Assignment #7

Daire, S.A. (2010). Celebrating mathematics all year 'round. Mathematics Teacher, 103 (7), Pages 509-513.

The authors main goal of this article is to promote, as the title suggests, the celebration of mathematics all year 'round. She talks about how her school has cultivated a love of math, in particular the number pi, all because she started celebrating pi day, March 14, every year. Through hard work, generous donations, and personal sacrifices the author was able to extend her pi day celebrations to involve a wider range of students and other faculty members. Events, such as a Monopoly tournament, Halloween themed story problems, and a Valentines Day Love of Mathematics contest, are now a regular part of the school's yearly schedule. Getting students involved in the voluntary events can be difficult, but the draw of prizes such as a graphing calculator, 5 x 5 x 5 Rubik's cube, trophies, and other gifts, especially in a lower income area, is a great way to encourage participation. The article ends stating the fact that due to the implementation of events such as these, the students at this school have had much higher scores in statewide tests and have a greater desire to participate in mathematical discoveries.

I feel that this article hit its main goal right on the head. After reading, I am now quite excited to try some of these ideas once I start teaching. I can see how there would be difficulties getting other faculty/staff members involved, but I'm sure that with time it could happen. One thing that I feel would be nice would be a follow-up article on how to get other people excited about it. What other ideas could work to get more people involved? How did she approach people, especially when she was asking for money our other resources? Can teachers give help to the students when they're trying to solve problems? These are some questions that I feel would be helpful to others when trying to implement these ideas. What a wonderful article!

Assignment #6

Otten, S., Herbel-Eisenmann, B. A., and Males, L. M. (2010). Proof in Algebra: reasoning beyond examples. Mathematics Teacher, 103(7), Page 514.

The goal of the authors of this article was to convey the idea that proofs could be utilized in beginning algebra classes, not just geometry. Through a case study of an algebra one class, the authors demonstrated how the cross-multiply rule is generally taught, and then presented an alternate version in which the use of proof could easily have been inserted into the discussion. Usually, students only encounter proofs when they come to geometry; however, the use of proofs in algebra can greatly assist students in their comprehension of difficult concepts. Also, the discovery of why rules work in algebra, will also lead students to a greater capacity to like math because it's no longer "a collection of procedures and rules" that students feel they have no ownership over, rather it provides the students the opportunity to "realize that mathematics is a state of mind characterized by inquiry and a thirst for justification."

Although I agree with what the article is arguing I feel that, due to the fact that they invented a hypothetical situtation instead of actually testing out their idea, they did not quite present as strong as an argument as they could have. It is slightly ironic to me that the article is written about proving things, as opposed to just showing examples, but then the authors present an example instead of setting out to prove their point. I do like the ease at which the teacher, in the hypothetical situation, was able to construct a proof. It really didn't take that much more time to generalize the cross-multiply situation to show that it works for all situations. Once again; however, I have a problem because of the fact that the cross-multiply rule is an easy situation to come up with a proof for. What about more complicated situations such as solving systems of equations or how we came up with the quadratic formula? In these situations it could take quite a bit more effort to show why they work. In summary, proof of things in algebra is a good thing that teachers should look into, but at the same time, it might just be better to provide students with examples.