Entry #7

Kaufmann, M.L., Bomer, M.A., & N.N. Powell. (2009). Want to play geometry? Mathematics Teacher, 103(3), 190.

In this article, the authors argue that students can learn to understand proofs through playing games. They explain that by setting, following, and disputing rules in a game, students can learn the main ideas covered by proofs. When students play games, they understand that rules are true, unchangeable, and if the rules contradict one another, the game is not fair. Also, by looking at the statement of the rules, students can prove whether or not a play or move was fair. Games draw the attention to students because they are familiar and they allow students the chance to play and be creative. In the article, the authors suggest game ideas that will help students be engaged while still allowing them to develop the skills to write proofs.

I think that games are a great idea to engage student’s interests while still helping them develop the skills necessary to write proofs. Many students have played lots of games in their lives, and they would be able to understand how rules work, and what is considered to be against the rules of a game. When students can recognize when someone has contradicted the rules of the game, they can also begin to understand that some things can contradict proofs. Also, they can see that all possible cases that could happen in a game need to be confronted in the rules. For example, in a dice game, all the possible rolls and combinations need to be discussed in the rules, so no holes are left in the explaination. This helps students understand that proofs need to cover all possible cases, as to leave no gaps in the proof. By comparing proofs to something familiar, the students can better understand the questions proofs need to cover and the information they should contain.

Entry #6

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.