# Diverse Worked Examples

All problems contain both surface features regarding general context (and are irrelevant to the solution) and deep structures (that are essential to the solution). Learners need to acquire information about the deep structures that determine a solution process.

Presenting a diverse range of examples demonstrates the surface features that may change while maintaining similarity in deep structures that determine a similar solution process.

As schemas develop, the diversity of worked examples should be increased to promote transfer across a wider range of contexts.

When a series of worked examples is presented for a similar problem type, incorporate diversity in the range of contexts where surface features change.

As learners progress through the series of worked examples, gradually increase the level of diversity in surface features.

When the content area is of higher complexity or when the learners level of expertise is lower (or both), initially provide a lower level of diversity in worked examples surface features and more gradually add diversity of surface features.

When presenting a series of worked examples, include diversity in the surface features of the problem statements.

Guide attention to the similarities in deep structures determining the solution processes, despite the differences in surface features.

As the learner progresses through a series of worked examples, gradually increase the diversity of surface features in worked examples.

Rather than demonstrating worked examples for four similar situations, such as:

- calculating the area of a rectangle that is 3 m x 4 m

- calculating the area of a piece of paper that is 20 cm x 35 cm

- calculating the area of a window has a frame of 2 m x 1.5 m

- calculating the area of a door that has a frame 2040 cm x 820 cm...,

demonstrate worked examples showing how to calculate for four diverse situations such as:

- calculating the area of a rectangle that is 3 m x 4 m

- calculating the area chocolate icing has to cover for the top of a birthday cake that is 20cm x 35 cm

- calculating the area of grass on a football field that is 100 metres long and 60 metre wide

- calculating the height of a fairies' back door which is 5 cm wide and has an area of 50 square centimetres.

Rather than demonstrating worked examples of how to calculate the mean, mode and median for the following four similar scenarios:

- a set a 10 scores in a maths test

- a set of 8 heights of students

- a set of 10 data points for maximum temperature over the last 10 years taken locally

- a set of 10 annual incomes...,

demonstrate worked examples of how to calculate the mean, mode and median for the following four diverse scenarios:

- a set a 10 scores in a maths test

- a set of 8 weights of chocolate cakes cooked by film stars

- a set of 10 data points for maximum temperature collected at the South Pole from 1950 to 1960, and compare these to another set of 10 data points collected at the South Pole

- a set of 24 maximum flying speeds recorded for bees returning to their hive after collecting honey.

Rather than demonstrating a set of 5 similar modifications using filter effects such as:

- slow down slightly

- speed up slightly

- lower pitch slightly

- play track with gain added (louder), and

- apply a reverb to introduce an echo...,

demonstrate a set of 5 diverse modifications such as:

- slow down slightly

- speed up substantially

- lower pitch substantially

- play track backwards, and

- apply an equaliser to produce a "robot voice".