Tuesday, September 30, 2014

Not what you do, but how you do it

Not what you do, but how you do it

By Bobby Neal Winters
Before you read any further, you should know that I do not support the Common Core Mathematics.  My reasons for not supporting it have nothing to do with the specifics of the curriculum.  Instead, my lack of support grows from general principles: I believe that teachers should be professionals and allowed to use their professional judgement regarding how to teach.
Students in different parts of the country have different expectations, different levels of preparations, different goals and aspirations. Professional teachers, along with the school district and parents, should be allowed to use teaching techniques appropriate for those particular circumstances.
This having been said, I find myself disturbed by the rhetoric being used to attack the Common Core.  A particular method of attack is being used which I believe has harmful consequences to the level of the debate.
Consider the following problem in subtraction: 342-97. One method to solve this coming from the Common Core is to perform the following calculation:
97+ 3 = 100
Since 3+200+42= 245, it follows that 342-97=245.  There are quicker ways to do this.  There is the standard method that most of us learned that yields that answer more quickly.  I don’t think anyone would argue that.  That having been said, in my opinion, the value of this technique lay elsewhere.
For example, if you get something that cost $15.23 and give the cashier a $20 bill, the cashier will give you 2 cents to make $15.25, then 3 quarters to make $16; then $4 to make $20. It is the same process.
What does this process do?  It allows us to subtract by doing addition.  Someone who knew only the algorithms for addition could pick up this technique and be able to subtract,  They would be doing it  more slowly than someone who knows the standard algorithm, but they would be learning about what the concept of subtraction means as it relates to addition.  They are also learning how to implement a rather simple algorithm that makes good use of the decimal system of numbers.
Lets look at another method that comes in for criticism.  Consider the addition problem 8 + 5.  Think of it as 8+2+3=10+3=13.  Yes, if you know your addition facts, you can just jump to the 8+5=13.  But look at what his technique does.  It shows us that we can manipulate our numbers.  The 5 isn’t just 5; it is 2+3 and that 2 can be very handy in getting the 8 up to 10.
If we go back to our first problem, we can say 342-97= 342-100+3= 242+3=245, to get a completely different way of doing the problem.
These techniques breed familiarity with numbers and provide a gateway for growth.
As a math teacher of many years, I do work with numbers, but not necessarily in the way one might expect.  When I give an exam, I put 100 points worth of problems on it.  I have a class of 40 or more students most of the time and over the years I’ve developed a system for grading these exams.  I grade one page at a time and at the bottom lefthand corner of each page I write the number missed on the page.  
When I am finished with all of the tests I will go through them and calculate the total points.  If a student has missed 14, 8, and 12 points on the first, second, and third pages, respectively, I will proceed with the following calculation:
100-10=90, 90-4=86, 86-8=78, 78-10=68, 68-2=66.  Sometimes, if I am looking ahead, I would combine the last few steps by recognizing that 8+12=20 and calculate that 86-20=66, and often, in a calculation like 86-8, I will hiccup on the usual subtraction fact and, in my head, do 86-8=86-6-2=78.
I do this all in my head without writing a single step down and I do it for 40 to 50 papers at a run.  It rarely takes me more than a few minutes.  The two techniques illustrated above lead to this sort of mental manipulation of numbers.  
Yes, the standard subtraction algorithm is an incredibly useful technique. It should be taught and mastered.  However, these other techniques which I’ve seen used consistently used as examples of why the Common Core is criminally stupid, are  useful techniques when taught correctly by teachers who are professionals and the techniques are given the correct emphasis.
With math, with teaching, and with rhetoric, it’s not only important what you do, but how you do it.   Of these three, the math is the easy part.
In math, we know a variety of techniques and the secret is which one to use at what time.  It is all between us and whatever problem we are working on.
Teaching is more difficult.  We have our techniques, but when we use them, we by necessity have to include the students.  Each student has different abilities, different preparation, and has a different level of support at home.  Rolling down a one-size-fits-all solution and not allowing teachers to use their best judgment is going to cause trouble.
But then we get to the rhetoric.  
One source I read, criticized the particular techniques because they made students cry. Crying is not a bad thing. I cried in long division to the point my mother just did my homework for me.  I cried even worse in trigonometry when she couldn’t help me at all.  Learning is often a struggle.  This appeal to the emotions is effective rhetoric, but it seems to assume we should never stretch ourselves in learning.
I can understand why these two particular techniques were attacked.  They appear to make difficult what can be done easily another way. Indeed, I was taken in myself at first until I sat down with pencil and paper and worked through the first technique I cited.  It looked stupid to me, someone who’s been teaching math for over 30 years, until I worked it through once.
It is easier to attack a technical package like this by pulling out the complicated looking bits and making sport of them out of context to a non-technical audience.  It is effective; is sews a lot of confusion; it’s harmful to the level of debate.
It’s not just the result that is important. It’s how you do it.  This is not a healthy way to argue against the Common Core.


Susan said...

I believe you meant to write that the cashier will give you 2 cents to make it $15.25, etc. Not 2 cents to make it $15.23. My mind automatically proofreads as it goes.

Janet said...

You have just taught the blind to see! Also, 30+40+5 sounds a lot less than 75.