How might we help students with learning and remembering without giving them 30 of the same math exercises each night?
This is a question that I had pondered for a while. I really enjoy reading about cognition, so in addition to my cognition book for grad school, I was also reading “Why Don’t Students Like School?” by Daniel Willingham (@DTWillingham) and “Make It Stick” by Peter C. Brown, Henry L. Roediger III, and Mark A. McDaniel. The topics of interleaving and spacing practice kept coming up. While it is more difficult for learners, it helps increase the “stickiness” of what they are learning. Willingham states, “But something else does protect against forgetting: continued practice” (p. 117).
Interleaving is the opposite of how most math teachers assign practice work. Typically, math teachers assign massed practice – students work out examples that are all on the same topic. Interleaving is mixing up the topics. This is much harder and slower for learners initially. From Make It Stick, “…research shows unequivocally that mastery and long-term retention are much better if you interleave practice than if you mass it” (p. 50).
Spacing is what it sounds like, spreading out practice instead of cramming. If you will study for 3 hours, it’s better to space out that 3 hours instead of doing it all at once the night before a test. You will forget less and remember longer by spacing. More from Willingham, “If, on the other hand, you study in several sessions with delays between them, you may not do quite as well on the immediate test but, unlike the crammer, you’ll remember the material longer of the test” (p. 119). Spacing is for the long term. As a teacher, I want my students to remember for the long term. The math they are doing in my class will continue to be built upon in future coursework.
Catalyst for change
Even with reading about this in 3 different books, I still hadn’t made any changes to the practice work I assigned to my students. Then in November 2014 I attended the NCSM Regional Conference in Richmond, VA and heard Steve Leinwand (@steve_leinwand) speak for the first time. (If you’ve never heard him live, I highly recommend rectifying that situation!) Steve also spoke about spacing, interleaving, and giving students no more than 8 practice problems per night. That was it, I was sold. I couldn’t escape that I was being directed to change my assignments. I try to have one major takeaway from any conference that I implement immediately – changing how I did practice was done my first day back at school after the conference. I told students what I was doing and why.
Here is how it looks (typically) in my classroom.
Day 1 – 8 problems – 4 are low-level on the new material, 2 are medium-level on review material, 2 are high-level on review material
Day 2 – 8 problems – 4 are low-level on the new material, 2 are medium-level on Day 1 material, 2 are high-level on review material
Day 3 – 8 problems – 4 are low-level on the new material, 2 are medium-level on Day 2 material, 2 are high-level on Day 1 material
This pattern repeats throughout the unit. It cuts down on end of unit review time because we’ve been reviewing all unit long. Additionally, we use ALEKS & I would assign some exercises on ALEKS that were review. I could see details of each student with each topic and use the weak topics as our warm up the next day in class. New this year: our math team has agreed to have all unit tests include some amount of material from previous units. We are hoping this shows students the importance of remembering what they’ve learned.
If you want to read more on this, I recommend the 3 books listed at the top of this blog post. In addition, read anything and everything by the incomparable Henri Picciotto (@hpicciotto). He has an excellent post on how he lags practice. I haven’t done lagging that way, yet! Finally, you may want to check out the #eduread thread on Twitter. A conversation I had there last week inspired this blog post!