Fractions are challenging for both typically achieving children and adults. Although some prior research has focused on fraction difficulties of children with mathematics difficulties (MD), persistent difficulties encountered by adults with MD remain unknown. It is possible that these adults may be able to compensate for some deficits. In this…

When learning about fractions, teaching usually follows certain topics -- e.g. part of the whole, fraction equivalence, and size comparison. Not yet answered is whether students' conceptual and procedural knowledge of fractions is coherent between those topics. To answer this question, we performed a latent profile analysis of data from N = 1005…

Background: Mapping fraction symbols to magnitudes is easier for students to master than comparing fraction magnitudes. Fraction mapping assesses students' understanding of part-whole interpretations of fractions; fractions represent the parts of an object or set of objects. Fraction comparison assesses students' understanding of measurement…

The purposes of this study are to report current Preservice Teachers' (PTs) decimal abilities regarding the types of error patterns that they commit and to analyze characteristics of the errors in the problems posed for multiplication and division in decimals. We have determined common concept- and procedure-based errors made by the PTs. 37 PTs in…

We analyzed the solution pathways and errors found in the written responses of 469 prospective teachers solving an equation containing fractions. The majority (332, or 70%) used an algebraic method; 141 of the 332 (42%) were correct, and 22% of the algebraic methods were abandoned before a solution was obtained. We identified the steps in the…

This study investigated understanding of and misconceptions with fractions in college students enrolled in a remedial mathematics course. Data were collected from 22 college students for one semester. The analysis of 41 fraction problems revealed that participants' common misconceptions were associated with a lack of understanding of basic…

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…

This study analyses the potential of a learning analytics (LA) based formative assessment to construct personalised teaching sequences in Mathematics for 5th-grade primary school students. A total of 127 students from Spanish public schools participated in the study. The quasi-experimental study was conducted over the course of six sessions, in…

One of the attributes of rational numbers that make them different from integers are the different symbolic modes (fraction, decimal and percentage) to which an identical number can be attributed (e.g. 1/4, 0.25 and 25%). Some research has identified students' difficulty in mental calculations with rational numbers as has also the switching to…

Online educational technologies offer opportunities for providing individualized feedback and detailed profiles of students' skills. Yet many technologies for mathematics education assess students based only on the correctness of either their final answers or responses to individual steps. In contrast, examining the choices students make for how…

The article deals with mathematical literacy in relation to mathematical knowledge and mathematical problems, and presents the Slovenian project NA-MA POTI, which aims to develop mathematical literacy at the national level, from kindergarten to secondary education. All of the topics treated represent starting points for our research, in which we…

This paper presents an analysis of fractions errors displayed by learners due to deficient mastery of prerequisite concepts. Fractions continue to pose a critical challenge for learners. Fractions can be a tricky concept for learners although they often use the concept of sharing in their daily lives. 30 purposefully sampled learners participated…

Adults use a variety of strategies to reason about fraction magnitudes, and this variability is adaptive. In two studies, we examined the relationships between mathematics anxiety, working memory, strategy variability and performance on two fraction tasks: fraction magnitude "comparison" and "estimation." Adults with higher…

The purpose of this study was to investigate what common errors and misconceptions about fractions exist among Saudi Arabian college students. Moreover, the study aimed at investigating the possible explanations for the existence of such misconceptions among students. A researcher developed mathematical test aimed at identifying common errors…