Monthly Archives: March 2012

I am very Barbie about math*

Why are High School Teachers Convinced that White Girls Can’t Do Math?: apparently, high school teachers rate white girls lower than boys when they are matched in grades and test scores. Therefore, sez the Forbes article and the study it reports on, high school math teachers are biased against white girls.

Okay, so first off, the headline and the study are absurdly biased, which is a tad ironic in an article about bias.

Using the Forbes article as a guide to the study, the study didn’t establish bias. What it established was that high school teachers consistently rate white girls a tad lower in ability than boys with the same grades and test scores. That’s not the same thing.

First off, throw out grades. I’ve written on this before, but it bears repeating: if a teacher counts homework as a significant part of the grade, the grade simply isn’t accurate. Moreover, grades skew dramatically based on population. Suburban schools with lots of high-achieving kids have a tougher grading standard than Title I schools.

I am hoping that this study focuses primarily on test scores. Let’s assume that teachers rate boys higher in ability than girls, even though they have the same test scores. Is that necessarily a sign of bias?

Hell, no. Girls do more homework than boys. Girls are, as a group, more worried about grades than boys. Girls, as a group, work harder than boys.

So suppose you have two students. One of them turns in every bit of homework, asks questions purely about methodology and algorithsm, works very hard to “get it”. The other student doesn’t do homework, asks questions about process and concept, and always grasps everything without any particular effort involved. They both get the same test scores.

Who will the teacher say is “better” at math?

That’s not bias. That’s a totally rational inference about the ease of understanding, grasp of concept, and underlying aptitude.

I have a good number of students who are entirely obsessed with grades and utterly uninterested in math. Most, but not all, of these students are girls. I have a large number of students who are fascinated by how math works, often praise an “interesting” question, ask all sorts of conceptual questions because they want to know how things work. Most, but not all, of these students are boys.

Spare me the sturm und drang. It’s not bias. Teachers are longing to find female students who are strong at math. They aren’t ignoring white female students with math talent. They are just less likely to confuse “slog” with “talent” than, say, your average researcher.

*I used to say that all the time, until I became a math teacher. I hate it when my cultural references start to date. (They should stay single for life. Hyuk.)

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Teaching Trig

(No, I am not in Alaska. Yes, I am overly fond of alliteration.)

My trig lessons were going pretty well, when I noticed that a good number of kids were having trouble identifying the opposite or adjacent side of the angle. This always seems trivial when you’re teaching a big, complicated subject. The kid gets SOHCAHTOA, gets the ratio, gets the concept of inverse, and just has a little bit of trouble figuring out which angle is which. Big deal, right? Lots of concepts grasped and a glitch on implementation. But from a testing and demonstrated knowledge standpoint, the implementation is the ball game.

It suddenly dawned on me that I was constantly guiding students on one point, and one point only, despite a lot of time spent explaining different ways to find opposite or adjacent sides. And that this seemed awfully familiar, a memory from teaching this two years ago. I couldn’t assume they’d finally pick it up, or that this was non-trivial. I realized I needed a different approach.

And so, I gave them a Kuta handout, magic markers, and an explanation:


“Suppose I ask you to find the trig ratios for angle A. You guys have shown me you know the ratios of SOHCAHTOA. But how many of you are still not quite sure which is the opposite, the adjacent, or the hypotenuse?” (Half the class had their hands up before I finished the last sentence.)

“Yeah, that’s what I thought. So we’re going to try this. In your notes, create a right triangle like this one. Using a marker, trace the two sides of angle A.” (I can see all the kids, not just the usual worker bees, busily creating triangles and marking angles, which is encouraging. They want this method; it’s clearly a hitch in their understanding they want fixed.)

“Now, here is an important concept. The angle is created by the hypotenuse and the adjacent. The opposite is not a part of the angle.” (I repeat this several times. I can hear several kids already saying “Oh, I get it!”)

“So, which side is NOT a part of angle A, Corinne?”

“B and C.”

