Blog Post 1: Weeks 1-3
Week 1
In class we discussed the growth mindset, as understanding we can all progress in our learning through practice and teacher support. I had always believed as a student that my intelligence was fixed, and subjects that I struggled in would never become easier. I believed that I would never become better at subjects like math because I just didn’t have a math and science brain. Instead I had an arts and English brain, and these were the subjects I would do well in. I wish a teacher had helped me to understand sooner that just like learning a musical instrument, I could become better at math through practice. I also believe as a teacher it is vital to show students’ they aren’t stupid if they cant complete a problem. To show students their minds can grow will help them become motivated to learn. Bell, Hill and Bass (2005), discuss that teachers should not just present math at the front while students listen, but explain fully, use models that are useful to students, and listen to the students. This kind of constructivist teaching would engage students as they are part of the math lesson. I think this kind of involvement would also help students see they can have math brains too!
Week 2
In class we discussed how students need to become patient problem solvers, meaning they don’t get discouraged the first time a problem seems difficult, but work through such challenges with varying strategies. I think it is very important in a technological age with instant gratification that we teach students that not all answers can be found at the click of a button. Students will face problems in their life, in and outside of math related content, that are more difficult to solve than a one step problem. Thus, teachers must prepare students to solve problems using a variety of strategies and to use perseverance and collaboration when problems seem to difficult. Part of helping students solve these problems is understanding how to teach in a way that promotes patient problem solving. This requires teachers to have not only math knowledge, but knowledge on how to teach math in a way that helps students succeed (Hoover et al., 2016). Teachers need to know how to construct open ended problems, work with students to create problem solving strategies and encourage collaboration for deeper thinking.
This news article discussed patient problem solving.
Week 3
In class we discussed the difference between instrumental understanding (understanding through procedural steps how to solve a problem) versus relational understanding (understanding the concept of how and why you solve a problem that way). While we discussed these types of teaching styles for math in opposition, I believe they need to be used together to create full understanding. Students need to understand the steps to solve a problem, but also have the deeper knowledge of how these steps work. I was taught using only instrumentally and it made me frustrated that I would never be given a why on how we completed problems. It also meant frustration that formulas only applied to one situation, so if a problem was ever worded differently, I struggled to be able to solve the problem. I want to be able to give my students the relational knowledge in order to understand math in a real-life context. However, I am concerned that I don’t have the content knowledge to complete this goal.
This Blog discusses instrumental vs relational understanding.
References
In class we discussed the growth mindset, as understanding we can all progress in our learning through practice and teacher support. I had always believed as a student that my intelligence was fixed, and subjects that I struggled in would never become easier. I believed that I would never become better at subjects like math because I just didn’t have a math and science brain. Instead I had an arts and English brain, and these were the subjects I would do well in. I wish a teacher had helped me to understand sooner that just like learning a musical instrument, I could become better at math through practice. I also believe as a teacher it is vital to show students’ they aren’t stupid if they cant complete a problem. To show students their minds can grow will help them become motivated to learn. Bell, Hill and Bass (2005), discuss that teachers should not just present math at the front while students listen, but explain fully, use models that are useful to students, and listen to the students. This kind of constructivist teaching would engage students as they are part of the math lesson. I think this kind of involvement would also help students see they can have math brains too!
Week 2
In class we discussed how students need to become patient problem solvers, meaning they don’t get discouraged the first time a problem seems difficult, but work through such challenges with varying strategies. I think it is very important in a technological age with instant gratification that we teach students that not all answers can be found at the click of a button. Students will face problems in their life, in and outside of math related content, that are more difficult to solve than a one step problem. Thus, teachers must prepare students to solve problems using a variety of strategies and to use perseverance and collaboration when problems seem to difficult. Part of helping students solve these problems is understanding how to teach in a way that promotes patient problem solving. This requires teachers to have not only math knowledge, but knowledge on how to teach math in a way that helps students succeed (Hoover et al., 2016). Teachers need to know how to construct open ended problems, work with students to create problem solving strategies and encourage collaboration for deeper thinking.
This news article discussed patient problem solving.
Week 3
In class we discussed the difference between instrumental understanding (understanding through procedural steps how to solve a problem) versus relational understanding (understanding the concept of how and why you solve a problem that way). While we discussed these types of teaching styles for math in opposition, I believe they need to be used together to create full understanding. Students need to understand the steps to solve a problem, but also have the deeper knowledge of how these steps work. I was taught using only instrumentally and it made me frustrated that I would never be given a why on how we completed problems. It also meant frustration that formulas only applied to one situation, so if a problem was ever worded differently, I struggled to be able to solve the problem. I want to be able to give my students the relational knowledge in order to understand math in a real-life context. However, I am concerned that I don’t have the content knowledge to complete this goal.
This Blog discusses instrumental vs relational understanding.
References
Small, M. (2013) 3nd Edition. Making Math Meaningful to Canadian Students, K-8. 3rd Edition, Toronto, Nelson.
Ontario Ministry of Education. (2005). The Ontario
curriculum grades 1‐8: Mathematics. Retrieved from http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf
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