Thirty-seven third graders and thirty-two first graders engaged in solving a tangram puzzle in the shape of a fox. They had five minutes to solve the puzzle, and after this time, they received guidance on the particular piece they had difficulties with. Through the lenses of navigating flexible abstraction, reinterpretation, combinations, and…

Mastering the ability for learning to learn is the most ambitious goal of modern educators. A distinction is made between two relatively independent components of this expertise: (a) the reflective component of the learning to learn ability that allows a person comprehend what knowledge and skills he or she lacks to act in the new situation; (b)…

Children in a first-grade class who were taking their first steps in formal mathematical knowledge were given a sequence of five modelling tasks during their regular mathematics lessons. These tasks were different in nature from the problems they encountered in their textbooks. They are more complex and challenging, requiring analysis of the…

Early elementary school students are expected to solve twelve distinct types of word problems. A math researcher and two teachers pose a structure for thinking about one problem type that has not been studied as closely as the other eleven. In this article, the authors share some of their discoveries with regard to the variety of…

A teaching team of three teachers aims to prepare students for 21st Century Learning Outcomes, which includes critical thinking, problem solving, and communication skills. Yet classroom experience has taught them that one of the most difficult aspects of teaching young children is that they have few experiences or prior knowledge to make sense of…

"Focus in Grade 1: Teaching with Curriculum Focal Points" describes and illustrates learning paths for the mathematical concepts and skills of each grade 1 Focal Point as presented in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It includes representational supports for teaching and learning that can facilitate…

Twenty-three children in each of 2 first-grade classrooms were observed as they worked in pairs with the computer language Logo in a learning-by-discovery context. Describes children's behaviors related to planning, correction of errors, reflection, causality, and procedure-writing. (RJC)

Forty-three first-grade children, who had received no formal instruction in addition and subtraction, were individually administered 20 problems that could be solved using addition or subtraction. The problems were selected to represent the following semantic types: joining, separating, part-part-whole, comparison, and equalizing. Responses were…

This study investigated a theoretical structure which attempts to explain the problem-solving strategies used by first-grade students who are successful in solving simple arithmetic story problems. The structure used describes the problem-solving procedure as consisting of a three-stage model building process: (1) comprehending the story, (2)…

Presents seven scenes showing everyday classroom situations that give students the options of applying their own problem-solving strategies to solve everyday problems of life and enable them to experience mathematical power coming from self-initiated insights into mathematical concepts. (MDH)

This book introduces journal-writing prompts in mathematics for grades 1-2. Content prompts, attitudinal or affective prompts, and process prompts are presented. Each of the content prompts relates or connects topics within and outside of mathematics, targeting important or meaningful concepts and skills. The content prompts also provide…

The contribution of decentration as an underlying component of discrimination learning and discrimination shift behavior was investigated in this study. In addition, the effect of verbal labeling and the relationship of academic achievement to discrimination learning and decentration was considered. The subjects were 120 first grade students who…

Evaluation results are reported for the Southwest Educational Development Laboratory's Thinking and Reasoning Program, designed to develop analytic thinking and problem-solving skills in young children in multicultural classroom settings. Results are based on a pilot test of the program conducted during the 1974-75 school year. Mastery activities,…

An experimental study compared the instructional effectiveness of Logo programming, commercially available software designed to aid composition and problem solving, and traditional teaching methods for low socioeconomic status first-grade students. Both software environments enhanced problem solving performance for a novel task, but Logo was most…