How to Practice
Vince Lombardi, one of the most successful American Football coaches of all time, once famously said that,
He sums up quite poignantly a very important aspect of what it means to practice, that how we do it is actually much more important than how much we do it. Practice is a part of every single skill and piece of knowledge we acquire every day. However, no matter what it is you are trying to achieve, good, efficient practice can mean the difference between success and failure.
The American Psychological Association performed a study analysing all the factors that led to high performance across disciplines and subjects. Throughout everything they considered the one thing that trumped all else in terms of peak performance levels was deliberate practice. However, “deliberate practice is not the same as rote repetition” they said. As opposed to rote learning, or simply repeating exercises, “deliberate practice involves attention, rehearsal and repetition and leads to new knowledge or skills that can later be developed into more complex knowledge and skills.”¹
Learning mathematics is no different. To be successful in mathematics one needs not only to practice but know how to practice. Too often rote learning becomes the norm but, as the APA discovered, this is not enough. Deliberate practice means being able to do extra attempts in similar but not the same questions. The opportunity to perform extra, similarly orientated attempts not only increases the possibility of immediate success but also self-confidence and therefore the probability for future success. Manu Kapur recently performed a study to assess the most effective way for students to learn maths. What he found was that students who made an attempt at a question, were unsuccessful, and then were provided with another attempt straight away had much steeper learning curves than those that were taught a concept and then only given one attempt.² This is the idea of variant learning – learning not simply through instruction, but variable, deliberate practice. Variant learning is one of the most effective ways for students to engage with, and gain conceptual understandings of, mathematics.
Summatic and Variant Learning
This is an area where Summatic has excelled. Summatic’s technology creates new question variants that offer students unlimited opportunities to test their understanding. The platform provides an opportunity to assess students with every question type including multiple-step longer form, matrices and written questions, not just multiple choice questions. Summatic also provides hints, links to interactive graphical depictions and immediate step-by-step feedback on attempts. This has large consequences for not only students, but schools and departments too.
Figure 1: Case Study with Cambridge Judge Business School³
One of the biggest challenges universities face is how to bring incoming students up to speed with quantitative skills more efficiently. As the scope of acceptance into Business Schools and quantitative heavy postgrad courses becomes larger, there is more of a need than ever to level the playing field before classes start. Random variant assessment has proven to be one of the most effective ways of doing this. The graph above describes the situation that was tested at the Cambridge University Judge Business School. As we can see, through random variant practice, students showed an 80% increase in learning by the third variant. This means that 80% of students who had initially answered incorrectly had corrected their mistake, and deepened their understanding, by the third variant – proving both efficient and beneficial for students.
As can be seen from the graph above, random variants also allow departments to gain a much more in-depth and student-specific understanding of learning paths. By providing diagnostics of the learning curves instantly, departments can focus more time on analysing their cohort’s performance and identifying and implementing strategies to bring students up to speed faster. Ultimately it is about giving students the greatest chance of success and giving university departments the tools to do so. Random variant practice provides both of these in the most efficient way possible and is becoming a necessity for all quantitative students and programmes looking to progress into the future.
¹ Brabeck, M., & Jeffrey, J. (2015), “Practice for knowledge acquisition (not drill and kill)”, American Psychological Association. [https://www.apa.org/education-career/k12/practice-acquisition]
² Kapur, M. (2014), “Productive Failure in Learning Math”, Cognitive science, 38(5), pp. 1008–1022.
³ Case Study with the University of Cambridge Judge Business School [https://summatic.co.uk/0469dc56-7dee-4f4c-9e6f-487a08f51434/Summatic.CJBS.MFin.Case.Study.pdf]