Think about a basketball team. To get better, players need to practice, and practice should incorporate a variety of drills to work on skills like dribbling, shooting, and layups—but practicing skills in isolation is unlikely to lead to a winning team. To be prepared for a game, practice needs to incorporate game-like situations that help players learn how to work strategies and make decisions under pressure.
Math practice works similarly. Practice needs to reinforce students’ abilities to apply procedures accurately, efficiently, and flexibly. However, students also need practice integrating concepts and techniques as well as opportunities to support and justify their choices of appropriate procedures. A rigorous math practice routine will include a mix of the fundamentals and scrimmage work.
In an earlier post, my colleague described five math practice myths that can lead to ineffective pratice. In this post, I’m going to explore the qualities that lead to effective practice, and, in turn, stronger, deeper learning and better “game day” results.
Good math practice . . .
1. Is Purposeful
Good math practice is so much more than busywork. Strong practice clearly aligns to lesson goals and is moderate in length or number of problems. Students don’t necessarily need to solve a lot of problems to understand a concept.
2. Looks Different Depending on Where Students Are in the Learning Progression
Students need practice opportunities that align with the steps of their learning progression. For example, when students are just being introduced to a concept, they need practice that helps them make connections between the new concept and their prior knowledge. At this point, giving students a worksheet with 30 skill and procedure problems might overwhelm and confuse them. The key is to have the focus of the practice align with where students are on their learning journey.
3. Provokes Discourse and Engagement
Meaningful math discourse engages students and helps them learn from one another. Practice that inspires students to talk about their problem solving and reasoning also helps teachers understand where students are in their different math journeys and adjust instruction accordingly.
4. Presents the Right Amount of Challenge
Practice should elicit productive struggle, but it should be accessible to all students. Strong practice questions promote math reasoning, advance problem-solving skills, and can be solved several different ways. The best kinds of practice offer students multiple entry points.
5. Continues beyond Proficiency
Research has shown that for practice to be effective, it should be distributed across topics over time—a practice that’s known as “spaced learning,” “distributive learning,” and/or “interleaved practice.” Once students have become proficient with a concept, they should practice recalling and using it across different types of problems months—and even years—into the future.
Interested in learning more about math practice?
Read “Math Practice Myths (and What Teachers Should Do Instead).”LEARN MORE
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