math rant

Math Rant: Screwy Stats

I have to say, I love me some statistics. Have I collected student scores and done a little analysis? Why, yes, I have. Have I collected and graphed data related to my writing? Oh, wait, you already know I have.

The thing is, I also know the limitations of statistics—what it takes for them to be meaningful, how far you can or can’t take the results. That data I analyze from my students? I use it to give me some direction as a teacher, figuring whether things are improving, whether a particular concept fell through the cracks, etc. Not much more than that.

As we all know, of course, statistics on education can get used for a lot more. I get the need for assessment (in some form) and accountability (in some form), but often when I see articles reporting school success/failure, I wonder if the people involved have the first clue about statistics.

Case in point: I recently saw an online report about the 50 best and 50 worst schools in the state, in reference to percentage of students achieving proficiency on the state’s high-stake testing. It reported results for Language Arts, Science, and Math.

The first thing that struck me was that whether looking at the 50 best or 50 worst, the percent passing math was WAY lower than the other two the majority of the time. That made me scratch my head, so I glanced down at the comments.

Several people noted that AP students didn’t take the state test.

I haven’t had a chance to dig into it yet, but if true, it makes those reported percentages almost meaningless. “We want to see how your school measures up … but we’re not going to count the top students.”

This is why when I see statistics reported, I have next-to-no reaction. Not until I know more about where the numbers are coming from. In broader situations, I ask myself questions like, who was included in the sample? How was the sample selected? How were questions worded?

Be careful when reporting statistics as part of an argument. They may or may not back you up as much as you think. Dig a little deeper to find the whole story.

ETA: Did my own digging-a-little-deeper, and it’s actually worse than I thought. The last math courses to participate in the state test are Algebra I and Geometry. The website was reporting on the results of high schools, many of which around here are only grades 10-12. By that time, even the “average” students are past those levels. So the published results only showed the proficiency of the lowest group. No wonder the math percentages were so much worse than the other subjects (which I believe test higher numbers of students in high school).

Have you run into questionable statistics? Any pet peeves on how you see them reported? Do you find yourself completely confuzzled when facing the numbers?

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Math Rant: Yes, Elementary Teachers, Math is in Your Job Description

Yikes, long time, no post. Not the first time it’s happened, but hopefully the last, because I’ve finally figured out a posting “schedule” that I think will work for me. What do you think?

You know I love my alliteration. Hopefully I can keep thinking of fitting topics each week.

So, that makes this a Mathematical Monday, and we have another math-rant. First, a disclaimer. Some elementary teachers are awesome. Some don’t match anything I’m about to say. I hope we get more of those.

Here are some actual quotes I’ve heard from elementary teachers.

“I hate math.”

“I wish I didn’t have to teach math.”

“I was lousy at math in school, but I figure elementary math is easy, so I can teach that.”

I have yet to hear an elementary teacher say they hate reading, wish they didn’t have to teach reading, or are lousy at reading. Many elementary teacher training programs are heavy on the literacy courses, and light (or non-existent) on the math pedagogy.

Don’t get me wrong. Reading and writing are hugely important. (Hello, I’m a writer!) But so is math. Even if a student will never have to divide fractions or graph a linear equation once they leave school, the associated thinking skills are valuable no matter what they do in life. They need a good math education to develop those skills of logic, problem solving, and number sense.

And guess what—when the teacher doesn’t like math, the kids know it. Doesn’t matter if the teacher doesn’t explicitly say so. It comes across.

It’s socially acceptable to say you’re bad at math, but this is something that needs to change, especially with the way technology is developing so rapidly these days. It used to be only the elite knew how to read, and now no one wants to admit being bad readers. (And yes, we need to keep working on ways to help those who have difficulty reading.) It’s time for math skills to have the same status, and it starts with those who are role models for the teeny-tiny kids—both parents and teachers.

