It was written by a Maryland math teacher in the throes of a Core-gasm. Before the Core her life was an empty desert, a Rub al-Khali, but now her life is Core-tastic. Core, core, core. I was doing fine with her story until she got to this one part--and I about blew a gasket:

As an instigator of thought, I try to ask the right question—one that enables unsure teenagers to progress to the next level of learning. I've learned to use "hook questions" to engage students' curiosity and encourage inquiry in math.Are you kidding me? This teacher doesn't know enough basic math to be in a classroom. This teacher is incompetent.

A hook question has no one right answer. It doesn't even have to be something to which you know the answer. A good hook question encourages students to become investigators and to seek the answer from outside resources—textbooks, the Internet, even their communities. This open-endedness might also lead students to use several of the Common Core's practice standards, such as, make sense of problems (Standard 1) or look for and make use of structure (Standard 7).

For example, as students learn how to solve inequalities, we tell them that if you multiply or divide by a negative number, you have to flip the sign of the inequality. As I explained this rule, one of my students asked, "Why?" As I thought about it, I realized I wasn't sure. I could show this rule with an example, but I couldn't explain why it existed.

I made discovering the answer to this question students' homework for the night and challenged them to find the answer before me.

I don't need students to spend an evening "researching" this. What a waste of time! I could explain and demonstrate

*why*this is so in a minute or two. Students will "get it" and we can move on without the false glory of having students pretend they've discovered some ancient truth that's been hidden for millenia. Seriously, that problem is barely more difficult than the concept of "borrowing" in subtraction (another skill and algorithm that's being cast aside by many who worship at the Altar of the Core).

I get that California has adopted new content standards, the Common Core. What I don't accept is when people tell me that those new standards will require me to fundamentally change the way I teach. How do they know? Do my students do poorly now? How do they know I'm not getting my students to think deeply on topics, or to persevere, or to attend to precision? Why would anyone possibly think I'm not already doing those things?

I'll tell you why. Because there are teachers like the incompetent I quoted above--and because

*she*exists,

*all*math teachers must be bad like her. We can throw out the bath water of our old content standards, but there's no reason to throw out the baby of good teaching just because some woman in Maryland doesn't understand the simplest of math concepts. It would be different altogether if she had forgotten, for example, how to manipulate a sine curve with a phase shift, but the level of her lack of knowledge is, quite simply, an embarrassment. It's unforgivable.

She thinks she's done some great and wonderful thing by having her students spend a bunch of time figuring out what she could and should have taught them in a minute or so if she were at all competent. "The Core" may be necessary for

*her*professional growth, but

*I*seem to know a bit more math than she does--and in addition I also know how to transmit that knowledge to students.

Teachers who revel in their own ignorance, who try to spin virtue out of vice? I can do without them and their ideas, thankyouverymuch.

## 11 comments:

OMG. My 16-year-old is laughing about this!

I need too argue, just a bit, because you are taking an obvious case of incompetence, which was self anointed. and expanded it too largely. But I don't think it's a fault of new standards ... I think it's a problem of hiring people who don't know math. I grew up never knowing why you flipped the inequality sign when you multiplied or divided by a negative ... you just did. When I started teaching it... I figured it would be nice to be able to defend that rule, so I learned. Fact is: math teachers are in such short supply, they can get a way with this crap. Fact is, I could correctly identify the students who had 'learned algebra' from a specific teacher because their strategy was to 'move the number to the other side and change the sign' , I think the bigger question / you shouldn't have to no everything immediately now thing is fine ... but that's for big questions. I've been asked things in econ that I couldn't answer; I I've given my guess, and researched it. I have no problems with that ... but ... basic functions in math? No excuse.

"How do they know? Do my students do poorly now? How do they know I'm not getting my students to think deeply on topics, or to persevere, or to attend to precision?"

It's not that they don't know but that they don't care. I was the science department head at a large urban high school. We were the only high school in the system where female enrollments exceeded male in all of the AP and honors science classes. We were the only one where the percentage of females in these high level classes was greater than the percentage of females in the school. We were the only one meeting the goals the system had set for females in science.

When the district science supervisor showed up to discuss our program was it to learn what we were doing to get these results? Of course not. The results didn't matter. We weren't doing it "right."

Well ... some digging suggests that her undergrad background is biology and psychology. My guess is that she was taught to "crank the machinery" of math to get the right answers, but doesn't actually understand *why* the machinery works. There are a *LOT* of places in the typical math curriculum where they "why" is very lightly touched on an then ignored in favor of a rule-based mechanical approach:

(a) Invert-and-multiply to divide fractions,

(b) Multiply as integers and move the decimal (to multiply decimals)

(c) Multiplying polynomials by FOILing (FOIL ... first, outer, inner, last)

This tends not to matter unless (a) one actually pursues a math career, or (b) one winds up teaching math.

Unfortunately, she's doing (b). Sorry that this is going to impact you :-(

-Mark Roulo

Sounds like a zen koan approach to education.

Mark -- FOIL drives me nuts. One of my personal pet peeves ... why not tust teach it as a derivative of the distributive property, which ruins the acronym, but strengthens the mathematical principle ... and is easier and quicker...

This is more seminar inspired doublespeak from the same folks that have brought us to our knees before with New Math, Whole Language, Open Classroom and whatever fashionable method has been sold by the snakeoil salesmen who speak to our administrators. A local middle school principal seeing the failing grades in her formerly Blue Ribbon school went back in the face of district head honchos and banned all phones, tablets or personal computers between classes or in class. Seems the little darlings are distracted by their technology. I'm waiting to see how long it is before the superintendent makes them back off.

Well, now you have me curious! How would you explain why the equality symbol is flipped when multiplying by a negative?

I'd show it on a number line.

Let's stick with positive numbers. If one number is larger than another, it's further from zero on a number line. It's farther to the right. Make the two numbers negative, and what had been the larger is still further from zero, but now it's further from zero to the left. Left is smaller. It's "less than". The sign changes.

Nothing earth-shattering. Just a brief explanation along with a visual. Doesn't take an evening of research.

thank god you don't teach our class like this.

Thanks for the clarification!

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