To troubleshoot any difficulty you first look at the broad area of that difficulty, and then you gradually narrow it down until you have defined the actual difficulty precisely.
So, to troubleshoot a difficulty in math you start with the broad area of Mathematics.
Mathema (Greek) = Learn
Mathematics = Tools for learning
Mathematics provides you with analytical tools for learning. When you are troubleshooting mathematics, you are troubleshooting the difficulties a person is having with learning analytically. You narrow down to the area of mathematics where the person cannot think analytically.
Mathematics is analytical learning and not just memorizing of materials.
If the student is having trouble with higher mathematics, such as, Trignometry, Analytical Geometry, or Calculus, then start from there. You may explain the area the student does not understand. But if the student cannot understand the explanation analytically, then the troubleshooting may lead to one of the three areas below.
When you select one of these areas, explain it per Math Overview. You do not have to explain that whole document. Keep to the trail of trouble.
Ask, “What part of this area you have most difficulty with?”
Use the answer to narrow down further to the area of difficulty. Quiz the student on the key math vocabulary in that area. From student’s answers you may narrow down the area of difficulty further.
If the student cannot answer the question, simply start with the first lesson
related to that area at Mathematics. Follow student’s attention to fish around for the actual difficulty.
As you narrow down the area of difficulty, keep asking, “What part of this area you have most difficulty with?”
Check the key math vocabulary in the narrowed down area. Soon you’ll reach the actual difficulty. Handle it using the right materials selected from the appropriate level at Mathematics, or from student’s own materials.
Once that area is handled, the student may come up with another area that he or she has attention on. Narrow down to the actual difficulty in that area as above, and handle it.
Otherwise, start all over again from the diagram above. This time you may follow a different trail to a different area of difficulty.
Ultimately, teach the student how to troubleshhoot difficulties. This is the best thing you can ever do for the student.
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