Okay, rant over. Now I can get back to looking for ways to bolster the math skills of the elementary teachers at my school so they can stop making excuses. 😉

Are you a math-phobe? What led to you feeling that way? If you’re a math-lover, how did that happen?

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Math Rant: College Professors

The subject of this particular rant is a few years behind me, but the effects linger. And now, the horrors are being inflicted on my former students, and it’s enough to make me want to inflict something of my own—a forceful *headdesk* on the perpetrators.

Through my undergrad and graduate schooling, I encountered a number of college mathematics professors. Here are two facts:

#1 Many of them are absolutely brilliant mathematicians.

#2 Hardly any of them can teach to save their lives.

I even had a few classmates who were likely to join their ranks in the future. Kids who could do multi-variable calculus without breaking a sweat and thought abstract algebra was a great weekend activity. Kids who could not teach it.

Make no mistake. Doing math and teaching math are two entirely different skill sets. Thing is, the teaching skill requires the doing skill, and then some. (Do I get tetchy with the old “Those who can, do; those who can’t, teach” line? Don’t get me started.)

A former student came by to visit the school the other day and we chatted about how her first semester at a new college is going. Because she has issues with test-taking, she didn’t do so hot on her placement exam, which landed her in a math class that’s dirt-simple for her. She understands the material, but then the teacher goes and confuses her by insisting she use his methods, which she didn’t understand. She tried to ask a question to clarify, and he cut her off.

Okay, this particular girl is very assertive and kind of blunt, so maybe she could have handled the exchange better. I don’t know—I wasn’t there. Then there’s the fact that he tried to hold her interpreter back after class to talk to the interpreter about the student needing an attitude adjustment. (Grr… don’t get me started on that, either. That’s a rant for another time.)

Bottom line, this student didn’t expect the same kind of bend-over-backwards-to-help teaching she got in high school. She just wanted to understand.

If there’s one thing I remember about several of my college math classes, it was the clear undercurrent: If you don’t understand the magic I’m performing on this blackboard, it’s your own fault, because you must be too stupid to grasp it. No one ever said it in words, but you felt it.

Thankfully, they’re not all like that. I found a handful who didn’t just want to get their teaching hours out of the way so they could get back to their “real” work. The kind you could ask a question, and they didn’t just repeat their last two statements. They elaborated on the in-between step, or what justified some conclusion.

If you find college math professors like that, add them to your Christmas card list for life. They’re rare, but they’re also golden.

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Math Rant: Subtraction

This will not be a rant about how even some kids in advanced math classes have to count on their fingers to subtract (or add). I’ll save that one for another time. (For the record, with deaf kids “counting on fingers” is fairly equivalent to tapping on the desk and counting in your head.)

No, this rant is about the failure of someone (or several someones) earlier along the line failing to address both types of subtraction.

Two types of subtraction? Whatever are you talking about, Miss Lewis?

Yes, two types.

If you think of beginner’s subtraction, what do you think of? Probably the idea of “take away.” Johnny has 10 apples, and Jimmy takes 4 of them away. How many does Johnny have left?

Nothing wrong with that. Totally valid interpretation of subtraction. But it’s not the only one, dagnabbit!

There is also the HOW FAR perspective. And I don’t have the stats to prove it, but my gut says this is the more frequently useful angle in real life.

Take the problem 11 minus 8. Here’s what I see over and over in my classroom:

*holds 11 on one hand, then starts counting off on the other*

10, 9, 8, 7, 6, 5, 4, 3. I counted 8 places before 11, and the answer is 3.

Why? WHY? Even if you must count, here’s all it takes:

*hold 11 on one hand, start counting off on the other*

10, 9, 8. I’ve arrived at 8 and it took 3 steps to do it, so the answer is 3.

To me, this says these kids were taught a procedure for subtracting and memorized it without really going deeper. So I need to dig in and do some remodeling in their heads.

Even better is when they see 11 – 8 on the paper and borrow. So the tens place becomes zero and the ones place becomes … 11. Fortunately, that’s a little more rare.

*sigh*

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