Trying to improve your math lessons? Two recent studies have implications for math instruction, especially in how teachers can more effectively design or choose problems and assessments. This research comes at a time when the 2023 National Assessment of Educational Progress (NAEP) math scores for 13-year-olds have declined steeply across all gender, racial, and ethnic groups.
First, students can learn more from analyzing worked-out example problems than simply problem-solving on their own, according to a meta-analysis in Educational Psychology Review. The authors examined nearly 100 math-intervention studies of math performance when students use worked-out example problems. They found that when students look at solved problems, especially those done incorrectly, and studied them alongside correct answers, they greatly improved their understanding of concepts more than if they used other approaches. To make this method work, the researchers say, educators should select math problems that have an explicit goal and detailed steps necessary for solving the problem.
Educators should also think about appropriate difficulty levels that fit students' needs to improve math performance. In a survey of 1,800 German students in grades 5–10, more than half said they were bored during math tests. Although students' boredom didn't influence outcomes during easy problems, the study in the Journal of Educational Psychology noted, it did negatively affect achievement when problems were challenging. Those students who were bored performed worse on difficult questions than those who reported feeling engaged.
By making math problems appropriately difficult and providing worked-out examples, educators can design instruction and assessments that better fit students' needs—and likely see improved achievement.
