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Learn Math by making mistakes!

April6

It has been a long couple of weeks setting exams, working out solutions and then marking. Of course, given the pressure that we are often under, mistakes do happen – both in the papers and solutions, and in the students’ answers. However, you do need to realise that making these mistakes is a real positive, but only if you learn from them! A group of sophomore students were seen recently by H3 pouring over a problem that they had got wrong. The real learning was taking place as they eventually figured out how to get the correct answer. They needed to revisit the wording in the question to understand it fully. It was an excellent exercise in making mistakes to learn!
math error
This reminded H3 of this helpful article:

“Success is Failure Inside Out!

“Think like a mathematician and learn from your previous mistakes. In order to do so, I would suggest that you keep a record or journal of the patterns of errors. Mathematics requires a lot of practice, so review the concepts that caused you grief from previous tests.

“Keep all of your marked test papers, this will assist you to prepare for ongoing summative tests. Diagnose problems immediately! When you are struggling with a specific concept, don’t wait to get assistance (that’s like going to the doctor three days after breaking your arm) but get immediate help when you need it, if your tutor or instructor isn’t available – take the initiative and go online, post to forums or look for interactive tutorials to guide you through.

Remember, mistakes in Mathematics can be your friends!” (adapted from a longer article here)

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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