Archives for category: Math Trailblazers

Math Curriculum Report – 12/2/2003

See page 15, which lists criteria for adoption of a math curriculum in IUFSD.

“Constructivist approach with modeling”

This was 2003, 12 years and 3 superintendents ago. “Constructivist” was a requirement for every math curriculum the district considered. Nobody even looked at Singapore Math. Or Saxon Math, or any of the other “instructivist” math curricula available on the market. 

Constructivism isn’t new.

It’s old.

The word “constructivism” has replaced “progressive education,” but it’s the same thing, only worse.

Constructivism is worse because after the 1960s, progressive education merged with postmodernism to produce radical constructivism

The progressive education movement, which began in the 1890s, was always anti-intellectual. But after the 1960s, progressive education became anti-“truth” as well. From the standpoint of radical constructivism, everything is relative, and there are no right answers. (And the right answer can be wrong.)

What’s different about what Kris and Raina are doing is that most administrators give lip service to constructivism while continuing to tolerate teacher-centered classrooms in practice. 

Kris and Raina intend to make classroom reality conform to ideology.

That’s what’s so dangerous.

Right answer is wrong - 10533__Standardized_Testing
Source: Facebook

Math Night
Our current curriculum director, then the principal of Main Street School, hosted the evening.

One question parents asked administrators: will Trailblazers allow my child to take AP calculus senior year?

The then-assistant superintendent did not know.

The Tri-State Consortium praised Math Trailblazers in 2007
The Banality of Deeper Learning by Tom Loveless May 29, 2013
..11:00am | The Brown Center Chalkboard | Brookings
Solutions Money Can’t Buy
Irvington Parents Forum at Yahoo
IUFSD Factoids
The Tri-State Consortium, a group of public school administrators and teachers from nominally high-performing districts, will soon be returning to Irvington, this time to evaluate our World Languages program.

Tri-State reports are constructivist* in nature: they focus on “21st century skills” and the like as opposed to knowledge.

Constructivists value “skills” (21st century skills, critical thinking skills, critical inquiry skills, noncognitive skills, etc.), which they believe can be taught separately from knowledge. (Another constructivist claim: whatever knowledge one may need in order to execute a skill can be looked up on Google.)

“Instructivists” value knowledge (which includes skills).

That is the conflict.

You can see Tri-State’s “skills” focus in the text below, which is drawn from its 2007 evaluation of the district’s math program. A translation follows the text.

From the report:

1. How effectively does the K-12 Mathematics program prepare students for higher level thinking skills required in the 21st century?

The structure of the Trailblazers program includes a comprehensive mathematics curriculum that contains embedded quantifiable evidence of critical thinking skills, an important part of preparing students for their futures. The program consists of an approach to mathematics that develops resourceful and competent problem-solvers who can use a variety of tools, from manipulatives through to calculators, graphs and data tables. Students, K-5, will transition into sixth grade with a common vocabulary, a consistency of performance-based assessments, and computational fluency.

The Tri-State team’s concern relates to the challenge to maintain the critical thinking skills that students have acquired in the K-5 program as they move into the district’s more traditional math environment. With a clearly articulated balance of integrated critical thinking skills and traditional math, the student results will be a deeper and more enduring understanding of mathematical procedures and concepts.

Currently, there is a wide range of 21st century skills defined as vital for students’ future success; critical thinking is just one of them. The Tri-State team suggests that the district identify, analyze, and select those skills that are relevant and developmentally appropriate to the K-12 program. A coherent plan that identifies specific thinking skills that are assigned by grade level and course, scaffolded to ensure consistency, and agreed upon by administrators and teachers, will establish the framework essential for sustainability.

Tri-State Consortium Irvington Visit Report
November 7-9, 2007

Obviously, these three paragraphs contain a great deal of jargon and obfuscation. In fact, the reason I read the report in the winter of 2008 was that a friend who had tried to read it and failed asked me to read it for him. Reading is all about background knowledge, and to read a Tri-State Consortium report you have to know the Tri-State Consortium world and words.


The first paragraph lavishes praise on Trailblazers. From the sound of it, Trailblazers would be a perfect choice for implementing Common Core standards (as our district interprets the standards).

Note that the report echoes Trailblazers marketing materials, which claimed students would achieve “computational fluency” without drill. Constructivism opposes memorization and drill.


