Friday, April 10, 2009

High School Math Adoption


At the School Board meeting on Wednesday night, 15 of the 20 public comments were about the high school math adoption. Of those 15 comments, 11 were comments from people opposed to the adoption of the Discovering Series and 4 were from people in favor of the adoption. I was in the opposed group. The 11 speakers opposed were from all over the district and included teachers, parents and math professors. Of the 4 people who spoke in favor, 3 of the people were on the adoption committee and the 4th person was Mr. Boyd, the Principal at Chief Sealth, who said that all the high school principals are in favor of the adoption of the Discovering Series. I have to say, I don't know why anyone would care what the principals think on this topic, they are not the ones who have to teach the class. I know that our principal never asked any of the math teachers here how we feel about Discovery. It was interesting that no one outside of the adoption committee came forward to speak for adopting Discovering.

I do believe that the Board listened to what was being said and will look very long and hard at this. I had to leave the meeting before the presentation was made to the Board by the staff, but I was told that the Board asked some good, hard questions and did not get good answers back from the staff. How this will play out in the end, I have no idea, but I believe that there is much skepticism on the part of many Board members and those that were around for the Everyday Math adoption feel they were sold a bill of goods on that adoption and they do not want that to happen again.

I am including what I said to the Board:

Good Evening
My name is Michael Rice. I teach mathematics at Rainier Beach High School. I am here this evening to speak to you about the proposed adoption of the Discovering Series by Key Curriculum Press as the math textbooks for the high schools in Seattle. I would like to encourage you to reject this recommendation. This is based on many factors, but since my time is limited, I will only share a couple with you.

1. Rainier Beach High School is known for many things. Besides being only one of three high schools in Seattle that is not on the Federal Needs Improvement list, every year, we have several student-athletes who earn athletic scholarships to college. I have found that my students really understand sports analogies. I use the analogy about how the football team practices Monday through Thursday, so they can be ready for the Friday night game. I tell my students that same sort of sustained effort is needed to be successful in a math class. When you are learning a new concept, you have to practice it (better known as classwork and homework), so that you are prepared for game day (better known as a quiz or exam). I share this with you because I have reviewed the Discovering Series, and I have found it to be lacking in practice problems to help prepare students to be ready for game day. When I inquired about this, a district official told me to “supplement” so the students will get enough practice. Any textbook where you have to “supplement” something as basic as practice problems, is a textbook series not worthy of being used in the classrooms of the Seattle Public Schools.

2. According to the SPS website: Mathematics is the language and science of patterns and connections. Learning and doing mathematics are active processes in which students construct meaning through exploration and inquiry of challenging problems.
That definition of mathematics makes no sense. It does not explain what math education is and what students need to know. A much better definition of what math education needs to be comes from California. Among other things, the goal in mathematics education is for students to:
a) Develop fluency in basic computational skills.
b) Develop an understanding of mathematical concepts.
c) Become mathematical problem solvers who can recognize and solve routine problems readily and can find ways to reach a solution or goal where no routine path is apparent.
These are much more understandable goals that actually discuss what math is and what students need to learn. In addition to the revised state standards, these are the kind of standards that Seattle Public Schools should be applying when it comes to math. When applying these standards, the Discovering Series lives up to its State Board of Education designation as “mathematically unsound.” Please reject the Discovering Series. Thank you for you time.


anonymous said...

Thanks for standing up for our students, Michael.

RBHS is truly lucky to have you!

Dorothy Neville said...

Yes, the folks that spoke in favor of the adoption included the woman who said we needed to replace the ratty textbooks because the kids think that broken bindings signify bad math. And as if mathematics has changed so much in the past 20 years we desperately need new materials. Someone should give her a carton of duct tape. (Although the text she was waving in the air was an Integrated 2 text. I don't love that text, but would find it acceptable in a pinch. Certainly more acceptable than Discovering Geometry.)

I also did not understand the deal with the principals being unanimous. RHS principal, whom I do not think has ever taught math, has drunk the UW Ed school kool-aid and speaks the inquiry-learning-is-the-one-true-path talk quite well. And interesting that the RHS math teachers have so far stuck to cherished ratty, tattered out of print traditional books *and* use the pre-calculus book developed by and used by UW Math department.

