Daire, S. A. (2010). Celebrating mathematics all year 'round. Mathematics Teacher, 103(7), 509-513.
When students are given excitement and motivation to participate in mathematical thinking activites, they are brought to a greater knowledge and understanding of mathematical concepts after the activity is completed. Sandra Arguelles Daire read a magazine article in her early years of teaching that inspired her to really help students understand pi through activities such as puzzles, story problems, and contests. Throughout the years, this celebration of pi turned into a "Mathletes Boot Camp" which consisted of year round festivites promoting students to gain a love and understanding for mathematics. Competitions and prizes along with the enthusiam from the school faculty continue to draw more students in every year.
Mind games, contests, and other activities are great ways to get students involved with mathematical concepts. Daire did an excellent job at going above and beyond the average math teacher. The article made it clear that more students participate in Daire's activities and contests each year than the year before. More educators need to bring a bright side to mathematics to get students excited about the subject and erase the underlying hatred there has always been for math classes. Daire put an intense amount of work into planning activities, but sometimes that is necessary to get students motivated. Every math teacher will have their own way to get students involved, so as long as they put effort in, both the teacher and the students will benefit, which is the goal of teaching.
Friday, March 26, 2010
Friday, March 19, 2010
Assignment #6
D’Ambrosio, B. S., Kastberg, S. E., & dos Santos, J. R. (2010). Learning from student approaches to algebraic proofs. Mathematics Teacher, 103 ( 7), 489-495.
This article discusses the idea that students are not well trained in using algebraic methods to write or create a sufficient proof. Educators can discover if this is the case for their own students by asking them to write up their own ideas on a general statement or theorem. What each student writes will give the educator an idea of the level of understanding the class has reached on proving that particular concept. A study was conducted where the students were given the assignment to write a general statement regarding a pattern that results from squaring numbers with a 5 in the ones place. The students were struggling, so they were each giving a hint consisting of the binomial (10n + 5)^2. Most students thought the statement was obvious and found no point in proving it, so they just wrote specific examples of when it is true. Others set the binomial equal to zero and solved for n. Few students actually used the binomial correctly to algebraically prove the statement. This evidence shows that the students are not experienced in creating sufficient proofs through algebraic means.
If students are more familiar with algebraic proofs they will be more likely to have the ability to create their own sufficient proofs. Through the study conducted above, it was obvious that the students who were tested were uncertain how to connect algebra with written work. In order for students to become familiarized with these proofs, the educator must take the time to see how much knowledge they already have on the subject. As stated in the article, this information can be obtained through written proofs on statements they have never seen proven before. When the educator understands where they students are in the understanding process, they will know which proofs to expose them to, so the students will be better prepared to create their own proofs.
This article discusses the idea that students are not well trained in using algebraic methods to write or create a sufficient proof. Educators can discover if this is the case for their own students by asking them to write up their own ideas on a general statement or theorem. What each student writes will give the educator an idea of the level of understanding the class has reached on proving that particular concept. A study was conducted where the students were given the assignment to write a general statement regarding a pattern that results from squaring numbers with a 5 in the ones place. The students were struggling, so they were each giving a hint consisting of the binomial (10n + 5)^2. Most students thought the statement was obvious and found no point in proving it, so they just wrote specific examples of when it is true. Others set the binomial equal to zero and solved for n. Few students actually used the binomial correctly to algebraically prove the statement. This evidence shows that the students are not experienced in creating sufficient proofs through algebraic means.
If students are more familiar with algebraic proofs they will be more likely to have the ability to create their own sufficient proofs. Through the study conducted above, it was obvious that the students who were tested were uncertain how to connect algebra with written work. In order for students to become familiarized with these proofs, the educator must take the time to see how much knowledge they already have on the subject. As stated in the article, this information can be obtained through written proofs on statements they have never seen proven before. When the educator understands where they students are in the understanding process, they will know which proofs to expose them to, so the students will be better prepared to create their own proofs.
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