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Interesting that Irvington reports "Math Trailblazers" as the "Elementary Math Program" for K-5, but then, under "Middle School Math Program," says "No specific program is used, however we follow the NY State curriculum."

Number one: last fall, at a school board meeting, our Assistant Superintendent for Curriculum, Instruction, and Technology told the assembled 2 or 3 parents seated in the audience that: "People say Trailblazers is our curriculum. Trailblazers isn't our curriculum. We write our own curriculum."

She rolled her eyes when she said "People say Trailblazers is our curriculum."

Number two: The middle school uses traditional math textbooks: Prentice Hall Pre-Algebra, Glencoe Algebra 1, Glencoe Geometry (for the accelerated kids in 8th grade). I've forgotten the others but, as I recall, they're not fuzzy.

Apparently to the Tri-State way of thinking, "not fuzzy" translates to "no specific program" and "Math Trailblazers," while not a curriculum, is a program.

Needless to say, I have suggested to the school board, the administration, and the PTSA that we save money in these uncertain times by declining to renew our membership in the Consortium.

Thus far my pleas have fallen upon deaf ears.

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## 22 comments:

"People say Trailblazers is our curriculum. Trailblazers isn't our curriculum. We write our own curriculum."

What a perfect opening. Please show me your curriculum. Show me the curriculum map and lesson plans. Show me sample homework and tests. Do all teachers cover the same material and give the same tests? What standards must be met for a student to move on to the next grade?

I am always surprised that my son's schools could never answer these questions. At best, they would tell me to talk to each teacher individually.

"Glencoe Algebra 1, Glencoe Geometry"

I'm using the Glencoe Algebra 1 book with my 7th grade son and it's pretty good. It's very methodical and perhaps a little slow. That's better than being too fast. I think we will be using the Glencoe Geometry book next year.

By the way, I am clearly seeing a difference between conceptual understanding and the understanding my son has when he masters the material. (no surprise) I'm not sure why many educators have a "rote" hangup about this. They can't seem to come to grips with "drill and kill". Drill and kill doesn't imply that mastery is wrong, it just says that there should be a different (slow) path to mastery. But some educators see mastery only in terms of speed. They talk about balance, but you either master the skills or you don't. Speed shows that you understand the material automatically.

My son received an algebra mid-term test that is used to place students in the proper math class in high school. It's ALL about skills mastery and speed. It's a two-day test with over 120 questions. That's less than one question per minute. Many questions are easy, but there are some word problems.

I never did see the school's 6th grade math placement test, but I'm sure it was based on skills too. So, for all of K-6, schools tell kids and parents that it's all about understanding and critical thinking and they avoid drill and kill. Then they turn around and slam the kids with tests that are ALL about mastery of skills.

The reality of real high school math meets the fantasyland of K-8 math education.

SteveH, I've become cynical in my old age. It's likely that the K-8 teachers are required to use the fuzzy math programs by their administrators, and that the high school teachers want to weed out the children who don't have a firm grasp of math facts. Experience probably shows that kids who don't know how to multiply & divide won't succeed in high school math.

It's the same district, so you'd think the superintendent would arrange for the k-8 teachers to prepare children for high school math. However, remember Attewell's study, which claimed that high schools in affluent towns restrict access to higher level math & science courses.

If you make placement in high school math classes contingent on performance on a test of math skills, you can cut down the numbers of children who are eligible for such courses. The parents who will be most troublesome are those who have made certain that their children know the standard math algorithms. Their children can populate the upper level math courses, the parents are happy, and that source of complaint has been neutralized.

The children who fail a test of automaticity have parents who trusted the school when it assured them that knowledge of math facts was overrated. They will still trust the school, and assume that their children were never that good at math anyway.

I seem to remember that Siegfried Engelmann reported that in their DI efforts, one school system noted that they had produced too many advanced math students.

It's not necessarily in the interest of the system to increase the number of advanced math students.

It's not necessarily in the interest of the system to increase the number of advanced math students.Meanwhile, it is absolutely in the best interest of important matters (such as our economy) to increase the number of advanced math students.

Is it me, or can the entire philosophy of K-6 education be summarized as:

1. It's not our fault.

2. It's not our problem.

3. We're underfunded.

If kids don't learn math, it's because they're not capable of learning it. And if they enter high school five years behind grade level, then it's up to the parents and the high schools to catch them up. Either way, they need more money so that they can facilitate kids learning on their own.

It's not necessarily in the interest of the system to increase the number of advanced math students.In fact, it's against a rich district's interests.

Oh yes, of course. Most school officials and politicians will pay lip service to the importance of education, as well. If you look at how the system really works, however, it's striking how many policies can be put in place to perpetuate the status quo.

Our high school is proud to have all of the AP exams receiving 4s and 5s. No 3s. They ascribe those results to excellent instruction. I feel that those results attest to artificially restricted access to challenging courses.

