Archive for December, 2010

Everyday Math

Dec 23 2010 Published by under borderland

Nothing says Happy Holidays quite like a good old-fashioned argument. This being the case, I’m reposting a comment left for me today by Karl Fisch on a post from a couple of weeks ago about math pacing guides, along with my response. I’m supposed to be on vacation, and I wasn’t around when Karl left the comment because I was out celebrating a minute gain in winter daylight. I wasn’t planning on writing anything, but I think this was worth doing because Karl’s comment is typical of what elementary teachers hear all too often from secondary teachers, and Everyday Math advocates. Besides, that other post was not really about Everyday Math, as such, and Karl’s comment is almost all about that. Almost. Except for the part where he blames elementary school teachers. My response is the best I could come up with on short notice, from my current happy place. Maybe some other people will have more enlightening things to say.

Hi everyone. Let me jump in briefly as a high school math teacher who has some basic familiarity with EDM.

1. It seems like so far in this discussion you"™ve basically been discussing arithmetic, not mathematics. I"™d be interested to see you discuss both.

2. As a high school teacher, I do want my students to know their multiplication facts, because that"™s part of being numerate and being able to think about more complicated mathematics.

3. But, as a high school teacher, I think it"™s just as important for students to understand multiplication and division. In my experience, many students who know their facts don"™t have a clue what multiplication and division is. I believe part of the reason that programs like EDM were developed were to attempt to address these very issues. Teachers were sending their kids forward thinking that they knew mathematics, when they really just knew arithmetic (and even "œknew" is probably too strong).

4. As a high school teacher, I really don"™t care that much about "œthe standard algorithms for multiplication and division, and tell them that these are the fastest way to get the job done." No, the fastest way to get the job done is to use a calculator (or Wolfram Alpha). They need to know facts (no algorithm required) because that helps them think about mathematics, have number sense, and be able to solve more complicated problems, but once you get past one-digit problems I want my students to understand the concept of multiplication and to be able to estimate, but I don"™t need them to use the algorithm. And long division? Not so much. So, as a high school teacher, I like the emphasis on multiple algorithms as a way to try to truly understand what"™s going on. That doesn"™t mean they can"™t eventually settle on the standard algorithm (because they aren"™t going to use it much anyway), it means that I value the understanding more than the algorithm.

5. From my understanding of EDM, the emphasis on "œfidelity to the program" is due to folks not understanding the program and picking and choosing too much. If you have a "œspiral" curriculum, but then you have teachers only choosing to do certain aspects of it, then that"™s a problem. Note that I"™m not saying that teachers can"™t use their judgment to adjust and make changes when necessary, but if teachers don"™t see the big picture of how it all fits together, then they can undermine the success of a program by leaving important parts of it out.

6. To address Sue"™s comment about teachers not being comfortable with math, I think this is the elephant in the room. Now, I"™m going to say this despite risking the wrath of everyone, but based on my decently large, but definitely still limited, sample size, we do have a problem with teaching math at the elementary level. What I see in my daughter"™s school (and many others) is that some of the teachers don"™t understand the mathematics well enough to teach it well. In schools and classrooms where this is the case (and I"™m not saying it"™s every school and classroom, but it is many), then a program like EDM is more of a problem than a help. Because what some of the teachers at my daughter"™s school (and others) are doing is throwing out the things in EDM they don"™t understand (or think is too much work, or that parents don"™t like or understand), and supplementing with more "œtraditional" mathematics that they are comfortable with. So many students are ending up with the worst of both "“ they don"™t have the automaticity that a more traditional math program would"™ve given them (when taught with "œfidelity"), and they don"™t have the understanding that a program like EDM is more likely to give them (when taught with "œfidelity"). Here"™s the wrath-inducing part: teachers are part of the problem here.

So, I"™m not saying that EDM is perfect. No program is. But from what I"™ve seen of it, it is definitely an improvement over previous programs. What I saw before is that students came out of elementary and middle school thinking they were good at mathematics because they were good at the arithmetic algorithms (and, frankly, most of their parents and teachers thought the same thing). Then when they got to high school they hit the wall, because they didn"™t have any understanding of what lay behind the algorithms, and because they had spent so much time "œmastering" the arithmetic they hadn"™t done very much problem solving or mathematical thinking. Some students were able to overcome this, many students could not. But if you had asked the parents or teachers when those kids left elementary school, they would"™ve said everything was fine. In my experience, we have a huge vertical articulation problem in mathematics (and other areas as well).

I understand and agree with the concerns about pacing guides and tests at pre-determined times, but that"™s more of a district problem, not a program problem (whether the program is EDM, Singapore, or whatever). I think we should definitely supplement EDM (or whatever program you have) in areas you think it"™s weak in, and slow down (or speed up) to meet the needs of individual students, but I think that needs to be part of a larger conversation about what mathematics is, and what we want our students to take away from it. I would strongly suggest that the arithmetic that most folks at the elementary level argue about the most is definitely a necessary part of what we do, but should not be what we spend most of our time thinking and talking about.