“Okay, remember that you describe segments by saying the two points together, like this: BC. And yes, you’re right. Segment BC is NOT a part of angle A. Sandy, what did I just say about a side NOT being being part of the angle?”

“The opposite. You said the opposite is NOT a part of the angle.”

“Awesome. So Marco, which side is NOT a part of the angle and so must be the OPPOSITE?”

“BC.”

“Great. So everyone mark BC as the opposite, like this:”

“Now. You’ve got a foolproof way of finding the opposite. Just trace over the angle, and then label the side you haven’t traced as the opposite. Now, what about the angle itself? What sides form the angle, class?”

“The adjacent and hypotenuse.”

“But how do you tell the difference between them?” asks a student.

“It’s opposite the right angle,” pops in another.

“True, and that’s a really helpful method. But if you’re worried about what “opposite” means, just do this. Take your pencil, start at the right angle. Draw a straight line through the interior, the inside, of the triangle, until you hit a side. That side is the hypotenuse.”

(Again, I can see that all the kids are doing this. It’s really friggin’ awesome to to realize how much the kids wanted to close this loophole and to have a method be so instantly useful.)

“And now, what’s left?”

“The adjacent!” the class choruses.

“There you go. That’s how you identify the sides. Helpful?”

“Yes!” (big response.)

We practiced it several more times and then I let them loose on the handout. I knew I was on the right track when one of my weakest students showed me his entire handout labelled correctly, but told me he wasn’t sure what to do next. We went through SOHCAHTOA and the light dawned. He worked every problem correctly.

From there, the next big teaching challenge was inverse, when I finally let them use calculators. Yes, up to now, they’d been using a trig table. I wanted them to fully internalize the fact that each trig value is a ratio. Their familiarity with the trig table really aided their comprehension of the inverse.

Next up was solving right triangles and figuring out what ratio to use. But this was much easier because they were now close to 100% accurate in identifying sides, so they weren’t compounding errors.

And then, the course-alike quiz:

This quiz is by another math teacher, and much easier than my quizzes. The kids nailed it. The mode–the MODE–was 100%. The mean was 83%. Only four kids failed the test, and one of them failed because he wasn’t trying.

To reward them for their great job, I still graded the quiz on a curve (meaning one of the Fs converted to a D), and weighted the quiz as 100 points instead of 50.

Then, the kids spent two days moving back and forth between the three methods of solving for sides: Pythagorean Theorem, special rights, and trig.

Once, when I was up front reviewing the results, a kid asked “So why can’t I just use trig instead of special rights?”

Another one chimed in. “Yes, I really don’t like the ratios.”

I said, “I’m fine with you using trig. But remember, you are expected to know the trig ratios for special rights, although we don’t call them by the same names. So if you really like using trig, take a little time to memorize certain values.” And then I went through the trig values for sin(30), cos(30), sin or cos(45).

“So just memorize these three, and you’re fine. And of course, you should never forget the tangent of a special right triangle.”

“ONE!” said a good number of the class. Yay.

We’re moving onto polygons, which will allow me to revisit trig when finding areas.

I’m psyched. If only I had a job next year!


Test Pattern

The polynomial quiz results were fantastic. Over half the class got a perfect score; no one outright failed–that is, all of the students did at least one of the four problems correctly.

Which brings up something that I’ve been bothered by for a while: around a dozen of my algebra II students are nailing the quizzes and failing the tests, or close to it.

All of the students showing this pattern are hard workers. Some have shown strong math skills; a few of them struggle but patiently work things out. I know they are discouraged by their low test scores, and I’ve been encouraging, but puzzled.

Certainly, I expect some fall-off between quizzes and tests. My quizzes are directly on point with no surprises. I give problems exactly like the ones we’ve been working in class. My tests slant off sideways and crisscross (my geometry students constantly whine about this). Some of the strugglers might get flummoxed when the problems don’t appear in exactly the same form, sure. But others of these students are well beyond that. They work the toughest problems of the day with minimal guidance; when they have questions, they are logical and structured.

