Troubling Students

My classes are easy to pass, hard to do really well in. I’m a pushover for a D, but think three or four times about giving out an A. I didn’t fail a single kid last year. Save for Year Two, All Algebra All the Time, I’ve failed fewer than six kids a year, and even Year Two I had the second lowest fail rate of the math teachers.

I teach mostly math at a comprehensive high school, and the previous paragraph is very near heresy. Some math teachers cheer me on as a brave, admirable soul, but I spot them making the Mano Pantea while they walk away, just in case the Overlord is Watching. Others think I’m What’s Wrong With Education Today. These teachers hold as gospel that math standards could be upheld if we teachers were just willing to fail 60-70% of our students. In contrast to Checker Finn, who thinks teachers like me are spreading out two years of math content over three years of instruction because we can’t be bothered, these folks don’t think I’m lazy. They think I’m soft. They think I’m damaging their ability to cover all the course content they could get through if there weren’t all these kids who shouldn’t be there.

I became a lot less conflicted about my high pass rate–not that I ever lost sleep over it–after teaching precalc and discovering that a third of the kids had forgotten how to graph a linear equation and half couldn’t graph a parabola. These were kids that those other teachers had, teachers who had covered everything. Meanwhile, my kids do well in subsequent classes, so I’m not doing any harm.

But I digress. The students who trouble me aren’t the strugglers. I can take a kid who hates math, doesn’t want to be in class, and get him (it’s usually a him) to try. I can get that kid to attack a projectile motion problem and, even while making multiple small mistakes, beam with pride because by god, he kind of gets this and who ever would have thought? Kids like that, I can pass with nary a qualm.

The worrisome ones pretend they understand, but don’t have a clue. They cheat whenever they can, and not just on tests. They copy classwork in the guise of “working together” or “getting help”, and do their best to sit next to strong students. I group students by ability and, unless they can cheat on my assessment test, they are outed and placed up front, where I can keep an eye on then. They will then ask if they can sit next to John, or Sally, or Patel, their friend, because “they explain it so well”. I say no.

But if they cheated on the test, they can sometimes escape notice for a while. I circle constantly, watching kids work, changing seating when I see too much “consulting” with little discussion. Still others are more clever, and it takes a while before I realize they’ve been cheating not only in classwork, but on the tests–even when I create multiple tests. As a new teacher, I would sometimes miss these kids through the first semester. My success rate at pegging them early has improved.

This isn’t a big group, thank god. I might run into one or two a year. They have a telltale bipolar profile: for example, failing English entirely one year, and passing it the next year with Bs. Passing algebra with straight As, failing geometry completely–and failing the mostly pre-algebra and algebra state graduation test with a spectacularly low score. They aren’t fooling all of the teachers all of the time.

These kids are not your Stuyvesant cheaters, conspiring with others to satisfy demanding parents and create a fraudulent resume to get into a good school. Nor are these the low achievers who just want to get a passing grade in these time units called classes organized into a larger time period called school that others apparently view as a place of learning but they see as little more than a community network in which they have invested considerable social capital.

In fact, they’re almost worse than identified low incentive low achievers, cheating or otherwise. These kids almost seem incapable of learning. I can’t get them to slow down. They often resist help from me. Typical conversation:

Me, stopping by: “Okay, let’s start this again. You’ve plotted these points….”

Student: “Oh, yeah, I see.” Frantically erases.

Me: “Well, hang on, I want to be sure…”

Student: “I got it I got it I got it.” Starts to plot a point, then pauses.

I realize the student is waiting for me to say where to plot it in order to say “Yes, I know, I know.” So I wait. The student takes a deep breath and plots the point then lifts his pencil. “No, that’s not right, duh…”

Me: “You aren’t sure how to plot points.”

Student: “Yes, I am.”

Me: “Great. Plot (7,-7).”

Student plots (-7, -7).

Me: “Stop there.” I go grab a handout I have specifically for these situations, a simple handout that explains plotting points with some amusing activities to drive the point home.

Student: “I don’t need this. I know how to do it!”

Me: “Great. Then it should just take you a few minutes.”

At this point, I get a variety of reactions. Some students become furious. Others get sulky. Still others do the handout, making many mistakes, all the while assuring me that this is easy. I obligingly correct the mistakes, make them do it correctly. The ones that get furious, I shrug and let them continue.

Regardless, within a day, they are making the same mistakes. Nothing sinks in. Don’t get overly focused on plotting points; the problem could be anything–factoring, solving multi-step equations, working with negatives, exponential properties, fractions, whatever. Or a new concept. They have absolutely no clue, and can’t do much of anything.

