Concept Rich Ch. 1/2

When reading the section on practice I remember that in my K-12 education we did a lot of drilling as practice. It was something that was never very beneficial to me because it did not usually solidify the content in my brain. A particular example of this for me was my multiplication facts. The only way I ever really learned my multiplication facts was through the timed multiplication tables which we had to fill out each day until we were able to do them in the time frame given. Those facts never really found a home in my brain that way and because of that I still sometimes have a difficult time recalling my multiplication facts on demand. I think it had also affected the ability for me to math quickly because I do not know these facts. I sometimes face similar struggles with my basic division and even the higher digit addition problems as they were never ingrained in my brain. This has also been a part of why I have struggled with my Praxis II test so much. With such a short period of time to solve each of these problems my inability to recall these basic math facts has left me to waste much of my time calculating out the basic math, or at least by taking the few extra seconds to type it into the calculator when every second is extremely important.

I’ve chosen to unpack the component of meaning. Meaning is when the concept isn’t taught using only one application, so that students are able to apply the concept to other applications. When you’ve given a concept meaning you have taught it as a generalization so that it can be applied to many situations. As it says on page 32, “Meaningful learning results in conceptualization,” and that is what made me decide to really categorize it as making the concept general so it can be used over and over again. I am a bit scared that I will not be able to accomplish this on topics that I do not have a huge interest in but must teach. I think that when I have a really big interest in the topic it is easy for me to accomplish this, such as with the Pythagorean Theorem, but when it is something which I am only moderately interested in I think that I will struggle to be able to do this and that scares me. Another fear for me that is from a different component is the fear that I will end up drilling my students constantly by accident like I talked about above and thus set them up to struggle the rest of their life with math. I am excited for the many opportunities for freedom which this offers us as teachers. Because it really encourages us to make the concepts general for use with many applications we are able to have a chance to explore all of those applications which we might not have had the chance to had we taught using drills. The components are all connected by the fact that they build on one another about how to help students truly learn the concepts at hand. They each discuss applications of the concepts and how to apply them usefully.

Citation: Meir, B. (2006) Concept-Rich Mathematics Instruction. ASCD: Alexandria, VA. ISBN 978-1-4166-0359-7