The first article I found corresponds with the first standard: Make sense of problems and persevere in solving them. The article is Quick Reads: Problem Solving with Laser Precision by Scott A. Goldthrop, published in Mathematics Teaching in the Middle School.
In this article, Scott explains how his students are given a problem and must find out a way to solve it. Students are divided up into small groups and are given a few tools to help them solve the problem. Two of the activities referenced in the article were to solve how high flags were in the gymnasium with the use of a mirror, ruler, and a laser pointer, and to determine the width of a soccer goal with only a paper towel roll, ruler, and trundle. These two activities definitely relate back to standard 1 because the students are having to plan out what they want to do and have to do some problem solving to get to their answer.
I thought these were great activities for a middle school classroom. In the beginning of the article the author discusses how with modern technology, students' attention spans are shrinking and students can readily gain information such as equations or formulas. He wanted his students to really grasp the concepts of mathematics, so he made his lessons more inquiry based and discussion based so students would be more likely to remember what they had learned.
I definitely agree with this. It will do students no good to just memorize formulas and to plug numbers into formulas to solve problem after problem on worksheets. With the use of technology, students would easily be able to look up a formula within seconds. I believe it is more valuable to teach students problem solving skills because these skills will be used every day for the rest of their lives. Using inquiry for students to learn concepts will allow students to become creative and discover on their own how to come to the solution. When classrooms are student centered, students are discovering about the topic on their own or in small groups by collaborating with others. When classrooms are more student centered, students will retain the information longer because they had discovered information on their own instead of just being given a formula. As a teacher, I want my students to retain as much information as possible as well as leave my classroom with various problem solving skills that they can use for the rest of their lives.
Goldthorp, S. A. (2013). Quick reads: Problem solving with laser precision.
Mathematics Teaching in the Middle School, 19(2). Retrieved from
http://www.nctm.org/Publications/mathematics-teaching-in-middle-school/2013/
Vol19/Issue2/Quick-Reads_-Problem-Solving-with-Laser-Precision/
The second article I found corresponds with the second standard: Reason abstractly and quantitatively. The article is Develop Reasoning Through Pictorial Representation by Wendy P. Ruchti and Cory A. Bennett, published in Mathematics Teaching in the Middle School.
In this article, the authors discuss the importance of using pictures to represent student work. They explain how it is much easier to follow a student's train of thought by looking at pictures of how they went about solving a problem. The pictures allow the teacher to see their students' problem solving techniques. This way teachers will be able to find where a student is struggling as well as see the different ways students approached the problem. Not only is this technique helpful for teachers, but it is also helpful for students. Drawing out pictures allows students to visually see the problem. If the problem is more of an abstract idea, the picture will allow the students to create a visual to help them understand what is going on in the problem.
I am a visual learner, so I find drawing pictures to be extremely helpful. I liked the problems presented within the article because they showed the student work examples of different ways to go about solving the problem. This is also a strategy that can be used at a wide range of grades. Teaching students as young as kindergarten students to draw when problem solving will only increase their ability and creativity in problem solving down the road.
Ruchti, W. P., & Bennett, C. A. (2013). Develop reasoning through pictorial
representation. Mathematics teaching in the middle school, 19(1), 31-36.
Retrieved from http://www.nctm.org/Publications/
mathematics-teaching-in-middle-school/2013/Vol19/Issue1/
Develop-Reasoning-through-Pictorial-Representations/
Nice job:) Thanks!
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