This qualitative review aims to describe the current status of problem-based learning (PBL) implementation in mathematics and identify research gaps in the area of investigation. Literature was searched using the ERIC and Google Scholar search engines. The inclusion/exclusion criteria included: articles published in reputable journals in English…

Rural schools face challenges that are often different than nonrural schools. Resource constraints are particularly acute in rural schools, and they struggle to offer advanced courses and extracurricular programs. The purpose of this paper is to present a descriptive, instrumental case study of an inclusive rural science, technology, engineering,…

A central goal of secondary mathematics is for students to learn to use powerful algebraic strategies appropriately. Research has demonstrated student difficulties in the transition to using such strategies. We examined strategies used by several thousand 8th-, 9th-, and 10th-grade students in five different school systems over three consecutive…

This paper describes the author's attempt to design assignments that engage preservice elementary teachers in original mathematical thinking. In particular, the choice of integer operations as the focus of a structured writing assignment that takes students two weeks to complete is explained and justified. Exemplary student work is quoted.…

Outlines a plan of action designed to enhance growth in problem-posing skills. The "blueprint" provides a model for teachers and teacher educators who wish to integrate more problem posing into their curriculum. Specific activities and instructional strategies are cited to illustrate the development of problem posing as a process in the classroom.…

Presents activities to demonstrate that current technology allows readily accessible representations in algebraic, numeric, and geometric forms. Argues that integrating these different representations into the curriculum helps students to think more critically about systems. Discusses problem solving using multiple representations, equivalent…

Student problem-solving behaviors are analyzed using a four-dimensional framework with related detrimental factors identified for each dimension. General approaches and specific techniques developed to address negative factors are reviewed. Examined are means of developing the components of problem-solving teaching. (KR)

Provided is a list of the needs of gifted and talented children. Delineates the concomitant relationship with science instruction and the stages in the model that are instrumental in meeting these needs. (RT)

Identified are reasons for discrepancies between desired states and actual practice of problem solving and reflective thinking. Issues discussed include describing the development of problem solving, using problem solving methods in instruction, outcome of developing students' problem solving abilities, and reasonable expectations of attaining the…