Problem-solving is a key aspect of mathematics instruction. Although it is part of several national curricula, its implementation is still being vastly explored. The present research, which is part of a larger project, aimed to investigate the effect of using problem-oriented instruction in grade 3 of primary school on students' mathematical…

This study investigated the extent to which domain-general and domain-specific antecedents contributed to pre-algebra's initial level and growth rate among students who experience word-problem difficulty (WPD). We examined if such a profile differs for English-language learners (ELLs; n = 75) and non-ELLs (n = 55) with WPD. We assessed 130 U.S.…

Central elements of adaptive expertise in arithmetic problem solving are flexibility, using multiple strategies, and adaptivity, selecting the optimal strategy. Research shows that the strategies children actually use do not fully reflect the strategies they know: there is hidden potential. In the current study a sample of 147 third graders from…

This research aims to explore students' learning obstacles in solving fraction problems in elementary school. This qualitative research used a case study method. The research subjects involved 30 third-grade elementary school students from two different schools in Bandung City, Indonesia. The instruments utilized were test and non-test. The test…

The relationships between visuo-spatial abilities and geometry performances in school-aged children were examined. A battery of tests assessing non-verbal reasoning, visuo-spatial mental imagery, and academic achievement in geometry (i.e., geometric knowledge and geometric problem-solving competencies) was presented to 162 8-9.5-year-old pupils…

This research examined whether children's construals of mathematical manipulatives -- as toys or as tools for doing mathematics -- influenced their learning from a lesson with the manipulatives. Children (grades 2 and 3) were presented with a set of buckets and beanbags, and they were either given no information about the manipulatives (control)…

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.…

The use of open problem-solving tasks in mathematics education challenges teachers' beliefs, knowledge and practices. This article examines the practices of two primary teachers and their 3rd to 5th grade classes during a three-year in-service teacher training project aiming to increase mathematical problem-solving in class. Three lesson videos…

Purpose: Math word problem solving, a form of reading comprehension, is complicated by mathematical lexical ambiguity (e.g., the word "difference" can mean "dissimilarity" in everyday discourse but "the answer in a subtraction problem" in math). This study examined the role of mathematical lexical ambiguity in math…

In this exploratory study, we documented teachers' knowledge of children's mathematical thinking as they engaged in the task of anticipating children's strategies for an equal sharing fraction problem. To elicit an array of knowledge, 18 teachers were deliberately selected with a variety of numbers of years participating in professional…

In this study, I examined the relation between various construct relevant and irrelevant variables and a math problem solving assessment. I used independent performance measures representing the variables of mathematics content knowledge, general ability, and reading fluency. Non-performance variables included gender, socioeconomic status,…

Providing exploratory activities prior to explicit instruction can facilitate learning. However, the level of guidance provided during the exploration has largely gone unstudied. In this study, we examined the effects of 1 form of guidance, feedback, during exploratory mathematics problem solving for children with varying levels of prior domain…

To date, a number of studies have demonstrated the existence of mismatches between children's "implicit" and "explicit" knowledge at certain points in development that become manifest by their gestures and gaze orientation in different problem solving contexts. Stimulated by this research, we used eye movement measurement to…

BRT Math Screening Measures focus on students' mathematics performance in grade-level standards for students in grades 1-8. A total of 24 test forms are available with three test forms per grade corresponding to fall, winter, and spring testing periods. Each form contains computation problems and application problems. BRT Math Screening Measures…