Another pro-Discovery woman said that her students wouldn't learn math without it, that they needed manipulatives. Well, gotta say that there are other possible conclusions that could be reached. Underprepared kids, inexperienced teacher, or something else. She didn't say anything to prove that this new textbook series would solve her particular teaching problems. Right now she is free to use any curriculum she wants and use the texts available or supplement at will.

The thing is, as Dan and others note. The Reform/Traditional debate is a false dichotomy. The Discovery series was a compromise that could be used (in the opinion of the committee) for both an inquiry approach or a more traditional exposition of material. However, as a stand-alone tool it is weak, abysmally weak. That's why one must supplement for comprehensive learning.

So, why couldn't one choose a solid text, such as Prentice Hall and use it to teach in an Inquiry based method? Truth is, one could. Truth is, math is often done by motivating topics, logically following from one to another so students see the connections and form connections on their own. HOWEVER, the Inquiry based folks don't see it that way. The salient feature of the inquiry based texts I have seen is that the authors purposefully hide the math. They purposefully do not teach the language, do not demonstrate algorithms or sample problems sufficiently to follow. While Discovering Algebra mentions y=mx in chapter two, they point out in the supplementary materials for teachers that they purposefully do not call m the slope until chapter 4. They call it the rate-of-change or simply rate, which is correct, but overly complicated at this stage.

And, one would think, that if one is espousing a discovery approach to math, one would also teach logic skills, deductive reasoning to help the students in accuracy of discovering concepts. But a speaker at the school board meeting pointed out that Discovering Geometry does *not* teach deductive reasoning. The first 12 chapters teach geometry informally and inductively. Only in chapter 13 are formal deductive methods used. Sort of like teaching science purely from inquiry, but going out of your way to ensure that students are not exposed to the scientific method.

Unrelated to pedagogy, there's the whole issue with whether or not Discovery Series is mathematically unsound. From what I have seen, it is clearly mathematically unsound.

How about adopting a strong text, a mathematically sound text, a text that can serve as a tool for curriculum and a reference tool for students. And then tell teachers that in order to facilitate a more inquiry based pedagogy, they are free to supplement, free to add lessons using manipulatives and whatever else they find useful to teach.

As I said in the comment on the open thread, DeBell was concerned that this sort of textbook, that hides the math, is unsound and cannot be a useful tool on its own, serves to put too much emphasis on the teacher for learning. While the teacher is an important part of learning, the teacher should be fully supported by the materials. The teacher should not be the gatekeeper of learning.

There is one point that DeBell made that I would like to dispute. It seems that most people accept that learning math includes conceptual understanding and computational fluency. DeBell and others seem to believe that while "reform" math is lacking in computational fluency it does lead to conceptual understanding. I dispute this. I see way too often that the middle school kids I tutor do form conclusions from their CMP work, but often it is the wrong conclusion. I spend as much time unteaching the wrong conclusions they formed as I do helping them form correct conclusions. And since they see all of math as a series of tricks and guesswork, they don't have the foundation to reason appropriately and build conceptual understanding.

I was heartened to hear the questions from DeBell and Sundquist. They've been paying attention and reading their email.

Please, if you are concerned. Watch the meeting yourself and then write the school board. There are three parts of the meeting addressing math. The public testimony, the presentation by de la Fuente and the TOPS teacher which included some questions and discussion among the board and then later after the break and consent agenda there was discussion and questions posed to Ms de la Fuente.

Melissa Westbrook said...

Good for you, Michael.

I, too, have been a bit dismayed at how easily the principals have fallen in line with these books (much though I respect and like my principal). He kind of waved off my concerns over the remarks about it being "mathematically unsound". I'm sorry but it's one thing for professionals to disagree on which book would be better to use but if you have some who have absolutely no faith in it, then I worry.

And all this supplementing stuff? Look, if you have to do extra work because the book is lacking, you have the wrong book. It's one thing if you want to cover something more deeply but to have each math teacher have to figure it out on their own is pointless.

dan dempsey said...

Check the money trail here:


Given Michael DeBell's comment about Carla Santorno and math as well as his questions on 4-08-09, hopefully on April 22, 2009 we will see the end of funding the SPS k-12 math plan to nowhere.

