*Out in Left Field proudly presents the eleventh in a series of letters by an aspiring math teacher formerly known as "John Dewey." All personal and place names, with the exception of Miss Katharine's, have been changed to protect privacy.
*

I have decided to take up my correspondence once more with
Miss Katharine about my experiences rafting along the ideological, political,
and cultural river known as math education. Some of you may dimly recall that
about a year ago I wrote some letters using the name Huck Finn, describing my
experiences as a student teacher. I am not yet teaching full time, but I am
subbing, so you’ll have to be satisfied with that for now. I’ve also abandoned
the raft for a canoe for easier maneuvering.

I chose the name Huck
Finn for two reasons: 1) I am looking to get hired as a teacher and because my
opinions may not be popular amongst those on the other side of the river, my
real name is best not told; and 2) the sheer poetry of it. My
experiences have for the most part been very positive and instructional. I missed my old class and my teacher from my
student teaching days and thought that no one would ever take their place in my
heart. For the most part it’s true, but I
do recall on one of my early subbing jobs at a middle school, the first student
entered boldly into the classroom, overjoyed at the prospect of having a sub
instead of the real teacher and cheerily announced: “Hi! My name is Lupita, but
you can call me ‘sexy’. ” I replied “Hi! My name is Mr. Finn, and I will call
you Lupita.” I was amazed at the
reflexive and automatic nature of this response.

It is the heart of
flu season and my greetings from students have gone from “call me ‘sexy’” to
“Can I go to the nurse’s office; I feel like I’m going to throw up.” In the
course of my work, things don’t get any more complicated than that. I usually don’t find myself in the thick of
political or ideological battles concerning math education with anyone. But the
other day, something did happen to make me aware once again of my trip down the
ideological river. I was subbing in a
high school geometry class, and preparing to put up a quiz on the projector
when I noticed on the table at the front of the class some extras of handouts.
One handout was titled “Standards for Mathematical Practice" which
consisted of the eight standards that relate to how math should be taught, per
the Common Core Math Standards, which have been adopted in 46 states. I picked it up, and realized it had been
handed out to students as a list of things for them to do in the course of “doing
math”.

With the handout in my hand, I was suddenly surprised
by the sound of my own voice. "I really hate to see stuff like this,” I
said. The students looked up. “It means nothing to you, I know, but it
comes from something called Common Core which will go into effect next year. It
is going to result in math being taught in certain ways. In fact, it’s where your teacher is today, at
a conference on how to teach the Common Core standards, learning the new ways
she has to teach you math.” Fortunately,
the piqued interest of the students had now turned into blank stares. Their years of acquired expertise had taught
them how to tune out teacher soliloquies.

The Standards of Mathematical Practice that got me so excited
are the following:

1. Make sense of problem solving and persevere in solving them

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others

4. Model with mathematics 5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

Taken at face value, they are as seemingly benign as when
the company you’re working for says that the latest reorganization will not
change anything and your life will continue as it always has. “Make sense of problem solving and persevere
in solving them” seems like good advice, and the way I interpret it is to help
students tackle problems by giving them the tools, instruction, guidance and
practice to do so. One of the many ways it
is being interpreted, however, is to require students to find multiple ways to
solve problems. (I say this because I
noticed in another classroom a poster bearing the logo of “Common Core” at the
top, showing multiple ways of doing particular types of algebra problems.)

There’s nothing wrong with finding multiple ways of solving
problems. But in early grades, students
find it more than a little frustrating to be told to find three ways of adding
17 + 69. Putting students in the position of not
satisfying the teacher by producing a correct answer and showing how they got
it unless they find multiple ways of doing it is a recipe for 1) disaster and
2) rote learning, the bugaboo of the purveyors of “find more than one way to
solve it”.

Now it’s true that during my recent assignment, I went over
a proof of a problem they had in their homework and, immediately after going
through the proof the teacher had provided, asked “There’s another way to do
this proof; can anyone see how?” I’m in a habit of doing that in high school
math classes, and I suppose that’s good, because if it comes to the point that
I actually teach full time and a strict principal decides to make sure I’m
following the Standards for Math Practice, he or she would likely conclude that I’m doing
it.

What I will not be doing is

*requiring*students to do things in multiple ways. I’m a bit stubborn on this point, but I tend to believe if a student can do a proof, or solve a problem and do so correctly by applying prior knowledge, then he or she doesn’t also have to do twenty five fingertip pushups.All in all, teaching high school is a bit more straightforward than the lower grades. By that, I mean that the span of content to be covered is such that there isn’t room for discovery- and inquiry-based group work and “read my mind—what answer am I looking for” type of catechisms. I hope that Common Core doesn’t bring that about. If it does, you can look for me along with flu-stricken students in the nurse’s office, trying to keep the nausea at bay and figuring out what my career options might be.

## 4 comments:

Welcome back!

Glad you are back. It's very hard to have a good math teacher. My daughter has had equal numbers of good and bad. The good are highly organized and really demonstrate the steps, make it accessible and promote mastery and interest. The bad make my kid need the nurses office and have really moved her backward in ability. Go California! J

Welcome back, Huckleberry. I'm proud of you!

I missed your blogs and hope you will write more. I also see nothing wrong with communicating to students there are multiple ways to solve a problem, but that they should not be forced to find multiple ways. I think that time can be much better spent on other things. At the moment, I'm dealing with high school students who still don't know even their three and four tables (much less the higher tables) because they were never asked to work on them, and no classroom time was ever devoted to helping the students learn them.

--Lynne Diligent

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