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Practice and understand · Lesson 5 of 11

Worked Examples and Mixed Practice: How to Practice Skills

Learn two habits for practicing a skill: study solved examples while a topic is new, then mix the kinds of problems you can already do.

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This lesson gives you two habits for practicing a skill, like solving math problems, working with a spreadsheet or applying rules to cases. First, study solved examples. Then, once each kind of problem makes sense, mix the kinds together. It matters because real tests, and real life, rarely tell you which kind of problem you are facing.

Start with worked examples

A worked example is a problem solved step by step, with every step shown. Study one before you try a problem alone: follow each step and ask yourself why it comes next. Then cover it and try a similar problem on your own.

A large review of math studies found that learners who studied worked examples did better, in studies ranging from elementary school to university.

Under the heading Worked examples, an Example problem solved in three numbered steps with a check, labeled Worked example, and a note: A large review of math studies, Did better. A learner stands in the middle, and on the right a second Example problem has empty steps and a question mark, with the label Then try one alone.(opens the full-size picture)
See every step first, then try a similar problem yourself.

Let the help shrink

That help should shrink as you improve. Beginners learn more with extra guidance. People who already know the subject do better with less. Researchers call this the expertise reversal effect.

So lean on worked examples while a topic is new. As you get more confident, look at the example less and less, and then solve problems yourself.

Three steps rising under the heading Let the help shrink: New, with a full worked example; Getting there; and Confident, with a learner on top and a problem left to solve. On the right, a Guidance slider set from A lot to A little, above Example cards, and a label: Lean on examples while it's new.(opens the full-size picture)
More help while it is new, less help as you get better.

Practice in blocks feels smooth

Now, how should you practice? Most people work in blocks: ten problems of one kind, then ten of the next. It feels smooth, because you already know which method to use each time. You just repeat it.

The catch is that a block does an important job for you. It tells you the method before you start.

An Example under the heading Practice in blocks: three cards marked A with circles, three marked B with squares and three marked C with triangles, each group labeled Same method. A learner stands at the end, and a label reads Blocked practice feels smooth.(opens the full-size picture)
In a block, you never have to decide which method fits.

Mix them up

Mixing, which researchers call interleaving, means shuffling different kinds of problems into one session. Now each problem asks a question first: which kind is this, and which method fits? A real test asks the same thing. An exam question rarely says which chapter it comes from.

Under the heading Mix them up, with an Interleaving tag, a row of nine cards in mixed order: A, C, B, B, A, C, B, C, A, labeled One session. Below, an Example practice sheet mixes a triangle, a circle and a square, and a label reads Mixed practice: you choose the method.(opens the full-size picture)
In a mixed session, choosing the method is part of the practice.

What one school trial found

In one trial, school math classes were given mostly mixed practice for four months. On a surprise test a month later, they scored about six in ten. Classes given mostly blocked practice scored about four in ten.

The researchers also noted that mixed practice takes longer, and may work less well when a skill is brand new and has not been practiced on its own first.

A bar chart headed One school trial. Mostly mixed, for 4 months, scored about 6 in 10, and Mostly blocked scored about 4 in 10 on a surprise test a month later. The axis label is Test score.(opens the full-size picture)
Classes that mixed their practice scored higher a month later.

Not for everything

Mixing is not a fix for everything. It helps most when you must tell similar things apart, such as two kinds of problem that look alike, or the styles of different painters. But a large review found that for learning words, keeping them in blocks worked better. And most of this research involves students.

Two cards under the heading Not for everything. The left Example shows two similar triangles, one under a magnifying glass, with the label Helps: telling similar things apart. The right card, A large review, shows a stack of Example word cards and the note Words: blocks worked better. A line below says Most research: students.(opens the full-size picture)
Mix kinds of problems; keep word lists in blocks.

Mix what you already know

Mixing feels harder and slower than blocks, and that effort is part of how it works. But don’t mix too early. Keep a new topic in its own block until you can answer its problems without help. Then shuffle it in with the kinds you already know.

An Example row of mixed cards, A, C, B, then a check card, then B, A, C, under the heading Mix what you know. A learner stands beside a tall Effort bar and a label that says Harder is fine. On the right, an empty dashed box says New topic, with the note Can do it alone.(opens the full-size picture)
A new topic joins the mix once you can do it alone.

Mixing different problems is not multitasking

Mixing means switching between kinds of problem on the same subject, inside one practice session. Jumping between unrelated tasks, like studying and checking messages, is something else, and it has a cost of its own.

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Read the full lesson script

In this lesson, you will learn two habits for practicing a skill. Study solved examples first, then mix different kinds of problems together. It matters, because real tests come mixed.

A worked example is a problem solved step by step, with every step shown. Study one before you try a problem alone. A large review of math studies found that learners who studied them did better.

That help should shrink as you improve. Beginners learn more with extra guidance. People who already know the subject do better with less. So lean on examples while a topic is new, then solve problems yourself.

Now, how should you practice? Most people work in blocks: ten problems of one kind, then ten of the next. It feels smooth, because you already know which method to use each time.

Mixing, which researchers call interleaving, means shuffling different kinds of problems into one session. Now each problem asks a question first. Which kind is this, and which method fits? A real test asks the same.

In one trial, school math classes were given mostly mixed practice for four months. On a surprise test a month later, they scored about six in ten. Classes given mostly blocked practice scored about four in ten.

Mixing is not a fix for everything. It helps most when you must tell similar things apart. But a large review found that for learning words, keeping them in blocks worked better. And most of this research involves students.

Mixing feels harder and slower, and that effort is part of how it works. But keep a new topic in its own block until you can answer without help. Then shuffle it in.

So, study solved examples while a topic is new, then mix the kinds of problems you can already do. In your next session, mix two kinds of question you already know. Next, you will explain an idea in plain words, to see what you understand.