Monthly Archives: February 2012

Homework and grades.

The NY Times rewinds the typical homework debate. The post gets predictable pro and con responses: “homework is ruining my kid’s life” vs. “homework is a necessary component to learning”.

As is often the case, the situation at hand involves middle and elementary school students. High school homework rarely gets much scrutiny, unless it’s high achieving students complaining (with a lot of justification) about the huge amount of work they have to stay on top of to stay competitive.

But outside the top 10%, homework’s impact on high school students is a much neglected issue, and it shouldn’t be. Few people seem to understand the inordinate influence homework has on student transcripts—and the results, for the most part, are near-fraudulent.

High school students are far less likely to do assigned homework and the consequences for non-compliance are much higher, because students who don’t do homework often fail—not for lack of demonstrated subject matter skills, but simply for not doing their homework.

Here’s a chart that pretty much any teacher in the country could produce, comparing achievement (test scores) to classwork and homework effort.

(from Reflections of a First Year Math Teacher)

Don’t be distracted by the positive correlation. This is for individual grades, so the individual points are what matter. Notice how many students work hard, yet have failing test results, and how many students don’t work much at all, yet ace the tests.

This graph reflects the reality I point out ad infinitum: effort is only tangentially related to achievement, and then only at the individual level. Students who try harder don’t do better than students who don’t try at all. The lurking variable, of course, is ability.

For this reason, teachers should not include homework as a significant part of a grade, and should never allow missing homework to lower a grade. (This means, English teachers, that if a student doesn’t do an assigned essay, you find another way to assess the student.)

But of course, teachers routinely include homework as 25, 35, 50% of the grade. Happens all the time, and no one calls teachers on this behavior because it’s so damn cheap and easy to argue that homework is essential, good for both discipline and achievement. Never mind that there’s no real evidence for the latter, and the former should not influence grading.

The “homework proxy for effort” skew is understandable, given that teachers really can’t grade students purely on demonstrated ability. Teachers would fail too many students if they set an absolute ability standard. (See the above chart again if you need reminding.)

Teachers tend to value effort anyway—it makes them feel needed. So this preference, coupled with the real dilemma imposed by teaching and assessing students whose skills are far below the required ability level, gives them license to reward effort, to some degree.

But the degree matters.

Boosting hardworking students’ grades just a bit (say from one grade’s “+” to another grade’s “-“) is fine. While some may raise an eyebrow at the idea of giving a failing student a D- because he shows up and tries, I not only forgive this, but engage in the practice frequently.

Giving a student with mediocre math skills an A or B simply because they work hard and finish all their homework is quite another matter and worst of all, giving a low grade to students with excellent test performance—in many cases even failing the student—is outright fraud.

This happens every day, although it’s drowned out by all the middle class parent whining about how much work their middle schoolers have.

In high school, teachers are assigning homework, students aren’t doing it, and teachers are giving lower grades—often failing students completely—even though their skills are strong, simply because they don’t do their homework. Teachers are a moralizing lot, by and large, and they are far more comfortable giving low grades, or outright failing, kids who don’t try and aren’t compliant than they are doing the same to hardworking kids with low skills.

This leads to astonishingly bizarre grade results. Two students might each have very weak algebra skills but one gets an A, because she goes to a school that weights homework as 50 or more percent of the grade and does extra credit, while the other fails at the same school simply for not doing his homework. Students who can read at basic proficiency can fail English for not doing their essays, while functionally illiterate students who earnestly string together sentences on books they didn’t understand get Bs.

Five of my algebra sophomore students last year scored Basic on their state tests–but failed algebra for not doing their homework. One of my best geometry students failed geometry last year for not doing his homework—at least, he was one of my best students until he left for alternative high school because he’d failed so many classes (all by not doing homework) that he can’t graduate on a normal schedule. Several of my top Algebra II students this year took Algebra II/Trig last year and scored basic—but, yes, failed for not doing their homework. Meanwhile, I have colleagues teaching AP Calculus to students who scored Below Basic on all their math state tests up to that point. How can that happen?

State universities don’t use test scores for basic admission, but grades. Which explains why remediation is such a huge problem, doesn’t it?

Of course, at this point in a conversation someone will say, condescendingly, that the students just need to learn how to put in some effort, go through the motions, and I have to fight the urge to go find a baseball bat. Really? We’re talking about a nationwide problem and some idiot treats this as a cheap sermon on morality and obedience? Seriously?

I mean, never mind the fraud that teachers are engaging in, failing competent students while giving good grades to functional illiterates. Consider the massive waste of money thrown away because so many teachers confuse homework obedience with academic achievement. And of course, because our nation is convinced that all kids must be on the college track, there’s so little room for error that one or two Fs ensure that a student is off-track and just marking time until alternative high school is an option.

Districts desperate to stop teachers from indiscriminately failing otherwise competent kids (compared to the kids who are passing) institute those policies that annoy eduformers and earn them lots of mocking catcalls—Fs can’t be less than 50%, homework can’t be more than 10% of the grade, and so on—but these policies make perfect sense when considered in light of the money districts lose to dropouts and quick credit factories that allow students to collect enough credits without learning a thing—even less than they learned from the teacher who gave them an F.

