Procedural flexibility is an important skill for algebra. Although prior work has focused on measuring students' procedural flexibility using arithmetic problems, word problems may also capture students' flexibility because of their open-ended nature. To date, no published study has examined the use of word problems as another measure of…

In the present study, we illuminate students' multiplicative reasoning in the context of their units-coordinating activity. Of particular interest is to investigate students' use of three levels of units as given material for problem-solving activity, which we regard as supporting a more advanced level of multiplicative reasoning. Among 13 middle…

This study aims to examine the effect of problem posing-based active learning activities on students' problem-posing skills and problem-solving achievement. To this aim, an experimental design with pre-test post-test control group was employed. The participants consisted of two groups of sixth graders, one experimental group (N=23) and one control…

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…

The purpose of this study was to examine the effects of a number line intervention with supported self-explanation on student understanding of fraction magnitude and quality of explanation. Participants were three U.S. middle school students with significant behavior problems. Participants were given eight lessons containing explicit instruction…

Background: Providing students with worked out problem solutions is a beneficial instructional technique in STEM disciplines, and studying examples that have been worked out incorrectly may be especially helpful for reducing misconceptions in students with low prior content knowledge. However, past results are inconclusive and the effects of…

This study was guided by the question, how do we understand the multiplicative reasoning of upper high school students and use that to give insight to their performance on a standardized test? After administering a partial ACT assessment to a class of high school students, we identified students to make comparisons between low and high scoring…

Identifying the knowledge resources teachers productively and unproductively draw upon can provide a means by which to create support structures to develop a more robust understanding of the content. To provide more informed grade-level support structures in teacher education programs, this study examined the knowledge resources 20 secondary…

Fraction knowledge and algebraic skill are closely linked. Algebra is a gatekeeper for advanced courses (Booth & Newton, 2012; Brown & Quinn, 2007). This study uses the person-centered approach of latent profile analysis to examine individual differences in middle schoolers' (N = 350) algebra performance at the end of the year (EOY). The…

Puzzles involving infinite networks of resistors are an engaging way for students to explore the idea of infinity and self-similarity in physics. Recently K Atkin has described one such puzzle, alongside a solution based on an equivalent finite network (2022 "Phys. Educ." 57 025015). Here we present a generalisation of this problem which…

This Spotlight explores effective strategies for improving math instruction and enhancing student achievement in K-8 classrooms. From making math more relevant and engaging and mastering word problem-solving to deepening conceptual understanding of fractions and nurturing students' ability to tackle challenges, these articles offer valuable…

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…

The current study assessed whether adding worked examples with self-explanation prompts focused on making connections between mathematical principles, procedures, and concepts of rational numbers to a curriculum focused on invented strategies improves pre-algebra students' fraction number line acuity, rational number concepts and procedures.…

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 study investigated relations between the distribution of practice problems in textbooks and students' learning of decimal arithmetic. In Study 1, we analyzed the distributions of decimal arithmetic practice problems that appeared in 3 leading math textbook series in the United States. Similar imbalances in the relative frequencies of decimal…