To improve understanding of identities and inverses, and to provide a stronger foundation for future mathematics, Sandra Miles designed a two-part lesson that makes the relationship between identities and inverses explicit. This article illustrates Miles' teaching of the first part of the lesson, focused on addition and subtraction, and then gives…

Introducing the distributivity property of multiplication over addition is a well-known challenge in mathematics education, especially in primary school. As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation and evaluation of a modelling activity in which 2nd-grade students are…

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…

The aim of this study is to design learning activities that can support students to develop strategies for the addition of number 1 to 20 in the first grade by involving students' spatial structuring ability. This study was conducted in Indonesia by involving 27 students. In this paper, one of three activities is discussed namely ten-box activity.…

When solving mathematical problems, many students know the procedure to get to the answer but cannot explain why they are doing it in that way. According to Skemp (1976) these students have instrumental understanding but not relational understanding of the problem. They have accepted the rules to arriving at the answer without questioning or…

A teacher describes an activity designed to help children understand the number concepts of the basic addition facts with sums of 11 or greater. (CL)

This manipulative model using counters involves balancing the number of counters on either side of the equals sign. (MP)

The article presents two teaching strategies for use with elementary age educable mentally retarded students. The first introduces the concept of the equivalence of a nickel and five pennies in terms of buying power. The second strategy involves teaching students the skill of adding various combinations of nickels and pennies. (PHR)

Recent research has provided a reasonably coherent picture of how children learn to add and subtract. There is clear evidence that children do not learn simply by mastering a procedure and storing in memory. Instead, learning is structured in meaningful ways, connected to previous knowledge, and adapted to new contexts. This view of learning has…

Helping teachers to build a strong bridge from concrete experiences to algorithms is the focus. A detailed sequence of activities is described. (MN)

A teaching sequence provides a guide to instruction on initial concepts of fractions, equivalent fractions, and addition with fractions. (MN)

Another way to add and subtract, in which the mental regrouping strategy is applied to an original 10-structure, is presented. Pupils use a visual model, called "little person," to move from counting to visualization. Originally designed for use with pupils with learning disabilities, this method has wider applicability. (KR)

The author argues that children not only can but should create their own computational algorithms and that the teacher's role is "merely" to help. How children in grades K-3 add and subtract is the focus of this article. Grouping, directionality, and exchange are highlighted. (MNS)

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)

Five-frames are proposed as manipulative material to increase children's ability to identify the number of objects without direct counting. How to use frames and beansticks to construct basic facts without counting is discussed. (MNS)