Many U.S. students possess only a weak knowledge of fraction arithmetic. I hypothesize that textbooks are a critical reason for students' poor performance on fraction arithmetic. This is not because of what textbooks contain but rather because of what they lack. Distributions of fraction arithmetic problems in textbooks are imbalanced, with…

How dyslexia students solve number operations is still challenging to unravel. This study aimed at revealing the types of errors conveyed by a dyslexic student in performing fractional operations on mathematical tasks that combined non-verbal text (symbols and pictures) and verbal text. The data were collected using a task-based interview with a…

Fraction arithmetic facility is fundamental to learning more advanced math topics. However, attaining the ability to add and subtract fractions is hard for many students. The present longitudinal study examined students' growth on simple addition and subtraction word problems between fourth and sixth grades (N = 536). Latent class growth analyses…

To explain children's difficulties learning fraction arithmetic, Braithwaite et al. (2017) proposed FARRA, a theory of fraction arithmetic implemented as a computational model. The present study tested predictions of the theory in a new domain, decimal arithmetic, and investigated children's use of conceptual knowledge in that domain. Sixth and…

To understand misconceptions with rational numbers (i.e., fractions, decimals, and percentages), we administered an assessment of rational numbers to 331 undergraduate students from a 4-year university. The assessment included 41 items categorized as measuring foundational understanding, calculations, or word problems. We coded each student's…

This study investigated the role of the bar model method, a significant aspect of the Singapore mathematics curriculum, in the remediation of seventh-grade students' errors on algebra word problems. To accomplish this purpose, we first assessed students' errors on a written test involving algebra problems and identified ten students based on the…

The adverse influence of the presence of an irrelevant number and language inconsistency in a word problem is well known. Our study focused on the combination of these two variables and on the position of the irrelevant number in the word problem for Grade 6 pupils. The study has a mixed design. Item Response Theory was used to make equally able…

Children need support in the early elementary grades to construct a deep, formal understanding of foundational prealgebraic concepts. In this article, the authors share recommendations for teaching one such foundational concept--mathematical equivalence. First, they define mathematical equivalence and discuss research supporting the benefits of…

This article investigates how students with mathematical difficulties (MD) differ from typically developing (TD) students in enumeration processes of small sets of objects (of 1 up to 9 dots). We present a study with 20 fifth-grade students of which ten were found to have MD in initial diagnostics. The students were supposed to exactly enumerate…

The purpose of this study is to investigate pre-service elementary teachers' realistic considerations and difficulties in solving "division with remainder" type of problems which focus on the measurement meaning of division operation. The qualitative research method of case study design was used for the study. The purposive sampling…

Understanding fractions is critical to mathematical development, yet many children struggle with fractions even after years of instruction. Fraction arithmetic is particularly challenging. The present study employed a computational model of fraction arithmetic learning, FARRA (Fraction Arithmetic Reflects Rules and Associations; Braithwaite, Pyke,…

This study reports errors and misconceptions about division operation in fractions made by eighth-grade students. To investigate these errors and misconceptions, the study examined students' understanding of division operation in fractions using a questionnaire and expectation table. Students' misconceptions were determined for each question and…

Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

Even in primary school, mathematics achievement depends upon the efficiency of cognitive, metacognitive and self-regulatory processes. Thus, for pupils to carry out a computation, such as a written calculation, metacognitive mechanisms play a crucial role, since children must employ self-regulation to assess the precision of their own thinking and…

An experiment was conducted over three recent semesters of an introductory calculus course to test whether it was possible to quantify the effect that difficulty with basic algebraic and arithmetic computation had on individual performance. Points lost during the term were classified as being due to either algebraic and arithmetic mistakes…