One of my fears as a future mathematics teacher is presenting my knowledge in a student friendly language that will help them best understand the content being taught. The reason why this is challenging is due to what I would call "mathematical perspective."
What is this "mathematical perspective" that I speak of? Well, in class this week we did an exercise that involved three rounds of a Tug of War between various creatures. The goal of the exercise was to figure out who would win the final Tug of War based on the outcome of the first two.
Figure retrieved from: http://www.fotosearch.com/illustration/tug-war.html
The first Tug of War was a tie between 4 frogs and 5 fairy godmothers. The second Tug of War was also a tie between a 1 dragon on one side and 2 fairy god mothers and 1 frog on the other side. The final round had 1 dragon and 3 fairy godmothers on one side and 4 frogs on the other side, but the outcome was unknown.
Like many mathematics problems, there is only one solution to this Tug of War but, there are multiple ways one could reach that solution (the dragon and fairy godmothers won). These multiple routes to the solution are based on your "mathematical perspective" or how you personally would solve a mathematical problem.
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When our class of nine students was given this problem there were about three different methods to solve this problem, all giving the correct answer. In a high school classroom, this same outcome will likely occur where many different students will have various perspectives at solving mathematics problems. This activity showed us how many students even with the same academic background can look at mathematical problems from different perspectives.
As a future mathematics teacher, I would like to become more familiar with methods that allow me to cater to the various different mathematical perspectives that will be present within my classroom. One of the most interesting and frightening things to me when becoming a teacher is how every student learns differently, but I would like to do the best I can to help each student achieve their full potential.
Ryan
Ryan
Ryan I am happy you brought up the importance and struggles of relating to the various methods students use to derive answers. This is one of the most fascinating parts of education! As a teacher candidate this also makes me a little nervous. The idea of not being able to relate to or understand how a student got the correct answer is difficult. A strategy I plan to implement is basic; slowing down and allowing the student to talk through/justify their reasoning.
ReplyDeleteThanks for the awesome post, it was great to read your thoughts on math!
Hey Ryan, I too found this very interesting. Although all of us in the class have been exposed higher level mathematics at the university level, most of us approached this very basic question in a unique manner. I think the most interesting part of the activity was the debriefing section where we all provided rationale as to why we did what we did. I think this portion of the lesson would be even more critical at the high-school level where every student may not arrive at the correct answer. Hearing their rationale might reveal where or where not they are struggling with mathematics concepts, and will help us as educators tailor our lessons to individual needs.
ReplyDeleteThanks Ry!
Hi Ryan,
ReplyDeleteI think worrying about presenting knowledge in such a way that will help our students best understand the material is a fear we can all relate to. However, I think the fact that we have become conscious that our students may all have a different perspective and approach will only be beneficial for us in the future! Since we are aware of this fact, we can actively work together with our students to approach and solve problems in a variety of ways. I believe that activities like “Tug of War” are beneficial not only for us as teachers, but for our students as well. I think exposure to these types of activities will not only teach our students that their approach may not be the same as ours or as their peers, but it will also teach them communication skills as they attempt to explain their mathematical reasoning.
Thanks for the post!