In the reading, the author made some good points about how teachers should teach math and how math can be a great language to communicate. His ideas on how we should "distinguish between using things in the world around us to do math, and using math to understand the world around us" really struck me. Many textbooks use "real-world examples" to put the topic into students' perspectives, however, such problems just make students wonder why they have to learn all that and eventually grow to hate the subject. Even though those problems have been made to link math to students' daily life, some even fail to address the importance of learning such math concepts and how those are applied to certain real-life situations. Rather than just introducing new math concepts and giving them problems to solve using those concepts, school textbooks should let students do more critical thinking about how they can relate math to the real world and how math can explain things around the world. Doing so, students will learn to make connections between math and social justice. Social justice issues are always around them, and if they learn that they could relate math to some of those, they will definitely show more interest in math.
The advantages of instrumental understanding Skemp lists in this article can be viewed as study strategies for students who want to have easier grades and see apparent progress. This type of learning could help students who have had serious problems with mathematics and just need the grades to pass a course. Although my teaching experience is very limited, I have witnessed quite a few students who say they hate mathematics, and some of those students even think that they would not need mathematics in the real world. They might be right in some way, but if they were taught to learn relationally rather than instrumentally, their mathematical approaches towards the world might have been very different. With instrumental mathematics taught, students might think they understand, but they are not able to apply those concepts they learned to different situations. Lack of this skill leads to memory work and eventually boring classes. In boring classes students tend to strive for ...
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