The authors document their experience of working with 6-year-olds over several weeks. They share some observations that arise from weekly sessions they conducted which have been under way for several years and which have been widely reported. These observations show the payoff of a problem-solving approach to learning.

As teachers plan instruction--even instruction about punctuation--they have the opportunity to engage students' minds and create new labels: question-asking, problem-solving. How teachers teach embeds a vision of who they think kids are and what they think kids are capable of. Are they destined for a future of critical thinking, questioning,…

Basic brain function is not a mystery. Given that neuroscientists understand the brain's basic functioning processes, one wonders what their research suggests to teachers of developmental algebra. What if we knew how to teach so as to improve understanding of the algebra taught to developmental algebra students? What if we knew how the brain…

This article draws out many mathematical ideas connected with a familiar game often used by middle school teachers. (Contains 5 figures and 1 table.)

The benefits of using data logging to teach "how science works" are presented. Pedagogical approaches that take advantage of other school ICT are briefly described. A series of simple, quick experiments are given together with their resulting charts. Examples of the questions that arise from the charts show how the rich data lead to the refinement…

The present work has its focus on university-level engineering education students that do not intend to major in computer science but still have to take a mandatory programming course. Phenomenography and variation theory are applied to empirical data from a study of students' conceptions of computer programming. A phenomenographic outcome space…

Virtually all mathematics is based on pattern and structure. A mathematical "pattern" is any predictable regularity, usually involving numbers or space. In every pattern, the various elements are organised in some regular fashion. The way a pattern is organised is called its "structure," which may be numerical or spatial. In…

This reprinted "Mathematics Teacher" article gives a brief history of the mathematics of Escher's art. (Contains 9 plates.)

Visual intelligence is a key element in the thought processes of the most capable and creative among individuals, and this intelligence is closely related to analogical thinking, a learner's ability to make connections between prior knowledge and newly presented information. This article describes an approach to teaching scientific inquiry at…

A strategy is presented for teaching arithmetic to students with mental retardation, based on subitizing, skill of recognizing number of objects in a set without actually counting, and pattern recognition. The strategy helps children understand concept of addition by representing number configurations on 5-frames and 10-frames, and reduces need…

An approach to teaching sequences is described. The method is based on finding generating functions. (SD)

Abstraction is a major concept in computer science and serves as a powerful tool in software development. Pattern-oriented instruction (POI) is a pedagogical approach that incorporates patterns in an introductory computer science course in order to structure the learning of algorithmic problem solving. This paper examines abstraction processes in…

Developed to provide supplementary instructional strategies for reading teachers at the kindergarten level, this booklet presents the instructional module for completing patterns, a component of the Comprehensive Reading Program of the Chicago Public Schools. After an overview of the module, activities are suggested for the following areas:…

Procedures using calculators are described for determining the recurring sequence of digits in the decimal representation of numbers of the form 1/n. (MN)

The relation between the area of a rectangle and its perimeter is clarified by looking at patterns. Several examples involving rectangles with integral sides are presented. (MNS)