29 Jan

Applying Maths In New Situations

One of my students really struggles to take her knowledge and use it in new situations. Any tips?

The way students usually learn new concepts is quite progressive. You can see this in the structure of any text book. Usually the first questions in an exercise are very simple questions based around performing the same arithmetic processes again and again. Then the questions become increasingly different such that the student is not able to succeed by applying the rule or formula in the same exact manner. This forces students to think about how the rule/formula/concept needs to be applied and creates meaning and comprehension. The hardest questions of course are those long worded ones where the student must make sense of the questions first and then figure out how to apply their knowledge.

You need to consider at which point on this spectrum the student usually starts to have challenges in applying knowledge. It is quite common that students have troubles with those long worded questions – mastery of these types of questions takes time and considerable effort. Problem solving is a serious skill and if this is where your student struggles then there are various approaches to start developing problem solving skills on this high level. However, if your student is starting to struggle on simple problems which vary only slightly from the most obvious application then it may be indicative of a variety of problems:

  • Perhaps the student does not have the confidence to think for themselves and continues to rely on the simple certainty of just applying a rule. Application in math requires for a student to do their own thinking and this always includes the possibility of being wrong which is a big deal for students who are insecure about their intelligence.
  • Perhaps they do not know how to seek understanding and when they learn a new concept or attempt questions they are incorrectly focussed. Attention needs to be on comprehension and understanding why a rule works the way it does, and then application becomes a lot easier. Many students approach math from the frame of mind “What do I do to get the answer” rather than “what does this mean, why does it work this way, what if I tried it with other numbers would it still work?” etc.
  • Perhaps the student is not correctly putting pen to paper and getting caught up in their own thoughts – tripping over their own feet in a manner of speaking. Putting pen to paper correctly and formatting skills are crucial in applying knowledge.

It is hard to answer your question because “trouble in applying concepts” is such a generic problem. However, the following skills are probably lacking to various extents:

  • It’s Ok To Be Wrong
  • Problem solving skills/methods such as self questioning, Understand-plan-do-review
  • Pen to paper/ format skills

Obviously it is hard to seriously work on all these problems while tutoring a student for only one hour per week and having to spend most of that time covering class content. You should evaluate what will be most useful for the student, discuss it with them and move in that direction.

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