Learning Mathematics Problem Solving through Test Practice: a Randomized Field Experiment on a Global Scale

Abstract

We measure the effect of a single test practice on 15-year-old students' ability to solve mathematics problems using large, representative samples of the schooled population in 32 countries. We exploit three unique features of the 2012 administration of the Programme for International Student Assessment (PISA), a large-scale, low-stakes international assessment. During the 2012 PISA administration, participating students were asked to sit two separate tests consisting of problem-solving tasks. Both tests included questions that covered the same internationally recognized and validated framework for mathematics assessment. Students were randomly assigned in the first, 2-h-long test to one of three test versions containing varying amounts of mathematics, reading, and science problems. We found that the amount of mathematics problems in the first test had a small positive effect on mean mathematics performance on the second test, but no effect on general reasoning and problem-solving ability. Subject-specific effects of test practice on subsequent test performance were found over both short lags (same day) and medium lags (1-7 days). The learning gains ascribed to mathematics problem-solving practice were larger for boys than for girls.

Leveraging process data to assess adults’ problem-solving skills: Using sequence mining to identify behavioral patterns across digital tasks

“…The sample used in the current study included all respondents who were administered problem-solving items at the end of a two-part test, irrespective of whether they had received literacy items, numeracy items or other problemsolving items in the first part of the test. It is therefore possible that individuals who had been allocated problem-solving items in the first stage of the assessment might have adopted different test-taking strategies as a result of being more familiar with the assessment domain (Avvisati & Borgonovi, 2020); unfortunately, the small sample size did not allow such examination.…”

A Case Study of Using Test-Enhanced Learning as a Formative Assessment in High School Mathematics

“…A large-sample investigation of Avvisati and Borgonovi (2020) examines the relationship between the testing effect and problem-solving in mathematics, on authentic educational material. They demonstrate that the amount of mathematical problems in the first test had a small positive effect on the average mathematics performance on the second test among fifteen-year-old students.…”

Undergraduate students’ emotions around a linear algebra oral practice test

“…Their utilization has been demonstrated to enhance recall and significantly boost long-term memory retention (Roediger & Karpicke, 2006), and that the use of practice tests is more beneficial for learning than restudying (Adesope et al, 2017). In the case of the teaching and learning of mathematics, evidence has been found that the use of practice tests that require students to practice the application of problem-solving principles, procedures and numeracy skills, is associated with an improved performance in standardized tests (Avvisati & Borgonovi, 2020;Thai et al, 2021). However, although some of the academic advantages of practice tests are known, it is less known about the emotions that undergraduate students experience during such practice tests.…”