8.3. Practice v final performance

What I used to think

My rationale for not breaking complex processes down into sub-processes was that students would never be assessed that way on the final exam. No exam paper was going to ask students to decide if two fractions were in a form ready to be added together, or challenge them to find an appropriate common denominator. Instead, students would be presented with questions in their entirety, and expected to carry out the full process.

Hence, if that is what they needed to do on the exam, then surely the best preparation was to ensure that their practice was a similar as possible? This way of thinking would extend to: the best way to prepare for exams is to do exam questions, and the best way to get good at solving problems is to solve lots of problems.

In short, I believed that practice must resemble the final performance.

Sources of inspiration

My takeaway

Our first clue that practice does not need to look like the final performance can be found outside the domain of mathematics. As already discussed, when preparing for a recital a professional musician does not play the entire piece over and over again. If they did it would be difficult to identify the areas in which they need to improve. Instead they may practise scales, arpeggios, and small sections of the piece over and over again. Indeed, they may well do so in the manner described by both Kris Boulton and Hin-Tai above, interleaving the practice of past drills and sections alongside the study of new ones.

Likewise, the best way for a footballer to prepare for a 90-minute 11-a-side match is not to play lots of 90-minute 11-a-side matches. If they did, then it would be very difficult to discern how they could improve. Is their weakness short passing, dribbling, shooting, positional play, coping under pressure, acceleration speed, stamina, vision, heading, crossing? All of these skills contribute to the success of the overall performance, but are difficult to pinpoint and assess in the rough and tumble of an 11-a-side game. Similarly, the opportunities in which to practise these areas, and the ability to control the practice in order to make it as effective as possible, are lost during a big game.

Musicians and footballers prepare for the final performance using carefully designed, controlled and monitored drills, precisely because the purpose of practice is not to model the final performance, but to improve the final performance. And findings outside of the world of the classroom have repeatedly shown that the best way to do that is to make the practice itself very different from the final performance.

Of course, we need to be incredibly careful making inferences about how the techniques used in fields such as sport and music apply to the classroom. But fortunately, there is some evidence that the same principles apply.

McDermott et al (2014) found that the format of the practice quizzes did not need to match the format of the critical test for the benefits of testing and retrieval that we will discuss in Chapter 12 to emerge. In a study of history and science students, the authors found that both short-answer questions and multiple-choice quizzes were effective in preparing students for the final end-of unit exam where the questions were in a much longer form. What is also interesting is that even though the final exam contained no multiple-choice elements, students who were given multiple-choice questions during practice performed just as well – or even better in some cases – than those given short-answer questions.

The finding that short-answer and multiple-choice questions are effective in preparing students for exams that do not contain questions in that format is great news for us teachers. It means we can break down complex processes into sub-processes as described in the previous section. Having isolated the sub-processes, we can then plan explanations and worked examples, control practice through intelligent question choice, and crucially identify misconceptions far easier than if we had to tackle the processes as a whole. Using the techniques I will describe in Chapter 11, it also means we can quickly and efficiently assess understanding, whilst also identifying, understanding and hopefully resolving any misconceptions.

The benefits become even clearer when we consider multi-step and multi-topic exam questions. Consider the sub-processes that a student would need to go through in order to answer the following question from AQA’s Summer 2017 GCSE Paper 1 Higher:

Figure 8.4 – Source: AQA 2017 GCSE Maths Higher Paper 1

I got to 14 before I stopped counting – and that is ignoring the issue of deciding what the question is asking in the first place, which we will consider in the next chapter.

Repeatedly exposing students to exam questions like this is not the best way to help them get good at answering them if they have not yet mastered each of the sub-processes involved. Trying to answer these questions in one go is fine (and even beneficial) for an expert, but for a novice without the relevant domain-specific knowledge readily available and automated in long-term memory, it is likely to lead to cognitive overload and no learning taking place. Far better is to break questions like this apart, and employ the five-stage process described in the previous section to develop the skills students will need.

There is an additional advantage to the Deliberate Practice approach. Students will rarely have practised multi-mark questions in the exact same format that they appear in high-stakes exams. Variety in the context and the way topics are combined means that these types of questions on exams are highly unpredictable. By following a Deliberate Practice approach, students gain access to a wide selection of individual skills that they have mastered and automated, and as such can develop experience in piecing them together in an appropriate manner to solve these problems, as opposed to hoping a question that looks exactly like one they have practised comes up.

Exam questions like this are the final performance. Practice does not – and should not – need to look the same.

What I do now

I practise complex skills using Deliberate Practice, and I am not at all worried if this practice looks nothing at all like the final process or exam we are working towards. More often than not, this practice will be in the form of short-answer, carefully varied questions as demonstrated earlier on in this chapter, or the diagnostic multiple-choice questions that we will cover in Chapter 11. I will also make use of goal-free problems and remove redundant information as discussed in Chapter 4. The full process and exam questions are the very last thing I look at once the sub-processes have been mastered

I also make sure I tell my students why we are doing it like this. Students can become frustrated that they are working on drills and multiple-choice questions that look nothing like what they will be studying on the exam. I have known parents get involved as well. I know students will reap the benefits in the long term when we put everything together, but that may not help in the here and now. Hence, I am keen to describe the rationale behind what we are doing, and putting it in the context of sport or music seems to help them understand my thinking. Of course, once students see how they perform at the end of the process and in subsequent tests of retention, the benefits speak for themselves.