Mixing the problems up

Practising one kind of problem twenty times in a row teaches the method; mixing several kinds teaches which method to pick, and picking is what a test and a job actually ask for.

Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.

What it is for

They could all do it in the lesson and none of them could do it on the paper, and nothing went wrong in between. In the lesson every question was the same kind, so nobody ever had to decide which method to use, and on the paper that decision is the question. Your own practice here is mixed rather than blocked for exactly this reason: you are never handed ten running records in a row.

How to think about it

Keep the first block of practice pure, so the method gets built. Then mix it with the two or three kinds it is most confusable with, and let the choosing be the difficulty.

Worked example

Block first: 6 items, adding fractions only

The method itself, while it is still new. Blocking is the right thing here.

Then mix: add, subtract, add, compare, subtract, add

The same number of items. Now the first move is deciding what kind of question it is.

Mix with what it is confused with

Adding fractions mixes with subtracting them, not with long division. Confusable, not random.

Expect the mixed set to feel worse

Fewer right in the lesson and more right three weeks later. Both of those are normal.

Your turn

A practice set has 6 blocked items and then 12 mixed items. Write the line that totals the set.

6 blocked + 12 mixed =  items

The trap

Mixing on day one. A method that is not built yet cannot be chosen between, so blocked practice comes first and mixed practice second, and that order matters more than the ratio.

Practise interleaving on HoneA question on it now, a real problem where there is one, and it is remembered for review. Free, no email needed.