Studying With AI? Mix the Problems So You Have to Choose the Method

A learner asks AI for ten questions on percentage change. By question four, they are working quickly. The next day they see a different worksheet: one question asks for a percentage increase, another asks what percentage one number is of another, and a third asks for the starting value before a discount. Suddenly the calculations seem harder. The first worksheet supplied a clue before every question: use the same method again.

There are two skills here. One is carrying out a method once you have chosen it. The other is noticing which method fits. If you need the second skill outside the lesson, give it room in the practice. An AI assistant can help create a mixed set, but only if the questions make you choose rather than quietly announcing the answer in a heading.

Why the order of examples matters

In blocked practice, problems of one kind sit together. In interleaved practice, different kinds appear among one another. A randomised classroom study by Doug Rohrer and colleagues, published in the January 2020 issue of the Journal of Educational Psychology, compared those arrangements in mathematics. The interleaved group performed better on a later test. That is evidence about the assignments and test used in that study. It does not establish that a random mixture is always better, or that AI is needed to prepare one.

A related 2008 study by Nate Kornell and Robert Bjork used paintings instead of maths. People studied examples from different artists, either with an artist’s work grouped together or with work by different artists mixed. When asked about new paintings, participants did better after the interleaved arrangement in the experiments reported. The task asked them to recognise a category from an example they had not seen before, a different kind of decision from repeating a calculation.

The practical lesson is to choose examples that are worth comparing. Mix things that are easy to confuse and give yourself a chance to explain the difference. Ten unrelated questions can be varied without training a useful distinction. Likewise, a short run of similar questions may still help while you are learning the steps for a new method. The point at which you mix them should follow what you are trying to practise.

Ask AI for a mixture with a reason

Suppose a shop owner is learning to read percentage figures in a weekly report. They can practise three decisions: find a new value after a stated change, work backwards to recover an original value, and express one amount as a share of a total. All three can be written about the same shop and use similar numbers. What distinguishes them is what the question gives you and what it asks you to find.

For example, a print priced at £40 is reduced by 25%; what is the sale price? A different print sells for £30 after a 25% reduction; what was its original price? And if £30 of a £40 order was for prints, what share of the order did the prints account for? The common numbers make it harder to choose by appearance. Before calculating, name the starting amount, the result you need and the relationship between them.

Ask the assistant to generate another set with the method names kept out of the questions, and ask for the key separately. Tell it to include plausible lookalikes: two questions may mention a discount while asking for different unknowns. Check the worked answers against the original question before sharing the set. A convincing explanation in the key can still be wrong or assume information the question never supplied.

Check the decision and the calculation separately

Start with a few problems you can solve with guidance if the methods are unfamiliar. Then close the example and try the mixed set. Write your choice before calculating, even if it is only a short note such as ‘I know the discounted price and need the original’. Mark both parts afterwards. If you chose well but made an arithmetic slip, you need a different kind of practice from someone who calculated accurately using the wrong relationship.

• Remove the heading clue. Use neutral question numbers, and avoid a predictable rotation of methods that gives away what comes next.
• Keep the comparisons close. Include similar-looking questions that require different methods, plus differently worded questions that need the same one.
• Use the error to plan the next set. If one pair keeps causing confusion, work through the contrast before adding more types.
• Save a fresh check for later. Try new questions without seeing the key first, as in our guide to checking what you know after closing an AI answer.

For a creator teaching someone else, the most useful feedback may be the explanation given before the calculation. ‘I divided because the question asked for the original’ is a start; ask what quantity the known number represents and what fraction of the original it is. That follow-up tells you whether the learner saw the relationship or guessed a rule from a familiar word.

When a practice set starts to feel easy, ask what made it easy. If you knew the method because the heading told you, keep a few questions that take the heading away. The aim is to recognise what a new problem is asking before you reach for a familiar calculation.

Sources

• Rohrer and colleagues, A Randomized Controlled Trial of Interleaved Mathematics Practice, Journal of Educational Psychology, January 2020 issue.
• Kornell and Bjork, Learning Concepts and Categories, Psychological Science, June 2008.