Students are led to believe that they'll get into colleges on the strength of their extracurriculars. Of course, the sports teams are the usual varsity/star system. Many parents are still running around transporting their kids to off campus, out-of-town ECs.

I sometimes wonder if the whole system arises from the desire on the part of the high schools to get kids into selective colleges. In some way, the Workshop model of writing is like practicing writing college application essays over and over again.

"It's not necessarily in the interest of the system to increase the number of advanced math students."

"In fact, it's against a rich district's interests."

I don't see any smoking gun of intent. Our K-8 schools see it mostly as proper math placement in high school. The K-8 schools want successful students in high school (at whatever level) so that they don't get bad feedback.

It seems more like incompetence than anything else. In K-6, they allow kids to achieve mastery at their own speed, as prescribed by Everyday Math. Then they hit them with the fact and skill-based math placement tests. Some kids do well, so they don't give it a thought. I almost wish they were smart enough to do this on purpose, but I don't see it.

As I've said before, if you wait long enough, it's easy to blame the student for just about everything. Just give them a math placement test and then point to those kids who did well. Perfect absolution. Do they do this on purpose? I don't think so, but schools don't go out of their way to ask the parents of good students for details.

So, "never ascribe to malice, that which can be explained to incompetence?" Well, sort of, kind of. Except, I'd presume that an administrator's job is to manage a school district. They could all be incompetent, although that's unlikely. They could be restricted by laws, guidelines, silly school boards, and a fear of lawsuits.

I see it as expectations guiding and shaping practice. If you've always had a "top group," a "middle group," and a "bottom group," that perception will persist. I think that, even if a high school administration were presented with a group of kids absolutely equal in ability, if they weren't explicitly informed of that fact, they would pretty soon create a grouping system which replicated the groupings. The associated rationing of educational opportunities would follow.

Yes, kids vary in their ability to learn. Many kids in American schools arrive at high school longing for the day when they can legally drop out. They don't want to learn, and it's counterproductive to punish teachers because they can't create the desire to learn.

However, I think the advice parents often hear, that students would be better off getting an A in a lower level class, rather than a B- in an honors level class, is counterproductive. Many kids could do more, if they were given the chance. Jaime Escalante's work is a case in point. I just read the Wikipedia entry, and it's noticeable that success or failure in his efforts were directly linked with administrative support.

The administrative resistance to achievement also exists in affluent districts. We have principals and a superintendent who consider excellence to be either harmful, or not in the best interests of the district. Our high school considers extracurriculars the key to college admissions. It might be, but I don't consider extracurricular activities to be central to a school's mission. These years are the only time most people have to concentrate on learning. To tell children that they shouldn't try to learn as much as they can is sabotage.

Our system also uses a math placement test. No one informed the parents that this would be one of the criteria used for placement. We happen to have a wonderful math teacher who brings the children through a rigorous year of math, which is great after the early, Everyday Math years. His teaching is not without controversy, though, because it is difficult to get good grades in his class. Parents don't like that, because they know that "bad" grades could affect placement in later classes.

So, could one say that higher expectations by or for the students means more work for the schools? But it shouldn't matter if they switch one teacher from general math to Algebra II, for example.

What is the downside for the school if they make sure that all kids and parents know exactly what material is on the math placement test years ahead or online? The only reason I can think of is that parents will see more clearly that K-6 math curricula don't get the job done. I guess this is a specific question I can ask my son's principal. Why are these placement test such a surprise for most students and parents?

"We have principals and a superintendent who consider excellence to be either harmful, or not in the best interests of the district."

I guess I don't understand what drives this notion in high school. In our K-8 schools, I see it in the form of "all kids are equal" sort of thing. My son absorbs knowledge like a sponge and I have heard all sorts of comments about "mere" facts versus "understanding". They don't seem to want to deal with reality. Of course, some teachers know and try to differentiate, but you can't differentiate acceleration.

In high school, I suppose they have to deal with the students they get and they just go with the flow, but do you have an example that would show how principals or superitendents consider excellence to be harmful? Does this mean that schools don't want kids to try harder because poor grades will reflect badly on their numbers? If so, what are some of the numbers that drive high schools?

We have principals and a superintendent who consider excellence to be either harmful, or not in the best interests of the district.Why is this?

The only rationale I can think of, which could apply to my predominately minority urban district, is that historically the kids who excelled were disproportionately white kids (i.e., the classic achievement gap). Holding down the top is a quicker way to close the achievement gap than bringing up the bottom.

What other benefit could there be to a district to avoid excellence or high achievement? I just can't fathom it.

Let's see. A friend with a very bright child swears that the superintendent of our district told her that "the district isn't a good place for bright children. The parents often go elsewhere."

