5 Strategies to Help Your Students Master Math Learning
Recently I read an article in EdWeek about the importance of mastery learning to helping students recover learning they might have lost during the pandemic (or over the summer). What struck me, and you know I love data, was that although 84% of teachers polled thought mastery learning was essential, only 53% use it in their classrooms. I agree that mastery learning is fundamental to math instruction as I believe that given the right instruction and support, every child can achieve math success. In fact, that’s one of the core tenets of the ORIGO philosophy.
Mastery learning states that students must demonstrate mastery of prerequisite concepts or skills prior to moving on to learn new content. This is particularly important in math as it builds upon itself, you need to have a strong understanding basic concepts before moving on to increasingly more complex content.
Given the importance of mastery learning to your students’ math success, I want to share five strategies that I believe are most essential to successfully implementing mastery learning in your math classroom.
Strategy 1—Adopt an Instructional Approach that Supports Mastery Learning
At ORIGO, we use a four-step instructional approach—introduce, reinforce, practice, extend—that provides students with a deep understanding of standards-aligned content. But whether you use ORGIO Stepping Stones 2.0 or another curriculum program, it’s important that you follow an instructional methodology that facilitates mastery learning as follows:
1. Introduce new skills by employing concrete and pictorial models that help students “see” the math and use context to make learning meaningful and relevant. At this stage, you are helping students begin to lay down an understanding of the underlying concepts.
2. Reinforce with games and activities that help students internalize their thinking and connect the visual models used to introduce new concepts to the symbolic representations of the practice stage. This connection, a critical step often overlooked in traditional programs, allows students to further cement their understanding and move toward abstract reasoning.
3. Allow students to practice the skills with symbols frequently and in short time periods to help them develop accuracy and speed. This stage also improves students’ ability to quickly retrieve information and reinforces math fluency.
4. Provide opportunities for students to extend their skills to new situations, which often involve greater numbers. At this stage, students are showing true mastery by applying what they have learned to connected, but more complex problems.
Strategy 2: Practice Spaced Learning
One of the things I hear over and over is that students just aren’t retaining previously taught information, an issue which has only become more prevalent during the last two years. Mastery learning (and math learning) requires that students use previously learned skills to understand new concepts. This is where spaced learning can help. Pacing short practice sessions of a particular skill over time (spaced learning) has been shown to help students learn faster and retain information better. According to John Hattie’s seminal research, spaced teaching and practice has an effect size of .60, which means that students realize 1.5 years of learning in one school year.
So, what does this actually look like? Here are a few examples:
Strategy 3: Encourage Math Talk
Finding the time for robust math discourse can be hard, but I think it’s essential to mastery learning. Having your students explain their approach to a problem and their reasoning behind choosing a particular strategy has been shown to improve memory, develop math language, boost confidence and interest in math, and enhance metacognitive development. Additionally, math discussions allow students to learn from other students’ thinking, promotes collaborative learning, and demonstrates that often there is more than one way to solve a problem. And, you will learn a lot about what your students know (and don’t know) about the underlying concepts being taught, a critical component of mastery learning.
Strategy 4: Give Your Students Regular Feedback
I can’t overstate the importance of regular feedback; it’s an essential component of mastery learning. Your students need to know how they’re doing and how they might improve. Let them know what they are doing correctly, and where they may need further practice, and be specific. Focus on the skill being taught, not the student. Try to give the feedback at the time they are showing what they’ve learned, so that they connect your input to the skill they are working on. Personalize your feedback to match each student’s learning style. And finally, remind students that learning from mistakes helps them be better mathematicians. Providing regular, student-focused feedback provides every student with the opportunity to learn and grow.
Strategy 5: Memorize & Rehearse
Yes, I said memorize. But only at the right time. Research shows us that memorization as an introductory instructional strategy simply doesn’t work. However, that same research states that memorization (or knowing something from memory) and rehearsal (mental techniques used for recall) when used at the end of instruction, to consolidate learning dramatically increases student learning. According to John Hattie, memorization and rehearsal to consolidate learning has an effect size of .73, which means that students realize 1.8 years of learning in one school year.
Casebourne, I., (2015). Spaced Learning: An approach to minimize the forgetting curve. Elements: Self-paced learning library
Talk Moves: A Teacher’s Guide to Using Classroom Discussions in Math. Suzanne H. Chapin, Catherine O’Connor, Nancy Anderson. Math Solutions. 2013.