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