The article synthesizes research from the mid-1980s to 2005 in the fields of linguistics and mathematics education. The article highlights several linguistic challenges of math learning:
1. Multi-semioticity: the construction of the meaning of math concepts is drawn from multiple sources including symbols, oral language, written language and visual representation, order, position, etc.
2. Specific grammar features in math language: One feature is that the math language uses noun-dense phrases such as “the volume of a rectangular prism with sides 8, 10, and 12cm”.
3. “Mathematics is highly technical, with characteristic patterns of vocabulary and grammar” (p. 142). An example was used to illustrate the idea. “George has twice as less money than Tina” is considered technically incorrect, in comparison with a newspaper report “traffic in Sydney during peak hours is nine times slower than in Melbourne”.
4. Precision of mathematical conjunctions to link logical elements: words such as if, when, then are used in precise ways in developing theorems and proofs and they represent different ideas compared to use in everyday life such as in “if I got an A, I would be very happy”.
I appreciate the notion that a key challenge in math teaching is to help students move form informal discourse to formal discourse which is necessary for disciplinary and interdisciplinary learning in school. Especially with the inquiry-based approach to encourage students to connect math concepts with everyday life, students are comfortable bringing their “everyday” language to participate in the activities. In addition to teaching formal technical terms and demonstrating the language used in mathematical discussion, the article suggests to explicitly teach the language and bring self-regulated awareness of “formal” math talk in classrooms. It is a very insightful article as it casts doubt on the common understanding of the independence of effective math learning over mathematics language.
Question:
As the author indicated, most teachers have recognized that technical vocabulary is a challenge, but many do not pay enough attention to the grammatical patterns. How should we offer help in the classroom to ELL learners who are new to both “everyday” English and “mathematics” English?
This is a great question that I find myself considering regularly. I have recently found myself reminding my students that, although I am not their English teacher, all their teachers are language teachers and proper grammar is still required in Math class. In my classroom, I remind students that although mathematics has its own vocabulary, it is complementary to their “regular” vocabulary. I have a word wall in my classroom with all the relevant terms for the current unit. I find this helpful for all the students, not only the ELL ones. But I do find it difficult to support their learning of everyday English. I focus a lot of both verbal and written communication and hove found that scaffolding the responses for the ELL students gives them a starting point and helps them to learn how to frame response and reflection pieces.
ReplyDeleteI think your question is crucial for the current mathematics classrooms in this global era. Please allow me answer with the case of Japanese Language Learners. When I see some teachers who have to teach mathematics for non-Japanese students, they are very enthusiastic for the students’ mathematics learning but they do not have any idea how teachers should help those students. When I asked an experienced teacher who have been working for this problem for many years, he said teacher should never describe by oral explanation only. They bring real (physical) objects in mathematics class so that those students can understand what this word/phrase/situation means in Japanese (For example, bring several balls to let them understand what sphere is). The students learn the word for daily-life and for mathematics through the experience that they see and touch the real objects.
ReplyDeleteThe other idea is a mathematics words dictionary. Some provinces or local autonomies in Japan issue the technical and academic word list of mathematics in both Japanese and several languages such as English, Chinese, Portuguese. I also have heard some textbooks in English include small dictionary of mathematics word between English and Spanish (But I am not sure if this is true).