Computational thinking can provide a basis for problem solving, for making evidence-based decisions, and for learning to code or create programs. Therefore, it is critical that all students across the K-12 continuum--including students in the early grades--have opportunities to begin developing problem solving and computational thinking skills.…

The importance of developing reasoning and justification has been highlighted in "Principles and Standards for School Mathematics" (NCTM 2000). The Common Core State Standards for Mathematics (CCSSI 2010) further reiterates the importance of reasoning and proof in several standards for mathematical practice. Students of all grades are…

In an activity sequence that took place over several days, the class learned about sound and how people hear sounds. Following each activity, students engaged in whole-group sharing sessions and individual journal-writing sessions that were designed to help them see the patterns that emerged from their explorations. The activities were carefully…

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

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…

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…

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:…

Pattern work is now undertaken as early as kindergarten, and both researchers and teachers have discovered that children engage in pattern work with great enthusiasm and innate ability. Having some flexibility in pattern perception and selecting mathematically useful patterns require some training, although there is nothing particularly algebraic…

The focus is on the problem-solving strategy of find a pattern, with a problem explored to illustrate how to use the strategy. Other tips concern classroom climate, checking skills, research, and type of problems. (MNS)

Activities on estimation and mental computation are presented. Patterns on a hundred chart, an amazing fact, teaching and testing tips, and other references are included. (MNS)

An activity project is described which encourages students to question and experiment. Appendices provide examples of student results. (MNS)

Discusses that Gestalt principles are especially well suited to teaching music. Identifies the laws of proximity, similarity, common direction, and simplicity in the notation system. Suggests that music teachers use these principles by following a logical progression to teach students to improve musical skills, solve problems, and think in…

Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)

Briefly presented are suggestions on using exercises in number patterns in second-year algebra and factoring quadratics in a 10th-grade enrichment class. (MNS)

Presented are 44 examples in which students are invited to guess what pattern of numbers is emerging and to decide whether the pattern will persist. Topics of examples include Pascal's triangle, integers, vertices, Fibonacci numbers, power series, partition functions, and Euler's theorem. The answers to all problems are included. (KR)