© 1996: The University of Newcastle: Faculty of Education
The Restaurant Problem
The now-familiar "restaurant problem" provides a suitable first example of the way in which a graduated help facility might be developed. While such a facility would be most appropriate within a computer-based learning environment, it is by no means restricted to this. Suitable support may be offered in a written format, or on cards, available to students when needed.
The problem is reproduced here from Clements and Ellerton (1991, p. 3).
Three women went into a restaurant and ordered a meal which, according to the menu, cost $10 per person. After finishing their meal, each person handed the waiter $10. The waiter then took the $30 (= $10 + $10 + $10) to the restaurant manager, who said to the waiter, `Those three are good customers - here, take $5 and give it back to them as a discount'. The waiter, on receiving the $5 note, thought to himself: `Hmm, it's a bit hard to share a $5 note between three people. What I'll do is I'll give them a $1 coin each, and tell them that the manager said that each of them was being given a discount of $1 because they were valued customers. Then I'll keep the remaining $2 for myself.'
The waiter did just what he said he would do. Hence, each customer paid $9 (= $10 - $1) for her meal. Now, 3 x $9 = $27, and the waiter kept $2 for himself, so $27 + $2 = $29. Where has the other dollar gone?
Graduated help may be developed for this problem as follows:
- * Level 1: General information
Read through the problem again, then see if you can identify the relevant information from the question which will help you to understand what is happening. (You might underline each piece of useful information).
- * Level 2: Specific information
Where does the problem occur? Explain in your own words to someone else what the question is asking.
- * Level 3: Suggest action
Try making a list of the money that changed hands in this situation. Who did it go to?
- * Level 4: Suggest sequence
You will need to be clear about money which is SPENT in this encounter (WHO spent money? How much?) and money which is EARNED (WHO earned money? How much?)
- * Level 5: Demonstrate
Think about the money SPENT: The three ladies spent $10 each, a total of $30. They received back $3, so a total of $27 was spent.
Both the waiter and the manager EARNED money. The waiter "earned" $2 and the manager earned $25 - a total of $27.
When thought about this way, there is no "missing dollar" - all money is accounted for.
The problem arises because the final description of the situation confuses money "earned" with money "spent", but does so in a way that sounds perfectly reasonable.
This is a problem situation which does not require a high level of mathematical knowledge or skill, but rather it requires clear thinking and a systematic approach. As such, the graduated help needs to lead the learner towards this systematic approach slowly, so that the student is encouraged to think carefully and to re-examine the problem situation. Many students will need only the first level or two of help, and then be able to produce an adequate solution themselves. In this way, they are encouraged to develop independence rather than reliance upon the support structure. For those who need greater assistance, however, this is available as required.
Graduated help.
Sample Problem 1.
Last updated: 1st May, 1996
Stephen Arnold
crsma@cc.newcastle.edu.au
© 1996 The University of Newcastle
© 1996: The University of Newcastle: Faculty of Education