Never forget: grades are a fraud. And in homework, stop wondering about how much is given, and start asking about how much it’s worth to the grade. Because if it’s more than 5%, it’s too much.

Modeling Linear Equations, Part 2

In Modeling Linear Equations, I described the first weeks of my effort to give my Algebra II students a more (lord save me) organic understanding of linear equations. These students have been through algebra I twice (8th and 9th grade), and then I taught them linear equations for the better part of a month last semester. Yet before this month, none of them could quickly generate a table of values for a linear equation in any form (slope intercept, standard form, or a verbal model). They did know how to read a slope from a graph, for the most part, but weren’t able to find an equation from a table. They didn’t understand how a graph of a line was related to a verbal model—what would the slope be, a starting price or a monthly rate? What sort of situations would have a meaningful x-intercept?

The assessment confirmed my hunch that I haven’t been wasting my time. I tried to focus on problems they could solve in multiple ways—up to and including plugging in the answers. I wanted them to be able to approach a problem “as if it were their money”, as I kept telling them when they were figuring out how many power bars and gatorade they could buy for $20.

Here’s the assessment, with the percentage of 83 students who answered correctly (click to enlarge).


  • Questions 1, 3, 8, and 10 were at or just above the “random guess” percentage. Everyone screwed up the first question, flipping rise and run (answering -2). 3, 8, and 10, however, were answered correctly by students who received a C or higher.
  • Question 11 makes me want to beat my head with a student whiteboard. Only 62% of the class knew what the slope of y=-10x + 7? Really? Some of the students who got it wrong then went on to accurately identify the slope from a table and pick the right equation in slope intercept form. It is to weep. But anyway, my guess is that 20% of the kids who got it wrong actually know it, leaving 20% who still aren’t sure. And that’s bad enough.
  • Very proud am I of the results for question 13, since we hadn’t done anything like that in class. Apart from the “read carefully” hint, I gave no assistance. Of course, I didn’t include the midpoint for AM, which would have cut the success rate in half. But it still shows the students are thinking and not giving up.
  • While the system of inequalities questions are barely at 50%, that’s a huge improvement over the semester final.
  • The students had trouble with question 19. This suggests that many of them are still just plugging the values into the equation rather than reading the slope from the table, since the slope is a fraction—and at least a third of the class still can’t multiply fractions.

I curve my multiple choice questions on a 15 point scale, so 85 and up is an A, 70-84 a B, down to 40-54 a D. A student could pass with a D- by answering 8 questions; I think getting 40% of a test that would not (for those students) include any gimmees is worth a low passing grade. On that scale, the average score was 70%—and that’s a first. Every other assessment, including the two on linear equations last semester, had average scores in the D range.

Only two As and four Bs. Many students who usually nail Bs got Cs, while the students who usually failed also got Cs or solid Ds. This too makes me think I’m on the right track. It tells me that some of the B students are used to memorizing methods—and since I didn’t give them one clear-cut method, they had a bit of trouble. The D and F students, who couldn’t memorize or even really understand the methods, were really able to benefit from the instruction and had solid results. (For many students, I consider a passing grade of D a great achievement, and tell them so.)

Several of the B students who did poorly came up to talk to me about it, and that, too, was revealing. Most of them understood realized that this new approach was exposing a weakness on their part and, instead of complaining, talked about their difficulties and asked how they could improve.

We’re doing quadratics in the same way—just spent three days learning how to create table values from descriptions. For some reason, the only quadratic word equations I can think of involve geometry—but then, most of my kids need four or five seconds to remember the formula for a triangle, so the review is win-win.

Bad Teachers

The NY Post fumes about another “bad teacher” story, carefully designed to outrage all good taxpaying citizens as to the nefarious slugs collecting our hard-won taxpayer dollars.

I’m a process freak. When I read the Post story, my eyes went straight to the section that many others ] probably glossed over:

Accused in 2001 of making lewd comments and ogling eighth-grade girls’ butts at IS 347 in Queens, Rosenfeld was slapped with a week off without pay after the DOE failed to produce enough witnesses at a hearing.

But instead of returning Rosenfeld to the classroom, the DOE kept him in one of its notorious “rubber rooms,” where teachers in misconduct cases sat idle or napped.


That let rubber-room granddaddy Roland Pierre make a mockery of the system. He finally retired at age 76 last year — 14 years after he was yanked from PS 138 in Brooklyn and never taught again. Criminal charges in 1997 that he molested a sixth-grade girl were dropped.

So….we don’t actually know if either of these guys are, in fact, oglers and molesters. We don’t know this because, perhaps, incompetent bureaucrats and law enforcement personnel (government workers, all) failed to make the case (just as the DA found insufficient evidence on Mark Berendt in 1994–and yes, Berendt, too, gets to retire with full benefits). Or, perhaps, we don’t know this because these guys aren’t actually guilty.

