Blog # 6 Whole Numbers

Chapter 10 to 12 are very useful for me as a Kindergarten teacher. We have practically two years to lay the foundation of mathematics for our young children and  we should do it right. As our friend Jerome Bruner suggested, teaching should start with concrete material ( enactive represetation ), then in pictorial forms  ( ikonic representation ) and finally in abstract terms ( symbolic representation ) . As I read through the chapter, I am mindful if I have been teaching numbers, tens and ones, addition and subtraction, etc., in a systematical way; and whether I have missed out any step that may be detrimental to children's understanding and learning process. I also ook out  for any class activities that I can use to reinforce the concepts.  It was a time for self reflection and do some serious stock taking.


Concepts  that are in place in preschool :

Ten and ones :
       Introducing the concept of 10s and 1s. First by counting in ones (unitary), then by grouping concrete materials into bundle of 10 and counting in 10s ( Base-ten).  Teacher will also match grouping by numerals, placed in labeled places and eventually written in standard form.

     BUT  we do not  expose children to equivalent or nonstandard base-ten approach. such as  that memtioned on p.189  ( Figure 11.1)   53 can also be represented by 3 tens and 23 ones.  In  fact, some teachers frown upon it when they see children represent tens and ones in this form, deeming it as unconventional , confusing, or not yet reach the undertanding of the tens and ones concept.  However, we should adopt Diene's idea of allowing variety in teaching mathematics, in the use of materials and in different ways of representing a math concept. THis kind of exposure provide opportunity for children to approach the concept in different angles and will eventually increase their uderstanding and facilitate the application   of the concept in the long run.

Introduction of traditional algorithm

     Teachers will definitely include  addition, subtration, multiplication and division  in the curriculum using the traditional algorithm. 

     But seldom will we encourage student-invented strategies in the math calculation. By observing children's explanantion and demonstration of their invented algorithm, teachers can have a glimpse of their processing skills  and understanding of concepts.  In fact, experts find that children make fewer error in self invented strategies, develop better number sense, forming basic of mental computation and estimation. Moreover, they are flexible and oftern faster methods of mathematic computation.  Thus, in Chapter 12 , the authors call for a delay in  the introduction of traditional agorithms but put in more time to understand how chldren derive they own solutions to the problems.

There are many more refreshing strategies fo teachng mathematic in the text. Happy exploring.

Tr Anita