Research School Network: Modelling and Worked Examples This article explores the importance worked examples as a modelling technique and some of the supporting research evidence.

Modelling is a technique mentioned in Barack Rosenshine’s Principles of Instruction:


4. Provide models: providing students with models and worked examples can help them learn to solve problems faster.


By working through a problem with students, modelling thinking and decision making at all points, students are made aware of the thought processes that we go through in order to solve a problem. This technique also ties in with Cognitive Load Theory as examples can be worked through in stages, thus reducing the cognitive load on the students, especially in a multi-step problem. Sweller (1986) also proposes that this helps problem solving schema to be built more easily.

This may seem quite obvious, and the use of modelling and worked examples is widespread particularly in subjects such as Maths. In this article I will concentrate particularly on the use of worked examples as a modelling technique and look at some of the research behind this.

Trafton and Reiser (1993) used examples and problems in computer programming to investigate two differing models of knowledge construction:

- Example generalisation model – the most important skills for problem solving are learned while studying examples

- Knowledge compilation model – the construction of knowledge critically relies on applying the knowledge to problems as it is in solving problems that the necessary rules are compiled

Their study used sets of examples and problems sometimes given in discrete blocks and sometimes interleaved together to find out whether students just need to study examples (Example Generalisation Model), or whether it is also vital those examples are built upon by solving their own problems (Knowledge Compilation Model). Subjects who solved problems interleaved with examples took less time and were more accurate on the target problems than subjects who studied in blocks, supporting the Knowledge Compilation model. They concluded that studying examples is a very effective method to improve learning, however the knowledge gained from studying examples needs to be applied to solving a new problem:


​“The most efficient way to present material to acquire a skill is to present an example, and then a similar problem immediately following”


They hypothesised that subjects construct rules general enough to work for both the example and the problem. This has led to Craig Barton (2018) to implement what he calls Example-Problem Pairs in his maths lessons.

Useful examples and models are however not always easy to find. Gick and Holyoak (1980) conducted a well-known study in which subjects were told a story about an attack on a fortress and then asked to solve an analogous problem about destroying a tumour. The differing surface details of the models proved so distracting that only 20% of subjects manage to use the model to solve the problem. However once given a hint that a previous story might help them, the success rate improved to 92%. Care must be taken that surface features do not drive attention away from the learning task.

In their study using mathematical problems, Atkinson et al (2000) concluded:


​“Examples should be presented in close proximity to matched practice problems”

​“Learners can be encouraged … to actively self-explain examples”


It has been suggested by Renkl and Atkinson (2003) that it is better for there to be a ​“fading out” effect when transitioning from examples to problem solving, where steps in the process are removed gradually forcing the students to complete more and more of the example by themselves.

Types of worked examples

Modelling has been looked at in greater detail in a number of studies and there has also been more specific investigation into the types of worked examples that are used.

Grosse and Renkl (2004) looked at how the use of both correct and incorrect examples can help in learning. Both turn out to be important, though care must be taken that understanding is secure before incorrect examples are used. In AlgebraByExample (https://www.serpinstitute.org/algebra-by-example) researchers have worked in partnership with teachers to produce a set of 42 freely available assignments designed and tested with students. These take the form of both correct and incorrect examples which can be used as starters, discussion points, exit tickets or homework.

In ​“Understanding how we learn”, Weinstein and Sumeracki (2018) suggest the following tips for teachers which make a useful summary:

- Use more than one concrete example to explain abstract concepts, ideally differing in surface structure to help students to generalise
- Help students make the link between various surface details and the underlying structure
- Make the relevant parts of the example explicit in your explanation
- Use visual as well as verbal examples

References

How I Wish I Taught Maths. Barton (2018)

Learning from Examples: Instructional Principles from the Worked Examples Research. Atkinson, Derry, Renkl, Wortham (2000)

Learning from Worked Examples: What happens if mistakes are included?. Grosse and Renkl (2004)

Structuring the Transition from Example Study to Problem Solving in Cognitive Skill Acquisition: A Cognitive Load Perspective, Renkl and Atkinson (2003)

The Contributions of Studying Examples and Solving Problems to Skill Acquisition. (Trafton and Reiser, 1993)

Understanding How We Learn: A Visual Guide. Sumeracki, Caviglioli and Weinstein (2018)


Deb Friis October 2019