Students' ability to operate with increasingly more complex units has been shown to be a key factor in their conceptual development. These abilities have been characterized as "stages of units coordination." This article focuses on the domain of composing and decomposing composite units. Using data from a teaching experiment with a…

The basic notions of combinatorics, including systematic listing and permutations, are important topics of mathematics that are recommended to be learned eventually from elementary schools. However, there is little research in mathematics education regarding elementary students' combinatorial strategies. The purpose of this research is to…

Students who exhibit mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly choose effective problem-solving strategies (McIntosh et al., 1997, https://ro.ecu.edu.au/ecuworks/6819). Due to its dispositional nature, mature number sense is typically measured through in-depth interviews or tests of…

Cover, Copy, Compare (CCC) has been shown to be an effective intervention at improving single-digit multiplication fluency within the academic intervention literature. The application of the three-term contingency trial embedded within CCC provides the intervention with several key components of evidence-based interventions. Given that teachers…

Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…

Teachers and teacher educators have been sharing strategies and resources for implementing mathematics routines in National Council of Teachers of Mathematics (NCTM) journals for years. A less commonly shared mathematics routine, especially with young learners, is "Clothesline Math" (Shore, 2017, 2018). In this routine, teachers create…

Instructional routines, like "Number Talks" and "Notice and Wonder," engage students in doing and then talking about their mathematical thinking. Number Talk routines are short mathematical discussions where students mentally solve and share the strategies they used to make sense of the problem. In comparison, the Notice and…

Increasingly, students must demonstrate knowledge in mathematics through mathematics writing, yet research lags in understanding how students engage in mathematics-writing tasks. Most available research on mathematics writing focuses on typically achieving students without considering students with mathematics difficulty (MD). In this study, we…

This study investigated how six Year Four (9-10 years old) students interacted with a dynamic (zoomable) digital number line to demonstrate knowledge and understandings of decimal fractions. Results from a task-based interview indicated that the zoomable number line is able to assist students in developing conceptual understandings of decimal…

While symbolic number processing is an important correlate for typical and low mathematics achievement, it remains to be determined whether children with high mathematics achievement also have excellent symbolic number processing abilities. We investigated this question in 64 children (aged 8 to 10), i.e., 32 children with persistent high…

Researchers in educational measurement use Differential Item Functioning (DIF) to examine whether test items are functioning uniquely across subgroups of test participants while taking into account their ability level. DIF is essential for test validity arguments, thus making it a necessary part of validity studies. This study examines DIF across…

This study aimed to examine whether a computational thinking (CT) intervention related to (a) number knowledge and arithmetic (b) algebra, and (c) geometry impacts students' learning performance in primary schools. To this end, a quasi-experimental, nonequivalent group design was employed, with 61 students assigned to the experimental group and 47…

The present study tests two predictions stemming from the hypothesis that a source of difficulty with rational numbers is interference from whole number magnitude knowledge. First, inhibitory control should be an independent predictor of fraction understanding, even after controlling for working memory. Second, if the source of interference is…

Purpose: Previous studies examining the inter-relations between serial and discrete naming with reading have found that the ability to efficiently process multiple items presented in a sequence (indexed by serial naming) is a unique predictor of word- and text-reading fluency. However, conclusions have been tempered by the concurrent nature of the…

In grade 3, students are expected to be able to represent a fraction on a number line by first identifying the interval from 0 to 1 as the unit and by partitioning the unit as needed on the basis of the denominator. This task extends these grade 3 fraction goals stated in the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010)…