Children often learn abstract mathematics concepts with concrete manipulatives. The current study compared different ways of using specific manipulatives -- base-ten blocks -- to support children's place value knowledge. Children (N = 112, M age = 6.88 years) engaged in place value learning activities in one of four randomly assigned conditions in…

This paper reports from a case study which explores kindergarten children's mathematical abstraction in a teaching--learning activity about reflection symmetry. From a dialectical perspective, abstraction is here conceived as a process, as a genuine part of human activity, where the learner establishes "a point of view from which the concrete…

To promote learning and transfer of abstract ideas, contemporary theories advocate that teachers and learners make explicit connections between concrete representations and the abstract ideas they are intended to represent. "Concreteness fading" is a theory of instruction that offers a solution for making these connections. As originally…

A fundamental aspect of statistical inference is representation of real-world data using statistical models. This article analyzes students' articulations of statistical models and modeling during their first steps in making informal statistical inferences. An integrated modeling approach (IMA) was designed and implemented to help students…

Empirical arguments rely on examples without necessarily addressing all cases. Students should be skeptical of empirical evidence and should seek more secure arguments for generalizations, such as those that explain why a generalization is true for all cases. Generalizing on the basis of patterns in data is an important mathematical practice;…

There are many reasons to be curious about the way people learn, and the past several decades have seen an explosion of research that has important implications for individual learning, schooling, workforce training, and policy. In 2000, "How People Learn: Brain, Mind, Experience, and School: Expanded Edition" was published and its…

Analogous thinking has been commonly discussed as being an inherent and distinguishing characteristic of human cognition (e.g., Gentner, 2010; Goldstone, Day, & Son, 2010; Holyoak, in press; Rittle-Johnson & Star, in press). Gentner (2003) has argued that as part of the human cognitive toolbox, comparison accompanied by the relational language to…

Together with other publications in this series, this handbook addresses the issue of humanizing education. Specifically, discussion focuses on the role of critical thinking and reasoning in the educational process. Part one outlines reasons, requirements, and methods for teaching critical thinking and reasoning and connects critical thinking with…

This study investigated the effect of two external conditions on the learning of principles by children. The external conditions were instruction on the major concepts related in the principle and the number of teaching examples and teaching nonexamples of the principle presented with a statement of the principle. Subjects were 159 fifth-grade…

This paper provides a brief overview of some of the current thought on teaching problem-solving and decision-making skills and presents selected exercises that have been used successfully in a graduate course in problem-solving and decision-making strategies. In addition to learning theories that are presented in order to help learners understand…

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,…

Differences in levels of subject matter learning at the university level were explored to determine how a learning task is approached between those who are successful and those who are less successful. Students read a selected social science text, (Paul Samuelson's "Economics", for example), related the material learned, answered content…