Sense of Belonging in Mathematics

The book states that “young people seek to fit in and belong in any way they can” (pg. 310). In the Goals for Achieving Diversity in Mathematics Classrooms, the author also discusses the importance of belonging and how it helps students succeed in mathematics. The author suggests that teachers take on a participation-view of learning, in which teachers and students participate in practicing mathematical concepts as a community (being the classroom in this case). This type of learning has three dimensions: a joint enterprise, a shared repertoire, and a mutual engagement.

A joint enterprise is a when the members of a community engage in activities together, such as producing solutions to problems. In interacting with each other, they acquire more mathematical knowledge. A shared repertoire includes unspoken norms, like studying, doing homework, and taking tests. The third dimension is when there is mutual engagement within the joint enterprise and shared repertoire. These are the ingredients of a classroom where students feel a sense of belonging. When students can use each other to gain mathematical knowledge, they connect with each other and grow as a community. Students can bring their background experiences and knowledge to the table to help solve problems. This way all students feel that sense of belonging.

Want to check out the article from National Council of Teachers of Mathematics?

http://www.nctm.org/resources/nea/mt2005-11-253a.pdf

Deficit Perspectives Challenged in the Mathematics Classroom

In the book, the authors address the idea of deficit perspectives, which is "the theory that genetic or cultural inferiority is the cause of academic failure" (pg. 257). This theory has been prevalent in the history of our education system. Low achievement is blamed on the home life of Blacks. Or low achievement is based on ancestry. Those are common deficit perspectives that still exist today and continue to influence policy. 

In the mathematics classroom, there are even further deficit views. In the article, Challenging the Math Box, the authors consider the deficit views. One view is the idea that women are not intellectually developed enough to aster math. This view is carried over to low-income family students and minorities. There is noticeable achievement gap for these three groups within the mathematics, science and technology classrooms. So, researches started into looking at how to teach math and what to expect?

Since curriculums have been less challenging in more impoverished and high minority schools, students are not expected to actually learn. Teachers have told them they are not smart enough to learn. Students begin to adopt that mentality and it became a self-fulfilling prophecy. If they think they are going to fail, they will fail.

Instead of low standards, the article suggests equity-based approaches. The National Council of Teachers of mathematics issued an equity principle with three aspects: “high expectations and worthwhile opportunities; accommodating differences to help everyone learn mathematics; resources and support for all classrooms and all students” (n.p.) This sounds nice and all, but it still need implementation.

That’s where programs like Math Smart! come in. This institute is a professional development program that helps teachers learn “out-of-the-box” approaches while also providing technological integrative support for the classroom. I think these new strategies definitely help put into action what we need in order to conquer these deficit perspectives.

Check this article out here: http://www.idra.org/IDRA_Newsletter/September_2005_Self_Renewing_Schools_Math/Challenging_the_Math_Box/

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 一, 二, 三, 四, 五 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.

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). 

Check this article out: http://www.promse.msu.edu/_documents/PROMSE%20Math%20Tracking-%20ResRep.pdf

Mathematics and Social Justice

This article explores the concept of critical pedagogy in mathematics. It addresses how critical pedagogy is underrated in the math world today, but really, math is the best place to utilize it. Often times, students have low self-efficacy is math, because they have been beaten down by not remembering the formulas or processes. However, when implementing critical pedagogy, an instructor can help spark student's self-efficacy as they open their eyes to worldly issues. Teachers can help students feel like their opinion matters about social issues - especially if students understand the math and facts behind those issues.

You know an article is good when it sparks an entire unit. After reading from Lawrence M Lesser and Sally Blake's "Mathematical Power: Exploring Critical Pedagogy In Mathematics and Statistics," I already have an entire unit on proportions planned revolving around the common doll or action figure with ties to social justice. When I learned about proportions, we were always given application questions that did not apply to our age level of adolescents. In the book, critical pedagogy is described as "the exploder of myths" (pg 55). So, how about exploding the myth of body image that is impressed upon the youth with the images of Barbie dolls and action figures? Have the class measure the size of Barbie's body parts and see if the life-size proportions are anything close to our size. I would bet that Barbie's head, breasts, and feet would not be normal. Same goes with action figures, the size of the muscles in comparison to the waist size is not proportional. Yet, many students grew up with these dolls modeling how they should look. Using critical pedagogy skills, such as analytical reasoning can help students see the real life issues - like body image in the media.

The author's push analytic reasoning even further "to explore several specific, concrete real-life scenarios which stimulate a sense of social justice could influence student empowerment" (pg. 4). To continue with the dolls and action figures, looking into where they are manufactured and discussing salaries of the sweatshop workers. A discussion about the injustice of sweatshop labor can expand students' view to other cultures and perspectives. As teachers, we are called to develop are students, prepare them for the real world, and not just ensure proficiency in content areas. We need to put critical pedagogy in action, in order to help our students critically think and act. Students need to be aware of the world in order to live in it.

Want to check out this article? View it here: http://www.jceps.com/PDFs/05-1-13.pdf

Multicultural Education in Mathematics

Before reading Frederick L. Uy's article, Teaching Mathematics Concepts Using a Multicultural Approach, I thought I would have to bend over backwards to incorporate multicultural education into my math class. But Frederick proved me wrong. In fact, it's pretty easy to connect math to culture. Frederick must have read from Chapter 5 as well, because he knows the benefits of multicultural education and takes it one step further by applying it to mathematics.

Frederick's article discusses the benefits of multicultural education in mathematics, which include: humanizing mathematics lessons and topics, the inclusion of all students and boosting confidence levels, provides holistic learning with a interdisciplinary approach, determines math usage in other societies, corrects inaccuracies within math, increases awareness of universality of math, recognizes existence of other approaches to math, promotes critical thinking, and is consistent with constructiveness. Frederick then explains the necessary people involved in multicultural education - not just the students and the teachers, but administrators, curriculum supervisors and even the parents at home. It’s a collective effort to teach with a multicultural perspective. Frederick offers guidance of where a multicultural approach in teaching mathematics can be implemented. These locations include: in the introduction of a lesson, providing the historical background of a concept, in the examples during a lesson, when connecting to interdisciplinary units, when celebrating holidays, etc. Finally, Frederick provides a few guidelines when planning: maintain focus on the mathematical content in the multiculturalism, uphold educational equity, develop collaboration and empowerment of entire learning community, promote inter-group harmony in the classroom, help increase knowledge of various cultures, and enable students to think and see from a multicultural perspective, and help correct misjudgments of inaccuracies of cultures.

This article proves that multicultural education can be effective if used effectively. One of the guidelines that I think is most important is to not lose the mathematical content in the multicultural approaches. I know I would probably try to oversell multiculturalism to the point where they would lose the math concepts. It’s key for all educators to recognize that the content comes first and all else comes second. But that does not mean educators are limited. That does not mean that only the content is what is learned in the classroom. Rather the content needs to be the core of the classroom. I think it’s a challenge that we need to optimize the content with the multicultural approach. we need to surround the core with layers of our students' backgrounds and interests; as well as layers of other cultures. That way, students will be able to see how these layers relate to the core - the content. One way I plan on implementing multicultural education into my classroom is in the explanation of the historical background and in examples of content. Instead of making up stories for word problems or making up statistics and such, why not use actual ones? Those actual examples can be connections to other cultures.

After reading this article and getting my gears turning, I accept the challenge of teaching mathematics with a multicultural approach.  

You can find Frederick L. Uy's article here:

http://www.ccd.rpi.edu/eglash/nasgem/ncsm04/Uy,%20Fred%20Teaching%20Concepts.pdf