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How to use:
Make It True is a web application to practice fundamental algebra procedures used when manipulating equations. The application generates arbitrary equations containing 1-4 variables. It is for the student to provide values for these variables which make the equation true. For example, in the screenshot above the equation is: 18-64-c*d=4. The student must choose values for c and d which result in a true statement. One approach would be to solve for the product "c*d" and then choose 2 numbers whose product satisfies what's needed. Like this: 18-64-c*d=4 18-64-4=c*d c*d=-50 Then the student could pick any two numbers with product of -50, like c=-25 and d=2. Another approach would be to pick any number for c, then express d in terms of that number. For example, if the student arbitrarily chose c=13 then: 18-64-c*d=4 18-64-13*d=4 d=(4-18+64)/(-13) One caveat: The second approach described above is usually preferable. Why? Because "Make It True" carries with it the implied caveat "Make It True according to the computer". The computer experiences round-off error, so whenever division is present in the problem (usually!) then this potential exists. This is a good thing, however, as it further serves to help students appreciate the subtleties of mathematics on the computer. The Importance of Feedback: If you have entered valid values for the variables then the program will increment the "correct" score (top right number in green). If your values don't work out, however, don't worry! The program will not let you proceed until you provide values that do work. This may seem like a subtle point, but I believe it is of upmost importance for a student to have instant feedback rather than being allowed to proceed thinking that they know what they are doing, if, in fact, they don't. In fact, I will briefly digress here to point out that this is an area where software is very well suited for use in schools: As any teacher knows, finding time to carefully grade every thing from every student is difficult, to say the least. However, giving a student credit for work done incorrectly sends the wrong message. In the context of spelling it can cause kids to store an incorrect spelling in their brains. In the case of math it might be worse: They know they solved the problem in somewhat of a mysterious (to them) way, and getting credit for it might confirm to them that math really is mysterious and cannot be understood. So, having lots of practice is important for students, but leads to lots of work to grade. Ungraded work (lack of feedback) can have unintended consequences. One solution to this phenomenon is to let computers provide both the practice and the feedback at the same time. Future features: 1. Exponents to numbers and variables, both 2. Use of parentheses in generated problems 3. Please email if you have any ideas |
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Last Updated Sunday, September 04 2011 @ 02:15 CDT|8,861 Hits 