Vision of Mathematics Statement
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School
University of Washington *
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Course
170
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
2
Uploaded by BrigadierMoleMaster3707
Mathematics should be taught in diverse ways to cater to individual learning styles. The first mathematical concept is important for me because everyone learns at different paces and ways. I remember my first math class at the University of Washington. I had always done well in high school in terms of math, but this course was nearly impossible for me to comprehend. I tried watching the lectures over and working with peers, but I could not understand and eventually failed. I ended up taking the course again later with a different teacher
and it was much more comprehensible. I think it’s important to acknowledge that learning styles are different, which is why educators need to teach in diverse ways if they want students to succeed. One example of this can be seen in the “Check Your Understanding: Measurement & Partitive Meanings of Division” on canvas. For example, “12 ÷ 3 = ?” is given in two different contexts in a story: measurement and partitive. Explaining to students different contexts, using story problems, and visual aids (i.e. direct modeling) are all tools that can help cater to the different learning styles of children. Another thing that’s important to acknowledge regarding unique ways of learning is that processes towards finding the answer can be different. For example, the four types of invented algorithms for division are used by and favored by individuals depending on their comfort level. In class, we practiced all four types: partial quotients, multiplying up, halving and halving, and the “Big 7” strategy”. While discussing with my table partner and comparing with the class, I noticed that some people are able to quickly solve the equation with one strategy but not the others. I realized this is because some people have practiced and utilized one method more than the others, so learning the new style was more challenging. This can be applied to all fields of math for any individual. Teachers do not know the previous knowledge a student holds when a course starts. Some individuals will be more confident in concepts, while others are learning it for the first time, so teaching the class in different styles will accommodate everyone and push towards conceptual understanding. I want educators to not generalize their students, so they can open their minds to different ways of teaching. Mathematics should be taught in a way that focuses on conceptual understanding.
This concept is important to me because I have struggled and succeeded in math classes based on the teaching style. As someone who memorized procedures and lacked conceptual understanding, I started to struggle at higher level math. Chapter 2, titled, “Equality” by Carpenter et al. further emphasizes the importance of foundational knowledge. When given the equation, 8 + 4 = ロ + 5, “fewer than 10 percent of the students in any grade gave the correct response of 7” (pg. 9). The data shown in chapter ultimately prove that “students harbor serious misconceptions about the meaning of the equal sign”. After reading, I thought about how educators should teach to accomplish relational understanding. This connects to the first mathematical statement because I think it’s important for teachers, tutors, and other childcare professionals to teach concepts in different ways. For example, in class, along with module three, we learned how to operate in
base six. During class, we used direct modeling as a tool to help us
understand. My table partner and I had a bag of coins and we worked together to solve problems the professor gave to us. Once we solved a set of
equations, the class came together and discussed their answers. This exercise allowed me to understand how our current number system works and interacts with each other. Understanding base 6 made me relearn mathematical concepts of bases so I can apply it to other bases such as base-10 or base-12. Educators should always look towards new ways of teaching, so their students can grasp the deeper concepts. I like how both of these resources allow me to better understand the importance of foundational understanding, because individuals can get away with memorization which will hurt them in the long run.
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