In a meeting with parents about a controversial program, a principal maintained that, in the past, the program pursued excellence. However, not all children can achieve excellence, so that's "divisive." The parents in this meeting weren't amused, but what could they do?

The high school doesn't track in the humanities, outside of a small, sheltered class for special needs. I have heard of a very bright student who had to take remedial classes in writing in college.

I sat in a meeting, years ago, in which the sped director claimed that classroom competitions to see who could complete their math facts most quickly would be harmful, because not all children have an equal chance to win. It's the effect of mainstreaming. To acknowledge individual accomplishments makes others "feel bad." It's a cultural thing. The high school decided not to publish the honor roll in the newspaper. Someone might feel bad.

Meanwhile, of course, every week the paper's filled with the exploits of the star athletes. It's o.k. to pursue excellence in sports.

Got it. Your school/district is pursuing equal outcomes. All the strategies you mentioned (plus more that you didn't, including group work resulting in grade averaging, subjective assessments and project work) are designed to equalize educational outcomes. It's intended to advance the social justice agenda. N.B.: ED Hirsch and others have made a good case that these efforts are not benefitting disadvantaged students.

The eye-opening book on this subject is by Cheri Pierson Yecke, The War Against Excellence: The Rising Tide of Mediocrity on America's Middle Schools."

We should do everything we can to achieve

equal opportunity.Striving for equal outcomes, on the other hand, seems wrong for more reasons than I have time to list!

group work resulting in grade averaging, subjective assessments and project workYes, they do that too. I'll have to reread

The War on Excellence. When I first read it, my eldest hadn't reached middle school yet, so I focused mainly on the enmity to tracking. Now, I think I'll see it with new eyes.Very soon, we won't have children left in the public schools. They'll be in private schools, as long as we can afford it. We've tried to advance the case that all children need to be academically challenged, but it's not possible to change a system which doesn't want to be changed. Other parents would tell us that they agreed with out opinions, but many parents were too busy researching private schools to speak up. They also were afraid of retaliation from the school if they did speak up.

Case in point. We just had to turn in our 'recommendations' for retentions. They are 'recommendations' you see, because there is no retention policy. Our recommendations are subsequently chewed on by our principal who will, no doubt, retain something as near to zero as possible.

We even have retention 'tryouts' where kids are held back for a month or two into a new year and then promoted for 'good behavior'. We were quite generous because any criteria having to do with meeting the grade level standards would have resulted in a 'recommendation' of perhaps half the class. Instead, we turned in about 6 names.

Then we were told that the list was too long! Huh? Just tell us how hot the porridge has to be and we'll make it so. A typical comment was that no possible good was to be served by retaining this individual. True of course if you think only of that individual. There is nothing like a remediation program to get a retained student back on track. But what of the remainder of the class that has to suffer through excruciatingly slow lessons while the kids who are way way behind eat up the majority of the teacher's time?

My kids live in a world with absolutely no consequence for doing well or doing nothing. The result is just a headlong rush into mediocrity. The best are squashed and the worst become festering wounds that eat the life out of your classroom. Every year they get farther behind as they are asked to catch up on their own.

what of the remainder of the class that has to suffer through excruciatingly slow lessons while the kids who are way way behind eat up the majority of the teacher's timeYes, and the same question could be asked about kids with disruptive behavioral disorders placed in the regular classroom.

I'm starting to think of the classroom as a zero-sum environment. When a teacher's attention is hijacked by a few kids who need immense amounts of help with either the academics or classroom behavior, this directly, and negatively, impacts the learning environment for the rest of the students.

In these wildly heterogenous classrooms there *is* a tradeoff, but few people want to talk about because it begins to sound politically incorrect. Peter is robbed to pay Paul. Students who are well-behaved and/or at grade level or above are ignored while the high maintenance kids are attended to. Or worse: some students (and teachers) must remain in hostile classroom environments that could form the basis for lawsuits if they were present in the real workplace! This can go on year after year, resulting in subpar performance and loss of motivation in the non-problem kids.

This is the real cost to heterogenous classes and full inclusion. These practices clearly do not benefit all students no matter what administration says. What if administrators would finally 'fess up and admit that, yup, sorry, we're not going give the kids who are without emotional or academic problems a whole lot of attention anymore. Our resources will be (or have to be--NCLB) directed primarily toward other kids.

That might get a lot of people riled up.

And what then? Well maybe, finally, new paradigms (many of which have been discussed here on other threads) would emerge that don't set the needs of one student off against the other. Approaches that work for all of the kids, not just some. We could move from zero-sum to win-win.

The buzzword in my district is 'access'. Every student must have access to teachers with high content knowledge and scrupulously equal curricula. Feels right until you scrape away the emotionally and politically correct dross.

