This week's reading was particularly interesting to me because of my current practice in my math classroom. I've been making an effort to help students better communicate mathematically (translation: getting better marks in the Communication category of their assessments) through three main methods.
1) Creating a word wall - I posted a chart paper at the front of the class and I add new or key vocabulary to it throughout the day's lesson
2) Communication questions - I add test-type questions to a list of "Communication" questions at the end of every lesson (e.g. Explain the similarities and differences between partially factoring and averaging the zeros methods of finding the max/min of a quadratic.)
3) Deconstructing the question stem - I've been making a conscientious effort to go through a word problem line by line, asking students to clarify what the question is asking them to find in mathematical terms
Reading Helen's exchange with her students and her reflections afterward made me think about my own teaching methods in the area of explicit mathematical language teaching. Am I driving my students crazy by telling them over and over again that proper mathematical language needs to be used? Of course. Did I think that I was doing the right thing by my students? I did. Now, however, I'm not so sure...does it matter that the students say "square root" instead of "radical"? Does it matter that they write precise "let statements"? I thought that it did, for proper mathematical form...but now I'm so confused!
I've been emphasizing so much mathematical language acquisition because I too believe that "being explicit about mathematical language benefited all pupils in their mathematics classes, irrespective of their language histories" (p.48). I've been further motivated to be explicit about mathematical language due to a third of my classes having recent Visa students from China; although these students (for the most part) know the math, they don't always know the correct terminology so I felt that the language focus would be most beneficial for them. However, I've also seen the result of having too much focus on the proper language "[obscuring] the mathematics under consideration" (p.62). I've yet to strike the balance and wish that I had some examples of how to properly teach language acquisition in the math classroom while at the same time ensuring that the math content is learned and not having a lesson or teaching style that is too confusing for students to grasp...
Hi Vivien,
ReplyDeleteI do not think that you are alone in ensuring that students 'get' the mathematical language, notation, etc. When looking at the Communication rubric for Ontario that seems to emphasise that very point. Yet, I agree with you after reading Helen's story I too wondered if I was putting too much emphasis on the mathematical language acquisition as opposed to ensuring that the math understanding was there. I guess as math teachers because we are so familiar with the language we want our students to 'talk' in the same manner as a way to 'prove' their understanding of the math concepts?
Trying to find the balance is the challenge as you acknowledged - perhaps these readings are to help remind us of this need for balance and a realisation that there are multitudes of ways to express understanding that should also be acknowledged (gestures, diagrams, everyday language & connections, etc.). Maybe the first step is to work with these constructions students used to show their understanding, and then over time help students to translate this knowledge in a more conventional and acceptable (?) mathematical language...
L
My Focus on Meaning
ReplyDeleteThanks Vivien and LM for so clearly sharing your experiences. I have the opposite concern-I probably don’t pay enough attention to verbal communication conventions.
I don’t know if that is my redneck upbringing where I don’t ever remember being corrected over style issues, or my background in language development where children don’t learn from corrections, but from problems with meaning, and increased participation in a linguistic community. When teaching French I focus on meaning and communication strategies not grammar. I really struggled when starting my PhD with the idea that others should critique my writing style.
I actually used to hate teaching the traditional geometry classes that focus on vocabulary. I have since found some activities that focus on using mathematical definitions which work better to me.
The Moschkovich article was an easy read- it really was a review of my courses and prior readings in language acquisition. However, I struggled initially with the Adler article: I thought I understood the dilemma of transparency with talk but didn’t understand the need for the article. I had difficulty reading the Helen’s entire transcript because it was so counter to how I teach. I wonder why Adler belaboured the point. And then I read the last page and the article made sense: teachers need to be aware of how they use talk, and how too much work on communication can interrupt the learning about mathematical reasoning.
And with this realisation, my thinking returns to the numerous students that I teach with communication difficulties- do I provide effective support (and enough of it) to improve my students ability to communicate their reasoning?
Thanks DT, Vivien and LM you've helped me see another perspective and have clarification. Many times as I read these articles I dismiss much of it as an American issue that may not be as vital here.
ReplyDeleteI wondered as I read Moschkovich's article what all the fuss was for. I thought, no one 'really' places that much emphasis on mathematical language to the detriment of the students' math reasoning do they? After reading Vivien and LM I changed my mind. I then felt maybe its because I am an elementary teacher why I didn't connect with what Moschokovich expressed as an urgent need to view and change "what counts as competent mathematical communication". Then reading DT I now see its not just a elementary thing, there are others who don't emphasize mathematical language to that degree as well. I now see there is some purpose to the article from a Canadian perspective, but I can't imagine not allowing code switching, gestures, use of objects etc. for my ESL students to have a comfort level of participation in math class. Well, I now have a name for what I do: It's a sociocultural perspective in teaching mathematics. My perspective needs tweaking, but I am working on it.
I had mixed reactions to the Adler article. I think that building communication skills and being able to define your terms is really important, but I agree that communication can overshadow the rest of the content that students need to learn. I think similar problems arise in English classes. Part of the point of an English class is to learn to communicate effectively, but that isn't the only thing students should get out of it.
ReplyDeleteI think that the main problem I had with Helen's situation was that she wasn't able to separate communication from whether or not students understood concepts. There were a few times when I thought it was clear that students understood the ideas of angles and side lengths in similar triangles, even if that didn't match what they had been saying earlier. She kept going back to the word "independent" even though the rest of what they said showed that they knew the angles were not independent of the side ratios. I think it would have been a good idea to go back to this problem they were having with terminology once she had made sure that everyone understood the basic concept. Instead, it seemed that the entire lesson was sidetracked.