The purpose of this research was to investigate students' mathematical understandings of fraction division with an ethnomathematics/STEM framework. A small group teaching study (Cobb et al., 2003) was conducted using design research methodology to examine how students interacted with the curriculum. The researcher served as interventionist and…

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…

This study explored whether initial skill moderated outcomes of Promoting Algebra Readiness, a Tier 2 sixth grade mathematics intervention targeting conceptual and procedural knowledge of fractions. The study analyzed data from a quasi-experimental pilot study in which at-risk students (n = 198) were assigned to the treatment or control condition…

This study explored whether initial skill moderated outcomes of Promoting Algebra Readiness, a Tier 2 sixth-grade mathematics intervention targeting conceptual and procedural knowledge of fractions. The study analyzed data from a quasi-experimental pilot study in which at-risk students (N = 198) from Oregon middle schools were assigned to the…

A one-on-one dialogue-based mathematics intelligent tutoring system (ITS) for learning multiplication and division of fractions was developed and evaluated in this study. This system could identify students' error types and misconceptions in real-time by using a block-based matching method. The adaptive dialogue-based instruction was supported by…

There is strong evidence from research conducted in the United States that fraction magnitude understanding supports mathematics achievement. Unfortunately, there has been little research that examines if this relation is present across educational contexts with different approaches to teaching fractions. The current study compared fourth and…

This pilot study examined the promise of a Tier 2 sixth grade intervention program for students at-risk for difficulties in mathematics. The study utilized a quasi-experimental design. The final sample included 112 students in treatment (Promoting Algebra Readiness) and 86 students in control (standard district practice) conditions. The Promoting…

This pilot study examined the promise of a Tier 2 Grade 6 intervention program for students at risk for difficulties in mathematics. The study utilized a quasi-experimental design. The final sample included 112 students in treatment (Promoting Algebra Readiness) and 86 students in control (standard district practice) conditions. The Promoting…

Prior work exploring preschool-aged children's reasoning with repeating patterns has shown that patterning ability is an important predictor of math achievement; however, there is limited research exploring older children's growing pattern task performance. The current study tested whether presentation format impacts performance on growing pattern…

People's attitudes toward mathematics are multifaceted. Across four studies, we found that children and adults have different attitudes about mathematics when asked specifically about whole numbers, as opposed to fractions. The vast majority of children and adults reported negative attitudes toward fractions despite having positive attitudes…

This study compares the effects of a concrete-representational-abstract (CRA) intervention against a modified CRA-Integrated (CRA-I) intervention using a pretest-posttest design with random assignment of matched pairs to intervention conditions. The researchers designed both interventions to improve participants' understanding of and ability to…

Self-efficacy in mathematics is related to engagement, persistence, and academic performance. Prior research focused mostly on examining changes to students' self-efficacy across large time intervals (months or years), and paid less attention to changes at the level of lesson sequences. Knowledge of how self-efficacy changes during a sequence of…

Reasoning about numerical magnitudes is a key aspect of mathematics learning. Most research examining the relation of magnitude understanding to general mathematics achievement has focused on whole number and fraction magnitudes. The present longitudinal study (N=435) used a 3-step latent class analysis to examine reasoning about magnitudes on a…

This study investigated the accuracy of three fraction measures (i.e., fraction number line estimation accuracy, general fraction concepts, and fraction arithmetic) for screening fourth graders who might be at risk for mathematics difficulties. Receiver operating characteristic (ROC) curve analyses assessed diagnostic accuracy of the fraction…