Kaufmann, M. L., Bomer, M. A., Powel., N. N., (2009). Want to play geometry? Mathematics Teacher, 103(3), 190-195.
The main idea of the article is that sometimes alternative, fun, and interactive methods in the classroom can be used to explain mathematical concepts and ideas. The authors demonstrate this by describing an approach they took when teaching kids the structure and meaning of a proper proof. They put the class into groups and gave each group a die, 5 marbles, an egg carton, and 15 chips. They asked each group to use the pieces to develop their own game, for which they would write the rules for. They groups then exchanged games and critiqued the games made by other groups, looking for contradictions, incompleteness, and repetition. After this activity the teachers discussed with the class the similarities between the rules of their games and the rules and axioms involved in writing correct geometrical proofs. They argue that this is a quick, inexpensive, and motivating way to teach students about "analysis, synthesis, and evaluation".
I would definitely use something like this in my classroom. It is easy to see from the article that the students 1) enjoyed the activity 2) developed a conceptual, relational understanding of proofs 3) could relate these principles to the world outside the classroom. One student was even able to relate the principles they learned to the United States legislature, and the rules outlined in the Constitution. For each new big concept I wish to convey to my class, I want to develop an interactive activity to first allow them to explore the concept on their own and obtain a relational understanding.
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You did a great job relaying one main idea the author had. You sounded professional and the way you wrote the first paragraph made me want to read that article. Your second paragraph went right with the first as well as you supported the main idea written about in the paragraph above. The use of the example from the paper in your own support in the 2nd paragraph was strong. Good job.
ReplyDeleteBibliography feedback: you need a "&" before Powel and no comma between the last initial and the year
ReplyDeleteI thought that the summary paragraph was strong. You have a clear topic sentence that identifies a main idea of the paper. You developed this idea throughout the remainder of the paragraph. I liked the level of detail that you included about what the teachers did to help their students understand proofs, and how this activity tied into the main idea for the paper. The only thing I would have appreciated is more detail about how they connected the games and the proofs. I'm not sure I really understand how this activity in designing and critiquing games would lead to appreciable increases in the students' understanding of proof.
For me, the structure of the second paragraph was less easy to understand and follow. The stance you are taking seems to be that you would use their activity. However, the rest of the paragraph doesn't necessarily seem to be entirely about this stance. Perhaps you could have written a different topic sentence that would have incorporated all the points you wanted to make in your second paragraph.
I felt like you summarized the article very well, a good balance between the main point and how the author achieved the main point. I was a little confused in the second paragraph, I felt like you were jumping around from point to point, maybe a little more explanation about each idea. I really like emphasis on the importance of games and other learning styles, I would enjoy reading this article.
ReplyDeleteYour summary was very clear. You pointed out the main idea of the article and what the author did to implement that idea. I also understood your opinion and standpoint on the article. This idea on teaching proofs is clever and I think students would benefit and enjoy learning this way.
ReplyDeleteYour summary was very clear and sounded professional. I liked the way you wrote your second paragraph, it was interesting and I could understand your view on the article. Good Job.
ReplyDelete