While research on specific math textbooks may not be readily available, a tremendous amount of research clearly shows what works well (and what doesn’t) regarding mathematics instruction and math achievement. I finally got the book recommended in an earlier post, Hattie’s (2009): Visible learning: A synthesis of over 800 meta-analyses relating to achievement. It is excellent, and clearly details what works in education.
By way of introduction, a meta-analysis take groups of studies that have been done on a particular topic, innovation, or approach and combines their findings into a summary measure called “effect size”. An effect size of d = 1.0 indicates an increase of one standard deviation on the outcome (e.g., achievement), or advancing kids’ achievement by two to three years, or improving the rate of learning by 50%. An effect size of 1.0 means that, on average, the performance of students receiving that treatment would exceed 84% of students not receiving that treatment.
What does Hattie report for mathematics programs? Combining 13 meta-analyses covering 677 studies and 8565 people (2370 effects), the effect for mathematics programs is 0.45, a medium effect size that means they DO have an effect. Specifically, the highest effects were found when teachers provide feedback data or recommendations to students (d = .71) and peer-assisted learning (.62), explicit teacher-led instruction (.65), direct instruction (.65), and concrete feedback to parents (.43). Hattie states that “modern” mathematics that stress real-world problems and a high level of use of manipulatives (e.g., constructivist approaches) has an effect size of .24. Effects are higher for teaching concepts (.36) and computation (.31) but not application (.06).
According to Hattie, “Overall, the presence of feedback, direct instruction, strategy-based methods, high levels of challenge and mastery has much effect on the learning of mathematics. That is, directive teaching makes the difference when teaching mathematics” (p. 147)
In a subsequent post, I’ll pull together Hattie’s findings regarding effect sizes for teachers as ‘activators’ and teachers as ‘facilitators’.