I don’t know what’s going on, but since all the students in question did excellent work on the last quiz, I decided it was time to step up to the problem. Rather than try to set up time with them individually, I just made an announcement in class when I returned the quiz.

“If you are a student who is looking down at an A on this quiz, but got a C or worse on the last test, I want you to know that I’ve noticed this pattern–great on quizzes, near-disaster on tests. So here’s the deal: I will be adjusting your grade on the next progress report. It’s now clear to me that something about the test is causing you problems, not the math itself.”

“BUT. You must schedule time to come in after our next test and work quietly, either at lunch or after school, so I can watch you and see what’s going on when you take tests. I’ve invited everyone to do that after every test, but for you guys, it’s mandatory if you want a grade adjustment. You can’t keep going through life tanking important tests when it’s clear you know more.”

In all three classes, I scanned the room as I said this, and every one of those dozen students looked up in hope and relief.

Which makes me a bit sad. It’s not like they haven’t had this option all along. Why don’t they take advantage of it? Why wait until I mandate it?

But it also reminds me that no matter how many times I think I’ve made it clear that my door is open, help is here, even on tests—I haven’t said it enough.


Busy schedule

Spring is my busiest time. In addition to my normal teaching job, I have four private instruction classes:

  1. English lit enrichment/PSAT: 3 hours, every Saturday. I wrote about ithere.
  2. ACT prep course: underprivileged kids and the ACT. I’ve done this every year but one of the past six. Nothing is more satisfying than teaching test prep. Every year, six or seven kids who wouldn’t otherwise have escaped remediation do so because they took my class. 3 hours.
  3. AP US History Survey: two classes, 3 hours each. I stand up and talk about US History for 3 hours. No notes, either. I love it. Every year I find something new to add.

So that’s close to 12 hours of private instruction. I also tutor 6-8 hours in a slow week, 10-12 on occasion.

Why, yes,I have a life. But I don’t sleep much.


Intelligence and Algebra

A few years back, I was reading up on an interesting theory about working memory, as it seemed hopeful that working memory, not IQ alone, had some predictive value in learning algebra. I periodically google for new results in any field I’m interested in—not interested enough to pay for access to the papers, but I can still find out quite a bit just from google.

Recently, I stumbled across this paper: Do Measures of working memory predict academic proficiency better than measures of intelligence?

If I understand the paper correctly, working memory has been shown to be more predictive than IQ in “hierarchical regression analyses conducted with observed variables”. In this study, by contrast,

we examined the relationships between measures of intelligence, working memory and academic proficiency using latent variables in structural equation models. One advantage in using latent versus observed variables is that measurement errors are modelled explicitly. It is widely acknowledged that measures of working memory and executive functioning are not pure (e.g., Rabbitt, 1997; Miyake et al., 2000). In regression analyses, measurement errors are confounded with true measures of the constructs in question. By using multiple indicators, extracting their common variance, and modelling measurement errors explicitly, latent level analyses provide a more precise examination of relationships between conceptual constructs.

This sort of stuff always makes my head hurt. But I believe they are saying that they used a different method that doesn’t rely on observed variables to see if working memory is actually more predictive than IQ.

They tested three models:

  1. “Model 1 assumed independence between the working memory and intelligence constructs.”
  2. “Model 2 is analogous to the hierarchical regression.” (that is, working memory is more predictive”
  3. “Model 3 postulated a direct path from the working memory latent variable to intelligence and the path from working memory to algebraic proficiency was fixed at zero.”

Their findings:

In summary, our analyses of the data from all three studies show good support for Model 3. Only intelligence has a significant direct path to algebraic proficiency. At best, working memory has only an indirect effect on algebraic proficiency.

Okay, so here’s the thing: whether it’s intelligence or working memory notwithstanding, algebra proficiency is linked to cognitive ability.