What we do know, according to the story, is the process for getting rid of bad teachers, as well as the process for putting sex offenders in jail, was followed. But the journalists who write “bad teacher” stories don’t agree with the outcome of that process. Journalists who write “bad teacher” stories have to mention the process, but they never blame the process. They blame the unions for doing the job they’re legally required to do, the teachers for not quitting or allowing themselves to be fired. But not the process. These stories always punch up the volume on the potential sex offender or near-abusive teachers, but it’s rare to see a “bad teacher” story that focuses on the effort to get rid of a teacher who just isn’t very good.

Eduformers, on the other hand, do blame the process. They don’t like it one bit. Eduformers often push the “bad teacher” sex offender stories, not because they think all teachers are sex offenders, but because, as they repeat ad nauseum, “we need to make it easier to fire bad teachers”. Gen up outrage to make it easier to fire sex offending teachers and hopefully the net will widen to pull in the other teachers the principal wants to fire as well.

But while eduformers do blame the process, they rarely talk about changing it. They want it gone. They point to the the process of firing teachers, which they clearly think is absurd, and call for a more executive approach, one that allows principals full discretion to fire “bad teachers”.

In fact, the process itself isn’t that ridiculous. In most districts, principals can visit classes any time they like. If they find a teacher asleep or reading the newspaper, they can write it up and put it in the teacher’s personnel file, where it can be used in the next evaluation. If students turn in absurd assignments that show the teacher is phoning it in, or record the teacher showing them movies daily, that, too, can be included in the evaluation. An aggressive principal can get a bad teacher fired—if, in fact, the teacher is a bad teacher.

But that’s not enough for eduformers. They don’t want a process, they want a system with executive control—one in which the principal is more powerful than the much-hated unions, one in which the principal gets to form his or her team and dump the naysayers. Dream on. I get the allure. It’s just not going to happen. Unions or no, teachers and principals are still paid with government money, and principals will never be able to have unilateral control as long as they’re spending taxpayer dollars. Because, just as there are really bad teachers, there are spectacularly awful principals1, and the job carries authority to do real damage with real money. Eduformers either can’t or won’t understand the futility of their dreams.

I know that eduformers don’t understand math, despite their protestations about math teacher competence, because bad teachers are a non-issue when it comes to their contributions to educational costs. Imagine, for a moment, that 10,000 horrible teachers sit idle in New York City, teachers so awful that they are all banished to the rubber room and are collecting $100K/year. They would be taking up 5% of the city’s operations budget for education. In fact, there are fewer than a thousand horrible teachers sitting idle, and the money spent is a fraction of 1% of the budget. So spare me the sturm und drang. When it comes to waste in education, bad teachers are a rounding error.

If principals wanted to make firing bad teachers a priority, they would. The fact that they don’t speaks volumes not about the difficulty of firing bad teachers, but rather the low priority it is for principals.

So. Should it be easier to fire spectacularly incompetent teachers? Sure. Is that what eduformers are interested in? No.

What eduformers say they want is improved educational outcomes, and that improving teacher quality is essential. If that’s really what they want, then no problem, as far as I’m concerned: eduformers, you’re wrong. Give it up. Bad teachers aren’t causing the problems you’re worried about, and they really aren’t that much of a problem to begin with.

What many progressives accuse eduformers of actually wanting is something quite different. Eduformers and their corporate funders are, say progressives, actively seeking to undermine all elements of the traditional educational power structure—unions and education schools—in order to remove teacher job protections and make education much cheaper. They want to turn teaching into a job like any other private sector job, with zero protections and guarantees, no pensions, getting turned out with a few weeks pay when a new boss comes in, no seniority rights. These protections, once guaranteed to many private sector workers, are now a sinecure of government jobs and need to be destroyed. Once teachers are stripped of the protections they have, say the progressives, eduformers will shrug and find a new culprit—and probably push for government to get out of schooling altogether.

I find this accusation extremely convincing. Many eduformers are no doubt well-meaning romantic fools being used by their corporate funders, while other eduformers are explicitly working towards this goal, openly or not.

The thing is, I’m not sure I disagree with that goal. Why should teachers and government workers be protected when private sector workers are not? Why should taxpayer dollars go straight from teacher paychecks to union funds that get handed directly to progressive causes that many teachers don’t support? While we can’t get better results with our current goals, we could undoubtedly get the same results for less money—not that much less, unless pensions got axed. But less.

If that’s the goal, then why not go for it directly? We could revamp the teaching job in all sorts of ways, many of which would give tons more power to good teachers in way eduformers can’t even dream of, cut costs, and—alas—send all the best teachers to the richest schools permanently.

Of course, if that is the goal, no one will admit it directly. Far more respectable to proclaim dedication to poor and underprivileged children everywhere and just incidentally–in the best interests of these children—go after those evil wicked teachers who are ruining childrens’ lives and our country’s future.

Just when I get to that point in the Machiavellian universe the progressives see, I shrug. Naw. Eduformers really are nothing more than naive dreamers who think they understand what’s wrong with our schools.

Not that their motives really matter. As long as they’re blaming teachers, they’re going to fail.

I’m not a fan of unions, so I do find it a tad ironic that I’m counting on unions and their invincibility to stop eduformers from further destroying our schools. At least I’m paying for it to the tune of a thousand or so a year.

1Not my principal, however, who is a paragon of principals.