It is not uncommon to see a sporting coach routinely stop their player to model a skill. This is often at the frustration of the athlete who just wants to get on with the game and play. I remember this when I played basketball. Instead of a free flowing game, our coach would stop play to correct a poor dribbling skill or an inadequate defensive technique. This is quite natural in sports and coaches intuitively know that regular feedback and practice is necessary to improve performance. Therefore, it’s not surprising that the same principle translates into the classroom. Teachers generally model new knowledge or skills, feedback on how to improve or what the next steps are and they provide pupils with an opportunity to practice old and new learning. However, is our planning for practice time efficient – can general practice improve pupil outcomes?
For instance, in mathematics, most textbooks will lead with a worked example (a step by step outline in how to solve the problem) which is then followed by pages of practice problems. Naturally, this sounds like a proficient method to help drill students in learning a math skill. Yet, it may not be as effective as you would expect. On the basketball court I would receive instant feedback. This may take the form of a verbal instruction or the coach demonstrating the solution. Doug Lemov et al (2012) refer to this as closing the feedback loop. He suggests that feedback during practice should be given regularly and responded to by the participant instantly. This helps avoid poor form or misconceptions from becoming engrained by repeated poor quality practice. Therefore, practice is not about quantity but its quality.
Let’s return to mathematics. In lesson the teacher explains how to factorise an algebraic expression then sets a task on a series of questions from the textbook to practice. The pupils complete the set task with the traditional worked example at the start. They may have found the work relatively easy or difficult or became increasingly frustrated and confused. It could also lead to a phenomenon in which pupils may feel they have mastered the skill after the first couple of problems but, in fact, they have not. Daniel Willingham talks about this as familiarity, which is when the pupil may have had some early success which gives them the illusion of knowing it. Consequently, the worked example for the pupil becomes obsolete and the outcome of the task may not be as positive as the pupil or teacher would have expected.
It sounds counterintuitive to suggest that this may be an example of the wrong type of planned practice. The pupils have been provided an instruction that includes a worked example and an ample number of questions to practice. How is this different from the sports analogy? A key difference is the space of time in which feedback is given between each practice question to correct any errors. In the sporting example the athlete receives feedback instantly, yet in the mathematics illustration the pupils received limited feedback, if any, until the questions are marked at the end. One source of feedback may be the worked example but that is at the start. Unfortunately, it is not a given that pupils will repeatedly refer back to it, in particular if they believe they have already mastered the skill. If the skill is misunderstood then some pupils may have either become frustrated and will lose the motivation to continue or they may start to encode misconceptions leading to errors being committed.
The increase in ratio of worked examples to problem solving questions structures the pupils’ practice to revisit the modelled steps more frequently, similar to a coach feeding back to a player. Focusing primarily on the planning of practice around worked examples is different than the conventional thinking which concentrates principally on a large number of questions to answer. The switch of focus to worked examples removes goal-directed problems, which in turn reduces cognitive load. This will allow pupils to study the processes necessary to develop a schema of understanding to solve the problem, as opposed to losing time searching for the answer (Sweller & Cooper 1985; Cooper & Sweller 1987). Therefore the regular insert of worked examples acts as a coach frequently remodelling and testing the pupil so to make the necessary changes to their understanding. As a result, in the mathematics classroom, less may be more.
Some studies suggest that the use of worked examples as opposed to conventional problem solving methods of practice may improve student outcomes and significantly speed up acquisition of a mathematical skill (Sweller & Cooper 1985; Zhu & Simon 1987). In one extreme, a middle school in Beijing, China, reports that by adopting a worked examples approach, mathematics teachers were able to complete a three year course of algebra and geometry in just two years (Zhu & Simon 1987). Although Zhu and Simon (1987) are cautious to suggest a worked example is the answer to teaching mathematics quickly, it does demonstrate that worked examples have a role to play in learning.
It appears that in some instances less is more. Conventional thinking that lots of practice of a particular skill may actually be an inefficient use of time and have less of an impact than originally thought. Athletes want to compete and just play but it’s the frequent interruptions to master a skill that improves performance, similar to worked examples. The use of worked examples may help to encode the knowledge needed to recognise the problem, the steps required to solve the problem and the consequences each step may have which is necessary for schema acquisition (Sweller & Cooper 1985). Once the schema is acquired it can be applied and tested on a smaller sample of problem solving. This would make completing long lists of questions redundant and the time saved could be invested in further skill development, in which over time will pay dividends.
A common saying is that practice makes perfect, yet the quality of practice needs to be carefully planned. Expecting someone to learn basketball by lots of general practice will result in some player improvement but it is the value of incisive modelling and feedback which drives expert performance. An increased focus on the value of worked examples in planning which are then utilised in the classroom can provide the effective practice needed for pupils to learn and improve their performance (Atkinson et al 2000).
Atkinson, R.K., Derry, S.J., Renkl, A., & Wortham, D.W. (2000). Learning from examples: Instructional principles from the worked examples research. Review of Educational Research, 70, 181-214.
Cooper, G., & Sweller, J. (1987). The effects of schema acquisition and rule automation on mathematical problem-solving transfer. Journal of Educational Psychology, 79, 347-362.
Lemov, L., Woolway, E., & Yezzi, K. (2012). Practice Perfect: 42 Rules for Getting Better at Getter Better. San Francisco: Jossey-Bass.
Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2, 59-89.
Willingham, D.T., Ask the Cognitive Scientist: Why Students Think They Understand – When They Don’t. American Educator. Access here http://www.aft.org/periodical/american-educator/winter-2003-2004/ask-cognitive-scientist
Zhu, X., & Simon, H. A. (1987). Leaning mathematics from examples and by doing. Cognition and Instruction, 4, 137-166.