Perhaps the WA math standards may actually become SPS math curriculum ... then all the SPS will need are appropriate instructional materials and the will to make it happen.

ROI = return on investment

Anyone care to calculate a math ROI for Ms. Santorno's three years here?

Most bizarre moment of testimony.
There was a lot made of the Mathematically Unsound rating of "Discovering" and the fact that no mathematicians were on the Core Committee. Prof John Lee, UW research mathematician had applied for the committee and not been selected. Prof Lee testified as to the "Discovering Geometry" defects.

The bizarre moment occurred when a Core Committee member testified that she was on the Core Committee and had a Bachelors degree in math and considered herself a mathematician.

I think I missed her peer reviewed articles on mathematics. When and where were those published?

The stacked committee, using the biased selection criteria selected the "Discovering Series". Then they provided No reasons for this selection .. other than the current books are old and need replacement now.
Is this a coincidence that Ms. Santorno is now headed south to Tacoma?
At the Everyday Math adoption a principal stood and read a statement of support for the Elementary Adoption of Everyday Math signed by all the elementary principals.

John Boyd's statement of all nineteen secondary principals supporting the math recommendation is hardly a comfort.

WoW!!! News Flash building based administration supports central administration's plans.

Boyd's statement was about district politics not math.

dan dempsey said...

Michael Rice wrote:
"That definition of mathematics makes no sense. It does not explain what math education is and what students need to know."

Little wonder that the SPS k-12 math program is a confused program to nowhere as it follows the SPS definition of Math.

Dorothy Neville said...

Dan, that was just one of the bizarre moments. Were you still there when the TOPS teacher gave praise to CMP, but said that there was one topic that he did not teach inquiry style, Symbolic Manipulation, as "he didn't leave that to chance."

Confirming that even teachers who like the "reform" pedagogy acknowledge that using it leaves the learning to chance.

dan dempsey said...


Great observation. Learning has been left to chance and it is now confirmed that it is a really small chance.

I liked Matt Grove's testimony about CMP ... it seems that CMP classes are more social event than instruction.

MoneyPenny said...

I think it is ridiculous that you give no weight to what Principals think. I watched the meeting on TV, and frankly thought that the vast majority of folks were arrogant and lacked insight on actual SPS students. Mr. Boyd and Ms. Nelson were two of the most crediable speakers. Plus, Ms. de la Fuente and Mr. Ellis were stellar in presenting thier reasoning.

dan dempsey said...

It is of particular interest that most of those testifying in the Pro "Discovering Series" camp were from Chief Sealth High School.

Sealth spring 2008 math WASL scores:
level 1 40% & no score 12%.
One of these Sealth Ladies on the core committee testified that: "My kids can not learn from lectures." .... So how can they learn? Does she know?

Sure looks like she might not actually satisfy the committee requirement to be open about student learning.

Hopefully the SPS math plan to nowhere is ending.
The district in the interest of data gathering has two elementary programs worth supporting for at least the next five years.
Saxon Math at North Beach and Singapore Math at Schmitz Park.

With Carla Santorno leaving perhaps these two schools will not need to live under the threat of having a waiver denied for permission to use their programs and then being forced into using Everyday Math.

dan dempsey said...

Dear MoneyPenny,

I like positive results.

You said: "Plus, Ms. de la Fuente and Mr. Ellis were stellar in presenting their reasoning".

I really like data that can back reasoning. I guess I missed the stellar reasoning. Would you please summarize it for me?

lacked insight on actual SPS students.

Please share those insights that are lacking.



ParentofThree said...

moneypenny, you are sounding more and more like a district insider...didn't you also say Michael Tolley knows this school system than anybody you know? Yikes, he's been here less than 2 years and does not, to my knowledge, have any children enrolled in SPS. Ya got to be in the trenches for at least 3 years, with a kid in the system to even begin to understand SPS.

MoneyPenny said...

Sorry, didn't know that only people with a particular viewpoint were allowed to post here. I have more than one child in high school
(at two different schools) and have been around for 15 years. I have been to many of the same meetings that Melissa and Charlie attend, I just don't lock step agree with them. And I am not bothering to respond to Mr. Dempsey, because having had a child have him as a teacher, don't put stock in what he has to say. That is my perogative, just like it is his perogative to post and repost the same things over and over again.