My response:

Hi Karl, thanks for the provocative comment. Worth interrupting my vacation to respond to, I suppose.

Before I say anything substantive about what you"™ve left us here, I should say that this isn"™t the first time I"™ve written about the pacing guide. That other post, though, didn"™t generate any discussion about EDM, but it does explain in a little more detail my point of view on what math instruction should be about. I called it Speaking Math, and I suggest that you read it because it may help to explain why I feel that the distinction you draw between math and arithmetic is really not an issue. If understanding is the goal, then it seems to me that drawing lines around concepts such as "œmath" and "œarithmetic" creates a false dichotomy that does not help us to get any closer to what is really going on. Likewise, I"™d say the same for the criticisms you and other high school teachers commonly hurl at elementary school teachers.

At the lower primary level, when students are learning basic number concepts, what you call "œarithmetic" is no different than what you call "œmath" for older students. Where do we draw this line that separates the two things? And blaming people who have worked with students previously is just too easy. The absurdity of doing so was brought home to me in crystal clear fashion when, during the first year I taught at my Title 1 school, in first-grade, I started thinking bad things about the kindergarten teachers! Where does the chain of responsibility begin and end?

Now, to anyone who wants to point at the failures of elementary teachers, I just say, "œBe my guest. Go do a better job." We spend a great deal of our time outside of the classroom marveling at the difficulty of teaching math, and I would love to see a pro from high school come in and show us how to do it right. Based on my experience, there are just as many poor math teachers at the secondary level. If the upper-level teachers are so great, why don"™t they simply fix all the problems they think the lower grade teachers are sending their way? I DO agree, however, there needs to be much more done with our professional development in mathematics instruction, but I wouldn"™t be too quick to say that the profession as a whole has dropped the ball, given the enormity of the problem.

Your defense of EDM is what I would call The Standard Defense, as it points to the program"™s use of a so-called "œconceptually based" approach. Since I am a sixth-grade teacher, at the end of the elementary school production line so to speak, I have no allegiance to the program for the sake of some other teacher at the next higher level. Also, I"™ve taught all the other grades, and I know what the kids are supposed to have been taught. The kids act like they"™ve never heard this stuff before, but I KNOW they have. What has happened is that they never learned it "“ and it was forgotten. They need to know the multiplication facts to simplify fractions and find common denominators. They need to know the facts in order to think mathematically. But the facts are not stressed. So I back up, I and stress them because I know that later on, teachers will not want to spend time doing that. The rest of that suff about "œconceptually-based" algorithms is all hoo-haw because the whole point of an algorithm is to take the thought-work out of calculating. And where is all the conceptual understanding with the "˜lattice method"™, which ignores place value altogether? None, n-o-n-e of the kids who use those alternate calculation methods have ever shown me that they have any understanding whatsoever about what they are doing.

My shorter version of what"™s going on: We teach math as if it was a dead language, like Latin. It relates to nothing in the real world. It is not relevant to anyone"™s everyday experience. Everyday Math is the most ironically-named math program out there.

Maybe others will have things to say here now. Thanks, again Karl, for the provocative comment. Merry Christmas.

26 responses so far

The Turning Point

Dec 19 2010 Published by under borderland

It’s the winter solstice, and I’m taking the next couple of weeks off. Completely. Snowboarding, reading books, laying low, watching the sky and waiting for the sun to start climbing again.

A view of the setting sun from my doorstep at 3:08 in the afternoon.

Here’s a time-lapse video of an entire day in the Tanana Valley, looking south from the University of Alaska.

Have a great holiday.

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Rothstein on Accountability in Schools

Dec 14 2010 Published by under commonplaces,curriculum,education,literacy,politics

Approximately 30 well-spent minutes with Richard Rothstein, who patiently spells out what is happening as a consequence of using narrow measures of accountability for schools vs. what really needs to happen.

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The Six Hells of the Pacing Guide

Dec 11 2010 Published by under borderland,curriculum,education


High expectations-hell
The district adopts a new mathematics curriculum, and selects a textbook series that "œEmphasizes conceptual understanding." It promises to explore a "œbroad mathematics spectrum, not just basic arithmetic" [pdf]. You eagerly anticipate stimulating new and deep mathematical understandings.

Indoctrination hell
Company reps lead grade-level cohorts of teachers in training sessions. The trainer emphasizes fidelity to the program, and predicts that conceptual mastery will develop gradually as the curricular "œspiral" widens, with students continuously encountering the material, lesson after lesson, year after year. You are warned not to linger too long upon any one lesson, or your students will fall behind, and the entire program will fall apart.