The second paragraph expresses “concern” over the “challenge” of K-5 students being able to “maintain the critical thinking skills” they possess when they enter “the more traditional math environment” of grades 6-12.

Translation: With the adoption of a constructivist math curriculum only in the early grades, K-5 is now on a collision course with 6-12.

The report is clear as to which math curriculum is superior: Trailblazers.

In Tri-State’s mind, the question is: How will Irvington students be able to “think mathematically” in middle school and high school if they use traditional math textbooks and are taught in traditional ways?


The third paragraph recommends that the district create a 21st century skills-style math program for all grades, K through 12.

The final reference to “sustainability” is an allusion to the sustainability of Trailblazers. If grades 6-12 are not brought into alignment with Trailblazers, the report warns, Trailblazers may not survive.

In the end, the Consortium was right about the sustainability of Trailblazers, wrong about the notion that children could acquire “computational fluency” without practice.

Eventually the middle school teachers, possibly encouraged by the then-curriculum director (I don’t know),** protested 6th graders’ lack of preparation, and timed worksheets were introduced in grades K-5. Since one of Trailblazer’s main selling points was its promise that children would learn the math facts without timed worksheets, the worksheets amounted to a repudiation of the curriculum.

Two years later, Math Trailblazers was unceremoniously dumped in favor of a math curriculum that had yet to be written.

* Also see: constructivism, excerpted from An Electronic Textbook on Instructional Technology by Irene Chen
**During a board meeting I attended, the then-curriculum director praised the middle school math teachers for their courage in coming forward. Of course, by that point parents had been coming forward for years, but there was no public acknowledgment that parents had been right.

Trailblazers “Math Night” in 2007
The Banality of Deeper Learning by Tom Loveless May 29, 2013
..11:00am | The Brown Center Chalkboard | Brookings
Irvington Parents Forum at Yahoo
IUFSD Factoids

Irvington Parents Forum at Facebook

Cross-posted on Yahoo:

  • For this year, the district abandoned its normal textbook-review process and adopted the new engageny math modules sight-unseen. (engageny)
  • Engageny math is still being written; the district is downloading units as they’re posted to the web.
  • The Engageny “modules” have not been field-tested. Irvington teachers and children are first adopters &, thus, are serving as test subjects.
  • Kids in higher grades (3rd & 4th) have gaps in their math knowledge because engageny & Math Trailblazers don’t match, but no one in the school can identify the children’s gaps, and no one has a plan to remedy the gaps.
  • The district has never had a “scope and sequence” of knowledge and skills students learn in each grade, so administrators don’t know what the kids know — and they have no simple means of comparing engageny math to the math that children have been learning here.
  • It was clear last Thursday night that administrators can’t fix the problem. None of them is expert in math; they don’t know what a proper sequence of math instruction is. Nor should they: no one can know everything about every subject. Normally “pedagogical content knowledge” (what to teach & when & how) is “purchased” when we adopt the best math textbook series we can find.
  • The solution, for now, is to drop engageny (or delay its adoption) and replace it either with the old Trailblazers books or with an ’emergency adoption’ of Saxon Math, the single most teacher-friendly math textbook on the market. (Here’s the homeschool edition.) UPDATE 11/9/2013: Or, better yet, we should do an emergency adoption of Singapore Math. Engageny math is, to some degree, modeled on Singapore Math, but Singapore Math has been field-tested and revised over many years’ time, and its Scope and Sequence can be understood by administrators, teachers, and parents alike.
  • Any teacher (& any parent) can pick up a Saxon Math textbook and teach math today. I know this because I chose Saxon when I realized I needed to re-teach my son 4th grade math. I hadn’t taken a math course since college, and I successfully used Saxon immediately to teach my son and re-teach myself.
  • An emergency adoption of Saxon would mean that this year serves as the pilot of Saxon; next fall the district could pilot Singapore Math (& perhaps engageny math, if we have good word on engageny from other districts).
  • Other children, in other districts, should serve as test subjects for engageny math, not ours.
  • For the time being, we can’t worry about the new Common Core tests. We have Trailblazers kids in a Common Core world; that’s the reality. (If we had Singapore Math kids — real Singapore Math, not Dobbs Ferry Singapore Math — in a Common Core world, things would be different. But we don’t.) The state requires kids to take the tests, and that’s fine: we should treat the results as information about gaps and proceed from there.
  • We have $2.16 million dollars in the fund balance to use for ’emergencies’; this should be seen as an emergency. Once kids develop gaps in math, it is very difficult for them to catch up to peers who have had a coherent math education. Our family knows this from direct personal experience.

