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)…

This paper presents the results of a study on Calculus students' use of web-based homework. We collected data from students' web-based homework usage, such as their grades, time spent, number of attempts used to solve problems, and problem solutions. We also collected grades on in-class quizzes, which were given the day after homework had been…

Students in a fully online learning environment have limited opportunities to talk about math problem solving. While discourse is an effective pedagogical model, less is known about how it translates to online math learning. We analyzed online platform data from two fully online virtual elementary schools in the United States to address the…

The use of mathematics performance tasks can provide a window into how a student is applying mathematics to various situations, how they are reasoning mathematically and how they are applying conceptual knowledge through problem solving and critical thinking. The purpose of this study was to investigate, according to the elementary mathematics…

Provides information for constructing two-dimensional performance graphs for students to assess their competencies and to diagnose difficulties in the important area of problem solving. (ASK)

This study investigated whether undergraduate students encode spurious correlations in memory and exhibit them during the learning process leading to ineffectual problem solving. Findings suggested that even experienced students relied on surface-structure feature-algorithm correlations for solving new problems. Findings pose implications for…

Fourth-grade students (n=45) either with or without learning disabilities and achieving or not achieving at grade level in math were asked to explain strategies used to solve computational problems. Strategies were classified as reproductive or reconstructive (which varied in applicability and efficiency). Significant group differences were found.…

Tenth graders solved mathematical problems assisted by varying amounts of help from their teacher. Significant differences occurred between students receiving aid and the unaided control group. Partial assistance resulted in better immediate performance, but this difference was less observable three weeks later. (Author/GDC)

This study was designed to determine if there were certain aspects of cognitive/personality style that affected prospective teachers' choice of problem-solving paradigm and presentation of inquiry. Fifty-six undergraduate elementary education majors were given the Paragraph Completion Test, which measures conceptual level, and the Group Embedded…

This study investigated several aspects of a teaching experiment which focused on five seventh grade students' performance on nonroutine number theory problem-solving with a close look at the role of heuristics, concrete models, and the relationships between these variables. In the experiment, students were given a series of lessons on number…

A pretest-posttest control group design was used in a classroom experiment designed to determine whether the problem-solving performance of second grade students would be affected by systematic instruction in estimation. Participants were 36 students in two groups who were given daily lessons in measurement. The experimental group received a daily…

This paper reports the results from one of a series of related, collaborative studies carried out in Sandy Bay, Tasmania, Australia, in 1979 and 1980, examining how young children acquire the skills to represent and solve addition and subtraction problems. The purpose of this study was to relate children's cognitive processing capabilities and…

This study, presented at the 1979 meeting of the American Educational Research Association (AERA) in San Francisco, examines the relationship between a student's mathematical problem-solving ability and the nature of the student's recall of information from previously-solved problems. Seventy-seven seventh-grade students completed tasks measuring…