Making mistakes during maths learning is a common step to mastery of its concept.
This is possible, provided the learners pick up the error made and understand them through detailed analysis.
I came across an error that puzzled me for quite some time.
The error made: Inverting y = 2x + (1/x) became 1/y = (1/2x) - x
What actually happen in the thinking during the math manipulation?
Understanding the thinking will definitely help in resolving the issue and prevent further mistakes made.
Here, I believe the student:
- confused "flipping" cards with the basic concept of maths (flipping the left y does not equate to individually flipping the right mathematical terms)
- confused the property of indices ( 1/a = a-1) with this operation, resulting in the last term having a shocking "-" appearing after the inversion of denominator to numerator placement.
- lack practices to enhance the algebraic manipulation during the learning phase. Knowledge is not retained.
Analysing maths error is not an easy task if done alone, and without guidance.
The thinking part is an abstract art of the mind. If there is no communication to reveal the mental procedure in solving the math question, a skilled guess has to be made especially by those teaching maths.
If guidance is not available, textbook will be the next best alternative to answer for the mistake encountered. Go back to basic to dig out more understanding.
The approach is to question and question till satisfied. It will cover most aspect of the learning objectives.
However, do note that identifying and analysing maths error is a great learning process.
It serves to filter out current bad learning habits and replaces the gap with proper systematic steps. This is of much importance especially in maths where every steps count.
Therefore, do enjoy "debugging" your maths error. It is fun and not meaningless!
Errors do tell many stories. Just be friendly to them.