Contribution: This article presents a new look at teaching the Laplace transform for engineering students by emphasizing the obsolescence of the current method of finding the inverse Laplace transform when solving differential equations, and by recognizing the important role of a computer-assisted environment in helping the students understand the…

There is a strong need for fifth-grade students to become proficient in mathematical problem-solving using fractional computations because it will have a lasting impact on student achievement. Traditionally, mathematics is taught inside a brick-and-mortar classroom, grounded in rote memorization of facts, rules, and formulas. In recent years, more…

A growing emphasis on computational thinking worldwide necessitates student proficiency in creating algorithms. Focusing on the use of counterexamples for developing student-invented algorithms, I reanalyze two pieces of data from previously published research, pertaining to two different cases of students' algorithmatizing activity. In both…

When, how, and why students use conceptual knowledge during math problem solving is not well understood. We propose that when solving routine problems, students are more likely to recruit conceptual knowledge if their procedural knowledge is weak than if it is strong, and that in this context, metacognitive processes, specifically feelings of…

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…

Developing an understanding of fractions is critical as a significant predictor for the learning progression of advanced domains; however, students face significant challenges in learning fractions because of their unique properties. To systematically approach remediation, this study examined the common error patterns committed by middle-school…

This article proposes a practical method of teaching the addition of unit fractions using a series of mirror equation experiments.

The purpose of this study was to analyze the problem-solving techniques that students in a fifth-grade classroom applied while solving mathematical word problems. Fifth-grade students in a private school with Ministry of Education curricula in Al Ain, Abu Dhabi, were given a set of 15-word problems to solve with detailed justifications. The…

This document includes instructional tips on: (1) Building on students' informal understanding of sharing and proportionality to develop initial fraction concepts; (2) Helping students recognize that fractions are numbers that expand the number system beyond whole numbers, and using number lines to teach this and other fraction concepts; (3)…

Whole Number Arithmetic (WNA) appears as the very first topic in school mathematics and establishes the foundation for later mathematical content. Without solid mastery of WNA, students may experience difficulties in learning fractions, ratio and proportion, and algebra. The challenge of students' learning and mastery of fractions, decimals, ratio…

Despite the importance of computational estimation skill for the improvement of number sense, little research exists on preservice teachers' estimation skills and their view on estimation in the US context. This study examined the computational estimation skill of 58 preservice elementary teachers (PSTs) and its relationship to their views of the…

The study has two primary purposes. The first was to examine the efficacy of the "Super Solvers" Fractions Intervention (SSFI) for third-grade students at risk for mathematics learning disabilities (MLD). The second was to test the added value of embedding self-regulation instruction into the SSFI. Students were randomly assigned to a…

The purposes of this study were twofold. The first was to test the efficacy of two versions of the "Super Solvers" (SS) intervention for fourth- and fifth-grade students at-risk for mathematics learning disabilities (MLD). The second was to test the value of adding an error analysis component to the SS intervention. Students were…

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…

Using Cuisenaire Rods, metric measurement, and mapping, students worked collaboratively to calculate, keep records, build, and problem solve with use of decimal fractions as a key element.