To Be Presented in the 11th Asian Technology Conference in Mathematics December 12-16, 2006, Hong Kong SAR, China |
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## Designing Applets to Build on Intuition
## Abstract You have a match box containing an unknown number of matches, and are
told that if you had 2 more matches then you would have 9 matches altogether:
how many matches are in the box? Even before studying linear equations,
most school students correctly answer 7 to this question. However, many
students find it difficult to explain clearly how they arrived at the
answer ¡V for example, a common response is ¡¥because 2 plus
7 is 9¡¦, which is a demonstration that the answer is correct rather
than a explanation of the method of solution. In this paper we consider
the issues underlying the creation of applets to specifically build on
this basic mathematical intuition. One beneficial outcome is that intuition
itself is enhanced. We illustrate the general ideas underlying the use
of ICT to help develop mathematical skills at the junior level by looking
at an applet created specifically to support learners¡¦ intuition
in solving simple linear equations like the matchbox problem above. The
aim is not only to help improve learners¡¦ skills in solving more
general linear equations, but also to let them become aware that these
skills (the appropriate use of the operations of addition, subtraction,
multiplication and division) have built upon, and grown out of, their
¡¥natural¡¦ intuitive approaches. |
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