September 27 Reflection

This week was another enriching week in my mathematics teacher education where I learned concepts that will alter my math teaching philosophy. The primary focus of the week was working with whole number operations and the algorithms we use in order to solve these operations. The more traditional approach to teaching these kinds of operations like multiplication or addition was to explain to students the most efficient algorithm and practice the process many times as a method of reinforcement. However, I have learned that this is not always the best method because it does not allow students to process the question in a way that makes sense to them. In my opinion, it is not only important to teach students the mathematical processes, but also help them understand why that process works. As Marian Small points out in her book Making Math Meaningful to Students, students should be encouraged to invent their own algorithms and use the ones that suit them. It is the job of the teacher to anticipate this occurrence and to ensure that the process used is one that can be effective for any similar question. Here are some examples that Marian Small provides for the alternative methods that can be used to prime factor numbers, the factor tree and the factor rainbow. 

Gill, Zachary. From Small, Marion Making Math Meaningful. (October 3, 2016) Factor Rainbow.

Gill, Zachary. From Small, Marion Making Math Meaningful. (October 3, 2016)  Factor Tree. 

This can also be demonstrated using multiplication, as shown in the picture below. 

Gill, Zachary. (September 27, 2016) 

From these pictures we can learn that there are multiple alternatives to solving equations and we as teachers need to be open to letting students explore these different avenues. Instead of focusing on efficiency, we need to equip our students with the ability to problem solve and learn about why mathematical processes work. 

On top of all of this information I also learned about how teachers need to educate students about why math is important. I believe that in order to get students to be focused and excited about math teachers need to show that math is meaningful to their everyday lives. I feel that another way students can get excited about math is to make it a fun experience! I believe that this can be done using manipulatives so students can see how mathematical processes work. It can also be accomplished through the use of educational games. For example, I got a chance to play Puppy Chase this week where the player answers fraction questions as fast as possible to get students to win the race. Finally, math can become a fun experience if the questions apply to events in their lives that they can relate to. In my teaching practice I like to create questions or use examples of math processes using the latest trends to grab attention. For instance, Pokemon Go can be incorporated into a math question so students have more motivation to solve it. Most importantly, all students need to know that they have the capability to excel at math if they place enough effort into it. Here is a fun video by a teacher who has grasped these ideas and made a presentation about how math is fun and meaningful.