kitchen table math, the sequel: rightwingprof: "I Would Like an Answer Now"

Thursday, February 18, 2010

rightwingprof: "I Would Like an Answer Now"

Clay Bond posted this to rightwingprof on March 29, 2006. It's a keeper.

'Yes, I posted this some time ago. However, the questions are not rhetorical. I really would like an answer from my colleagues in the primary and secondary school system — particularly those in the education union establishment. And I’d like an answer because I really do want to know why I have to do your job as well as mine.

Thanks ahead of time for your response. Here it is:

I don’t want anyone to get the wrong idea. I’ve had many extremely bright students. Many. Some had the necessary knowledge for the class, and some did not; of those who did not, most worked their butts off and did well. I also don’t want you to think smarts are what I care most about.

My favorite students are the ones who aren’t that bright, but work their tails off to do as well as they can. My least favorite students are the ones who are extremely sharp, but don’t work.

Sometimes, however, there’s too much missing knowledge, so much that the best thing the student can do is drop the class. It breaks my heart when I get a student like this.

I had a student some time back I’ll call Mark. Mark was bright, though his high school had cheated him, and he was lost almost from the first day. He worked hard, and came to my office hours. But … well, there was too much missing, as I discovered early in the semester when he was in my office.

I asked him what he wanted me to clarify, and he said he didn’t understand the 68-95-99 Rule. The conversation went something like this:

Me: “In a normal distribution, 68% of the data fall within one standard deviation in either direction of the mean. So here’s our distribution,” I drew a bell curve on the whiteboard, “And here’s our mean,” I drew a dashed line bisecting the curve. “Our mean is 50, and our standard deviation is 2, so 68% of the data fall between 50-2 and 50+2, 48 and 52.” I drew lines and arrows, and a 68% beneath.

Mark: “I don’t understand. Wouldn’t it be 75?”

Me: “Wouldn’t what be 75?”

Mark: “The mean.”

Me: “Why would it be 75?”

Mark: “That’s what you said in class.”

Ah. He was stuck on the example — and being a firm believer in introducing concepts in contexts familiar to students, I introduce basic descriptive stats in terms of grades, since what else are students more familiar with?

Me: “The mean could be 75, sure. In this particular distribution,” I pointed to the curve on the whiteboard, “the mean is 50.” I then erased the 50. “But let’s say the mean is 75,” and I wrote 75 after the x-bar, “then 68% of the data falls between 75-2 and 75+2, 73 and 77.”

Mark: “How do you know if the mean is 50 or 75?”

One of the difficult parts of teaching is diagnosing the problem. Students have questions, but the problem may actually be more fundamental than what they are asking about, as I was beginning to understand here.

Mark was having two basic problems: He didn’t understand what a mean was, and he was having trouble abstracting the idea out of the example. The former is easy to fix; the latter is not.

Me: “Can I erase this?” I pointed to the whiteboard, and he nodded. I erased the curve, and wrote a series of numbers on the board in a vertical column: 90, 85, 70, 65, and 50. “These are test scores,” I said, “How do you calcualate the mean, or average?”

Mark didn’t volunteer an answer.

Me: “Okay, let’s say the whole class takes an exam, and these are the scores. An average, or mean, tells me how well the class did overall. To calculate the average, I add all the scores, then divide by the number of scores. Here, you do it.” I have him the marker.

Mark added the numbers, then stopped.

Me: “How many scores are there?”

Mark: “Five.”

Me: “Okay, divide the total by five.”

Mark complied.

Me: “What’s the mean?”

Mark: “Seventy-two.” He looked at the numbers for a minute, then smiled. “I get it!” he said.

That’s when I realized what I’d suspected: Mark was a university freshman who had not, until just now, understood the concept of an average. I found that disturbing, but Mark was on a roll.

Mark: “So what’s a median?”

Me: “The middle score.” I pointed to the five numbers. “Half of the scores will fall above the median, and half will fall below the median. What’s the median of these scores?”

Mark: “Seventy.”

Mark was in my office three hours. No wonder he’d been lost. He didn’t understand an average. He didn’t understand sampling or distributions. We didn’t get to the 68-95-99 rule that day, because there was too much he didn’t understand.

I worked with him twice every week, and he got a B in the class. He worked harder than nearly any other student I’ve had. But if he had not come to my office every chance he got, he would never have passed.

