Interleaving: mix problem types once you know the basics
Practising a mix of problem types feels harder than doing one type at a time, and it teaches you more, because it trains the skill of choosing which method applies.
The evidence
In Rohrer & Taylor (2007), The shuffling of mathematics problems improves learning, Instructional Science 35, 481–498, students who practised shuffled mathematics problems did worse during practice than students who practised one type at a time, and much better on a test a week later.
In Kornell & Bjork (2008), Learning Concepts and Categories, Psychological Science 19, 585–592, people learned painters' styles from examples. Those who saw the painters mixed together were better at identifying the artist of new paintings. Most of them still believed that seeing one painter at a time had worked better.
Dunlosky, Rawson, Marsh, Nathan & Willingham (2013), Improving Students' Learning With Effective Learning Techniques, Psychological Science in the Public Interest 14, 4–58 rated interleaved practice as moderately useful: promising, with a narrower evidence base than testing or spacing.
How to do it
- Learn each method on its own first. Interleaving helps you discriminate between things you already half-know.
- Then shuffle. Mix old and new problem types so each one first asks "which tool is this?"
- Expect it to feel worse. That difficulty is the point.
Sources
- Rohrer & Taylor (2007), The shuffling of mathematics problems improves learning, Instructional Science 35, 481–498
- Kornell & Bjork (2008), Learning Concepts and Categories, Psychological Science 19, 585–592
- Dunlosky, Rawson, Marsh, Nathan & Willingham (2013), Improving Students' Learning With Effective Learning Techniques, Psychological Science in the Public Interest 14, 4–58