Enhancing the approach for Teaching Mathematics (Week 4 Reflection)

As a prospective teacher, I have learned various high-level mathematical concepts throughout the many math courses required in my program. However, I have gained little knowledge on how to teach mathematics to students effectively, since very few of these courses were relevant to the grade level I will be teaching.  The article 'Toward a Practice-Base Theory of Mathematical Knowledge for Teaching' argues the notion that learning more advanced mathematics does not necessarily contribute to a prospective teacher’s effectiveness with young students. Therefore, knowing and understanding high-level math does not benefit a teacher’s quality of teaching mathematics. A problem is that prospective teachers do not review or thoroughly study the material that they will actually be teaching in the classroom. Thus, they are not becoming experts on how to teach this material in the most effective way to engage a variety of learners.

 I often hear prospective teachers say that they are worried to teach in their second teachable during their upcoming teaching block because they “haven’t seen some of that material since High School”. It is shocking that even though we have taken many courses related to the subject we will be teaching, we still do not feel prepared or comfortable enough to begin teaching it to students. It seems that inadequate opportunities exist for teachers to learn mathematics in ways that prepare them for work.

            I feel that in order to fix this problem, the concurrent education program should dedicate part of it’s program to courses that review the High School mathematics program and teach us various teaching strategies on how to best teach that material in a variety of ways. We should become experts in the material we will be teaching and be prepared on how to answer any question a student poses during our lessons. Based on the reading 'Toward a Practice-Base Theory of Mathematical Knowledge for Teaching' a teacher successfully showed students how to multiply and divide, however when a child asked for an explanation on why the invert-and-multiply algorithm for dividing fractions works, the teacher could not provide an answer and told the student to just use it as a rule for now.  It is critical that prospective teachers have a strong understanding of the fundamentals of mathematical principles, so that they can properly educate their students on mathematical concepts. Having more mathematical knowledge is useless unless you have the ability to facilitate students learning. It would be most beneficial for prospective teachers to have plenty of practice teaching content to their peers before getting thrown into their teaching blocks. 

            As a student I have not had the opportunity to experience many teachers who were able to properly explain why we use the rules and methods that were being applied. This was very difficult as a learner because I was just memorizing how to do the math instead of realizing when and why certain rules should be used. The teachers that were able to provide explanations had the most positive effect on my learning because remembering the reason why you use a rule has a more lasting impact then simply memorizing when to use it. The understanding of how mathematical principles were derived ensured that I had a deeper and more complete understanding of the material.