Challenge and Support Index

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© 1996: The University of Newcastle: Faculty of Education


Sample Problem 1

The next three examples are drawn from the computer-based learning environment, Exploring Algebra (Arnold, 1993). They would be suitable for high school students and assume access to computer or graphics calculator facilities.

If x = 2 and x - 2 = 0 are identical mathematical statements, then why does squaring one produce an equation with TWO real solutions, while squaring the other produces only one? Investigate.

Now try to solve the equation

Graduated help was developed for this problem in the following format:

Constructing graduated help in this way is no simple task. It is important to avoid "giving the game away", even at the last level, while at the same time, providing increasingly clear directions which will assist in the solution process. Notice that level 1 provides broad, general mathematical information which (while relevant to the problem) does little to move the learner towards a solution, and level 2 is effectively a rewording of the problem. Both are important since students must be given every opportunity to provide a solution themselves, and often this simply involves re-reading the task. The increasing levels of support then move from a single action to a sequence, before finally giving fairly explicit instructions.

The restaurant problem. Sample Problem 2.


Last updated: 1st May, 1996
Stephen Arnold
crsma@cc.newcastle.edu.au
© 1996 The University of Newcastle


Challenge and Support Index

Courses | Software | Readings | Links | Comments?

© 1996: The University of Newcastle: Faculty of Education