Math101 · Independent Ontario learning library
Math101How to Practise Mathematics
Mathematical practice is deliberate when each item has a purpose: acquire a new procedure, strengthen recall, discriminate among methods, or transfer an idea to a new setting.
Make practice deliberate: choose a purpose, attempt independently, use timely feedback, classify errors, and test the correction on a changed problem.
Intuition and core definition
Mathematical practice is deliberate when each item has a purpose: acquire a new procedure, strengthen recall, discriminate among methods, or transfer an idea to a new setting. Quality comes from attempting, receiving timely feedback, explaining errors, and varying the problem—not from the raw number of exercises completed.
Notation, language, and conditions
A blocked set contains one problem type; a mixed set interleaves types. A near-transfer item changes surface details while preserving the method, whereas a far-transfer item places the idea in a less familiar context. Accuracy, independence, explanation, and time are separate measures; speed should not be pursued by sacrificing the first three.
Why this idea matters
Practice becomes deliberate when each attempt has a target, receives diagnostic feedback, and is followed by another problem that tests the corrected reasoning.
A dependable method
- Choose the purpose of the set and a small number of representative problems.
- For a new skill, solve one example with support and then one closely matched item without support.
- Mark confidence before checking so guesses and secure answers are not treated alike.
- Classify each error as concept, method selection, execution, notation, or interpretation.
- Retry corrected items after a delay and include one variation that changes the required decision.
