Can students learn how to solve mathematics problems by taking maths tests?

By Francesco Avvisati, Analyst, OECD, Directorate for Education and Skills, and Francesca Borgonovi, British Academy Global Professor, Institute of Education, University College London

Few subjects in education spark as much controversy as tests. Many people recognise that tests are useful to students because they provide a strong incentive to study rather than procrastinate; they can help teachers because they provide information about what students know and what they do not know; and they are useful to education policy makers because they promote accountability. But most people consider tests as little more than a bitter medicine that one needs to swallow to get better; and many worry that, as with medicine, too much testing may have toxic effects – so much so that “teaching to the test” and “learning for a test” are seen as diverting valuable time and resources from education.

Many people believe too much testing may have toxic effects – so much so that “teaching to the test” and “learning for a test” are seen as diverting valuable time and resources from education

But tests are, in essence, problem sets that students are asked to solve in a controlled setting. As the famous mathematician Paul Halmos once wrote, “The best way to learn is to do; the worst way to teach is to talk. ” By attempting to solve problems that appear in a practice test, students do mathematics. Indeed, in the study, Learning Mathematics Problem Solving through Test Practice: a Randomized Field Experiment on a Global Scale, we find that tests are not neutral events; they can be powerful learning experiences. Using data on almost 20 000 15-year-old students who participated in the 2012 round of the Programme for International Student Assessment (PISA) we show that participating in a single low-stakes test leads to a small gain in mathematical problem-solving skills, even in the absence of feedback from teachers. We also find that learning effects persist over the short term – between one and seven days. Crucially, we find that the effect of sitting a test on subsequent performance reflects more than just the power of recall or the effect associated with having learnt test-taking strategies.

How large is the learning gain in mathematics associated with sitting a maths test?

Granted, the learning effects that we found were small – but that was to be expected given that the difference in the amount of test practice within our sample was tiny. One additional hour of test-taking practice was associated with an improved performance of about 2% of a standard deviation in a final test designed to identify how well students know how to apply mathematical principles and procedures. In a real classroom setting, the effects may be greater if, for example, several short practice tests were organised over a period of a few weeks.

Although test-practice effects in mathematics were positive, on average, we also show that the benefits of testing accrue mostly to boys.

How can we make the most of the effect of practice tests?

Our study suggests that lessons that include practice tests bear the promise of improving students’ ability to apply their knowledge of principles and procedures to new, real-world problems, although the effects are not large and appear to accrue, in the absence of feedback, mostly to boys. If teachers provide corrective feedback and schedule several short test-practice sessions throughout a given period, the effect of test-taking on subsequent performance could be even greater. Girls might benefit more, too, if their teachers give them high-quality feedback. Evidence from other research shows that teachers’ feedback plays an important role in boosting girls’ confidence in their ability to succeed in mathematics.

This post also appeared in the UCL Institute of Education Blog

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