Irvington Parents Forum at Yahoo
IUFSD Factoids

Just back from the Common Core meeting at Main Street School tonight.

One factoid that leapt out at me: the price of a new K-5 math textbook series, RK reported, is roughly $100K. That is the reason, she said, or a reason, we do not have math textbooks. Normally, at this point in the cycle,* we would be vetting published textbooks, piloting them in the classroom, and choosing the one that works best, but not now, not with Common Core.

Today we’re using the free “math modules” being posted on engageny, downloading each module as it’s posted. The math modules are new, so new they are being written as we speak. They have never been taught by a teacher, or field-tested with a child. But they are free, and they carry the Common Core brand, so we are using them.

The ancient tradition of textbook adoption and 10-year textbook adoption cycles is gone with the wind.

Meanwhile we have over $2 million dollars sitting in the fund balance, as the district’s auditor confirmed three board meetings ago. The sum in the IUFSD fund balance, he said, is the “maximum allowable under the law.”

(He also mentioned that the law did not require an audit of our federal funds because we received less than $500K from the federal government.)

So. $2.16 million in the fund balance and we’re downloading never-before-taught math modules from the internet because they’re aligned with Common Core and they’re free.

Meanwhile Singapore and Saxon Math have been around for years, have been extensively field-tested, and have at least some reasonably sound data to show their effectiveness. And the Singapore series (Primary Mathematics) is universally endorsed by real mathematicians, as opposed to “math educators” (the term of art in ed-school precincts). Singapore Math may be the best math curriculum available in the English language.

For $100K Irvington children could learn math from the best math curriculum in the English language, or, for $0 Irvington children can learn math from engageny math modules the district downloads from the web.

We chose Door Number 2.

Here’s a question.

If we did not have a Curriculum Director, would we have math textbooks?

Would classroom teachers, acting on their own, choose to teach math without a textbook?

I don’t believe they would. Teaching math from packets is as hard as learning math from packets, or can be. I know because I teach grammar and writing from packets. My students need a good textbook, and so do I.

But education schools dislike textbooks, which they see as old-fashioned, sage-on-the-stage affairs, and curriculum directors are trained by education schools.

Untested math modules on the internet are “21st century” (a compliment in the education world), just like the position of “Curriculum Director itself,” which, like the math modules, did not exist at all in days gone by.


We’ve still got timed worksheets, which is more than most districts can say. And we’re going to continue to have timed worksheets: RK mentioned “fluency” several times. I wouldn’t be surprised to see the concept of fluency incorporated into other subjects: a very good idea. We desperately need to give kids fluency in reading and writing (something I’m working on myself in my own teaching).

Things could be worse. (See, e.g.: Dobbs Ferry)

UPDATE: “Fluency” = “automaticity.” Both words describe actions — and “thoughts” — you can perform rapidly, accurately, and largely or entirely outside of conscious awareness.

People who are fluent in a skill or area of content are fluent. This is why the requirement that children “explain” how they reached their answer in math is so wrong. Very often, a student who is really good at math just “gets it” without having to resort to effort-filled, conscious  reasoning. When you force that student to “explain his reasoning,” you force him or her to “translate” his correct answer into words; you force him or her to function in the way a less talented student does.

Contra RK’s assertion last night, in the real world, NOT having to “think” is the goal. We need to acquire sufficient knowledge, and sufficient “automaticity” in our knowledge, that we look at a problem and know.

We should save thinking, which is tremendously effortful and rapidly drains mental resources, for advanced questions, and strive for fluency in everything else.

Fluency is reached through knowledge stored in long-term memory.

* UPDATE 10/26/2013: A friend reminds me that we do not have a 10-year textbook adoption cycle, as mentioned during the presentation. We have a 3-year curriculum cycle (or curriculum-review cycle). The 3-year cycle, as I recall, does not require that we change textbooks; we revisit textbook choices and review.

Fund balance could pay for $385K administrative offices