

Lubin, A., Vidal, J., Lanoë, C., Houdé, O., & Borst, G. (2013). Inhibitory control is needed for the resolution of arithmetic word problems:A developmental negative priming study. Journal of Educational Psychology, 105, 701-708.

Meert, G., Grégoire, J., & Noël, M. (2010). Comparing the magnitude of two fractions with common components:Which representations are used by 10-and 12-year-olds? Journal of Experimental Child Psychology, 107, 244-259.

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.

Osman, M., & Stavy, R. (2006). Development of intuitive rules:Evaluating the application of the dual-system framework to understanding children's intuitive reasoning. Psychonomic Bulletin & Review, 13, 935-953.

Pritchard, V. E., & Neumann, E. (2009). Avoiding the potential pitfalls of using negative priming tasks in developmental studies:Assessing inhibitory control in children, adolescents, and adults. Developmental Psychology, 45, 272-283.

Stavy, R., & Babai, R. (2010). Overcoming intuitive interference in mathematics:Insights from behavioral, brain imaging and intervention studies. ZDM, 42, 621-633.

Tipper, S. P., Bourque, T. A., Anderson, S. H., & Brehaut, J. C. (1989). Mechanisms of attention:A developmental study. Journal of Experimental Child Psychology, 48, 353-378.

Tjoe, H., & de la Torre, J. (2014). On recognizing proportionality:Does the ability to solve missing value proportional problems presuppose the conception of proportional reasoning? The Journal of Mathematical Behavior, 33, 1-7.

van Dooren, W., De Bock, D., Evers, M., & Verschaffel, L. (2009). Students' overuse of proportionality on missing-value problems:How numbers may change solutions. Jouranl for Research in Mathematics Education, 40(2), 187-211.

van Dooren, W., De Bock, D., Vleugels, K., & Verschaffel, L. (2010). Just answering… or thinking? Contrasting pupils' solutions and classifications of missing-value word problems. Mathematical Thinking and Learning, 12, 20-35.

van Dooren, W., & Inglis, M. (2015). Inhibitory control in mathematical thinking, learning and problem solving:A survey. ZDM, 47, 713-721.

Volckaert, A. M. S., & Noël, M. P. (2015). Training executive function in preschoolers reduce externalizing behaviors. Trends in Neuroscience and Education, 4, 37-47.

Vuilleumier, P., Schwartz, S., Duhoux, S., Dolan, R. J., & Driver, J. (2005). Selective attention modulates neural substrates of repetition priming and "implicit" visual memory:Suppressions and enhancements revealed by FMRI. Journal of Cognitive Neuroscience, 17, 1245-1260.

Zelazo, P. D., & Müller, U. (2010). Executive function in typical and atypical development. In U. Goswami (Ed.), The wiley-blackwell handbook of childhood cognitive development (2nd ed., pp. 574-603). Oxford:Wiley-Blackwell.

Zhang, L., Xin, Z. Q., Wang, Q., & Li, H. (2012). The influence of constituent integers on the processing of fractions. Psychological Development and Education, 28(1), 31-38.

[张丽, 辛自强, 王琦, 李红. (2012). 整数构成对分数加工的影响. 心理发展与教育, 28(1), 31-38.]