Education headlines rarely permeate the cultural discourse, though there are exceptions. Over the last four years, one seismic exception has been the surge of interest in the Science of Reading. I’d estimate that most average-to-well-educated Americans could articulate at least its central claim – that direct phonics instruction is key to developing competent readers. Of course, additional—and crucial—elements to the science, including explicit vocabulary instruction and the building of comprehensive background knowledge, are less well known.
FCI is a staunch advocate of the Science of Reading. While we don’t believe in reinventing the wheel on K-2 instructional best practices for “teaching to read” since the space is full of fantastic curriculum and professional learning providers, we offer support in the less well-known elements mentioned above. Through our workshops (including our annual Science of Reading session focused on grades 3-12) and blogs, we spotlight best practices in explicit vocabulary instruction and background knowledge.
Surprisingly, the natural extension of the Science of Reading work – the Science of Math – has yet to captivate the attention of education experts and the country at large in quite the same way. That said, it is no less important: 2024 NAEP data shows less than 30% of 8th graders are at or above proficient in math nationwide, a deeply troubling metric for our nation’s future. So, we’ve been thinking: What does cognitive science tell us about learning math? And how can we make these takeaways applicable and actionable at the school and classroom level?
In this and subsequent posts, we’ll share a slice of the research and corresponding best practices, which we’re excited to turn into our newest workshop offering during the fall of the 25-26 school year. Read on for our first installment.
Retrieval Practice to Develop Fluency
A central question in math circles comes down to one of depth vs. volume: should students spend hours each day “killing and drilling” problem sets, or should they practice “three perfect problems” and call it a day?
The Research
The dynamics of memory encoding are at the heart of any conversation about instructional best practices. Essentially, our working memories are finite, but our long-term memories are infinite.
So, someone who wants to tackle increasingly complex math needs to have exceptional fluency across the swath of math skills (at its basic, the four operations – but also decimals/fractions/percentages, algebraic thinking, systems of equations, etc.) The more fluent you are in these areas, the less overloaded your working memory becomes as the math becomes more challenging, freeing up space for problem-solving. (For more in-depth, we recommend two great books: Daniel Willingham’s Why Don’t Students Like School? and Hector Ruiz Martin’s How We Learn.)
The answer then lies in how we encode information into our long-term memories, which happens via regular, thoughtful retrieval practice – or the active recalling of information from memory.
Effective Retrieval
Two elements play a role in effective retrieval: the content of the practice and the intervals between practice sessions. Research tells us that the retrieval should be designed to create spaced interleaving of microskills.
Spaced practice refers to practicing the same or similar skills at regular intervals with some time lapse between rounds. While intuitively true, think about the number of times you’ve known you had two weeks to study for a final exam, planned to do an hour every other day over the fourteen days, and still found yourself cramming in a single study session the night before. However, research confirms the difference: the single metastudy of the effects of distributed vs. massed practice (Donovan and Radosevich) found undeniable benefits to distributed practice.
Interleaving, or mixing topics within a single session, is also intuitively true and research-backed. As teachers, we’ve all assessed students on a single topic and seen signs of “mastery,” only to reassess that topic within a mixed problem set or larger exam only to find clear evidence of struggle. Studies into the conditions of effective practice demonstrate that skills need to be integrated before we can declare true mastery.
In Practice
Bringing mixed interleaving of microskills into every math classroom isn’t hard–but it does require pre-planning. First, ensure dedicated time for retrieval in every lesson. In many classes, this takes the form of a do now or bell ringer; it can also present as an out-loud questioning sequence (“oral drill” style – see here for one such example from the classroom of math-great, Denarius Frazier), mini launch questions at the start of new material, nightly homework, or a weekly round-up quiz.
Next, create a scope and sequence for retrieval. While there should be open space in the sequence to be responsive to data needs as they arise, much can be planned before the start of a year. Review the grade level and precursor standards as well as the final exam, and space microskills across daily retrieval opportunities so that each is touched on a minimum of four times in the year (and ideally more!).
Finally, create a system to track mastery—even a simple Excel sheet reviewed every few weeks in department meetings or with instructional coaches can do the trick. Teachers looking to take this to the next level can publicly share fluency data with students and use it to create challenges and competitions to promote both class and individual growth. The options here are endless!
So try it out! Including regular fluency opportunities for your students can help free up cognitive resources to attend to new and increasingly complex math, which is key to achieving at the highest levels. And if you liked this post, join us here next month for our newest installment on methods for introducing this increasingly complex new material with students – we’ll see you then!