Teaching of Number Sense

I agree with the Van de Walle (2010, p. 125) that children come to school with their ideas about number and our task is to help them develop "new relationships" and extend their understanding.

The framework of the Mathematics curriculum by Ministry of Education (MOE, 2006) states the learning of mathematics involves more than learning of concepts; it involves the understanding of underlying mathematical thinking, the strategies to problem solve, the positive attitudes, and the appreciation of mathematics as an important and powerful tool in everyday life. This is congruent to the big ideas by Van de Walle (2010, p.125) when he states that the "number concepts are intimately tied to the world around us" and by applying number relationships to the real world settings, it marks the "beginning of making sense of the world".

In the preschool, the number concepts that we introduced are:
1) the relationships of more, less, and same
This is one concept that we can introduce to the preschool children. Children as young as 3 year olds are able to tell that a tray with five bear counters is more than a tray that contains 1 bear counter.

2) Problem structures
Be it join problems, separate problems, part-part-whole problems or compare problems, our school curriculum only covers the simplier problem structures that require less than 3 steps to solve the questions given.

In the preschool years, children learn from concrete to pictorial to abstract (CPA approach by Jerome Bruner). When doing the problem sums, we use concrete materials (e.g. unifix cubes or counters) to help children understand and reinforce learning through the introduction of models. We did not use the number line concept to solve story problems. I believe, both methods work equally well, as long as we introduce the appropriate tools to the appropriate age group to help them understand what is happening in the story problem.

Other mathematical concepts that we taught in the preschool are:

1) Numeral writing and recognition

2) Counting on and counting back

3) Patterned set recognition

4) Part-part-whole relationships (based on single number)

5) Addition and subtraction

6) Estimation and Measurement

7) Data Collection and Analysis

In my school, we did not teach the following concepts:
a) Doubles and near-doubles
This is an interesting concept and I would like to try this out. When children understand part-part-whole concept, the doubles and near-doubles strategies strengthen children's understanding of basic addition facts. However, this can be challenging, even for the K2 children.

b) Anchoring numbers to 5 and 10
Though teaching the anchoring numbers to 5 and 10 is an useful way to help develop thinking about various combinations of numbers, it is not an easy task for the 6 year olds children. The five-frame or ten-frame provide opportunities to train children to "see" the relationships among numbers, and when the children are familiar with the relationships among numbers, we have also trained them in terms of mental computation skills.

The development of number concepts and number sense cannot be underestimated, and children need to have a good foundational ideas in order to extend their learning to larger numbers and computation.