Sunday, October 13, 2013

Mathematics in Another Language

One of my high school teachers explained to me that math was another language in and of itself. The beauty of the language of math is that it is universal. If you know math in one language, you know it in all languages. However, that is not necessarily true. Perhaps the concepts are universal, the theorems are universal, the laws and properties are universal, the procedures are universal. But the language? Hardly universal. In the English language, my numbers are 1, 2, 3, 4, 5, and so on. In the Chinese language, numbers are  and so on. Therefore the concept of integers increasing infinitely is universal, but they are hardly the same. Also, consider that in the English language, we may also say one, two, three, four, five, and so on. However, in the Chinese language the symbols stay the same for numbers.

In middle school, a transfer student from Russia joined us. We were all curious if she would have to start way back in Kindergarten and learn how to count. As middle school students, we just assumed she would have to learn a completely new mathematics system. However, the book addresses the idea of an additive bilingual perspective. This perspective disagrees with my middle school self and states that rather than subtracting an existing framework, that educators and students to add a new language framework (pg. 232).

In the article, Mathematics and Bilingual Brain, Cindy Tumiel considers the common idea that bilingual people are at a disadvantage when processing mathematical concepts. According to other research within her article, bilingual people process mathematics in the original language they learned it. Despite a bilingual student’s proficiency in English as a second language, they will still process the mathematics in their first language. However, most people assume they only process in their first language. Tumiel addresses the idea that bilingual students can process math in their second language. I think this important to consider when accommodating bilingual students.

Friday, October 4, 2013

Tracking in the Mathematics Curriculum

There are many myths of effective strategies in education; tracking is among them. A research report titled "Dividing Opportunities: Tracking in High School Mathematics," discusses the detrimental effects of tracking. Tracking has been said to match students with a suitable curriculum for their teaching and learning (pg. 2). However, tracking has instead created barriers between low-achieving and high-achieving students. Instead of a more suitable curriculum, Affirming Diversity addresses how low-achieving students “are most likely to be subjected to rote memorization and static teaching methods because their teachers often feel that these are the children who most need to master the ‘basics’” (pg. 111). 

In the article, they found that there are 270 different mathematics courses in secondary education in only 30 schools (pg. 6)! There are so many different courses, teaching at different levels based on student achievement. Yet, aren’t they all teaching the same topic? I remember my high school offered Pre-Algebra, Algebra I, Honors Algebra, Algebra II, Applied Algebra, Honors Algebra II, etc. You were not able to be in Honors Algebra II if you were in Applied Algebra and only students that were deemed exceptional by the teacher in Algebra I were able to be in Honors Algebra II. The only students automatically enrolled Honors Algebra II were in Honors Algebra I. However, the standards and track for my high school is different than another district’s high school. The idea of tracking, especially for systems like in my high school, does not allow students to progress or improve. Instead, students just conform to the level they are at and do not believe they can excel or improve their skills. Tracking was supposed to even the playing field; yet, “perhaps a more appropriate metaphor should be that schooling in America is played on a field laid out on the side of a mountain” (pg. 11).