It’s Time for Algebra Class … Do You Know Where Your Linguist Is?

We’ve heard … and many of us say … “math is a language” or “algebra is like a foreign language”.  In our classrooms, these statements are often intended to motivate students to pay attention to vocabulary and syntax.  In general, I think the net result is neutral or even negative.  [Students are told to attend to something that they do not understand, and also lack a structure for learning.]

Twenty-five years ago, the Center for Applied Linguistics (http://www.cal.org/) published a pair of books on “English Skills for Algebra”, authored by Joann Crandall et al (Crandall, Dale, Rhodes, and Spanos).  One book was a student workbook … the other a tutor guide; the goals were:

“provide practice in manipulating the specialized language of mathematics and algebra through listening, speaking, reading, and writing activities in English; and

“provide practice in using language as a vehicle through which they can think about and discuss the processes used to perform basic operations in beginning algebra.”

I notice that the authors (linguists) include four modes of langauge usage (active — speaking & writing; passive — listening & reading).  I suspect that this is obvious to linguists … but not to mathematicians … that fluency depends on prolonged and deliberate efforts in all four modes.  Our math classes tend to focus on the passive modes; we consider ourselves progressive if we include talking in small groups. 

You probably will have difficulty finding the books mentioned.  I am adopting some of the content for my beginning algebra classes, and can provide a sample of one activity.  This is a worksheet, delivered through our course management system, with the purpose being to understand both one correct meaning for an algebraic statement AND to identify a correct paraphrasing.  Here is an image (you may need to right click on it, and open separately so you can enlarge it):

This activity has 7 questions, and I have a series of 3 for students to use. 

As you can see, this still works on the passive modes.  For active modes, here are two things I do in class:

Speaking — I ‘cold-call’ on students to have them explain how to do problems (they have had a couple of minutes to work on the problem, which is related to an example I have worked with verbal explanations).  I am able to encourage correct spoken language, as well as identify gaps in language or understanding.

Writing — I use “no-talk quizzes’, where students review other student’s work and provide feedback in writing phrases or sentences.  The focus is on explanations; feedback must be verbal (can not be symbolic).” (pg iv)

I encourage you to think more deeply about ‘algebra is a language’.  If you are fortunate enough to have a linguist nearby (which I was for a few years), talk to them; you might need to draw an analogy to learning a foreign language.  [Most linguists actually have some background in applied mathematics, but not so much in learning issues in mathematics.]  My own work in this regard is unfinished … I am most concerned about getting a process for spoken algebra with feedback, and I want to add more writing with feedback.

Writing across the curriculum is wonderful; however, the language within mathematics is more fundamental to our work.  If we conceptualize algebra as a language, we should have a deliberate plan for developing the fluency of our students in all modes of usage.  Just saying “it is a language” is a bit like saying “don’t you understand this yet?”.  The langauge learning process is not just a matter of a label like that, or motivation; language learning has its own processes.

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