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

On Sat, 1 Jul 1995 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.

Kevin J. Maguire
School of Education Telephone: 61 3 9479 2080
La Trobe University