Say what you mean, the importance of language in a math class

“Why?” asked a student on some day in that one class.  The teacher replied, “Because.”  Often this conversation goes on without even a word spoken aloud.  Teachers develop routines in the classroom, and students learn to follow them.  The cliche at home of “Do as I say, not as I do,” doesn’t always fit into the classroom structure of I do, we do, you do (which may not be the best method either).  It might have transformed into more of a modeling-focused perspective of “Do as I do [, not as I say].”  Words in the classroom can get confusing, leading many teachers to struggle using proper language with students and instead depending on visual aids and demonstrations.  These conversations can get even more complicated when the students jump in.

Students are true artists when it comes to words and interpreting directions.  They are the best peer-editing service, often exposing any fault or loophole left open in an activity.  A skilled teacher can anticipate these attempts for learners to go off script and plan accordingly.  An even more skilled teacher can say less with more, only giving a few cleverly designed guidelines that allow students to explore and still arrive at some type of expected outcome.  For example, an assignment may have required students to write 1-2 page research paper on the topic of proportional relationships and its applications in scaling up or expanding a business.  This guideline is specific but has too many holes.  Through various interpretations of format, the students can complete the task without demonstrating any understanding.  Some think that more detail in the directions is the remedy for this situation.  I’m on the other side, preferring to give directions that would say something like, “In enough words and/or pictures, show me how proportional reasoning can help expand a business.”

Many view math as an objective and direct subject, being so reasonable and having one answer (or at least a best answer).  Some also say that one method is the best method and should be the only one that any true mathematician should use.  There is a strong movement to have a more open middle lead by dynamic educators such as Dan Meyer.  Math still has structure, and such structure should be highlighted.  I think it’s just foolish of us to attempt to summarize that structure into discrete, specific statements and expect the statements to transfer the understanding directly and objectively.  Math is just as much abstract as it is concrete.

This entire preface is to address one major issue with the most common prompt given in a math activity: “Solve it.”  First of all, we might even need clarification on the it that needs to be solved.  More importantly what does it mean (in the context of a math activity) to solve.  I ask this question to my students every year, sometimes multiple times a year, and their most common responses often include:

  • work it out
  • break it down
  • simplify it
  • find the solution
  • or everyone’s favorite Nike slogan (yeah, that one you’re thinking of right now)
So we wait, and see if students can come up with anything else.  Usually it gets really quiet; maybe because students aren’t quite sure why we are talking about words in a math class.  I start the scaffolding by reminding them that the meaning of a word can be found in its root.  I highlight the root, solve, and then ask the students to brainstorm other words with the same root.  This list is often populated by:
  • solution
  • solved
  • solver
  • solving
  • and sometimes an unrelated word like sold
I try to edit the list and ask the students to think of a word that’s only four letters that is pronounced the same, spelled the same, and has the same meaning in both english and spanish.  At this point students have sometimes guessed the word soul, or they forgot that I said four letters and go back to their originals from the first round of guessing.  The tension is building, both for myself and for the students.  The students are still confused but at least interested.  The gears are turning but not really going anywhere for most.  Usually one or a few that listened carefully to the clues asks in a half certain tone, “solo?”
Like a dam that’s been waiting to burst, I holler like I just found out I won the championship of lawn bowling, “Yes!”  Many of the student are finally relieved that the wait is over, and some are still confused.  So I expand the list, “How about isolate, would that have the same root meaning?”  This is when the clarity starts to cut through.  We have a brief discussion/venting session about why hasn’t anyone else brought this up before.  We move on and settle on the idea that when directions for a math exercises say solve,  it means to manipulate the equation so that something was by itself (solo).  This word association of solve and solo then becomes part of the routine in working out a solution to an equation.
Because of this confusion in the purpose of solve, the prompt is often overused incorrectly or in an inappropriate context.  An educator needs to raise his/her own awareness of this prompt and any others to make sure that directions are clear.
Solving an equation, one of the most common mathematics skills, has the clever design of leaving the options in the middle open, yet having a specific endpoint.  The only problem is, that many have not been able to articulate what this specific endpoint was in layman’s terms that make sense to students.  Too often has the open middle been restricted to the instructor’s preferred method as well.
My wife, another math educator, was in a conversation on the following exercise:
Solve : 14n=28.  
Her response was, “That’s just as good as giving a student a sentence and directions say ‘read’.”   I’m not saying that a teacher needs to add more detail that could possibly complicate and/or restrict the process, but every teacher should have an understanding of the core purpose of a particular prompt.  Just to stir it up even more, has the student satisfied the prompt if his/her response shows n=28/14?  Is simplifying a fraction implied?  Should it be (ever)?  Is it technically solved? 
What do you think about all this?  What other contexts highlight similar issues of communication and language in the classroom?
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About Mr-Butler

Math Geek Volleyballer Crochet Crazy

Posted on January 7, 2014, in Algebra, Good Teaching, Language and tagged , , . Bookmark the permalink. Leave a comment.

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