In the primary grades, engaging in counting collections provides students with regular opportunities to make sense of numbers in dynamic ways, build social skills, and communicate about mathematics. This article aims to guide elementary educators through a team's process of planning and implementing counting collections in kindergarten. Counting…

Children with mathematical difficulties need to spend more time than typically achieving children on solving even simple equations. Since these tasks already require a larger share of their cognitive resources, additional demands imposed by the need to switch between tasks may lead to a greater decline of performance in children with mathematical…

There is a call for enabling students to use a range of efficient mental and written strategies when solving addition and subtraction problems. To do so, students should recognise numerical structures and be able to change a problem to an equivalent problem. The purpose of this article is to suggest an activity to facilitate such understanding in…

This is the second of three articles that draw on findings from Nunes, Watson and Bryant (2009): "Key understandings in school mathematics: a report to the Nuffield Foundation". The report was soundly based on research about how children learn mathematics, much of it done in the UK in the '80s. Most of the findings about algebra are very…

Students around the world have difficulties in learning about fractions. In many countries, the average student never gains a conceptual knowledge of fractions. This research guide provides suggestions for teachers and administrators looking to improve fraction instruction in their classrooms or schools. The recommendations are based on a…

A program is presented which enables a programable calculator to become a device to check the arithmetic computational skills of students. (MP)

The framework of Tharp and Gallimore (1988) was adapted to form a ZPD (Zone of Proximal Development) Model of Mathematical Proficiency that identifies two interacting kinds of learning activities: instructional conversations that assist understanding and practice that develops fluency. A Class Learning Path was conceptualized as a classroom path…

This document is a collection of activity-based mathematics lessons for grades K-4 from the "Ideas" department in "Arithmetic Teacher: Mathematics Education through the Middle Grades." Each lesson includes background information, objectives, directions, extensions, and student worksheets. A matrix is included which correlates…

The author recommends allowing elementary students to use pocket calculators, so that they may concentrate on the sense of a math problem without getting bogged down in computation. He presents calculator activities on place value, estimation, and arithmetic operations, suitable for grades 1-6. (SJL)

Included are activities published in this regular column in the "Arithmetic Teacher" from 1980-90 organized by topics and presented in a month-by-month format. Topics include estimation, fractions and decimals, geometry and spatial sense, measurement, number sense and numeration, problem solving, statistics and probability, and whole number…

Provides instructions and worksheets for activities on: (1) sorting sets (grades K-one); (2) telling place values of two-/three-digit numbers (grades two-four); (3) recognizing multiplication/division facts (grades four-six); and (4) computing problems that contain multiples of 10, place value problems, and subtraction problems with many zeros…

The NCTM Standards regarding whole number computation and computation and estimation are reviewed and explored. Activities for implementing this portion of the Standards in grades K-4 and 5-8 are suggested. (CW)

Students who can compute mathematical problems in their heads have learned a skill that is important for estimating and for understanding the number system. Practice activities that can help students master mental computation skills are described. (PP)

Presented is a problem involving a real-life situation involving simple ideas, computation, and a proof. A variety of other situations in which this type of problem may be applied are discussed. (CW)

Activities that illustrate a problem-solving approach to teaching grouping symbols, such as parentheses and brackets, are described. Suggested exercises, answers to those exercises, and variations of this activity are included. (KR)