Date: Jul 1, 1995 2:14 AM Author: Kevin J.Maguire Subject: Re: What are the "basic" facts?

On Sat, 1 Jul 1995 MCotton@aol.com wrote in response to Norm Krumper:

> How can students understand the above concepts if they don't know their

times tables?

> By pushing buttons on a calculator so that the magic black box can give

them some numbers?

Marge raises a very fundamental question in teaching/learning. What

comes first? To teach the number facts and then the concepts underlying

them? Or the other way round?

I guess that most of us either involved in primary (elementary)

education or interested in the learning growth of young children realise

that when children first come to school they possess "intuitive"

strategies which helps them to solve word-problems in the four

operations. The preparatory year (kindergarten) children I have been

involved with over the last month or so constantly amaze me with their

ability to solve quite complex word problems (for them) without having

the "formal" number fact knowledge. Perhaps we can blend the two

approaches to help all children grow to love and use mathematics as a part of their

daily life.

In regard to the use of calculators the following example may

throw some light on (or cloud?) the issue. I wanted to introduce the

inter-relationship between the four operations to a group of year three

children. We sat down on the floor with a pile of "counters" in front of

us. I had produced a sheet with a number of word problems which required

the use of one of the operations. These problems were inter-related such

that each was a re-phrasing of the other but in each case the unknown was

different. As these children had previously been in a rather "formal"

class they were not accustomed to manipulatives and modelling. Their

knowledge of number facts was rather limited and their ability to derive

facts from the known was also limited. As a group we read the problems a

couple of time as I asked these children what we had to find out.

This was followed by modelling (in Aust. we double the "l" when adding

"-ing") the problem. The calculator was used to "solve" the algorithm as

I was not so much interested in "getting the right answer" as I was in

helping these children develop the concepts of inter-relationship between

the four operations.

I hope to think that these children - now a few years down the

track - have a better understanding of these concepts. What I am saying

is that calculators *do* have a use but one should always be cognizant of

the aims.

Regards,

K.

Kevin J. Maguire

School of Education Telephone: 61 3 9479 2080

La Trobe University

Melbourne

Victoria