Findings
I have decided to focus on two main findings based off of my research:
1. Building upon mathematical concepts strengthens procedural ability.
This is the same finding from my first phase, but strengthened because of the data I collected on the pre- and post-tests. In the pre-test, most students were unable to solve for the multiplication equations and show them using concepts. After instruction on different concepts on how to break down multiplication, the students performed much better on the post-test. I believe this is a direct correlation of the instruction on mathematical concepts.
2. Providing varying solving methods affords students a better chance to solve problems
When showing the two different ways to show the multiplication, the students all used different methods in showing how to solve. This tells me that different concepts resonated differently with different students. I believe that it is important to note that students did not all use the same method. By teaching the different methods, it is possible that at different points students begin to understand the concepts. Each student might connect differently, and by giving them an arsenal to choose from we are providing each student with the best opportunity for success.
Phase 2 was an opportunity to tackle one of the building blocks of mathematics: multiplication. By addressing some of the concepts, it was a unique experience to see how this aided the students in their problem solving ability. I would love to see how this addressing of the concepts holds up over time, as well as to see how the students utilize their new knowledge. With more time permitting, I would love to see if the students still draw upon these concepts to solve in future math problems.
1. Building upon mathematical concepts strengthens procedural ability.
This is the same finding from my first phase, but strengthened because of the data I collected on the pre- and post-tests. In the pre-test, most students were unable to solve for the multiplication equations and show them using concepts. After instruction on different concepts on how to break down multiplication, the students performed much better on the post-test. I believe this is a direct correlation of the instruction on mathematical concepts.
2. Providing varying solving methods affords students a better chance to solve problems
When showing the two different ways to show the multiplication, the students all used different methods in showing how to solve. This tells me that different concepts resonated differently with different students. I believe that it is important to note that students did not all use the same method. By teaching the different methods, it is possible that at different points students begin to understand the concepts. Each student might connect differently, and by giving them an arsenal to choose from we are providing each student with the best opportunity for success.
Phase 2 was an opportunity to tackle one of the building blocks of mathematics: multiplication. By addressing some of the concepts, it was a unique experience to see how this aided the students in their problem solving ability. I would love to see how this addressing of the concepts holds up over time, as well as to see how the students utilize their new knowledge. With more time permitting, I would love to see if the students still draw upon these concepts to solve in future math problems.