She did not transfer spontaneously from TopoMath to Solver. I had to keep reminding her to use schemas and to name her variables appropriately. Need to add the transfer text that I made for my class. it was emailed to Sara & Jananie today. I wish the solver could give feedback on compliance with these criteria, but that’s hard. Below the text but the formatting is screwed up. It should be added before the first Solver problmes used in training. and abbreviated, reminder versions should be included before the other solver training problems, and before the post-test of the TopoMath students.
When using the Solver, a problem is considered correctly solved if one of the variables has the correct, sought value. For example, suppose the problem is:
Jack and Jill like to exercise together. Jack ran 5 miles at 10 mph. Jill walked 2 miles at 3 mph. They started at the same time, and Jack got finished first. So while Jill was walking, Jack spent part of his time running and part of his time waiting. How long was his wait time?
The correct wait time is 0.166666 hours. Here are three correct solutions that could be entered into the Solver:
Cryptic solution:
2=3(5/10+x)
Good solution:
5=10TJack
2=3TJill
TJill = TJack + Wait
Best solution:
DJack=RJackTJack
DJill=RJill*TJill
TJill = TJack + Wait
DJack = 5
RJack = 10
DJill = 2
RJill = 3
In the Cryptic solution, x=0.16666 so it is correct. In the other two solutions, Wait=0.16666 so they are both correct. All these solutions would get full marks.
However, the Best solution is easiest to understand and thus less likely to have a mistake. A Best solution has three properties:
Every equation corresponds to one single additive or multiplicative relationship.
Every variable has a descriptive name.
The numbers in the system description (parameters) are also assigned descriptive names.
A Good solution has the first two properties but not the third. The TopoMath training module, which only some of you are required to take, teaches you to create solutions with all 3 properties. That is, it teaches you to create Best solutions.
However, even if you know what a Best solution is, when you use the Solver, you can enter any solution you like: Best, Good, Cryptic, whatever. As long as one of the variables ends up with the right value, you’ll get full marks on that problem.
However, you are less likely to make mistakes when you enter a Best solution. In order to convince you of this, I analyzed the 29 Solver problems that students in the class have finished in the last two TopoMath units as of noon today. Of these 29 problems, 23 were solved using the three principles above, and 87% of them were correct. The remaining 6 problems had solutions that lacked the three properties, and only 50% were correct.
So if you want a high score on the exam on Tuesday 9/10, I recommend using Best solutions. If you use the solution methods you learned in high school, which tend to generate short, Cryptic solutions, then your exam score may suffer.
Why does this matter in the long run? All three solutions are models of the Jack & Jill system, but the Best solution is a much better model than the others. It is like the difference between a well-written computer program that is easy to understand and maintain, and a cryptic computer program that even its author can’t maintain. In this course, I want you to learn how to make good, clear models.
She did not transfer spontaneously from TopoMath to Solver. I had to keep reminding her to use schemas and to name her variables appropriately. Need to add the transfer text that I made for my class. it was emailed to Sara & Jananie today. I wish the solver could give feedback on compliance with these criteria, but that’s hard. Below the text but the formatting is screwed up. It should be added before the first Solver problmes used in training. and abbreviated, reminder versions should be included before the other solver training problems, and before the post-test of the TopoMath students.
When using the Solver, a problem is considered correctly solved if one of the variables has the correct, sought value. For example, suppose the problem is: Jack and Jill like to exercise together. Jack ran 5 miles at 10 mph. Jill walked 2 miles at 3 mph. They started at the same time, and Jack got finished first. So while Jill was walking, Jack spent part of his time running and part of his time waiting. How long was his wait time? The correct wait time is 0.166666 hours. Here are three correct solutions that could be entered into the Solver: Cryptic solution: 2=3(5/10+x) Good solution: 5=10TJack 2=3TJill TJill = TJack + Wait Best solution: DJack=RJackTJack DJill=RJill*TJill TJill = TJack + Wait DJack = 5 RJack = 10 DJill = 2 RJill = 3 In the Cryptic solution, x=0.16666 so it is correct. In the other two solutions, Wait=0.16666 so they are both correct. All these solutions would get full marks. However, the Best solution is easiest to understand and thus less likely to have a mistake. A Best solution has three properties: