Spaced Practice with Math Topics:
During my first year teaching Engage NY Math, we went step by step though the curriculum and we all discovered its Achilles heel (real talk: the Achilles heel of all currics): its speed and desire to “do it all”. Students are presented with many new strategies in immediate sequence, and those who struggle or lack foundational concepts are given little time to gain understanding of the first approach.(In the words of a former colleague, “They need to grapple? All they do is grapple. They’re like butterfingers! They can’t get a hold on anything!”) It was a big issue, and one I am still wrapping my head around. To deal with this curriculum problem, I needed deep understanding of the standards, my students, and developmental progressions in math learning. Not easy.
In my second year teaching the curriculum, though, I noticed something else about EngageNY that seemed to go against the research I'd been reading: the heart of 2nd grade math -- place value in addition and subtraction -- is addressed in a spurt of several months (those all important Modules 4 and 5) after which it is barely touched again.
I had been reading a lot about Spaced Practice thanks to the Learning Scientists and I realized that this might be an easy fix -- a fix that might even help me to address the larger issue I described above. According to a pretty serious body of research, spacing out the teaching and learning a given topic over time significantly increases long term retention (without increasing the total number of hours of instruction/study). A few reasons that this is the case: recall boosts memory, so we are forcing students to recall things more if we break up the instruction over time; returns to extra hours or lessons on the same topic might be low if students tune out -- and they might tune out less if it feels fresh again after having taken a break to learn something else.
So I wondered if spaced practice would help ease the "extreme grappling" that our second graders seemed to be experiencing with Engage's myriad place value strategies.
Rather than following the modules in the written order, we stopped addition and subtraction after Module 4 (adding and subtracting within 200) to do other things. We spend a few weeks on arrays, a few weeks on measurement, some time on data and graphs, some time on shapes and fractions.
Finally, at the end of May, we returned to addition and subtraction in Module 5. Sure enough, the majority of the class looked pretty shaky with composing tens and was making a mess of decomposition. We had given them enough time to un-learn their strategies.
But within a couple days, they were back on their feet, and were able to manipulate and solve problems with large numbers using the underlying principles they had learned in Module 4. With the passage of time, many of them were able to use even more sophisticated strategies, which were a bit over their heads on the first go around. And they were excited to come back to these strategies after a long hiatus – it was like seeing an old friend again.
Importantly, during the interval between modules, I had time to work more closely and more slowly with strugglers on some critical underlying concepts (place value, fluency in counting by tens, etc.) so that they were better able to attack the new problems. Even for them, the familiarity of an old strategy had something warm and comforting about it, though they had struggled the first time around.
It was amazing to see the power of simply switching the order of a module.
Looking forward to hearing others’ experiences with spacing, especially in the primary classroom!
(Check out The Learning Scientists and Effortful Educator for more on the research and classroom application of these ideas!)