In the USA, the Common Core Standards in Mathematics for the early grades (K-3) are designed to build on and develop students' number sense as students gain understanding of the structures of addition, subtraction, multiplication and division. It is well understood in teaching circles that subtraction is notoriously more difficult for students…

It is frequently surprising to new teachers (and even those with experience) when they find that not only do some children need to recount the group they have just counted to be assured of the total but also that this need seems to be resistant to intervention. Although moving from "counting-all" to "count-on" is sometimes…

Jill Cheeseman and Deborah Michels let us eavesdrop on a young child's attempt to solve a four-digit subtraction. In the process they describe the use of an empty number line as a tool for describing the calculation process. If you haven't tried using an empty number line, then the authors outline some compelling reasons for using empty number…

Action research (AR) is defined by Macintyre to be: "an investigation, where, as a result of rigorous self-appraisal of current practice, the researcher focuses on a problem,or a topic or an issue which needs to be explained, and on the basis of information, plans, implements, then evaluates an action then draws conclusions on the basis of…

Compares methods of subtraction used by children and teachers. Suggests ways to encourage children to invent their own subtraction algorithms. (CCM)

In this article, the author presents a new maths aid for teaching place value, addition and subtraction up to 1 million. The need for a resource to help his wife understand place value motivated the author to create "Counting Cards". Here, he shares his invention, in the hope that it will help others. (Contains 4 figures.)