a calculus professor's email exchange with a parent

Number 2 Pencil links to this exchange of emails between a math professor and one of his students, who is flunking calculus.

The professor is using a pedagogy known as Process Guided-Inquiry Learning, or POGIL:

I mentioned in an earlier post that one of the more controversial -- and to me, appealing -- aspects of POGIL instruction is that the instructor is not seen as a source of knowledge but rather as a facilitator of learning. In non-eduspeak, this means that the instructor is there to observe and to guide, rather than to tell students what to do or think.

I also mentioned, and one commenter pointed out, that students HATE this (at least at first). Typically, students -- even upper-level students in the major who have been around the block -- just want to get the darn problem done, and when people like me insist on students asking the right questions rather than just forking over the answers, things can get heated.

In practical terms, POGIL means that when 'Pat' comes to his professor's office for help, the professor refuses all requests for one-on-one demonstration of the problems being taught in class:

…when Pat would ask me a question such as, "Can you tell me how to do problem 7?", I would say: Let's start by asking the right questions. What are you being asked to do in this problem? What information is given to you in the problem statement? And what do you know from the course, your reading, or your work on other exercises that will help get you to the goal? I made it a point to NEVER give Pat explicit help on content unless it was a last resort -- Pat absolutely HAD to cut the apron-strings from me an learn how to approach, analyze, and solve a problem alone, or else Pat's chances for success in a future career or even making it through college didn't look good.

This goes nowhere.

Finally 'Pat' sends an email explaining that he requires direct instruction in order to learn.

The professor tells him he is wrong.

Pat sent me an email just after midterms that said something like: I now understand why I am not doing well in your class. My learning style is such that you have to show me exactly what to do, or else I can't do it. But you always answer my questions with more questions, which isn't showing me exactly what to do. So from now on, please show me exactly what to do first, and then I should be able to do it. My response was something like: Pat, we've been doing this every day in class -- I work a few problems at the board all the way through during lecture, and then I give you exercises that are based on the stuff you've seen. So you are seeing me show you what to do, and yet you're still having difficulty solving problems on your own. So perhaps your assessment wasn't quite right, and we should be working on your problem-solving skills in office hours.

Then Pat's mother gets into the picture.

(via email): I know [Pat] tried to explain to you that when [Pat] asks questions [Pat] needs answers not another question. We had [Pat] tested at [a local university] in January through the suggestion of [an academic counselor at my college].

During this testing we found out [Pat] has a learning disability. [Pat] does better with visual explanations then being asked another question. [Pat] needs to see how to physically work a problem so he can comprehend it. [Pat] is a slow reader which also frustrates [Pat]. If it is a word problem [Pat] has problems figuring out what are the essential parts of the question to find the answer.

This infuriates the professor, and, subsequently, all of his commenters as well, who pretty much stomp mom to death in the comments thread.

Pat fails the class.

The commenters are united in their view that Pat is a lucky guy to have experienced POGIL calculus, and he had no business hosing the course.

Memo to self: the time to begin instilling core take no course from professor who blogs principle in 10-year old son is now.

POGIL

POGIL, POGIL, POGIL

This does not sound good, POGIL.

I should reserve judgment.

I should, but every one of the little-red-light thingies on my Constructivist Nightmare Detector is flashing wildly, and all the sirens are going off—

So I’m not doing a very good job of reserving judgment.

POGIL is a student-centered method of instruction that is based on recent developments in cognitive learning theory and results from classroom research that suggest [sic] most students experience improved learning when they are actively engaged, working together, and given the opportunity to construct their own understanding. POGIL emphasizes that learning is an interactive process of thinking carefully, discussing ideas, refining understanding, practicing skills, reflecting on progress, and assessing performance. In a POGIL classroom or laboratory, students work on specially designed guided-inquiry materials in small self-managed groups. The instructor serves as facilitator of learning rather than as a source of information. The objective is to develop skills as well as mastery of discipline-specific content simultaneously. (Emphasis added)

OK, that does not sound good.

homeschool mom with common sense-y

I'll get to the professor’s various posts on POGIL as soon as I can.

I do want to read them.

But in the meantime, there's one homeschooling mom on the thread (son has LD) whose comments make sense to me:

Pat says clearly that your Socratic style doesn't work for [him]. Why do you then believe that it does work? You (rightly) want [him] to learn problem solving, but just because your method of teaching ... works for others doesn't mean it works for [him]. Maybe [he] needs repetition, repetition, repetition of the underlying content before [he's] ready for process. Other students may grasp the process after going through the underlying solutions three times, or six times, but maybe [he] needs thirty times.

You model the problem solving that you want [him] to do-- Where have you seen a problem like this? What rule did we use?-- but in a sense that's no better than modeling the actual rule for Problem 13. You want [him] to intuit that [he] is supposed to be asking [himself] those questions. But what if, as seems to be the case, [he] isn't intuiting that? Then [he's] not learning anything.

