Measures and References: References: Proportional Reasoning

Return to References: Proportional Reasoning factor page.

Measures

Numerous measures exist to gain a full picture of a student's learning strengths and challenges. Following are examples of measures used to assess this Learner Factor. These measures should be administered and interpreted by experienced professionals.

Ranking Proportions Task: (e.g., Mazzocco & Devlin, 2008): Magnitude comparison for fractions and rational numbers where students rank order different representations of fractions including shaded circles, numerical fractions, and decimals.

Missing value problems: (e.g., Lamon, 2007): Students are asked to determine which value is missing in a ratio equivalence context (e.g., how many sugars do you need to add to 6 lemons so your lemonade is the same sweetness as my lemonade with 2 sugars and 3 lemons?).

References

Agostino, A., Johnson, J., & Pascual-Leone, J. (2010). Executive functions underlying multiplicative reasoning: Problem type matters. Journal of Experimental Child Psychology, 105(4), 286–305.

Bailey, D. H., Siegler, R. S., & Geary, D. C. (2014). Early predictors of middle school fraction knowledge. Developmental Science, 17(5), 775–785.

Booth, J. L., Newton, K. J., & Twiss-Garrity, L. K. (2014). The impact of fraction magnitude knowledge on algebra performance and learning. Journal of Experimental Child Psychology, 118(1), 110–118.

Bulgar, S. (2009). A longitudinal study of students' representations for division of fractions. The Math Enthusiast, 6(1), 165–200.

Carney, M. B., Smith, E., Hughes, G. R., Brendefur, J. L., & Crawford, A. (2016). Influence of proportional number relationships on item accessibility and students' strategies. Mathematics Education Research Journal, 28(4), 503–522.

Cirino, P. T., Tolar, T. D., Fuchs, L. S., & Huston-Warren, E. (2016). Cognitive and numerosity predictors of mathematical skills in middle school. Journal of Experimental Child Psychology, 145, 95–119.

DeJarnette, A. F., Walczak, M., & González, G. (2014). Students' concepts- and theorems-in-action on a novel task about similarity. School Sciences and Mathematics, 114(8), 405–414.

Froiland, J. M., & Davison, M. L. (2016). The longitudinal influences of peers, parents, motivation, and mathematics course-taking on high school math achievement. Learning and Individual Differences, 50, 252-259.

Hansen, N., Jordan, N. C., Fernandez, E., Siegler, R. S., Fuchs, L., Gersten, R., & Micklos, D. (2015). General and math-specific predictors of sixth-graders' knowledge of fractions. Cognitive Development, 35, 34–49.

Hecht S., Close L., & Santisi, M. (2003). Sources of individual differences in fraction skills. Journal of Experimental Child Psychology, (86), 277–302.

​​Keller, J. (2002). Blatant stereotype threat and women's math performance: Self-handicapping as a strategic means to cope with obtrusive negative performance expectations. Sex Roles, 47(3-4), 193-198.

Lamon, S. J., (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. Lester (Ed.), Second handbook of research on teaching and learning mathematics, Vol. I (pp. 629 – 667). Reston, VA: National Council of Teachers of Mathematics.

Lortie-Forgues, H., Tian, J., & Siegler, R. S. (2015). Why is learning fraction and decimal arithmetic so difficult? Developmental Review, 38, 201–221.

Mazzocco, M. M. M., & Devlin, K. T. (2008). Parts and “holes”: Gaps in rational number sense among children with vs. without mathematical learning disabilities. Developmental Science, 11(5), 681–691.

Mazzocco, M. M. M., Myers, G. F., Lewis, K. E., Hanich, L. B., & Murphy, M. M. (2013). Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) versus low mathematics achievement. Journal of Experimental Child Psychology, 115(2), 371–387.

Namkung, J., Fuchs, L. S., & Koziol, N. (2018). Does initial learning about the meaning of fractions present similar challenges for students with and without adequate whole-number skill? Learning and Individual Differences, 61, 165–171.

National Research Council, & Mathematics Learning Study Committee. (2001). Adding it up: Helping children learn mathematics. National Academies Press.

Panaoura, A., Gagatsis, A., Deliyianni, E., & Elia, I. (2009). The structure of students' beliefs about the use of representations and their performance on the learning of fractions. Educational Psychology, 29(6), 713–728.

Post, T., Behr, M., & Lesh, R. (1988). Proportionality and the development of prealgebra understandings In algebraic concepts in the curriculum K-12. Reston, VA: National Council of Teachers of Mathematics.

Siegler, R. S., Fazio, L. K., Bailey, D. H., & Zhou, X. (2013). Fractions: The new frontier for theories of numerical development. Trends in Cognitive Sciences, 17(1), 13–19.

Thomas, N. (2004). The development of structure in the number system. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education 4, 305-.312.

Thompson, P. W., & Saldanha, L. A. (2003). Fractions and Multiplicative Reasoning. In J. Kilpatrick, G. Martin, & Schif (Eds.), Research companion to the Principles and Standards for School Mathematics (pp. 95–114).

Ye, A., Resnick, I., Hansen, N., Rodrigues, J., Rinne, L., & Jordan, N. C. (2016). Pathways to fraction learning: Numerical abilities mediate the relation between early cognitive competencies and later fraction knowledge. Journal of Experimental Child Psychology, 152, 242–263.