Lege, J. (2009). Fences, forms, and mathematical modeling. Mathematics Teacher, 103(3), 184-189.
In his article, Jerry Lege focuses on the idea that when students use models to represent mathematics, they can better understand functions and what they look like. He begins by explaining that students can look at different kinds of fences, and see what kinds of functions they represent. The four main types he talked about were constant functions, step functions, absolute value functions, and the sine function. He explained how students could better understand the functions when they can connect the ideas to a familiar image in their heads. A second big point he made, was that students can work from the graph of a function to the fence. When they understand the graph, students can model a fence from that information. He says that these two ideas help students develop the ability to apply mathematics in different contexts, and use models to identify relationships in mathematics.
Mathematical modeling does help students gain a greater understanding of the concepts addressed. When students learn to use models, they can more easily recall the images in their head, so they can better remember the concepts involved. Thus, they can also explain their reasoning to other people better because they have a more solid understanding of the concept. I think that when students have a concrete mental image, they can connect the ideas to others more easily. Also, when students use models, they can see mathematical ideas in real world contexts. This causes the students to gain a better understanding of the importance of mathematics. When students can see mathematical ideas in real world situations, they find mathematics more interesting and feel more that math has a purpose. Modeling mathematical ideas helps students have more interest in understanding mathematical concepts, and therefore the students become more engaged in learning and they have a deeper understanding of the concepts taught in class.
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I'm not sure that I quite understand the author's main point after reading your summary paragraph. I didn't understand how the different types of functions were related to fences. Was there a fence problem the students were working on, and each type of fencing led to a particular type of function? Or were fences used to draw graphs? A clarification on how the fences were being used would have helped me.
ReplyDeleteI thought that the second paragraph was strong. You took a clear stance in your topic sentence toward the value of modeling. I thought the rest of the paragraph contained several compelling reasons for the importance and value of modeling.
I think you did a very good job at addressing the main point of the article. Although I did have a hard time understanding the fence analogy. I'm not sure what was meant with it. I really liked your second paragraph and I want to go read the article now. Good job :)
ReplyDeleteI think you summarized the article very well, it seems you captured the main point and then elaborated on it. I am a little confused about your mention of fences, maybe a bit more explanation connecting this example to the main point would make for a stronger paragraph. I am curious to read this article because I think that using real world situations as mathematical models can be helpful for some, but overwhelming for others. I am curious to see what this author has to say.
ReplyDeleteI feel that the tone of your paragraphs were very professional sounding and your second paragraph was especially strong. You had topic sentence and elaborated on your point of view with several good reasons.
ReplyDeleteYour first paragraph was good as well, but like the other comments have mentioned, I was a little confused about the fence analogy, so if you went into a little more explanation it would have been easier for me to follow.