The learning of multiplication facts has long been an important focus of the primary grades, but lasting mastery of facts requires a meaningful approach that develops all four components of mathematical proficiency (understanding, fluency, problem-solving, and reasoning). This article shares how visual imagery in the form of Quick Looks with dot…

This article considers the development of synthetic landscapes of multiplicative reasoning constructed by student teachers (pre-service teachers). It explores the implications of working in a way that integrates literature from Maths Recovery, Cognitively Guided Instruction and Realistic Mathematics Education approaches. The aim is to better…

"That was the day I decided I was bad at math." Countless times, preservice and in-service teachers make statements such as this after sharing vivid memories of learning multiplication facts. Timed tests; public competitive games, such as Around the World; and visible displays of who has and has not mastered groups of facts still…

We examine a 4th grade teacher's development of a constructivist-based, adaptive pedagogy (AP) approach--and its contribution to student multiplicative reasoning and outcomes, mixing qualitative analysis of segments from her interviews with quantitative analysis of her student outcomes on the state-mandated test. Her reflections indicate a shift…

The purpose of this study was to determine if a typical third-grade boy and fifth-grade girl and a boy with learning disabilities could benefit from the combined use of Direct Instruction (DI) flashcard and math racetrack procedures in an after-school program. The dependent variable was accuracy and fluency of saying basic multiplication facts. A…

This study aimed at investigating the progress of students' learning on multiplication fractions with natural numbers through the five activity levels based on Realistic Mathematics Education (RME) approach proposed by Streefland. Design research was chosen to achieve this research goal. In design research, the Hypothetical Learning Trajectory…

"Concept study" is described in this article as a collaboration of teachers to investigate images, analogies, metaphors, exercises, and other experiences that are used to support students' understandings of concepts. The discussion is illustrated with the examples of multiplication and prime numbers. (Contains 3 figures.)

Learning mathematics has traditionally been thought of as a sequential progression. Children learn to count to 10, then to 20, and then to 100. They learn to add without regrouping and then with regrouping. The authors teach addition before multiplication and the two-times table before the six-times table. They usually teach division as a separate…

Provides four pages of practice problems covering the skills of multiplication, addition, and subtraction. Follows the premise that many arithmetic operations be done in working toward a solution. The sheets could be photocopied as worksheets or handouts. (JM)

Presented is an activity where students determine the multiplication tables of groups of small order. How this can be used to help develop an understanding of the concept of group isomorphism is explained. (KR)

Problem Solving in Mathematics (PSM), a program of problem-solving lessons for grades 4-9, is designed to be integrated into the regular mathematics curriculum. Although the content objectives of the lessons are similar to those of most textbooks, PSM emphasizes problem-solving skills and a variety of instructional strategies which foster the…

Presents five activities focusing on mental computation and estimation for the K-3, 3-5, 4-6, and 6-8 grade levels that require the student, acting as a judge, to review solutions to problems and to pronounce and justify a verdict. Provides suggested materials, questions, possible extensions, answers, and worksheets for each activity. (MDH)

Presents four innovative game-oriented activities designed to reinforce computational and place value skills involving whole and rational numbers. The games ask students to use randomly chosen numerals to formulate problems involving given operations or concepts whose responses come closest to target responses. (MDH)

This publication is a resource for those who teach basic mathematics to adults. It assumes very little knowledge or formal mathematics by teachers, tutors and students and provides background, strategies and rationale for people inexperienced in teaching adult numeracy as well as new ideas for the experienced teacher. The worksheets and activities…