Mark had no sense of entitlement. He wanted to understand, and he wanted a good grade, and he worked for both. He was bright. The thing is, I pretty much ran him through a high school math program in the office during the course of the semester.

I’m a teacher, so I can ask the obvious question, and some other teacher can’t come back with any of the usual non-answers.

I did it. Why couldn’t you, when Mark was in high school? It’s not money. I got no extra pay for helping Mark. It’s not time. I spent many hours in the office working with him. It’s not his intelligence or ability to learn. He’s smart, and he learned quickly, once we got started.

So I’ll ask again: Why couldn’t you do your job? It wasn’t my job to teach Mark high school math, but I did. Why did I have to? How did Mark get through all the required high school math courses without understanding what an average is? How did Mark get through all the required math courses without ever having seen y=mx+b? How did Mark get through all the required math courses and not understand that each flip of the coin is independent of all others? Most of all, how did you, his teachers, let such a bright, hard-working, motivated student slip through the cracks?

What’s going on there?


farmwifetwo said...

They don't care beyond their 3+mths of holidays, their $75-90,000/yr paycheques.

Anything else... they don't have to do. As I work to find a better class for my youngest.

YET, my son was asked what his fav class was a couple of days ago and the answer was.... Math...

Go MOM :)

lgm said...

Their union has the teachers work to rule.

The ethics situation is bizarre. I've seen situations where a child was struggling, but didn't qualify for help via rTi. Parents are told to get a private tutor - for elementary school. Sometimes they hire the classroom teacher their child is assigned to.

Allison said...

I'll add one slightly off-center-topic to this piece: sometimes kids don't work hard because they feel entitled.

But sometimes, bright kids don't work hard, esp. in college, because they feel Hopeless. They just can't see how they can get from here to there given all of the gaps.

And unless you go back, really back, to where you get that they don't get the mean or the median, they you might mistake their hopelessness for entitlement.

Most kids who make it to college without seeing y=mx+b are going to feel hopeless at some point. It's often really late to tell them it's not hopeless. It takes real optimist and encouragement, where by that I mean, you actually give them the courage to work hard. Baby steps are needed then.

K9Sasha said...

The problem is more deep seated than teachers not caring (most do - deeply) or even unions. The problem is the whole ed school culture. Change is good. There doesn't need to be evidence that the change works, it only needs to sound good, and "feel like" it'll be good for the kids.

In a teacher's staff meeting on Wednesday, a third grade teacher at my table made a telling comment. "How can we know what works? The standards change every three years. To have an idea of what works the standards would have to stay the same for at least 12 years - from the time a kid is in kindergarten until he graduates. As it is, we're creating gaps all over the place."

palisadesk said...

Work-to-rule only happens when there is a stalemate in collective bargaining. A very effective principal once told me she loved work-to-rule periods because all the useless meetings that waste everyone's time and energy are canceled and we can actually concentrate on teaching and working with students, and principals can be in their schools!

I have often wished that the union would make one simple resolution for a work-to-rule campaign: have teachers remove all their personal property from the school. In many schools, especially in low-SES areas, the difference would be shocking. SOme classrooms would suddenly have NO learning materials, no pencils, markers, classroom books, even much furniture. In one school I taught at, everything in the room (even all the textbooks) were mine, bought by me. The only exception was the student desks and chairs. The tables, the computer, the shelves, and everything else was mine. Elementary teachers spend an average of $500-$1000 per year of after tax income on materials for the students, and some spend far more.

I look on it as an investment. If I have the tools I need to work with the students, it's going to be a better situation for everyone. Of course health care practitioners in a hospital don't have to bring their own x-ray machines or suturing material, but it is often the case that teachers must buy their own materials to teach with. At my last school my budget was $50 for the year. That didn't even keep us in pencils!

Affluent schools of course do not have these issues and a work-to-rule of the kind I envision would produce no effect. That's perhaps why the unions have never considered it.

momof4 said...

I remember a work-to-the-rule episode in Montgomery County, MD during the mid-late 80s.It's a very affluent area, with schools sending many kids to Ivies, Duke etc. every year. Apparently, nothing in the contract mentioned writing letters of recommendation for kids applying to college. Some teachers refused to write them and some refused to do so unless the parents gave the teacher an unsealed letter to the school board supporting the union position, which the teacher would read before mailing. There was a perfectly predictable and justifiable and public outcry, so I'm not sure how many teachers were involved, but I knew parents whose kids were told this by their teachers.

