Annotated Bibliography
Original Research:
Winsor, M.S. (2007). Bridging the language barrier in mathematics. Mathematics Teacher (101)5, 372-378. Retrieved from www.tsusmell.org/downloads/Products/.../MELL_Winsor_MT_Article.pdf
The author of this article sought to find the relationship between learning English and learning mathematics, in order to provide an equitable math education for ELL students. He came up with the system “MSL” or “Math as a Second Language”, which focuses on communicating math, learning in groups, and using real life examples (p. 373). His method involved conducting tests in math and vocabulary before and after MSL strategies were used, using a scoring rubric on students’ math journals, and observing group projects to determine growth and understanding. He then compared results from an all Spanish-speaking class with an English-speaking class using the same strategies. Results indicate that MSL improved communication “about” and “in” mathematics, meaning that classroom discussion became student initiated and that students used proper math terms, but it did not improve their ability to communicate “through” mathematics, as problem solving skills did not increase (pp. 376-377). This article provides many teaching strategies for English language learners, such as using group projects based on real life examples, which I could use to engage and create an inclusive environment for English language learners. However, because the author’s classroom was entirely comprised of ELL students, it does not address how to use these strategies in a mixed classroom.
Moschkovich, J. (1999). Supporting the participation of English language learners in mathematical discussions. For the Learning of Mathematics (19)1, 11-19. Retrieved from http://www.jstor.org/stable /40248284
The author of this article studied the ways that a teacher can support English language learners in a math class through discussion by observing and transcribing a third grade math lesson. Moschkovich noted how the teacher promoted discussion, deciphered the mathematical content in the students’ speech, and then repeated it back to the students using correct terms. The study shows that by focusing more highly on the mathematical ideas within the students’ discussions, rather than correcting grammar, the teacher was able to engage his students in class discussions and promote proper mathematical discourse among English language learners. This study is not generally applicable to all classrooms, because it was only a sample of one class where the population was mostly Latino. However, it is useful to my research because it proposes that visual aids, which are typically recommended in teaching language learners, are not substitutes for language and can exclude them from participating. Rather, the emphasis is on how discussions can be facilitated, not replaced.
Gutierrez, R. (2002). Beyond essentialism: The complexity of language in teaching mathematics to Latina/o students. American Educational Research Journal (39)4, 1047-1088. Retrieved from http://www.jstor.org/stable/3202454
The author of this research paper sought to find the commonalities in the practice of teachers who are highly effective with bilingual Hispanic students (as defined by an exceptionally high enrollment in calculus) by observing three of these teachers at Union High School in Chicago. The study took place over a thirteen month period and data was collected through interviews with the teachers, the whole math department, the principal and twenty students, as well as regularly observing the classrooms. The research reveals that effectively teaching students at varying levels of English proficiency means viewing students’ needs on an individual basis, encouraging group work to be completed in primary languages, and stressing mathematical language in class discussions. While this research only reflects teachers and students at one high school, I believe that it can inform my inquiry question, as the teachers model practices that can be applied in any school, with any language. Whether I am working with Spanish-speaking students, or students with other language backgrounds, I can implement their strategy of consistently incorporating group work into homework, tests and projects. Lastly, two of the three teachers that were studied are white and monolingual, showing that this does not have to be a barrier in creating a more equitable classroom for language learners.
Pedagogical Resources:
Bresser, R., Felux, K., Melanese, K., Sphare, C. & Willig, C. (2010). 10 ways to help ELLs succeed in math. Instructor 119(5), 27-29. Retrieved from http://uri-englishlanguagearts.wikispaces.com/file /view/ELL+Math+10+ways.pdf
This pedagogical resource provides teachers with ten ways to support ELLs in a mainstream classroom, with recommendations varying from creating sentence frames to carefully designing questions in class discussions. Three really important points from this article are to group students by mixed levels of language and math skills, to ask questions that model the format of a well-formed answer based on the language proficiency level, and to utilize choral or nonverbal responses. These are all ways to create a more equitable classroom for ELLs, as they make class discussions more approachable and promote positive peer relationships. The authors do not focus specifically on the academic achievement of ELLs, but instead are oriented toward creating an environment that gives them opportunities to participate, organize their thoughts, and learn from their peers. The methods can be adjusted for proficiency levels and are also beneficial to English-speaking students, making them extremely useful in promoting equity in any mainstream class with ELLs.
Chen, X. & Li, Y. (2008). Research in brief: Language proficiency and mathematics learning. School Science and Mathematics 108(3), 90-93. Retrieved from http://vnweb.hwwilsonweb.com /hww/results/external_link_maincontentframe.jhtml?_DARGS=/hww/results /results_common.jhtml.44
The authors of this paper examined the recent body of research on the relationship between language proficiency and mathematical performance, as well the implications for teaching English language learners. The authors recommends that teachers have a knowledge of the inherent advantages and disadvantages that certain languages have for understanding concepts. Further, they recommend that teachers encourage students to understand mathematical concepts in their primary language first and promote a collaborative learning environment. The methods take into account the many languages that students might speak, and are applicable at all levels of math education. I would use these suggestions in my class, as they focus on creating equity for ELLs through showing how to use their language as a resource, thereby promoting participation in class and peer discussions.