urban teaching
urban teaching
Chelsea High School has put a lot of resources into reading and comprehension, and teachers have been requested to stress reading and vocabulary in all courses. During the 2006-2007 school year, my last year at Chelsea High School, my desk was in an open office area where I enjoyed being surrounded by, and learning much from, reading specialists.
Often, my observations about my students were that they might appear to read a problem statement perfectly well but then their behavior suggested that they didn’t understand what they had just read. I decided I needed to understand that better. I designed and gave my students various tests and other measuring instruments to learn what was going on.
Putting it all together, this is what I learned.
1.My students’ general level of comprehension of Geometry problems and test questions was surprisingly low.
2.Creating math problems and test questions that do not unfairly penalize students depending on their language abilities is very difficult, and the textbook system from which I was teaching was not good at it. I suspect that issues of language comprehension were not major factors in the selection of these materials, because we are still learning about the extent of these problems.
3.Possibly related to the above, possibly not, my students’ absorption and retention of Geometry concepts was also surprisingly low.
4.My attempts to teach specifically to counter the language disadvantages I was seeing in many of my students were not successful. Nor did I see evidence that the emphasis on reading and comprehension being placed by others all over the school was having any effect on my students’ performance in my classes.
At our department meetings the mathematics teachers were aware of, and were attempting to deal with, these issues. Some teachers voiced the view that “math reading” is different from the kind of reading that is being taught in English classes, and they were actually experimenting with this idea in their teaching. In this essay I seek to carry this important idea forward a bit.
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The following diagram presents a model of what I shall call here the “classroom language hypothesis,” namely that there are three distinct language processing skills that we expect our students to acquire successfully. I call these three language processing skills Literary language processing, Conversational language processing, and Formal language processing.
The left-hand circle encloses the two skills that are taught and used in English classes, and the right-hand circle encloses the two skills that are taught and used in Mathematics classes. That is, students in English classes are taught, and are expected to use successfully, Literary and Conversational language processing skills, and students in Mathematics classes are taught, and are expected to use successfully, Formal and Conversational language processing skills. The words inside the circles characterize some of the “products” of using these skills: Poems are manifestations of Literary language processing, ordinary I/You talk is the manifestation of Conversational language processing, and Theorem proofs are manifestations of Formal language processing.
In contrast to the other two languages, formal languages are typically only written, not spoken, although it is usually possible to read out loud an expression in a formal language. A formal language has a finite “alphabet” of basic symbols, and a set of clear “grammar” rules for creating correct expressions from these symbols. Examples are computer programming languages and algebra.
The model above gives me a way to describe what I have observed in the classroom.
•Most of my students, even many who do not hear English at home, are still convincingly fluent, for practical purposes, in Conversational language processing skills.
•Literally all of my students have poor Formal language processing skills.
I think we have been tempted to believe that, because “they are both English,” there is a connection between conversational language processing skill and formal language processing skill. My experience informs me that, even though conversational language skills are often necessary if a student is to describe his or her formal thinking, training in conversational and literary language processing contributes nothing to skill in formal language processing.
Here is my sad conclusion from my most recent four years of teaching high-school mathematics. All my students came to me having had practically no useful training in formal language processing skills. This is something that needs to be taught before high school, and my evidence is that it is not happening. Please believe that I am not singling out Chelsea Public Schools here; although most of my recent experience has been at Chelsea High School, my observations as a citizen tell me that this problem is pandemic. Furthermore, I believe that Chelsea is an exceptional place in that it is working, as hard as it knows how, to do what works best for its children.
I propose the following high-priority research program. Just because our nation’s high schools are clogged with students who were not adequately trained in formal language processing skills, we must not give up on these students. We must find ways to give students these skills even later in their lives than when they should have received them. If we can find out how to do that, we will have discovered a constructive and non-punitive way, at least in part, to leave no child behind.
© Copyright 2008 Mel Conway PhD
The Classroom Language Hypothesis
Monday, January 28, 2008