Yet they don’t have the profile of a low ability student. Test scores, yes. Profile, no. They often have As, win praise from teachers for their teamwork and effort. They are heavily invested in appearing “normal”. Serious control freaks. Sometimes, but not always, with parents who expect success. More often, but not always, Asian. All races. Both genders.

I haven’t taught freshmen since oh, lord, fall 2012.1 I teach relatively few sophomores these days, running into them only in Algebra 2.

That matters because when I taught freshmen and sophomores, I would go full-scale intervention. I might talk to a counselor to see if they should be assessed for a learning disability. I would insist that they stop lying to me and themselves. I had no small success at getting some of them to acknowledge their desperate attempts at fraud, get them to work at their actual level, deal with the discomfort. They didn’t make much progress, but it was real progress, and they had skills to move forward. I ran into some of them again the next year, and we could start on an honest basis and make additional progress. Those who didn’t acknowledge their issues were among the few students I failed.

But that’s a lot harder to do when dealing with juniors taking trigonometry or, god forbid, precalc. Should I fail them? They will probably do better in a class with teachers who give “practice tests”, study guides that have exactly the same questions as the eventual real test but with different numbers. They will definitely do better with teachers who actually grade homework and count it as 25% of the overall.

A small problem. This approach turns my grading policy into: work hard and honestly acknowledge your ignorance and I’ll pass you. Lie and do your best to cheat with similar ignorance and I’ll fail you. I’m comfortable with holistic grading at the bottom of the scale, but I don’t like morality plays.

Then I remember that kids who honestly acknowledge their inability in a trig or pre-calc class are usually seniors, off to junior college and a placement test that will accurately put them in remedial math. I’m only ensuring they are learning as much as possible for free before paying. If they are juniors, I always have a talk with them about their next steps, telling them not to take the next course in the sequence but maybe stats or something else that will keep them working math, but not out of their league.

The kids who cheat and fake it in trig and precalc are usually juniors, and they will be going onto another course. They will not listen to me when I tell them under no circumstances should they continue into pre-calc or, god forbid, calculus. I might be teaching that course, which just gives me the same problem again. Or they’ll be cheating their way through with another teacher–or, that teacher will do what I should have done and flunked them.

This quandary doesn’t make any sense unless you realize that in my view, these kids are pathologically terrified of facing reality, the sort of thing that some of them, forced to face up, might not survive in good form. These aren’t blithe liars gaming the system to look good. Then I remind myself that they’ve been caught before, they’ve flunked other classes, they’ll survive. But I still don’t like the quandary, because these are kids who literally can’t learn. (And remember, I’ve seen them in my non-math classes, too). By junior year, given their denial and fear, does it do any good to make them aware of this? They’re going to be able to point to any number of teachers who disagree with my assessment, and have all sorts of excuses for why they got those Fs. Besides, they just don’t test well. It’s always been a problem.

At times like this, I envy my colleagues who never notice the cheating, or who focus purely on achievement and aren’t interested in the distinctions I’m making.

But these are the students who trouble me.

************************************
1Holy Crap. That’s an amazing realization. New math teachers doing your time in the algebra/geometry trenches, take heed. If you want variety, it will come.

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33 responses to “Troubling Students

  • Mark Roulo

    “Then I remember that kids who honestly acknowledge their inability in a trig or pre-calc class are usually seniors, off to junior college and a placement test that will accurately put them in remedial math.”

    Okay, so I’m slow.

    I hadn’t realized that a non-trivial percentage of the kids from your high school were college bound (junior college is college …). What percentage go off to college (as opposed, I guess, to “getting a job” or “apprenticing to a trade” or “joining the military” or whatever other options one has)?

    • educationrealist

      About 50% are officially deemed “college ready” by the state, but I’d say close to 80% go to some sort of college. I might be overestimating, but not by much. Our school has an *excellent* vocational program, and many of our kids go to intern and trade schools in cooking, firefighting, and the like.

      Most of my kids who are in pre-calc and trig their senior year are going to college–mostly state 4 years, some junior college. Most will be deemed college ready at trig or pre-calc level (one or two of my pre-calc kids actually place into calculus). The very weakest will probably test into one level of remedial (that is, one course before college ready). . Most of my kids in Algebra 2 as seniors are also going to college, usually junior college. The best are testing into college ready classes, the rest one level back, and the weakest will still test into an achievable level of remediation.

      I’ve had both excellent and weaker kids go into the military; I’ve prepared a good 20 for the ASVAB. One kid is a weak tester, and got a low score. His sped teacher and I convinced him to go to junior college for a semester, take another math course and practice. He took it again and tested in at a much higher level (I don’t know how these work, but it qualified him for far better options).

    • educationrealist

      Put another way: In Michael Brown’s high school district, 279 blacks were taking precalc, trig, or stats, or 10% of the black population, while 13% of white kids were taking same.

