Bridges & Meaningful Distributive Practice
Meaningful Distributed Practice (MDP), is a technique incorporating big ideas of a grade level via short instructional tasks. Research from the University of Iowa has shown that implementing MDP increased students' conceptual understanding and skill development. These brief tasks improve classroom discourse because they provide students time to think and share their ideas in large and small group settings.
In distributed practice, the student distributes their study effort in a given course over many study sessions of relatively short duration. In contrast, massed practice (otherwise known as cramming), uses fewer but longer study sessions. Distributed practice promotes meaningful learning, while massed practice promotes rote learning.
Any classroom teacher knows that one unit on place value or fractions generally does not result in meaningful learning for all students. That’s why in Bridges we return to concepts and skills in multiple units, Work Places, and Number Corner throughout the year.
To see the progression in your current unit of study, check the Correlations document or the Skills Across the Grade Level chart. Use the tools to determine when the standard was introduced (which might have been in the previous year) and where and when the concept returns in future units and months. Throughout the year we revisit the concept in new settings, with new materials, models, strategies, and expectations for mastery. This approach distributes the practice over time, in a variety of ways, and contributes to a deeper conceptual understanding and procedural fluency.
In first grade, for example, standard 1.OA.C.6 from the Operations & Algebraic Thinking domain requires the following:
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on, making ten, decomposing a number leading to a ten, using the relationship between addition and subtraction, and creating equivalent but easier or known sums.
This standard requires deep understanding, developed over time. That is why first grade develops strategies for adding and subtracting within 10 and then 20 over the course of the year—in all eight units and many Work Place games as well as in Calendar Grid, Computational Fluency, Days in School, and Number Line workouts in Number Corner. Meaningful learning is distributed over time to give students an opportunity to make sense of the strategies, the inverse relationship between addition and subtraction, and the properties of operations.
For a fourth grade example, consider standard 4.NF.A.2 from the Number & Operations—Fractions domain. It requires the following:
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Again, deep understanding of this standard develops over time. Fourth graders explore fractions in Units 3–7 and several Work Places. They also practice these understandings in Number Corner’s Calendar Grid, Calendar Collector, and Computational Fluency, which pre-teach and re-teach the standard. This spaced practice helps students “know and remember” as they encounter a variety of rich experiences over time.
We remain focused on the critical areas, the major work of the grade, and the rigor and coherence implied by the new standards. We also understand how children learn. If we tried to teach these concepts by cramming, students wouldn’t remember what they heard. Interesting and engaging tasks, spaced over time, increase their cognitive demand and long-term understanding.
Pia Hansen is the director of professional development for The Math Learning Center.