Stanford professor, Dr. Jo Boaler, recently published an article titled, "Memorizers are the lowest achievers...". In it she makes the point that some students are really good at memorizing math facts and memorizing math procedures, but (sometimes) these same students are very poor at understanding the concepts connected to these math procedures. To those who believe that "mathematics" is nothing more than adding and multiplying, it may seem odd that we (educators) view this issue of memorizing as a bad thing. It may also seem untrue that these memorizers are low achievers.
Dr. Boaler goes on say that here in the United States, we (often times) reward students for being good at memorizing math facts, but offer very few compliments and rewards for being good thinkers and reasoners. She says that, "We need students who can ask good questions, map out pathways, reason about complex solutions, set up models, and communicate in different forms." These are the skills that help students to be good and successful learners, as well as helping them to understand the abstract, higher-math skills taught in upper Algebra classes and Calculus.
NCTM (National Council of Teachers of Mathematics) President, Cathy Seeley, wrote a great book titled, Faster Is Not Smarter. In this book, Ms. Seeley stresses the importance of teaching mathematics for understanding and not just for "getting the right answer".
High school mathematics teachers will tell you that it is a common situation to have students in (say) an Algebra 2 class or a Pre-Calculus class that were consider great "math students" in elementary and (maybe) in middle school, but then suddenly began to struggle in mathematics in high school because they never really "learned" and understood the mathematics; instead, they just did their best to memorize facts and procedures. This sort of "learning" is not permanent. The basic skills of (say) operations with fractions and integers (positive and negative numbers) are quickly forgotten because they were never really learned in the first place.
But this situation can be changed. For some it is a huge change from the way we were taught and from the trainers we received as teachers. For others, it is a very welcome change to the way mathematics teaching needs to be.
It isn't about grades. It's about learning. We need to have a good balance between procedural knowledge and conceptual knowledge. If we intend to truly prepare our students the best we can for their futures, we need to equip them with the tools to success. It isn't fair to give students (and their parents) the false impression that they are highly-able just because they are good at memorizing or getting the answers fast.
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