In this set of tips, parents and caregivers will learn how to: (1) support children's understanding of fractions at home with activities on dividing objects (recommended for grades K-5); (2) support children's understanding of fractions at home with measurement activities (recommended for grades K-4); (3) support children's understanding of…

Research suggests that special education teachers lack the pedagogical expertise and content knowledge needed to teach core mathematics standards and to develop the mathematical reasoning of fifth- and sixth-grade students with a mathematics learning disability (MLD). This study used a multiple-baseline design with randomization to examine the…

An understanding of fractions eludes many U.S. students, and research-based knowledge about fraction, such as the utility of linear representations, has not broadly influenced instruction. This randomized trial of lesson study supported by mathematical resources assigned 39 educator teams across the United States to locally managed lesson study…

Fractional approximations of e and p are discovered by searching for repetitions or partial repetitions of digit strings in their expansions in different number bases. The discovery of such fractional approximations is suggested for students and teachers as an entry point into mathematics research.

The purposes of this study were to (a) explore whether early fractions understanding at 4th grade is differentially challenging for students with versus without adequate whole-number competence and (b) identify specific whole-number skill associated with difficulty in fractions understanding. Based on initial whole-number competence, 1,108 4th…

Two content topics will be described. One deals with geometric measurement: length, area, and volume. These are important topics and they have not been learned very well. In particular, what types of relations can one consider when dealing with these three aspects of geometric measurement? The second topic is fractions, and different views of what…

This article provides an example of how one sixth-grade classroom teacher and an instructional coach built a bridge for students in a grade 6 self-contained classroom to support their conceptual understanding and procedural fluency with dividing fractions. Baseline data showed that most of the students in this class had mastered only the…

In this paper, we analyse the results of an experience designed and implemented to evaluate the epistemic and cognitive conflicts identified in the study of proportionality, carried out by a group of 21 students in their last year of primary education. Initially the students exhibit difficulties to recognize situations where proportionality can be…

In a previous study, we validated the fractions schemes and operations trajectory (Norton and Wilkins 2012; Steffe in J Math Behav 20(3): 267-307, 2002; Steffe and Olive Children's fractional knowledge. Springer, New York, 2010; Wilkins and Norton 2011) with PreK-8 prospective teachers and explored PreK-8 prospective teachers' understanding of…

A randomized controlled trial investigated the research question: Do students who participate in online tutoring and a related mathematical game learn more about fractions than students who only have access to the game? Participants were 144 students from four schools, all serving low-income students with low prior mathematics achievement. In the…

The purpose of this causal-comparative study was to gain insight into whether teaching fractions improves teachers' understanding of fractions. University master's students (n = 25) conducted tutoring focused on fraction magnitude using number line representations across 39 sessions (3 per week) at grades 3-5. The contrast condition, 17 master's…

This study explores students' mathematical reasoning within a novel technological environment designed to support understanding of relationships between quantities and adjustable measuring units. In particular, 30 elementary students (grade 3-5) engaged in a series of measurement tasks in which they used a "dynamic virtual ruler" that…

In this article, we introduce the term "vulnerability to achievement stressors," which refers to differentially low achievement when shifts in the educational environment "stress" or threaten the capacity of an individual or a group of individuals to make academic progress. We also introduce a methodological framework for…

Pre-algebra mathematical competencies were assessed for a large and diverse sample of sixth graders (n = 1,926), including whole number and fractions arithmetic, conceptual understanding of equality and fractions magnitudes, and the fractions number line. The goal was to determine if there were clusters of students with similar patterns of…

This study examines the collective mathematical reasoning when students and teachers in grades 3, 4, and 5 explore fractions derived from length comparisons, in a task inspired by the Elkonin and Davydov curriculum. The analysis showed that the mathematical reasoning was mainly anchored in mathematical properties related to fractional or algebraic…