The researchers are using “only” in the context of the comparison with working memory, but it’s still an amazing statement. Of course, there’s no follow-up research to determine the depth of algebra proficiency’s link to cognitive ability. We don’t know if there’s a basement to the cognitive ability needed to learn algebra We haven’t investigated whether different curriculum or instruction methods are needed for high vs. low cognitive ability students.

Any such research might explain the achievement gap in a most compelling and entirely unsatisfactory manner. So we won’t do the research.

Only intelligence has a significant direct path to algebraic proficiency.

I understand the genuine difficulties in acknowledging reality. I understand the fear of potential outcomes. But we’re spending billions, wasting lives, and causing tremendous unhappiness.

Only intelligence has a significant direct path to algebraic proficiency.

I’ve said it before: I don’t teach groups. I teach individuals. And I see so many individuals who are lost at school, who have given up. It’s not the teachers. It’s not the students. It’s the expectations.

Only intelligence has a significant direct path to algebraic proficiency.

So it is written. But it can’t be said.


Discovery Doesn’t Work

I had trouble in ed school because (well, at least in my view of it) I openly disdained the primary tenets of progressive education. I am pro-tracking, anti-constructivist, and pro-testing, all of which put me at odds with progressives. Here is the irony: I mention often that I am a squishy teacher (squishy=touchy feely). I am not just squishy for a math teacher, I’m the squishiest damn math teacher from my cohort at the elite, relatively progressive ed school that made my life very difficult. My supervisor, who knew me first as a student in a curriculum class, was genuinely shocked to learn that I didn’t talk at my kids in lecture form for 45 minutes or more, given my oft-expressed disagreement with discovery. Even my lectures are more classroom back and forth than me yammering for minutes on end. (In fact, my teaching style did much to save me at ed school, but that’s a different story.)

Here is what I mean by squishy: My kids sit in groups, not rows. When I set them to practicing, which is usually 20-35 minutes of class, they are allowed to work independently, in pairs, or as a group of four. I often use manipulatives to demonstrate important math facts. My explanations are, god help me, “accessible”. I don’t just identify the opposite, adjacent, and hypotenuse and then lay out the ratios. No, I’ve been mentioning opposite, adjacent and hypotenuse for weeks, whenever I talked about special rights. I introduce trig by drawing a line with a rise of 4, a run of 3, and demonstrate how every right triangle made in which one leg is 3 and the other 4 (that is, have a “slope” of .75) must have the same angle forming it. I spend a great deal of time trying to think of a way to help kids file away knowledge under images, concepts, pictures, anything that will help them access the right method for the problem or subject at hand. (For more info, see How I Teach and The Virtues of Last Minute Planning.)

However, I am not in any sense a constructivist as progressive educators use it. I use discovery as illustration, not learning method. I don’t let kids puzzle over a situation and see if they can “construct” meaning. I explain, give specific instructions, and by god, my classroom is teacher centered. I am the sage on stage, baby. And that’s why I got in trouble in ed school, despite my highly accessible, extremely concept-oriented teaching style; I routinely argued against constructivist philosophy, and emphasized the importance of telling kids what to do.

Anyway. I was incredibly excited to read an article that openly states the obvious: Putting Students on the Path to Learning: The Case for Guided Instruction. This article is just so dead on right. To pick one of many great excerpts–click to enlarge, but why can’t I copy text from pdf files any more?:

Yes. Low ability kids like discovery; it is less work for them, yet they feel they are doing something important—but in fact, they aren’t learning very much. High ability kids tend to be “for chrissake, give me the algorithm”, when they would be better off puzzling through the math for themselves.

The article talks about the importance of worked-out examples. I read the article this morning and had a worked out example on the board the same day—step by step factoring of a quadratic. Here’s the weird thing: the kids who need the help with factoring had to be prompted to use the example, but the kids who got factoring were clamoring for worked examples in the area they had trouble with.

This would be a great thing for notebooks. But how do you get the kids who need help to keep the notebooks?

Great article, that changed my teaching immediately. How often does that happen?


Trig Progress

Last week, I mentioned my plans to help my students understand the ratio element in right triangle trig.