When you do, you'll find classrooms staffed with the wrong people delivering the wrong curricula to most of the student body. What purpose is served by accessing material that is manifestly over a child's head? What good is a content expert in a setting where you need behaviorists, autism specialists, disabilities specialists, and police? Specialists in my classroom? Zero!

It's a zero sum game alright and our inability to openly and honestly debate these disparities has everybody doing a Kabuki dance. Nobody wins.

"new paradigms"

I agree. Schools need to "'fess up". One charter school in our area talks about full inclusion environments rather than full inclusion classrooms. The core academic classes are homogeneous, and everything else (art, music, gym, lunch, etc.) are heterogeneous. I think the school still has issues with allowing kids to get too far ahead, and they still like fuzzy math, but it's going in the right direction.

At our full inclusion public school, kids know what's going on. The school is not fooling anyone. Some classes use team teaching in a big room and they often separate the kids who need the most help and put them with the teacher who has the special training. Even though they are separated like this many times, the more able kids are not allowed to get ahead. They get enrichment. Schools need to 'fess up about this too. Enrichment is no substitute for acceleration. However, if your educational philosophy does not value mere facts or skills, then you would see no problem at all. One teacher told me once that in the end, most students even out by 4th grade. I felt like telling her that it was because many students weren't allowed to get ahead.

Enrichment is no substitute for acceleration.Amen to that.

It's like pedaling, but not getting anywhere. Ever ride your bike on an indoor trainer? You don't get very far, and it's pretty boring.

An example of an Everyday Math enrichment at our former public school was for the advanced 5th graders to make a picture book that would explain operations with fractions to a second grader.

Gee, sign me up for that!

I taught in my district's Gifted program for a couple of years. Administration admonished me (and others teaching in the program) that "parents will be asking for acceleration" but we were explicitly told

notto accede to these demands, but to provide "enrichment" instead.Thus, in mathematics, instead of moving forward into algebra, operations with rational numbers etc, we had "enrichment" activities involving simulations, games and puzzles (Mancala, Nim, Tower of Hanoi, logic puzzles requiring exclusion grids) and so on.

I was interested in math and managed to work in some other topics that possibly did provide additional development of mathematical knowledge and understanding -- I did units on set theory, topology and modular arithmetic, among other things. But while some of that was beneficial, clearly many of the students were starved for real

challengeand wanted to move ahead. They were chomping the bit, so to speak.I think we do these students a real disservice by artificially holding them back. Richard Feynman (who according to his IQ was not gifted, merely "superior" -- so much for IQ) was teaching himself calculus, with some help from his father, at the same age. My students did not have parents with the necessary background to advance their mathematics learning, but they had the ability, and the district even allocated the time -- and then forbade the teachers to take advantage of it.

It appeared to me that the hidden agenda was to

look likewe were addressing the issue of gifted students, while maintaining the equality of outcomes.I got out of that program as fast as I could, but it took three years. Surprisingly, there were not many teachers who wanted to teach it, or stay in it.

"'parents will be asking for acceleration' but we were explicitly told not to accede to these demands, but to provide 'enrichment' instead"

Do they really want to hold students back to keep the academic gap low, or is something else going on?

In my son's old private school, the headmaster specifically didn't tell parents when their kids qualified to take the Johns Hopkins CTY test. Even though parents had to pay for the courses, it turned out that the school really didn't want to deal with a bunch of exceptions and parents asking them to do more. Their students go off to fancy prep schools, so why offer anything else.

The principal at my son's current public school knows that there are limitations with full inclusion and struggles to find real solutions, especially in 7th and 8th grades. She was the one who worked with my son's schedule to allow him to skip 6th grade EM and move directly to Glencoe Pre-Algebra. My son's old private school would never allow that.

However, his current school is not set up to provide widespread acceleration for all core courses, so now instead of having a screwed up schedule this year, he has all of his normal classes, but I teach him algebra. I give the principal an 'A', because now the precedent has been set and other parents see what's going on. Unfortunately, the standard solution seems to be to move them to a separate room and have them take an online course.

The principal also struggles with providing any sort of differentiated instruction in the earlier grades. Many of the teachers still view education in more social and equality terms. I think the administration still has hope that differentiated instruction can be pulled off, but they've now watched it for more than 10 years. Some kids will do well no matter what, but it's the bright kids in the middle that will be hurt the most. They will be the ones who get tracked to the lower level math to nowhere.

Our state mandates that all gifted/talented instruction has to be done as part of the full inclusion process. It seems to me that they fall in love with an idea, implement it, and then try to figure out how to get it to work. In my son's school, they can't get it to work in class, so the approach is to offer special after-school projects, like the First Lego League, Science Olympiad, and MathCounts. That's great for the older kids, but what about the K-6 kids or the kids who can't go to the after-school groups?

Much more progress would be possible if schools dealt realistically with the core philosophical issues.

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