**By Francesca Borgonovi, British Academy Global Professor, UCL Institute of Education and Francesco Avvisati, Analyst, Directorate for Education and Skills, OECD.**

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.

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 a study we recently published, 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 appears at: https://oecdedutoday.com/solve-mathematics-problems-with-maths-tests/*

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