All Articles Education Educational Leadership How spaced learning solves a key math problem

How spaced learning solves a key math problem

Having students continually practice recently learned math skills in the midst of trying new ones makes learning easier, Sara Delano Moore writes.

7 min read

EducationEducational Leadership

Happy African American schoolgirl showing her A grade on a test at elementary school and looking at camera. for article on spaced learning

(Skynesher/Getty Images)

If you think about how we learn skills outside of school, we don’t achieve mastery by taking a crash course on a topic. Instead, we develop our skills a little bit at a time, stretching them further with each new exposure.

SmartBrief Education Insights blurbTake basketball, for instance. When you’re learning how to play basketball, you don’t master each skill, like dribbling, before moving on to the next one. Instead, you are shown how to dribble, and you practice this skill for a few minutes each day while also learning other skills and concepts. Over time, you learn more advanced applications of each skill, such as dribbling with your off-hand or crossing over.

In school, however, we typically engage in mass learning of a subject, where students learn a skill and are expected to master it before moving on to the next unit. In a third-grade math class, for instance, the teacher might introduce basic multiplication facts in early October and expect students to master them by Thanksgiving.

This type of learning is like cramming for a test. Students might learn these skills in the short term, but they often don’t transfer this knowledge to their long-term memory. Teaching everything all at once doesn’t result in expertise; instead, our brains need time to practice the information and to consolidate learning.

the forgetting curve for article on spaced learning in math
(Image from Sara Delano Moore)

This is why so many students don’t retain key math learning as their teachers and parents would want. It’s called the forgetting curve. As a result, teachers find themselves having to re-teach earlier material, and they run out of time to address the full curriculum for the current year. 

Spaced learning is a simple method to address this problem, and it’s supported by research.

What is spaced learning?

In spaced learning (also called distributed learning), teachers teach about a topic in smaller doses spread out over time. Students are also given multiple opportunities to practice retrieving and applying their learning, leading to better long-term learning.

Spaced learning intuitively makes sense, as it more closely resembles how we learn in real life. 

In a spaced approach to learning multiplication facts, students might learn these facts in smaller chunks, interspersed with other grade-level learning. For example, students might learn first about doubling for multiplying by two and then extend that idea to multiply by four and eight. These three learning sessions (of several days each) would be interspersed with other grade-level topics (e.g., extending place value understanding or generalizing approaches to adding and subtracting whole numbers). 

During the in-between times, students would be engaging in deliberate practice of the multiplication strategy and facts, allowing them to practice retrieving and using their learning. 

Over time, the teacher will continue to address multiplication facts by strategy, again with deliberate practice after each new learning session. Students will begin to learn about area and division (both using their newly learned multiplication facts) during the instruction between multiplication sessions, providing additional retrieval practice in a different context. 

By the end of the year, students will have addressed the same grade-level content as they would in a more massed approach. By spacing the learning and carefully distributing the practice, students have greater success toward long-term learning.  

Examples of success

Spaced learning has been shown to help students learn faster and retain information better. According to John Hattie’s seminal research on the effectiveness of various teaching strategies, spaced learning has an effect size of 0.60 on student learning. Given that the average effect size of an entire year’s instruction is 0.40, students can retain 1.5 years of growth from this approach in a single year.

“Not all kids are ready to learn a whole concept at the same rate,” a fifth-grade teacher from Virginia told me. “Since we started using spaced learning with the key concepts broken into smaller chunks, kids have the time and the space they need to master a piece of that concept. Because they have time to process and make sense of smaller pieces of content, they build confidence with critical concepts and feel ready to move on when the concept comes back again.”

Maryland’s Worcester County Schools saw what Coordinator of Math Instruction Kristen Danisavich called “amazing” results when piloting an elementary math curriculum with a spaced learning approach.

“One first-grade teacher who helped pilot the program in her Tier 1 inclusion classroom of special-ed and general-ed students reported that, by the end of the year, all her students were at grade level in math,” she said. “In fact, in all five first-grade classrooms that participated in the pilot, the special-ed students actually outgrew their general-ed counterparts.”

Taking a spaced approach to learning also had a remarkable effect on teachers’ attitudes toward teaching math. “Some really didn’t love teaching math at the beginning of the school year,” Danisavich said. “By the end of the school year, their enthusiasm for teaching math had skyrocketed. One teacher told us, ‘It was the easiest time I’ve ever had teaching math. I love teaching math now.’”

4 tips for using spaced learning

Spaced learning can be challenging to wrap one’s head around. Here are four practical ideas for applying this technique in the classroom.

Spread out instruction and practice over time

Break instruction into smaller chunks of information and have students practice using shorter and regular sessions. Students can practice a few problems at a time every other day while they are learning about a different topic in order to practice retrieving and using their recent new learning. This helps consolidate learning for the long term. 

Focus practice on both new and old material

Don’t just focus on new content. Students should practice new learning daily.  In addition, distributed practice, as described above, focuses on retrieving and using past learning. This should include a mix of tasks from recent learning and learning farther in the past. To create his daily homework assignments, one colleague I worked with would assign two or three problems from that day’s lesson, a few problems from the previous week’s content, and a few problems from material introduced the month before.

Help students make connections between concepts

Talking about how the skills and concepts students learn relate to material covered earlier is an excellent way to revisit and reinforce their prior learning. It also helps students amplify their understanding and apply those skills within new contexts.

Look for curriculum materials that take a spaced approach to learning

Spaced learning can take longer to prepare because teachers must thoughtfully design their instruction to pace students’ learning over time. A commercial curriculum product that has been carefully developed with spaced learning in mind can save teachers time in planning and make this process easier.

Too often, students don’t have a chance to review older material until they begin preparing for end-of-year exams. As a result, they don’t retain what they learned earlier in the year. Spaced learning solves this challenge and ensures that students learn and remember key math concepts more effectively — so teachers can simply teach instead of reteaching.

Opinions expressed by SmartBrief contributors are their own. 


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