It worked! I didn’t let anyone call out the answer; the kids had to discuss it in their groups first. As I walked round the room, I could hear them tussling with the question. In some cases, one or two of the students figured it out and explained it to everyone else; in others, the group “got” it while talking about it.

I gave them triangles with clearly distinguished cosine and sine ratios, and could start to see it click. Then I drew a 30-60-90 and 45-45-90 triangles, asking them which had a tangent of 1. Half the class figured out it was the isosceles right.

Seriously, it’s sinking in. All of the students in both classes were successfully solving for unknown sides by the time we tabled trig to focus on the state tests.

Now, the next big checkpoint: will they all be able to move between solving using trig ratios vs. the Pythagorean theorem vs. special rights. Here’s hoping.


Teaching Polynomials

When I met with my new supervisor in ed school (the second one), I told her that I didn’t feel like I was introducing topics well. She was extremely supportive, and it became one of our favorite discussion points. How do you introduce a math topic? And in my two plus years of teaching, I think I’ve become good at it–particularly in first year algebra, which I’ve taught more than any other. When I taught CPM Geometry, I hated everything about it except the way it introduced tangents (as a slope). I often spend several days mulling a good intro, and have been known to toss in a few days of review just to get my story right.

The story is usually a problem the kids can understand—and understand that they don’t have the tools to solve it. Or sometimes it’s a parallel. Either way, I try to give them an image, a reference, a bucket. Maybe it will help them trigger memories, because retention is a huge issue in teaching math.

It’s weird, the quick descriptors that teachers use. When I say I’m “teaching polynomials” in Algebra II, any math teacher knows I’m teaching everything but quadratics in their binomial/trinomial form, since quadratics is its own unit. Teaching polynomials means the kids are learning polynomial multiplication, polynomial division, synthetic division, maybe some binomial expansion, certainly some brute force factoring In general, the polynomials unit in Algebra II doesn’t have any obvious purpose other than to prepare the kids for pre-calculus. It’s just “let’s learn how to manipulate polynomials to no immediate purpose”. And that makes the intro tough.

Over half my students will not go on to pre-calc next year. Some will be taking Algebra II again, either with or without Trig. Others will be going into remedial college classes. So even leaving aside the intro, how do I help the kids make sense of this? I don’t care if they can expound on function notation or binomial expansion, but I do want to be sure they know the difference between multiplying two trinomials vs. two binomials, and when to factor. And for god’s sakes, I want them to know that they can’t “cancel out” the x2 term when presented with a rational expression.

I started the unit by explaining the preparatory nature of some of this—that they won’t really see how it’s used until pre-calc, that they just need to recognize these equations and know what to do. Multiplication, they’ve been doing for a while. Factoring, too. But then there’s division proper, which most of them won’t use again. I thought about not covering it, until I realized that I could use the lessons as a way to get them to think about division and factoring.

And so, the introduction:

I don’t present this all at once. I start with the first fraction, then ask what could we do. Someone will reliably say “reduce it”, and so we’ll reduce it. I then introduce the term “relatively prime”.

So then, I say, we do the same thing with variables and fractions, and we go through this step by step:

This isn’t the actual whiteboard example; I just wrote it up and took a picture. But it’s the idea.

And it worked. It gave the kids a great point of reference and most of them were able to divide a simple polynomial on a quiz a few days later.

I’m trying to build on that now. Thus far, I’ve taught them two forms of division and factoring. Ideally, they should be able to identify when to factor, when to divide and when, please, synthetic substitution is a good idea. So I went through the pros and cons of each:

  1. Factoring: the default. Pros: It’s fun to cancel out the common terms. In a test situation, you can pretty much assume that the terms will factor. Cons: Only works with first and second degree polynomials. After that, it’s brute force. Limited: if you can’t factor, you can’t. Nothing to tweak.
  2. Division: you don’t have to use it much, unless asked. Pros: It’s the easiest to relate to–works just like number division (most know this already. Most). It’s extremely flexible, works in every situation. Cons: you don’t have to use it much.
  3. Synthetic division: you never really have to use it. Pros: Incredibly useful for evaluating terms, which is what we’ve been using it for. Quickest method to find factors in higher order polynomials. Cons: It’s the most difficult to learn. Unless you use it often, it’s easy to forget. You have to know what it means in order to find it meaningful.

