This week one of the articles that we read was called “Tying It All Together: Classroom Practices That Promote Mathematical Proficiency for All Students”. The article talks about a lot of important concepts that teachers can utilize to help create proficient math learners but there was one that stood out to me the most. One of the concepts covered was called “Modeling Math Meaningfully”. The idea behind this is that when students use multiple ways of showing their work and the answer to a math problem, they create more connections. This technique has students using manipulatives, pictures, real-life scenarios, verbal symbols, and written symbols in order to create connections and understanding.
Why does using multiple ways of solving the same problem work? It works because more understanding is being created. When we solve a math problem only one way, a lot of times we aren’t really sure what we did or why we did it. When students have to prove their answer in more than one way they are proving that they truly understand the concept at hand. If they can show understanding through drawing a picture, talking about it, and showing it with manipulatives, there is a deeper level of understanding and more confidence. Many of the math students who are not confident in their abilities (ME!!!) feel that way because they lack true understanding of the math that they are working with. Even if they can solve a problem and/or work through different formulas and problems they don’t truly understand. It is essential that students know what they are doing, why they are doing it, how they are doing it, and how to apply those things outside of a structured classroom activity.
What does all of this mean for my future classroom? After reading this article I http://www.blogger.com/img/blank.gifwill be using the method that the author suggested for modeling math meaningfully. My students will not only be required to show their work but they will be required to show it in multiple ways. If I am holding them accountable to showing their work I also need to hold myself accountable. I need to provide plenty of opportunities for students to explore math and allow time for them to work out the problems at hand and really think about what they are doing and why.
One of the ways that students can solve problems is with manipulatives. Often times teachers can run out of ideas or not know how to use them in the classroom. Scholastic provides some excellent links to provide teachers with tips and ideas about how to use manipulatives effectively.
Hi, I am an Elementary Education major and am in the semester where we learn about teaching math! This blog post really helped me realize how important modeling is and along with that modeling meaningfully. I reminisced about my elementary math experience and all I could think was how helpful these strategies would have been! These practices give the students the opportunity to explore on their own and form their own conclusions. It's amazing how much I have learned already about how much more effective the instruction is for the students when they get that time to explore the manipulatives and relating it to real life problems. These connections are so important for the students. I skimmed over the article you mentioned and one section really struck me. There is such a bad stigma associated with math. I had a bad experience with math in high school, it was Geometry. The teacher didn't make it interesting for us, it was just worksheet after worksheet, I didn't make any connections that made her instruction meaningful. However when I was in Algebra 2, I excelled and was even a tutor for some students. The teacher explained it in a way that made sense to me and I still remember most to this day. Also from the article she would make us prove how we got the answer in a variety of different ways. She said if you are able to figure out the answers using different strategies this will ensure that mastered the skill and you will be able to consistently solve these problems.
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