I received several interesting comments on my second post about IMP. One of them is below. I am preparing an answer to others.
Andre Toom Department of Mathematics firstname.lastname@example.org University of the Incarnate Word Tel. 210-646-0500 (h) 4301 Broadway 210-829-3170 (o) San Antonio, Texas 78209-6318 Fax 210-829-3153
---------- Forwarded message ---------- Date: Tue, 15 Apr 1997 13:40:35 +1000 From: Jan Thomas <JanThomas@fox.vut.edu.au> To: Andre TOOM <email@example.com> Subject: Re: IMP (fwd)
I was interested in the actual reading of the problems. In the following for example: > >Example 1. On p. 67 there is the problem `A Fractional Life': >``Demochares has lived a fourth of his life as a boy, a fifth as >a youth, a third as a man, and has spent 13 years in his dotage. >How old is he?''
I suspect that many students would get stuck on 'dotage' - how often have you heard students use it? So unless they have some strategies that tell them (for example) to read the problem, underline or highlight words they don't understand and find the answers to those questions, then ask what does this question say and what do I have to do, they never get to the mathematics.
This is common in solving word problems of all types. Students have no reading attack skills so they never actually get to the mathematics.
Re: >``Pete spends 1/3 of his time for study. 1/4 for soccer, >1/5 for misic, 1/6 for TV, 1/7 for solving math problems. >Is it possible to live in this way?'' I think this is more funny.
Not only is this funnier, it uses language students would see as 'friendly'. > Re:
>Example 2. `The Haybaler Problem' on p. 198. Full text: >``The Situation. >You have five bales of hay. >For some reason, instead of being weighed individually, >they were weighed in all possible combinations of two: >bales 1 and 2, bales 1 and 3, bales 1 and 4, bales 1 and 5, >bales 2 and 3, bales 2 and 4, and so on. >The weights of each of these combinations were written down and >arranged in numerical order, without keeping track of which weight >matched which pair of bales. The weights in kilograms were >80, 82, 83, 84, 85, 86, 87, 88, 90, and 91. >Your Task >Your initial task is to find out how much each bale weights. >In particular, you should determine if there is more than one >possible set of weights, and explain how you know. >Once you are done looking for solutions, look back over the >problem to see if you can find some easier or more efficient >way to find the weights. >Write-up. >1. Problem Statement. >2. Process: This is especially important in this problem. >Include a description of any materials you used. >Be sure to discuss ways in which you tried to attack >the problem but which didn't lead anywhere. >Also discuss any insights you had after working on >the problem about other ways you might have solved it. >3. Solution: Show both how you know your weights work and how >you know that you have not missed some other possibilities. >4. Extensions. >5. Evaluation. >Adapted from Problem of the Week by Lyle Fisher and Bill >Medigovich (Dale Seymour Publications, 1981).'' > >Ooh, I have typed all the problem. >It takes two pages in the IMP book.
This, of course is not a real problem. In fact it is so silly it may as well just be presented without a context. If it takes 2 pages, it becomes a reading task, not a mathematical task and most students would rebel at the amount of writing they are expected to do in their report. Yes, students do have to read and write mathematics but we can't afford to turn mathematics into writing classes.
Re: >Soifer's formulation: >Problem 10.2. Four Knights. >Four knights are placed on a $3 \times 3$ chessboard: >two white knights in the upper corners, and two black ones in the >lower corners. In one step we are allowed to move any knight >in accordance with the chess rules to any empty square. >(One knight's move is a result of first taking it two squares >in horizintal or vertical direction, and then moving in one square >in the direction perpendicular to the first direction.) >Is there a series of steps that ends up with the white knights in >diagonally opposite corners, and the black knights in another pair >of the opposite corners ?
This runs into culture/background problems. If half the class don't know anything about chess, that will immediately upset comprehension. There is a lot of information in each sentence. This one looks to me like a linguistic mine-field.
So, if sudents have no reading skills specific to tackling these problems, I think there are real problems with them actually being able to do them without a great deal of help to get to the mathematics. Research in reading this type of material seems to be almost non-existant. So are teachers who have any idea of how to give kids some strategies.
Please share with the rest of the group if you think this is relevant.
Jan Thomas JanThomas@vut.edu.au Department of Education 61-3-9688 4401 (Business) VUT Footscray 61-3-9688 4646 (Fax) PO Box 14428 MCMC 041 900 6205 (mobile) Melbourne 8001 61-3-9328 1722 (Home)