by Douglas Grudzina
I’ve been reviewing statistics—test data—Delaware student test data …
… DELAWARE STUDENT FOURTH GRADE MATHEMATICS TEST DATA …
(Don’t ask me why.)
But in reviewing this data, I got to thinking about how mathematics kind of _is_ a language (my future son-in-law is a high school mathematics and physics teacher, so he’d be happy to hear me admit that), and perhaps mathematics teachers experience some of the same frustrations—often for some of the same reasons—as other language teachers. And maybe the solution is the same as well.
Here’s the backstory, the exposition, whatever you want to call it:
While reviewing this data, I encountered a young woman (fourth grade). She was tested once in the fall of 2010 and once in the winter of 2011. She was probably also tested in the spring of 2011, but I don’t have that data. Her scores in three categories were reported: _Numeric Reasoning_, _Algebraic Reasoning_, and _Geometric Reasoning_.
Now, keep in mind that this is fourth grade, and when I was in fourth grade, I was memorizing multiplication tables and trying to transition from long to short division. (Maybe that was fifth grade, and I never did successfully make the transition.)
I have no idea what “Algebraic Reasoning” or “Geometric Reasoning” might look like in the fourth grade.
But that’s not the point.
This young woman scored “Well Below” the performance standard in the fall (with an overall score of 642) and “Below” the performance standard in the winter (with an overall score of 696). 700 is the cut score for “Meets the Standard,” so she is almost there.
In both tests, her Numeric Reasoning score was the highest; Algebraic Reasoning was the lowest. Geometric Reasoning was very close to the Numeric Reasoning and showed the biggest gain from the fall to winter tests.
Now here’s the point…(and thank you for your kind indulgence).
Geometry is a readily-applied math. It’s gallons of paint, square feet of floor tile, yards of fabric. Algebra…not so much. Algebra is merely a set of _tools_ by which we calculate gallons of paint, square feet of floor tile, yards of fabric.
Yet, I think, math teachers teach algebra in much the same way they teach geometry. Here are some “rules.” Here are some equations. Here’s what parentheses mean in an equation, and here’s what you do if you encounter parentheses in an equation.
You give me any equation, tell me to solve for X, and I’m on it!
But…so what? When I order floor tile or paint, unless I’ve had someone else come in a measure for me, I invariably order too much (excess not refundable) or too little (sorry, that was the end of the lot run, so your next order will not match).
But I _can_ solve for X.
OKAY, now here’s (_really_) my point … (And _really_, thank you for your extreme patience.)
The English language has all sorts of tools—like algebraic equations—all of which _help us_ formulate thoughts, communicate those thoughts to others, and understand the thoughts that others have communicated to us. I’m thinking things like verb tenses, pronoun-antecedent agreement, subordinate clauses.
These tools, however, are pretty pointless on their own.
Imagine practicing “hammer.” Next week we’ll get to “nails.”
Solve for X.
But why do I care about X unless I need to know how many cubic yards of non-refundable decorative gravel I need to order for my driveway?
If we give a kid a list of 20 sentences, some with the subordinate clause at the beginning and some with the subordinate clause at the end, and we tell him to draw in the commas where they are needed, what have we taught him? Will he now never again write an unintentional sentence fragment? Will he never again subordinate the wrong bit of information and create an illogical sentence?
_Because he kindly stopped for me, I could not stop for death._
I learned a little bit of sentence diagramming in the fourth grade (when we weren’t trying to transition to short division). To this day, some 45 years later, I still hear the occasional lament that “they” stopped teaching sentence diagramming.
But what I remember about diagramming sentences was being tested on whether or not the line was straight or diagonal, whether it went all the way through the horizontal line or not, whether it was solid or dashed. On these tests, we would lose points if we did not put a word in parentheses that was supposed to be in parentheses.
We were tested on our knowledge of sentence-diagramming techniques.
But I do not remember _ever_ having a teacher (or professor or editor) sit down with me and diagram one of my own sentences to diagnose structural problems. That _is_ the proper use of the tool, isn’t it?
I can’t help but think that that poor little fourth-grade girl, who is _so close_ to meeting her fourth-grade standard in mathematics might do so much better in “algebraic reasoning” if someone would help her to realize that “algebra” is nothing more than realizing what piece of information she doesn’t have and finding a way to figure it out.
You know length and width; solve for area.
You know area and desired depth of stones in your driveway; solve for volume or number of cubic yards you need to order.
And I am even more certain that our most reluctant writers and readers might do so much better in the “grammar and mechanics” aspects of their language use if those aspects were made the _means to the end_ and not the ends in itself.
Solve for X.
Diagram the following sentences.
Decline the following irregular verbs.
Is it any wonder so many of our kids zone out before they ever get to the payoff of actual communication?