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A recent research review (by Paul L. Morgan, George Farkas, and Steve Maczuga) finds that teacher-directed mathematics instruction in first grade is superior to other methods for students with “math difficulties.” Specifically, routine practice and drill was more effective than the use of manipulatives, calculators, music, or movement for students with math difficulties.

For students without math difficulties, teacher-directed and student-centered approaches performed about the same.

In the words of the researchers:

In sum, teacher-directed activities were associated with greater achievement by both MD and non-MD students, and student-centered activities were associated with greater achievement only by non-MD students. Activities emphasizing manipulatives/calculators or movement/music to learn mathematics had no observed positive association with mathematics achievement.

For students without MD, more frequent use of either teacher-directed or student-centered instructional practices was associated with achievement gains. In contrast, more frequent use of manipulatives/calculator or movement/music activities was not associated with significant gains for any of the groups.

Interestingly, classes with higher proportions of students with math difficulties were actually less likely to be taught with teacher-directed methods — the very methods that would be most helpful!

Will’s Reflection (for both Education and Training)

These findings fit in with a substantial body of research that shows that learners who are novices in a topic area will benefit most from highly-directed instructional activities. They will NOT benefit from discovery learning, problem-based learning, and similar non-directive learning events.

See for example:

  • Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching. Educational Psychologist, 41(2), 75-86.
  • Mayer, R. E. (2004). Should There Be a Three-Strikes Rule Against Pure Discovery Learning? American Psychologist, 59(1), 14-19.

As a research translator, I look for ways to make complicated research findings usable for practitioners. One model that seems to be helpful is to divide learning activities into two phases:

  1. Early in Learning (When learners are new to a topic, or the topic is very complex)
    The goal here is to help the learners UNDERSTAND the content. Here we provide lots of learning support, including repetitions, useful metaphors, worked examples, immediate feedback.
  2. Later in Learning (When learners are experienced with a topic, or when the topic is simple)
    The goal here is to help the learners REMEMBER the content or DEEPEN they’re learning. To support remembering, we provide lots of retrieval practice, preferably set in realistic situations the learners will likely encounter — where they can use what they learned. We provide delayed feedback. We space repetitions over time, varying the background context while keeping the learning nugget the same. To deepen learning, we engage contingencies, we enable learners to explore the topic space on their own, we add additional knowledge.

What Elementary Mathematics Teachers Should Stop Doing

Elementary-school teachers should stop assuming that drill-and-practice is counterproductive. They should create lesson plans that guide their learners in understanding the concepts to be learned. They should limit the use of manipulatives, calculators, music, and movement. Ideas about “arts integration” should be pushed to the back burner. This doesn’t mean that teachers should NEVER use these other methods, but they should be used to create occasional, short, and rare moments of variety. Spending hours using manipulatives, for example, is certainly harmful in comparison with more teacher-directed activities.