So they all copied it down. Did they get it? I gave them a quiz—a pop quiz, no less.

And with one exception, they did pretty well.

Question 2. It got to them. First, they saw the division sign. So they divide, right? No! Don’t they remember? “Division is…..” I prompt. “Oh, yeah, you flip it!” They flipped it. But then they multiplied, which made sense because they were being tested on that too, right?

Argggghhhh.

Still, it was a good quiz. Once I reminded them, they worked it correctly. Few misconceptions. I’ll need another week to beat in the triggers to tell them what to do when. But it’s working.

I think.


Texting on Tangents

I don’t collect homework. My students take a picture of it and text or email it to me, or they have me take a picture of it. Then I go through and mark the homework done when I have time. In other words, my students have my email and phone number. To date, they have only used the information for good.

Like this text exchange with a freshman geometry student as he sent me an image of his homework, which was a simple right triangle trig task. I’d sketched two triangles, marked an angle on each, gave them three sides (a,b, and c) and asked them the sine, cosine, and tangent for each angle on each triangle.


Student: For both answers, the tan cos sine were the same angles.

Me: Yep! But the ratios were different.

Student: I don’t even know what I was solving for. Was it right?

Me: Does it matter if it’s right if you don’t know what you’re solving for?

Student: Of course it would matter. If it was right I could assume that what I did to come to that answer was correct.

Me: But if you knew what you were doing, you would not have to wonder. You would know why all the angles found for each identity were the same. And you would have an easier time with tests. Do you know what tan(52) means? That’s the big question.

Student: Don’t think you ever told me and when I asked you didn’t give me a straight answer.

Me: You wound me! I did give you a straight answer. I even brought the question up before the class because I thought it was so important and discussed it. But thanks to our conversation, I will revisit it tomorrow. I appreciate your questions and your honesty. Oh, in answer to your question, the tan(52) is the ratio of the opposite leg to an adjacent leg for a 52 degree angle in a right triangle.

When he asked me that question, I took it to the class and asked three students randomly, “what is a tangent”? Two were able to answer that it was a ratio; the third was able to somewhat explain what, exactly a ratio was.

This particular student is one much more interested in getting the right answer than in understanding the question or any part of it, but it’s still telling that he’s just going through the motions.

How do I get them to think of a trig ratio as a value, rather than just a step in a procedure?

So tomorrow, I’m going to post this diagram and question:

I have changed so dramatically on this point since I began teaching that it boggles the mind. I used to say that it was fine to teach the procedure—to teach the context, the meaning, of course, but if they didn’t get the meaning who cared, so long as they got the answer?

Believe me, I’d still hold to that position if the kids would get the answer. But consider the problems that I think any teacher would recognize:

  1. Students use the quadratic formula for everything–and I mean, everything. Give them a linear equation, two four-term polynomials to add, or a rational expression in fraction form and they’d define an a, b, and c, and plug it in. It’s crazy-making.
  2. Half my students still stumble over the area formula for a triangle.
  3. Students either use the Pythagorean Theorem for everything involving a triangle, or nothing.

That’s a short list. Slowly, I realized that kids who can learn and apply the formulas by rote are not the low ability kids, but close to the strongest in the class. The low ability students just seize on any formula they can remember and plug it in—and much of the time, they won’t remember any formula at all.

They feel better with formulas. When I work with students individually, I’ll prompt them for explanations of their understanding, while they roll their eyes and demand the formula so they can just plug it in. I’ve shut that down by telling them that they’ve been taught the formulas for the past four years, so if they don’t remember it by now why should I waste my time? (Yes, I’m a bit brutal.)