      So even in a school that is seriously malfunctioning, you have a (to me) unimaginable percentage that still make it through to advanced courses. Our numbers are around 47% and 55%, and even our Asian population is below 60%. Those numbers are much lower than non-Title I schools.

      So there’s a whole huge range of lower-achieving populations. I try to point that out. Remember the time I wrote about the only two kids I’ve worked with that had IQs lower than 90? Ferguson, on the other hand, probably has over half a population with IQs lower than 90. At the same time, kids with IQs of 95-110 are still going to struggle with precalc, trig, etc.

      • JH

        Ferguson-Florissant was considered a relatively okay district until last summer.

      • Mark Roulo

        Thank you.

        “I don’t know how these work, but it qualified him for far better options”

        The Wikipedia article on the ASVAB is good. In short, you need a certain “general” score to get into the military at all (slightly different cut line for the different branches). Then you need specific combined scores in various areas to get into specialties (Artillery, for example, cares about “mechanical reasoning”). If you don’t get into a specialty (or don’t want to go into one), for the army you get to start off in the infantry. Some folks are fine with this, but if your goal is to get some job training while in the army, a ASVAB score that lets you go into some sort of Maintenance job is probably better. Working on jeeps for two years is probably more valuable for future civilian jobs than two years lugging an M-16 and shooting bad guys.

  • Mark Roulo

    “I became a lot less conflicted about my high pass rate–not that I ever lost sleep over it–after teaching precalc and discovering that a third of the kids had forgotten how to graph a linear equation and half couldn’t graph a parabola.”

    For more depressing wonderfulness, you can read this:

    http://www.math.jhu.edu/~wsw/papers2/education/24-arith-elite-11.pdf

    The money quote is:

    In the fall of 2007 I gave a 10 question arithmetic test to my 229
    Calculus III (multi-variable calculus) students on the first day of class.
    Among other things, this means they already had credit for a full year
    of Calculus. The vast majority of these students were freshmen and
    were not about to question what happens on the first day of class in
    college. They had plenty of time. The average math SAT score was
    about 740.

    … [what follows are 10 arithmetic questions such as “Multiply 5.78 by 0.390” and “70 is what percent of 250?”] …

    Seven of these problems were each missed by 8% or more of my students and 69 students, or 30%, missed more than 1 problem.

    It isn’t just the kids in your high school 😦

    • educationrealist

      That’s really interesting.

      I’m happy to say that the bulk of my kids, when I run into them in pre-calc, are able to graph a line AND factor AND remember at least vaguely how to graph a parabola. I also run into my geometry students in trig, and they do pretty well.

      Some forgetting is inevitable. But I’m kind of surprised that MVC kids couldn’t do better.

  • educationrealist

    You know, someone just posted comments so utterly ill-informed that I didn’t approve them because taking the time to respond to them would have raised my blood pressure.

    In short, the idiot said that I work at an elite school with tracking, that there are ways to deal with cheating (as if that was the issue), and that Johns Hopkins wasn’t *truly* elite, so that’s why they couldn’t divide.

    I just…phhht. Couldn’t do it.

    • Mark Roulo

      “…Johns Hopkins wasn’t *truly* elite…”

      From Wikipedia: “Johns Hopkins is also ranked #12 in the U.S. News and World Report undergraduate program rankings for 2014 ”

      Well, if *truly* elite means top-10, then Johns Hopkins misses the cut. And I *totally* understand only expecting the top 0.1% or so college freshmen in the country to be able to work well with decimals, fractions and percentages. Expecting more is unreasonable. W. Stephen Wilson should know that …

      🙂

      • educationrealist

        Yeah, it was kind of crazy making.. I’m getting a bit tired of people only seeing what they want to see in my articles. I’m not always clear, but sometimes they go 180 degrees opposite. See comment below–I didn’t say my kids do group work. In fact, I’ve often said they don’t. I mean.

  • cryptonymousbill

    30% missed more than one problem? Ok, but nothing in the paper mentions a time limit.

    It would not surprise me if a group of students who hadn’t used pencil-and-paper in years, if ever, flubbed a few decimal multiplications if only given 10 minutes to solve them. I’d bet 30% of them would miss at least ten problems on the Wonderlic, too.

    But maybe I leap to their defense because that rejected comment disparaging Hopkins hurt my pride.

  • Hattie

    Is “doesn’t test well” *ever* valid?

    • Mark Roulo

      “Is ‘doesn’t test well’ *ever* valid?”

      In *general*, I don’t think so. If you know the test format and can practice, I have a hard time seeing the difference between “doesn’t test well” and “doesn’t know the material.”