The bad news here is that, clearly, constructivists are giving lots of workshops to math professors.

Even worse, math professors are attending them.

inflexible knowledge, flexible knowledge, and expertise

One of the problems with constructivism (and, apparently, with POGILism) is that it tries to teach higher-order problem solving first, instead of second.

That option probably isn't on the menu.

According to Daniel Willingham, knowledge is always inflexible before it's flexible. You can't hopscotch over the inflexible stage by teaching process, or asking students to discover addition.

Problem solving and critical thinking seem to grow out of extensive practice of surface, shallow, inflexible knowledge.

I’d like to know more about how this happens.

At a minimum I’d like to know what cognitive psychologists (psych department cognitive psychologists, I mean) understand about the process at this point.


And I hope that Robert, who writes the brightMystery blog, will join us at KTM once in awhile to think about these things.

update

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This sounds a bit like "reform calculus" that is being taught on various campuses. To use the vernacular, it sucks. One of the places where it was pioneered, I'm sorry to say, is my Alma Mater U of Michigan. One of the people involved in its promotion is a woman (instructor not professor) named Pat Shure, who is buddies with Glenda Lappan of Michigan State U, who was one of the big forces behind Connected Math (CMP). I communicated with Pat Shure briefly, before I knew about the math wars. I was asking about how certain aspects of calculus were being taught, and her answer was snippy and downright insulting. Now I know why. She thought I was snooping around, trying to undermine the reform calculus program.

On a slightly related but admittedly tangential topic, if there are lawyers out there, can you put in your two cents regarding whether any of this, whether at college level, but particularly at K-12, constitutes educational malpractice? I am writing an op-ed conjecturing on this possibility, and the more facts I have, the more dangerous that makes me.

-- BarryGarelick - 29 Jun 2005

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Barry, I'll email you the name of the man who is suing the state of MA.

-- CatherineJohnson - 29 Jun 2005

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I can state with certainty that the majority of math professors don't know squat about learning disabilities.

Unless they've been made to do seminars since my time. But the thing about having tenure is that there really isn't that much that you can make a tenured professor do.

I know I've said this before. But I still wish I knew, back when I was teaching, what I know now about learning disabilities.

-- CarolynJohnston - 29 Jun 2005

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I read Robert's post, and Number 2 pencil. Here is what I posted at Number 2 Pencil:

Robert's interaction with his LD student reminds me so much of my own ignorant interactions with mine, ten years ago when I was a college mathematics professor. Reading what he wrote makes me practically ache with guilt.

Let's try to evaluate Pat The Student fairly. Did he genuinely try to learn the stuff? Was he putting in the time, and failing anyway? Was he able to learn when the material was approached in the way that he and his mother suggested? Did Robert fail to even give their suggestions a try?

I had a few LD students like this. Some passed my course in the end, with the help of tutors (not mine, for the most part, I'm sad to say); some couldn't, even with the help of tutors.

I wish I knew then what I know now. And I wish Robert knew now what I know now.

-- CarolynJohnston - 30 Jun 2005

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I know I've said this before. But I still wish I knew, back when I was teaching, what I know now about learning disabilities.

You're definitely going to have to fill us in as you go along.

I wish I knew more.

-- CatherineJohnson - 30 Jun 2005

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Wow--Carolyn--you ROCK.

I'm so glad you posted that.

I had a strongly negative reaction to the whole saga...but I just couldn't quite tell whether I was on target or not.

On the one hand, by the time you get to college, you do have to be 'responsible' for your learning.

On the other hand, this professor was utterly unbending and frankly self-congratulatory.

Did you read the homeschool mom's comments?

Every one was good.

-- CatherineJohnson - 30 Jun 2005

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The mom is 'Cardinal Fang.'

I made a post to the Mystery blog, but he hasn't let it through yet. (I assume he will--I posted Willingham's article link.)

-- CatherineJohnson - 30 Jun 2005

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Oh good for you! I wanted to do that -- but didn't know the syntax (speaking of inflexible knowledge...)

I will post on this at length in time, though it's sort of a sore spot for me. I really do feel guilty about it.

Professors in math -- probably in all the other fields as well -- often don't know a thing about learning disabilities, and can't tell the difference between someone with an LD and someone who is just not trying. I am afraid I just didn't really believe in LDs, even in those kids whom I knew were trying hard and not getting it.

Never mind LDs, on some level I just didn't really believe in hidden disabilities. And I imagine I failed to hide my attitude very well.

So of course I get a kid with a serious hidden disability. Honestly, I've had to re-evaluate my beliefs and eat my words so often in my life, I think the fates must be using me as some kind of poster child.

-- CarolynJohnston - 30 Jun 2005