In many Western countries, there has been an emphasis on ways in which to support teachers to shift practice from traditional mathematics instruction to inquiry-based classrooms. As a form of professional learning and development, lesson study offers the potential for teachers to develop their ability to respond to students' thinking through…

The relationship between mathematical creativity (MC) and mathematical problem-solving performance (MP) has often been studied but the causal relation between these two constructs has yet to be clearly reported. The main purpose of this study was to define the causal relationship between MC and MP. Data from a representative sample of 480…

Like algebra at any level, early algebra is a way to explore, analyze, represent, and generalize mathematical ideas and relationships. This book shows that children can and do engage in generalizing about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential…

This study of fourth-grade students and teachers explores mathematics teaching and learning that focuses on discovering and modeling algebraic relationships. The study has two parts: an investigation of how students learn to construct algebraic statements and models for comparisons and measurement situations in the multiplicative domain, and an…

This study addressed predictors of the development of word problem solving (WPS) across the intermediate grades. At beginning of 3rd grade, 4 cohorts of students (N = 261) were measured on computation, language, nonverbal reasoning skills, and attentive behavior and were assessed 4 times from beginning of 3rd through end of 5th grade on 2 measures…

Four students participated in a two year study (fifth- and sixth-grade) focused on the development of their understanding of multiplication of fractions. During the first year, all students received individualized instruction designed to encourage them to build on their informal knowledge of partitioning to solve problems involving multiplication…

This report investigated to what extent a curriculum designed to actively teach critical thinking skills resulted in students utilizing higher-order thinking skills (e.g., analysis, synthesis and evaluation). An intervention strategy was designed for a sixth grade class located in a diverse suburban community in northern Illinois. The intervention…

Suggests that the differences existing between the view of algebra as a mandated course at a specified grade level and the view of algebra as a way of mathematical thinking and reasoning developed gradually over time must be positively integrated to help students develop a genuine capacity for algebraic thinking and reasoning. (AIM)

This book contains a classroom-tested approach to the teaching of problem solving to all students in Grades 4-6, regardless of ability. Information on problem solving in general is provided, then mathematical problems on logic, whole numbers, number theory, fractions, decimals, geometry, ratio, proportion, percent, probability, sets, and…

Presents a problem for students in grades 4-6 on Venn diagrams with or without manipulatives. Lists questions for teachers to reflect upon during the problem-solving process concerning student understanding of problems, problem-solving strategies, assessment, and reasoning skills. (ASK)

The view of the researcher is that students in the upper elementary to middle school range need to increase their problem-solving skills by making logical deductions and organizing and structuring their thoughts through the use of word problems. Giving children a daily word problem challenged and introduced them to the lesson. This activity…

Describes a variation on a problem from the history of mathematics in which the class is divided into cooperative learning groups of four students each. Each group is challenged to find a procedure for resolving the situation with several solutions emerging. Emphasizes the importance of examining "incorrect" answers and discussing the…

Focuses on mental strategies for computing in the middle grades. Describes what they are and why they are important. Refers to relevant research and presents some teaching ideas for developing these strategies beyond the primary grades. Includes a discussion of the role of mental calculation in everyday life both past and future. Contains 27…

Spreadsheets have become popular tools for exploring mathematical patterns and building conceptual understanding of variables and functional relationships. Presents examples of students' work to illustrate multiple paths of inquiry, generalization, and mathematical reasoning. Supports effective investigation of patterns and functions for students…

The purpose of this study was to investigate students developing understanding of concepts related to rate of change. Twenty students first participated in a rate of change curriculum unit as part of an after school math and technology program. During the unit, students used motion detectors and related graphing software to create and analyze…