New answers tagged reference-request
1
As far as "just practice", you shouldn't trivialize this or think of it as so simple as yes, no. Your job is to train the trainee. Many errors are common and repeated. So? This is not so different from sports or music. Develop a set of drills, games, etc. Try different things with different people.
The problem here is not so Boolean as math ...
4
When there is an obvious way to check the final result, don't give partial credit to students who make a mistake and fail to catch it. If they're solving a system of equations, they should be checking by substituting back in. If they're integrating, they should be checking by differentiation. Do give partial credit if they do the check on an exam, but run ...
1
I remember getting my first 18 inch slide ruler. I had worked hard, poison oak filled, hours making fire breaks in the Oakland hills to make enough money to get it. It was aluminum, had a spring loaded cursor that slid like it was greased, and the C and D scales (I think) lined up perfectly. It was huge and had scales I was never going to use. I loved it.
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3
Teach methods for verifying results.
Often once you have an answer, there are simple calculations to check its correctness. For example:
Numerical calculations: round the results and compute backwards. Example: if you get 1234 * 56 / (789 - 987) = 349, compute e.g. 300 * (700 - 900) / 50 = -1200 which is not close to 1234, because of the dropped minus sign.
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1
I believe that the majority of students with this problem are doing what is called "end-gaining" in the Alexander Technique:
https://www.hilaryking.net/glossary/end-gaining
I'm not an expert, but I think that in this case, it means that they are overly focused on getting to the end of the exercise, and they have a mistaken belief that the means for ...
14
I used to have this problem. What helps me more than anything is:
Solve it two different ways if you can and make sure they agree
If you are finding a general formula, test it on some examples
If neither of the above are possible, re-read every step of your work with an attitude like it's trying to sell you a used car.
Adopt the useful exaggeration that ...
0
When I was thinking about a similar question, I found the article "What is an equation" by S. Marcus and S.M. Watt ( https://www.academia.edu/3287674/What_is_an_Equation ) As far as I understand they discuss the difference between "equation" and "equality" in some languages. In some language (like english) there is no difference,...
21
Ask the student to "talk through" their calculations
Having a student verbalize their calculation may force them to pay more attention (or a different kind of attention) to their work that causes them to catch the errors as they make them. This feels very related to rubber duck debugging. At the very least, if you're working with a student one-on-...
2
Allow and promote using a calculator
This is one of the recommendations listed for accommodating students with dyscalculia, but this could help whether or not a student has dyscalculia. It's not really coaching and it doesn't address the underlying source of errors, but at the very least it will keep those arithmetic errors from cropping up and getting in ...
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As pointed out by @AmyB and @DanielRCollins, an equation is simply a statement that two expressions are equal.
@Adam remarks that the equation-identity distinction doesn't seem useful; on the contrary, it is instructive to distinguish an identity from a mere equation:
Let $z\in\mathbb C,$ $\;C_n$ denote $\left(z^2-2z\cos\left(\frac{n\pi}9\right)+1\right),$ ...
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