Does the title pique your interest? Or does it just make you want to move on to another blog? Give me just a moment to share a simple idea that may improve your students’ achievement dramatically!
Let’s begin with a golfing analogy: The typical golfer will practice by going to the range, grab a club, and then hit a bunch of balls with that club. Then after feeling good about that club, the golfer will grab a different club and hit another 20 or 30 balls with that club. This process will continue until the bucket of balls is depleted. This “...repetitive drilling on the same task is called ‘block practice.’ You do the same thing, over and over, in one block of activity. Schmidt argues that a better way to learn is to practice several new things in succession, a technique called ‘variable practice’ or ‘interleaving.’ So a golfer would interleave her exercises at the range by aiming at different targets each time, by mixing up the kinds of shots she takes or switching the clubs she uses.” (see here for the entire article)
It turns out that this concept can be applied to practicing mathematics. Traditionally, the teacher teaches a skill and then assigns 20 or 30 problems. This is blocking.
What might interleaving look like? One professor “... designed a simple experiment to interleave homework in [three teacher’s] classrooms. Half of the class’s homework assignments would stay the same. But for the other half, [the professor] would take all the homework questions the teachers had used last year and mix them up. So the interleaved assignments would have some questions about what the class was currently studying, and some questions about things they had studied earlier in the year.”
What were the results? “For the kinds of problems they learned with interleaved practice, the kids averaged 72 percent correct. With blocked practice, they averaged only 38 percent.” (Read the actual report here.) What is amazing is how little time, effort, or money was required to attain the more than 100% improvement! The curriculum stayed the same. The pedagogy stayed the same. The only thing that changed was the interleaving of the questions. This is a cheap, easy, and fast way to improve student achievement!
This news about interleaving versus blocking should not be particularly surprising. We have long known strategies that engage students in comparative thinking have the greatest effect on student achievement. More recently, Dr. Robert Marzano's research in The Art and Science of Teaching (2007) reconfirmed that asking students to identify similarities and differences through comparative analysis leads to eye-opening gains in student achievement.
Interleaving homework problems is just another way to create student opportunities to identify similarities and differences (and thereby the relationships) of the math topics being learned.
Please listen to the American Radioworks Podcast from which I learned all this.
For the segment on interleaving, scroll ahead to 28:42.
If you have an hour, please listen to the entire podcast. It is brilliant!
UPDATE (March 30, 2015):
The above is a quotation from a 4th grade textbook written in 1901. Clearly, mathematics teachers have long had the intuitive belief that interleaving is best for our students.