Skepticism hell
The spiral troubles you. You wonder about the difference between being a teacher and a program administrator. Every month or so, a "œmentor teacher" visits the classroom to model teaching with the new textbooks. He is upbeat and fun, but only one-fourth of your students know what he is talking about. Problems with parents crop up across the district. They have never seen these new algorithms [pdf] and they can"™t help their kids with homework. The district begins hosting parent nights. You note the irony that a wave of math phobia erupts because students are taught "œnatural problem-solving strategies" intended to eliminate math phobia.

Coercion hell
In order to ensure that teachers make it through the entire book, the district distributes pacing guides that specify how much time should be spent on each lesson. Math is to be taught for an hour and a half each day, doubling the time that had been previously allotted. Central office administration responds to teachers"™ concerns by clarifying that it is "œjust a guide" and teachers should continue to exercise professional judgment. Nonetheless, a midyear test is administered to all elementary school students in December as a form of program monitoring.

Guilt hell
After a few years, the pacing guide is revised; lessons that are not tested are dropped. Overall, some students get it; most do not. Nonetheless, each day you move on. Grades on unit tests are abysmal, but standardized test scores get a boost, overall. There is alignment between standards and curriculum; the district celebrates their success. High-achieving students are doing well. The low achievers are lost. Nobody seems to notice.

Torpor hell
After several years, students who have been exposed to this curriculum come to sixth grade with spotty basic skills. The multiplication facts are not automatic for most, and they have difficulty finding common denominators and simplifying fractions. A range of algorithms for multiplication and division are in use, and most take way too long to complete a reasonable amount of work. Concepts that they"™ve studied since third or fourth grade have to be taught from the beginning. You notice that many of them use repeated addition for simple multiplication problems. You bite your tongue and bang your head on your desk again and again. Year after year, they"™ve been hurried along, and they understand very little about math. Most of them hate math.

Hacking hell
You ignore the pacing guide. You institute a daily regimen of 100 multiplication facts, and promise the students that anyone who finishes them in under two minutes can be done with them for the year. You tell them that the multiplication facts are tools they need to do math, and practicing them each day is the same as a musician who practices scales in order to play music. Students are motivated; gradually they notice that they are learning the multiplication facts.

You spend more time on each lesson than the guide specifies. You teach them the standard algorithms for multiplication and division, and tell them that these are the fastest way to get the job done. Most learn to multiply and divide accurately and efficiently. Problem-solving, however, remains a major challenge.

At mid-year, the students are a chapter and a half behind. No way will they do well on the district test. You tell yourself that it doesn"™t matter since there is no consequence for failing the test, and if you"™d stuck with the pacing guide, no way would they have done well on the test. You tell them that they will be taking a test for which they are not prepared, that it doesn"™t count for anything, and you don"™t care how well they do.

But you do care.

You are a program administrator. You hate teaching math.

updated: broken links repaired

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A Brief Comment on Technophilia

Dec 04 2010 Published by under borderland

This post is taken from one that I left on Michael Doyle’s post, A response to a technophile, but which may have gotten lost in the intertubes, so I’m reposting an edited version of it here.

We were living in an unfinished three-room cabin with no electricity, phone, or running water 20 miles from downtown Fairbanks when my three (now teen-aged) kids were born. Gradually, civilization has wormed its way out to where we live, with most of its pluses and minuses. As it came, we took advantage of the pluses and resisted the minuses. The kids have never owned any video games, and they are not interested in them.

I took the two older girls to a movie, A Bug’s Life, when they were still toddlers, and their younger brother was home with Mom. We left half-way through because they did not “get” that this was a story like the ones they read in books. I learned that people have to learn how to “read” a story on a screen just as they have to learn to read books. Practice, practice, practice. They never saw a television until one day in February when they all had chicken pox, and their mom was tired of entertaining all three of them endlessly indoors. We got only one channel, PBS, because we are so far out of town. So they were not exposed to much advertising or daytime TV nonsense, and mostly watched Sesame St. and the like.

They are not now, by any means, technologically crippled. In fact, my son enjoys making snowboarding videos. But this is because his first passion is snowboarding.

additionally: Neil Postman’s “Teaching as a Conserving Activity” recommends an approach to education in which schools function like thermostats, regulating and moderating the influences of the general culture. It’s a good read, if you like Postman.

Larry Cuban posted something today about technology integration in the classroom and concludes with: “In my experience and research, most teachers have adapted their pedagogy by drawing from both teacher- and student-centered repertoires and crafted hybrids in lesson after lesson. Techno-centrists need to shed their blinders.

In my experience, also.

For the record, here’s one of Peter’s videos:

12 responses so far