Bostonian said...

The prof assumes that Mark was never taught about averages and other basic concepts, but it's also possible that Mark was taught about them but later forgot everything. Confirming this theory, the SAT math section does have questions about averages: . If Mark were college material he would have studied for the SAT and mastered the concept of averages on his own, even if his teachers botched the job.

One difference between more and less intelligent people is that the former retain more of what they learn for a long time afterward. I think Charles Murray discusses this in his book "Real Education".

Allison said...

Bostonian, I have no doubt that some retain more than others, and that sometimes things are "taught" in such a manner as no one could possibly remember having been taught it because it was incoherent. But I'm willing to hazard that RWP didn't just assume he'd never been taught this. Over the course of a term, he would have had time to tell the difference between not having been taught it and having forgotten. If you've forgotten something, then when you see it again, you have recognition. RWP would have seen this recognition--"oh, right, that's a mean", or "oh, right m is a slope." something, somewhere would have been recalled. RWP never saw this recognition. Whatever this student had been "taught", it wasn't even coherent enough to hang the tiniest bits on.

Anonymous said...

To analyze and fill in the gaps of students requires a teacher with talent and time. RWP certainly had trouble suffering fools (and others as many of us have experienced firsthand when we disagreed with him), but he always appeared to be a thoughtful and patient teacher with his students.

It still goes back to "they don't know what they don't know."

Mark really couldn't tell him where the gap was, RWP had to find it. Like Allison pointed out, a student's demeanor may mean nothing. They can appear quite entitled, but not really realize why a big wall appeared.


Redkudu said...

"They don't care beyond their 3+mths of holidays, their $75-90,000/yr paycheques."

Where is this magical land you speak of? I would like to teach there. :)

Seriously though, K9Sasha's comment is more on-point: "There doesn't need to be evidence that the change works, it only needs to sound good, and "feel like" it'll be good for the kids."

Teachers' "feelings" often dominate the classroom where teacher autonomy is respected over curriculum. These are people who, as K9Sasha said, care deeply. Unfortunately, when having to hand-craft a curriculum straight out of ed school teachers, especially new teachers, often equate engagement with their exciting new lesson as equal to mastery of the material. I've talked so many new teachers through their desolation when it came to testing time and the results are dismal. They often regard folks like me, who get results but are more inclined toward direct teaching and repetition, as dinosaurs who are actively harming students by making them learn in more traditional ways, irregardless of the fact that my students still move around, laugh, and think deeply. (They just don't make posters, puppets, tri-folds, or foldables.)

Not only do *students* "not know what they don't know," but without a consistent curriculum *teachers* don't know what they don't know.

Teaching, as we've set it up, is the ultimate discovery learning project. Maybe that's why schools like them so much - it's the reality we've created for ourselves.

concerned said...
This comment has been removed by the author.
concerned said...

Take TWO!

I would like an answer too!

I spend many hours filling in math gaps for students in the high school too. It's extremely difficult for students to master new concepts when so much of their time is spent trying to catch up.

We have to expect mastery at every stage in order to best serve the students and help them reach their fullest potential. Keep in mind though, that with mediocre math texts compounding the problem all over the country, new and unsuspecting teachers may not realize how detrimental the LACK OF REAL CONTENT is to the child's future.

If they knew, I'm absolutely sure that they would NEVER use those "instructional materials"

Every classroom teacher I know cares deeply about preparing students for a successful transition to college courses.

Christopher Walker said...

Thank you for re-posting this.
Though I lived with RWP for 29 years, I actually have not read very much of his writing on education, mostly because I had heard it at my dinner table. This posting made me think about the difference between a teacher and a trainer. I was a teacher years ago (when RWP & I met), but am 'only' a trainer, now.

As a trainer my mission is to impart complete mastery, if possible, of a discrete skill or set of skills. I have no obligation toward the general cognitive development of my students.

One of RWP's supervisors once described him as a master teacher. He never dropped into a classroom routine or taught a class by rote. And he believed, as this posting suggests, that when you get an opportunity to help a student learn something that will really help that person get more out of life itself, you should take it.

Because god knows, it's short. His was. He was 53 when he died.

Thanks for making his postings here easy to find.

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