In this commentary, I examine some of the distinctive, foundational difficulties in learning fractions and other types of rational numbers encountered by students with a mathematical learning disability and how these differ from the struggles experienced by students classified as low achieving in math. I discuss evidence indicating that students with math disabilities exhibit a significant delay or deficit in the numerical transcoding of decimal fractions, and I further maintain that they may face unique challenges in developing the ability to effectively translate between different types of fractions and other rational number notational formats—what I call conceptual transcoding. I also argue that characterizing this level of comprehensive understanding of rational numbers as rational number sense is irrational, as it misrepresents this flexible and adaptive collection of skills as a biologically based percept rather than a convergence of higher-order competencies that require intensive, formal instruction.
FuchsL. S.MaloneA. S.SchumacherR. F.NamkungJ.WangA. (2017). Fraction intervention for students with mathematics difficulties: Lessons learned from five randomized control trials. Journal of Learning Disabilities, 50, 631–639.
2.
GearyD. C. (2011). Consequences, characteristics, and causes of mathematical learning disabilities and persistent low achievement in mathematics. Journal of Developmental and Behavioral Pediatrics, 32, 250–263.
3.
GearyD. C. (2013). Early foundations for mathematics learning and their relations to learning disabilities. Current Directions in Psychological Science, 22, 23–27.
4.
GearyD. C. (2015). The classification and cognitive characteristics of mathematical disabilities in children. In KadoshR. C.DowkerA. (Eds.), Oxford handbook of numerical cognition (pp. 767–786). Oxford, UK: Oxford University Press.
JordanN. C.ResnickI.RodriguesJ.HansenN.DysonN. (2017). The Delaware Longitudinal Study of Fraction Learning: Implications for helping children with mathematics difficulties. Journal of Learning Disabilities, 50, 621–630.
7.
MatthewsP. G.ChesneyD. L. (2015). Fractions as percepts? Exploring cross-format distance effects for fractional magnitudes. Cognitive Psychology, 78, 28–56.
8.
MatthewsP. G.HubbardE. M. (2017). Making space for spatial proportions. Journal of Learning Disabilities, 50, 644–647
.
9.
MazzoccoM. M. M.DevlinK. T. (2008). Parts and “holes”: Gaps in rational number sense among children with vs. without mathematical learning disabilities. Developmental Science, 11, 681–691.
10.
MossJ. (2003). Research, reflections, practice: Introducing percents in linear measurement to foster an understanding of rational-number operations. Teaching Children Mathematics, 9, 335–339.
11.
MossJ. (2005). Pipes, tubes, and beakers: New approaches to teaching the rational number system. In DonovanM. S.BransfordJ. D. (Eds.), How children learn: Science in the classroom (pp. 309–349). Washington, DC: National Academies Press.
12.
MurrayE.HillaireG.JohnsonM.Rappolt-SchlichtmannG. (2015). Representing, acting, and engaging: UDL mathematics. In ChinnS. (Ed.), The Routledge international handbook of dyscalculia and mathematical learning difficulties (pp. 393–405). London, UK: Routledge.
13.
ObersteinerA.van DoorenW.van HoofJ.VerschaffelL. (2013). The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learning and Instruction, 28, 64–72.
14.
PowellS. R.FuchsL. S.FuchsD. (2013). Reaching the mountaintop: Addressing the common core standards in mathematics for students with mathematics difficulties. Learning Disabilities Research & Practice, 28, 38–48.
15.
SieglerR. S.PykeA. A. (2013). Developmental and individual differences in understanding of fractions. Developmental Psychology, 49, 1994–2004.
16.
SowderJ. T. (1992). Making sense of numbers in school mathematics. In LeinhardtG.PutnamR.HattrupR. (Eds.), Analysis of arithmetic for mathematics teaching (pp. 1–51). Hillsdale, NJ: Erlbaum.
17.
SowderJ. T.BezukN.SowderL. K. (1993). Using principles from cognitive psychology to guide rational number instruction for prospective teachers. In CarpenderT. P.FennemaE.RomberT. A. (Eds.), Rational numbers: An integration of research (pp. 239–259). Hillsdale, NJ: Erlbaum.
18.
TianJ.SieglerR. S. (2017). Fractions learning in children with mathematics difficulties. Journal of Learning Disabilities, 50, 614–620.
19.
UtleyJ.ReederS. (2011). Prospective elementary teachers’ development of fraction number sense. In International Group for the Psychology of Mathematics Education proceedings (pp. 1148–1154). Cape Town, South Africa: International Group for the Psychology of Mathematics Education.
20.
VamvakoussiX. (2015). The development of rational number knowledge: Old topic, new insights. Learning and Instruction, 37, 50–55.
21.
WongT. T.-Y.HoC. S.-H.WangJ. (2014). Identification of children with mathematics learning disabilities (MLDs) using latent class growth analysis. Research in Developmental Disabilities, 35, 2906–2920.