MoneyPenny said...

And what I said was Michael Tolley has impressed me and that I think he knows an awful lot more about high schools than armchair quarterbacks, not that he "knows this school system better than anybody." That a problem for you?

reader said...

I agree with MoneyPenny, lamenting "new math" has been a pastime since the beginning of math. People have always complained that the younger generation wasn't learning math the good old way. The fact that a bunch of math college professors complain isn't the least bit persuasive. And certainly when I was a kid, Dam Dempsey style whiners were everywhere. In the day, the butts in seats, long worksheets full of problems didn't seem to be all that successful either.

My kids do (and have done) Terc, which was great. Worked great, was fun. Now they're doing EDM... which is less great, but works. It isn't about the curriculum.

And the crybaby stuff that minorities can't learn new math (or constructivist math)... is plain racist. It's not like other methods have worked all so well.

dan dempsey said...

Dear Reader,

I am hardly a proponent for long work sheets. Take a look at the WA math data. The direction of math in WA, Seattle, and the USA is hardly going well. Internationally competitive math is hardly advocating for a return to the past. Pick up a Singapore Math book or buy one for $7 and have a look.
There were no good old days in math teaching of which I am aware.

Interesting that this has now degraded into personal attacks rather than a discussion of issues.

For the record I find Mr Tolley very talented and well informed.

MoneyPenny there is no requirement for ideology to post here. I taught at WSHS in the Pathways math program in 2006-2007, sorry you were unhappy. It would have been great to have communicated that concern to me during that school year.



ds said...

I think that the point that a particular teacher may not work for a particular kid is a valid one (sounds like Mr. Dempsey wasn’t a good match for MoneyPenny’s child) ...and this is exactly why the textbook needs to be something that the kids can use to try to figure things out on their own (e.g., as they’re working on their homework).

Both Discovering and Prentice Hall include elements of “reform” math (e.g., real world problems, and investigations...yes, there are even investigations in Prentice Hall) and “traditional” math (e.g., definitions, exercises)....if you look at the committee’s report on the 3 finalists (Discovering and PH included), it indicates that all had a “Balance between investigation and skill building” and “Real world applications.”

The problem with Discovering is that the “investigations” form the basis of the instruction; the main points/conclusions are often not laid out and, as Dorothy pointed out, kids often form incorrect conclusions from this type of presentation. So, if a kid tunes out his/her teacher, there’s little to fall back on with Discovering. Let’s say, though, that a kid has a “bad” teacher but has Prentice Hall...at least the materials will present the information in a straight-forward way; that kid will have a chance of “getting it” if s/he can use the textbook as a guide.

As for Reader’s reference to “crybaby stuff that minorities can't learn new math,” I don’t think the point being made is that disadvantaged kids (not necessarily minority kids) can’t learn from the constructivist/reform approach. There are going to be plenty of kids (minority or not) who can learn from the constructivist/reform approach; but there are many who will get lost. The point is that, because the Discovering series does not state conclusions clearly, kids with fewer resources at home (minority or not) are more likely to struggle because their parents are less likely to have the resources to help them make sense of the vague, indirect lessons. I have talked to soooo many parents whose kids have been frustrated by unclear (yes, reform-based) materials, and they have all been able to help their kids make sense of them either by working with them at home or by hiring a tutor, Kumon, etc. But not everyone has access to these resources. If the textbooks were more straight-forward, there would be less need for such extra resources.

Please, everyone, let’s stick to the issues and avoid name-calling and put-downs.

dan dempsey said...

Reader said:
"And the crybaby stuff that minorities can't learn new math (or constructivist math)... is plain racist. It's not like other methods have worked all so well."

There are methods and instructional materials that have worked well. The largest study in the history of education was Project Follow Through it specifically addressed primary school performance of disadvantaged learners.

Check the Cognitive model of explore and inquire with the Direct Instruction model here:


dan dempsey said...

"If the textbooks were more straight-forward, there would be less need for such extra resources."

