This article describes techniques to help students learn from their mathematical mistakes and so improve their approach to solving mathematical problems..
What are mistakes and how do they occur?
(1) Be clear to distinguish a mistake (which is about a correction) from a competency gap(which is about skill acquisition)
(2) mistakes-in-thinking (in concept formation and experimentation)
i. misuse or wrong selection of formulae
ii. misunderstanding of a question
iii. misunderstanding of core concept(s)
- Is this a common-error made by the student ?
iv. lack of competency with electronic calculator
(3) errors-in-solutions (in summative assessment)
v. silly written (elementary arithmetic or algebraic) slip
vi. lack of (intermediate) working
- Is this caused by a lack of competency in solution layout ?
- Is this caused by exam time-pressure ?
vii. silly electronic calculation slip
viii. misunderstanding of a question
What can a student learn from making a mistake ?
(1) shows they have tried
(2) gives them ownership of the learning
(3) shows them what doesn’t work
(4) they might notice a concept or pattern
(5) can understand andtalk about the problem a little better
(6) understanding WHY amethod didn’t work can lead the student to the correct solution
(7) makes the eventual moment the solution is found so much sweeter!