This was a fascinating lecture on mathematics and understanding. Dr. Clarke’s warning was this: conceptual knowledge may be extinguished (even lost) in the process of gaining procedural knowledge.
I can really understand the truth behind this message. We are teaching students to understand mathematics in the younger grades. But, when these same students reach the older grades, sometimes we are expecting them to memorize conventional math algorithms instead of remembering the knowledge and the “why does this make sense” behind them.
I can certainly understand how this might be the “easier” route for a teacher to take. Today in our 5th grade math class, we were working on the metric system. This system being based on 10’s and easy to understand. Some of the students who were having trouble converting mm to km or cm to m were asking me for the “formula” or “method”. I told them that I still got confused when converting measurements within the metric system if I didn’t stop to think which way the conversion was going. Meaning, that I have to think through are there more millimeters in a meter or vice versa; then should my measurement number be increasing or decreasing to follow this logic? Some of the students who were struggling just wanted me to give them a formula to follow whether to multiply or divide instead of thinking through the reasoning. We watched a video about “King Henry Died unexpectedly Drinking Chocolate Milk” (K – kilo, H – hecto, D deka, U – unit [meter, liter, gram], D – deci, C – centi, M – milli) to give them a method to remember the order. But then, I told them about how I didn’t remember if I should divide or multiply but remembered what order they were in and how the relevant size would determine getting “larger” or “smaller”. I really wanted the students to understand the concept behind the conversions and not just formula. Not because I’m against formula, but because I know it is difficult for me to remember which way a formula should “go” but I can remember the concept behind the idea.
I love that Dr. Clarke is reminding us (pre-service teachers) to teach concepts and understanding and not just formula and memorization. Students should know the “why” and understand the sense-making of math and not just numbers/figures/formula.
Katie, how do you feel about this topic? You are a science major and much more comfortable with math than I am. Does this change your view on the subject? And further, does there come a point in mathematics where we must say “do it this way because that’s what you need to know to pass the test”? I don’t know; but, I hope not 😦