According to Dr. Daniel Ansari, there has been a fearsome ongoing debate about the most effective way to teach math—rote learning tactics versus discovery-based strategies—that has failed to take into account the vast research findings about how children learn math.
The side that advocates “procedural knowledge” emphasizes explicit teaching of strategies and encourages students to memorize facts while the side advocating “conceptual knowledge” focuses on student construction of knowledge through hands-on materials, strategic-invention, and solving of open-ended questions that do not involve memorization. Neither side, in this polarized and emotional debate, has any use for the other. Keeping the previous blog post in mind (that some mathematical procedures are not intuitive and the subsequent symbols are not mental representations), it would seem that conceptual knowledge could only carry us so far. It seems we require the environment (in this case the math symbols as objects and procedures) to carry some of the cognitive weight. But any observer in today’s classroom can witness the limitations of rote memorization as well. Indeed, Daniel Ansari’s investigation found that children learn best when procedural and conceptual approaches are combined. “Researchers [like Bethany Rittle-Johnson] have demonstrated that an effective use of instructional time in math education involves alternation of lessons focused on concepts with those concentrated on instructing students on procedures.” It turns out that different parts of the brain are used in the various methods such that both approaches are interrelated and mutually determine successful outcomes in math acquisition. One of the specific arguments by the discovery-based camp targets time limits in math education: they oppose tactics such as the commonly known as “mad-minutes” wherein students must calculate multiplication products quickly. Ansari points out that there is no evidence that “speeded instruction necessarily has negative consequences.” In a study to which Ansari contributed, he found that young adults who performed better on high school math tests had more areas of the brain active: specifically, the fact retrieval area located in the left hemisphere was active whereas the students who achieved lower scores “recruited brain regions associated with less efficient strategies, such as counting and decomposition in areas of the right parietal cortex.” The “data suggests that math fluency and its neural correlates contribute to higher-level math abilities.” Since speeded practice in combination with other approaches results in “larger gains” it is thus useful for helping “low-achieving students in overcoming their math reasoning difficulties.” With his emphasis on research-based evidence, Ansari advises us to consider what is appropriate for the developmental level of the student when considering the sequence and content of learning. He leaves us with this important reminder: “[l]earning math is a cumulative process—early skills build on the foundations for later abilities.” If students enter the classroom without the necessary background in mathematics, if numbers and patterns are largely unfamiliar to students, then we must go back to square one with them. The next blog takes a peak at what that might look like in the classroom. References Ansari, D. (2015). No more math wars: An evidence-based, developmental perspective on math education. Education Canada, 55 (3), 16-19.
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AuthorNatalie Nickerson; that's me. Archives
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