      Having said that, I can come up with some exceptions:

      (a) When my now-teenager was very young he was at his pediatrician for a regular checkup (year three, I think). To test vision, they had a chart with shapes and animals and wanted him to tell them the various shapes/animals in each line. He was struggling mightily, when my wife and I intervened with “We’re not sure that he knows the *names* for what you want … can you give him one with letters?” Letters went well. In this case he “didn’t test well” for what they cared about (his vision), but also if we had known we would have practiced with him so that he knew what they wanted. If tests often don’t resemble the in-class material, I can see “doesn’t test well” as short-hand for “can have a difficult time figuring out what the questions are supposed to be.” Imagine someone who has never taken a multiple-choice test, for example.

      These cases shouldn’t be ongoing, though …

      (b) I can imagine some kids who know the material *VERY* well, but simply go slowly. They might flunk a one hour test (with a 50%), but get 100% if given 2 hours. I’m reluctant to give this kid the same score as a kid who really doesn’t know how to work with the material at all (but might get a bunch of partial credit).

      (c) I can imagine some sort of “test anxiety” … but have a difficult time accepting that experience and practice won’t make this go away. If real, then I still don’t know what to do for the kid. Alternative assessments simply aren’t comparable with what everyone else did.

      Ed? Any examples from your teaching of kids who actually knew the material but consistently “tested poorly?”

    • Roger Sweeny

      In my very small college major (at a pretty selective school), I knew a guy who “didn’t test well” because of some sort of anxiety. As far as I could tell, he was as smart and hard-working as any of us. He became a very successful lawyer.

      • plunatic

        I have far less experience teaching than the blog author, but my guess is that it sometimes is.

        An uncommon example that I encountered a lot was for people who were hesitant speakers and readers of English. Sometimes, they simply couldn’t make sense of longer questions, I thought it might have been a working memory thing. I think this is partly “not knowing the material”, as to demonstrate knowledge of something you need to be able to communicate it, but it might contribute to “maths ability” and “test scores” being slightly further apart than ususal.

        Other than that, when you see a lot of kids you learn that all sorts of unlikely pathologies are at least occasionally present. Hates tests, struggles with a particular part of questions that happens to be really common etc.

    • educationrealist

      As I think I’ve posted before, “doesn’t test well” is absolutely something that exists, but it’s far less frequent than most people think. I’m talking about cases where the kids can demonstrably do problems, unassisted, no cues, in a classroom situation and then doubts kick in during a test.

      However, I am not talking about kids who don’t test well. I’m talking about kids who don’t understand the material at all, at any point, who refuse to even try to let learning in because of anxiety, who seem incapable of learning.

    • DensityDuck

      “Doesn’t test well” = He does well on homework because his parents stand there and feed him the answers, thinking that they’re ‘helping’ or ‘coaching’, and he’s learned that if he just sits and stares at the paper then he’ll be given the answers, which of course doesn’t work on a test.

  • plunatic

    How much do you think it’s a defense against looking stupid? My experience is that the behaviour you describe is far more common when most students struggle with the work than when most can get through it. That is, there are a number of students who would be “fine” if not for the fact that they can actually do the work.

    • educationrealist

      Sorry, just saw this. I absolutely think it is an long-engrained reflexive defense against “looking stupid”. Skill level, they are probably equivalent to the low-skilled kids who *do* progress slightly. But because of this reflexive defensiveness, they can’t even do that much.

  • anonymousse

    “They copy classwork in the guise of “working together” or “getting help”, and do their best to sit next to strong students. I group students by ability and, unless they can cheat on my assessment test, they are outed and placed up front, where I can keep an eye on then. They will then ask if they can sit next to John, or Sally, or Patel, their friend, because “they explain it so well””

    What is this group work to which you are referring? I don’t recall a single instance of group work in my math experience (admittedly, 30-40 years ago).

    Since ‘groupwork’ is all about mooching off the smart kids, why, as an education ‘realist,’ do you use it?

    anonymousse

    • educationrealist

      “What is this group work to which you are referring?”

      I didn’t refer to group work. I don’t use group work.

      • Roger Sweeny

        I think anonymousse is asking, “If you don’t use ‘group work,’ how can students ‘work together’ or ‘get help’ from another student?” Your post can be read as saying that your students do that, and to people not in the business, any work not done individually is “group work.”

      • educationrealist

        Well, since he’s a teacher, I think he’s one of those who hates “complex instruction” (aka group work). I hate complex instruction too. Where I differ with the people who lump all “sitting in groups” together with “group work”, where the group is responsible for the success of everyone. I don’t do that.

        I was thinking I should write that up.

  • DensityDuck

    Some kids would rather jump off a cliff than admit that they made a wrong choice. I know this because I was one of those kids. I ended up making my parents pay for a trip to Europe because I didn’t want to admit that I’d misheard the time for an informational meeting and went to the wrong one.

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