Teaching with Worked Examples – Save learner time and effort while increasing performance!

I’ve done a lot of study in cognitive theory, specifically cognitive load theory, during my graduate work.  One of the best take-home lessons I learned (and immediately implemented in my classroom with great success) was how and when to use worked examples.

I taught chemistry, and even though I tried really hard to make sure I had a conceptually-focused course, there’s still many, many skills students needed to learn and practice (writing and naming chemical formulas, balancing equations, various mathematical calculations, etc.)

What is a worked example?

A worked example is exactly what it sounds like – an example problem that is worked out step-by-step.  They work well in areas with well-defined tasks and problems (math such as algebra, geometry or statistics, computer programming, science tasks such as naming or writing chemical formulas).

What evidence is there that they are beneficial?

I’m a scientist and I love research…what evidence is there that I should employ this method before I take the time and energy to do so?  There’s LOTS of studies and evidence on the benefit of worked examples.

Here’s a study that I find pretty compelling (Paas, 1992)…

One group had 12 conventional geometry problems and another group had the same problems but 8 of them were “worked example” and 4 of them were problems to solve.

Students in the worked-example group: (1) spent significantly less time working on the learning activity, (2) scored higher on a test with similar types of problems (“near transfer problems”) and (3) scored higher on tests of problems that require application of the content in a different way (“far transfer problems”)

Zhu and Simon (1987) showed students could go through a three-year math sequence in two years using the study of worked examples.

When to use worked examples

When the task is well-defined.

When it’s a skill to practice.

When the learner is new to the task/problem.  The expertise-reversal effect shows, believe it or not, that what works for novices to make learning efficient actually hinders more advanced learners.  Being required to study examples of a problem type that the learner already knows how to solve actually makes their learning less efficient.  (All the more evidence for mastery learning courses and dynamic computerized tools that adjust to the learner’s ability level to provide individualized instruction!)

How to use worked examples

Trafton and Reiser (1993) found that it’s better to show a worked example (or set of them of the same type of problem) and then have students practice that type of problem and repeat this for each type of problem rather than show all the worked examples of various problem-types first, followed by all the practice problems (which unfortunately is how most books are set up…even within a section or lesson, they still show all the examples first and then show all the practice rather than grouping like problems, both examples and practice, together).

How to get STUDENTS to use worked examples

In order to see the effects (faster learning, better performance) of worked examples, the students must use them instead of just skipping over them and jumping into the problems they have to solve (like most of my students would do).

Teaching students to self-explain as they study a worked example is one way.  As they go through a worked example, ask themselves questions like “where did that number come from?” or “why did they do that step next?”

One way to get students to self-explain, or to teach them how to, is by using faded worksheets.  This is where you show a fully worked out example.  Then the next problem is worked out except for the last step.  The next problem is worked out except for the last two steps.  You can “fade” one or more steps at a time (depending on the difficulty of the steps you’re fading or the level of your students) from the END of the problems as students go down the page.  When they have to fill in those missing steps and they don’t know how, they’ll refer to the worked out problems above and ask themselves those questions of “where did that step come from.”

If you change types of problems or make it harder, you may need to put some of the completed steps back in (see my example here…when I go to 2-step dimensional analysis, I fill back in steps for them temporarily to support this jump in difficulty).

An example from my classroom
Here’s an example of my old worksheet on dimensional analysis (a standard thing in any chemistry or physics courses).  This worksheet usually took quite a bit of time for students to do, lots of frustration, lots of irritation and general bad feelings about chemistry at that point.  They would take a quiz after completing it and still not do very well.  I hated this lesson!

Then I switched the same worksheet to a backwards-faded worksheet and the students would complete the worksheet and pass the quiz all within one 90 minute class period (and I required all students to pass with an 80% or better before moving on).  So to go from a multi-day, torturous process to a 90-min we all pass process is a miracle in my mind!

Why are they beneficial?
If you’re interested in why they have this enormous benefit on learning, like I always am, you can read up on the information on cognitive load theory and see that basically worked examples produce a much lower cognitive load that free problem solving and this lower cognitive load allows room for germane load (learning).

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