Of course, I teach the formulas. I love algorithms. I often outline methods step by step. I want them to be able to solve problems with the algorithms. But I remind them how useless the formulas can be by asking them questions that require understanding, not just answers.

I’d like to think this is helping their understanding and their long-term math ability. But if it isn’t, at least they are growing uncomfortably aware that the formulas and procedures aren’t as much good as they thought they were unless they take the time to understand the math itself.

And I know I have at least one ex-instructor who’s chortling in his beer at this confession.

I will report back.


Just one more way we pay to play

I am certainly not the first to observe that we jump through time and money hoops to become teachers, and that these hoops seemed designed to ensure not so much quality as inconvenience, the better to ensure that only the patient with no other options make it through. Heaven forfend that the state make it easy for smart people to get into the classroom. For all the talk about “alternative paths”, the reality is that all teachers have to go through a whole host of utterly useless classes, both before and after getting the credential.

After? Oh, yes, after, in at least 11 states, a horrible process that any recent teacher shudders to recall. This process, called induction, is the subject of a new report by the New Teacher Center.

Beginning teachers are, on average, less effective than more experienced ones. High-quality induction programs accelerate new teachers’ professional growth, making them more effective faster. Research evidence suggests that comprehensive, multi-year induction programs accelerate the professional growth
of new teachers, reduce the rate of new teacher attrition, provide a positive return on investment, and improve student learning.

As to the first sentence, sure. So what? New lawyers and doctors are, on average, less effective than more experienced ones. As to the second and third sentences, hold on a minute: a randomized controlled study of induction programs run by the Department of Education showed:

  • There were no impacts on teacher retention rates after each of the three years of follow-up.
  • There were no impacts on teachers’ classroom practices, which were measured during teachers’ first year in the classroom.
  • For teachers offered one year of comprehensive induction, there were no impacts on student achievement in any of the teachers’ first three years in the classroom.
  • For teachers offered two years of comprehensive induction, there were no impacts on student achievement in either of the first two years. However, in the third year, there were positive impacts on student achievement, based on the sample of teachers whose students had both pre-test and post-test scores. These impacts were equivalent to moving the average student from the 50th percentile to the 54th percentile in reading and the 58th percentile in math.

So if teachers jump through two years of hoops, a sample shows a very minor improvement in test scores, but no impact on retention and it doesn’t change a thing in our teaching practice. I’m sure New Teacher Center has other studies, but whatever.

Naturally, even in the face of this weak evidence, the New Teacher Center calls for more spending, more induction, more rules, more time spent.

Am I the only teacher who thinks that induction is a nightmare at worst, a waste of time at best? I don’t think so. I was lucky, too, since I taught at a small district the first year and induction was a formality. My second year, though, was at a big district, adding a good 50+ hours of work to an already unpleasant workload. Best case, you get a good mentor and at least have some quality discussions while going through the meaningless paperwork. I did have good mentors, although neither of them were math teachers.

And new teachers who don’t finish induction don’t get a permanent credential, or “clear”. Missing the two year window to get cleared renders a teacher largely unemployable at any district that pays for induction. Teachers who don’t get their clear in a given window have very little recourse. Teachers who go through an alternate program and get an internship credential have it even worse—if they don’t finish and get their clear in the five-year window, it’s as if none of it happened. Coursework, student teaching, all for nothing. Yet one more reason I went through the formal ed school program—it gave me a level of protection if something went wrong.

Last year, I was far more concerned that I get my clear than I keep my job for a second year—and I wanted a second year at the job pretty badly, which says something about how important the clear was.

As Steven Sawchuk observes, given how soft the data is in support of induction, why bother?

For my two cents, this review raises a lot of cost-benefit questions for policymakers and key supporters of induction, including teachers’ unions. Where should induction fall in the list of budget priorities? Is preserving and strengthening these programs the role of states or districts? How should it be weighed in comparison to other budget items, such as professional development, curricula, and salaries?

Exactly. Do teachers a favor—dump induction and give them a mentor or support group. Cheaper and far more valuable.