“Mathematical Fluency: The Nature of Practice and the Role of Subordination”
Question #1:
Throughout his article Dave Hewitt argues that practice is not always the best way to learn a mathematical concept. He believes that learning math by just doing practice questions is not a very good way to retain knowledge. Practicing math by doing question after question helps students remember the concept for a short period; therefore, this type of practice helps students do well on tests. However, this type of practice does not help the students remember the concept after an extended period of time. Hence, students always need to review math concepts they learned during previous years at the beginning of a school year because they are not retaining the information in their long-term memory. Furthermore, Hewitt argues that giving students more questions to do and having them practice a task more often is not practical nor does it help them remember the concept. Additionally, Hewitt argues that children do not become good walkers by just practicing walking on flat surfaces. They become good walkers by practicing walking up stairs and trying to run.
Overall, I agree with some of Hewitt’s argument, but I disagree with others. I think that just practicing something for a short period of time will not allow a person to retain what is being practiced in his/her long-term memory. I think that, with only a little practice, a person can retain information in his/her long-term memory if he/she has a “deep” understanding of what is being practiced. However, unlike Hewitt, I believe that if a person practices something a lot or for a very long time he/she is retaining the information in his/her long-term memory. For example, I think a person will excel at hockey if he/she starts practicing at a young age and practices a lot. However, similarly to Hewitt, I think it is not always practical to do hundreds of questions for practice. Therefore, I think that to retain mathematical knowledge for a long period of time, a person had to have a deep understanding of the topic.
Question #2:
According to Hewitt, subordination is an excellent tool in learning and math learning. Hewitt argues that through subordination a person can learn a skill so well that when he/she carries out the skill he/she does not have to pay much attention to what he/she is doing. Hewitt believes that tools and methods are remembered faster and a better understanding exists of them if they are practiced through subordination to another task. Therefore, concepts and methods that are learned through subordination of another task are retained longer than if the concept or method is the focus of attention. Therefore, math students should be taught mathematical topics and concepts through subordination. According to Hewitt, if math is taught through subordination then the student will remember the concept for a longer period of time and not constantly need to review the concept.
I found Hewitt’s argument about subordination to be very interesting. Before reading this article I had never heard of subordination being used to teach a concept or topic. I think learning a concept/topic through subordination can help a person retain the information for a long period of time. I really liked the way Hewitt used subordination to teach his students linear equations. I would really like to use the method that he used to teach my students about linear equations because I think by using this method students will get a better understanding of linear equations and how to solve them. Moreover, I feel that through the use of subordination in learning, students are not just using memorization – which is a good thing. Overall, I agree with what Hewitt has to say about subordination.
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