We report here on an intervention implementing a structural approach to arithmetic problem-solving in relation to learning outcomes among preschoolers. Using the fundamental principles of the variation theory of learning for developing the intervention and as an analytical framework, we discuss teaching and learning in commensurable terms. The…

This article draws on some ideas explored during and after a writing workshop to develop classroom resources for the reSolve: Mathematics by Inquiry (www.resolve.edu.au) project. The project develops classroom and professional learning resources that will promote a spirit of inquiry in school mathematics from Foundation to year ten. The…

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…

The concept of exponents has been shown to be problematic for students, especially when expanding it from the domain of positive whole numbers to that of exponents that are negative and later rational. This paper presents a theoretical analysis of the concept of exponentiation as a continuous operation and examines the deficiencies of existing…

This article describes how teachers address issues and tensions that students meet in learning division of fractions. First, students must make sense of division of fractions on their own by working individually and in small groups, using concrete or pictorial representations, inventing their own processes, and presenting and justifying their…

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…

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…

Number sense has been recognised as central to young children's development of mathematics for a number of decades. A student with a "good" sense of number normally has a thorough understanding of relationships among numbers and operations--being able flexibly to partition and combine numbers in convenient ways to allow appropriate…

The author cites research from students' misconceptions of decimal notation that indicates that many students treat decimals as another whole number to the right of the decimal point. This "whole number thinking" leads some students to believe, in the context of comparing decimals, that "longer is larger" (for example, 0.45 is…

This book of supplemental exercises is one of a series of books designed to provide educational materials for students in addition to the instructional texts in the Adult Learning Skills Program. Exercises in this basic level book are for the mathematics subject area. Course numbers and exercise topics are: 101 (shapes, sizes, numerals, sequencing…

Suggests techniques for teaching students about Arabic contributions to arithmetic and to the English language. Students are involved in figuring out English derivations of 12 Arabic words and in deciphering Arabic symbols. (Author/DB)

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 booklet describes basic counting principles and provides activities designed to develop basic skills in: (l) stable ordering; (2) one-to-one matching; (3) total number; (4) different objects; and (5) different order. These are extended to more advanced strategies aimed at building counting skills strong enough to provide a basis for adding,…

Presents reviews of the following mathematics software designed to teach young children counting, number recognition, visual discrimination, matching, addition, and subtraction skills; Stickybear Numbers, Learning with Leeper, Getting Ready to Read and Add, Counting Parade, Early Games for Young Children, Charlie Brown's 1,2,3's, Let's Go Fishing,…

This is an effective drill and practice activity that does not use consumable materials. It does not teach math facts, algorithms or concepts. It provides immediate feedback to the learner and can be easily modified for use in many curriculum areas. It is self correcting because the student can identify errors without assistance and provides…