EDM, CMP2, and Discovering are not straight forward. There is no reason to select materials that make learning more difficult.

Rose M said...

The problem with disregarding university math & science professors is that many of our kids want to succeed at university. Kids who sail successfully through SPS math program often end up in remedial math at UW. That is enough to make sure you are never accepted to the college of engineering.

I don't know what SPS is preparing kids for, but I want kids to have a choice of pursuing math or science or engineering at university and not be prohibited because SPS doesn't like the math requirements of those programs and refuses to teach those skills.

dan dempsey said...

Three thoughts:
Michael Rice --I know that our principal never asked any of the math teachers here how we feel about Discovery. That is why John Boyd's comment about all the principals are in agreement is not about math.
Rose -- I want kids to have a choice of pursuing math or science or engineering at university
TERC/Investigations may have been fun for some but lacks content. At the end of Grade 5 TERC students are slightly behind students coming out of Singapore Math grade 3. Singapore Math builds enormous conceptual understanding ... TERC just claims to do so .. and at the expense of skills. EDM just check the dissatisfaction with the results. EDM was presented as going to eliminate the achievement gap in 5 years. Significant expansion of the gap for Hispanics in grade 4.
Disadvantaged learners profit from a straight forward presentation.
The comments from ds are spot on.
Michael DeBell mentioned San Diego dropping "Discovering" and going to Prentice Hall.
Check this for why...


and this...for some information on those disadvantaged learners.

As ds points out Prentice Hall hardly precludes an inquiry approach if a teacher chooses to use it that way. It does give the student a straight forward presentation that is missing from "Discovering".

Dorothy Neville said...

I may be an armchair quarterback, but I have a BA, MS and ABD in Mathematics, seven years experience teaching high school and undergraduate math, one son in 10th grade with 8 years of SSD math (we homeschooled math a bit) taking precalculus and a math tutoring business that I keep small but could grow overnight if I wished.

Reader, I am glad your kids are doing well in elementary school math. With a good teacher, EDM can be fine. I would like to hear from more parents of students in grades 8 and up who are as satisfied.

Mr Ellis, the TOPS teacher, disagrees with DS. Go watch his presentation (It starts somewhere around 90 minute mark). He claims repeatedly that Discovering is the only text flexible enough for either instructional methodology. As DS states, it is in fact the most extreme in its Inquiry based approach. How flexible is that? Why couldn't a teacher teach in an Inquiry style using Prentice Hall? That's a question he should be asked. The answer would be telling.

(Yes, Discovering does have "Condensed Lessons" for parents and tutors. Free on the publisher's website. They are more explicit, although a bit condensed. We could save a million bucks and use those, eh?)

Also, look for yourself, right at the 100 minute mark of the board meeting, where Mr Ellis candidly states that he teaches Symbolic Manipulation (pretty much the key to algebra) in a direct instruction method because he doesn't "leave that to chance." Isn't that a telling comment? Let me offer an analogy. What if I were to say "I never drive drunk to church, no, I would never do that." Kinda makes you think, eh?

Neither Ms de la Fuente or Mr Ellis pointed out that TOPS 8th grade parents routinely pay tuition for a different teacher (a math professor) to come after school to teach their kids traditional algebra.

Yes, teacher-student relationship, a good fit there is important. Ms de la Fuente agreed over and over. Sometimes it doesn't work out. That's going to happen and students need to be able to deal with it. And as Ms de la Fuente also pointed out several times, SSD doesn't have enough excellent math teachers and we have an imbalance north and south. Success in an extreme Inquiry based approach will depend heavily on the student-teacher relationship and on the teacher's mastery of the material (and on the student's ability to pay attention and keep up with the pace, the teacher's ability to maintain discipline during all the group activity, the other students' willingness to participate and ability to learn...)

Why not choose a textbook that allows the most flexibility by providing decent explanations and sample problems just in case not all those conditions can be met?

anonymous said...

I don't know a lot about math, and won't even pretend to be an expert.

What I do know is what I have seen with my own children. My youngest son has a fantastic math teacher this year, really top notch. She likes EDM and thinks it works well. We are a college educated, middle class family, and my son is very bright.

My son keeps up in math, but needs a lot of assistance from us. He is rarely able to complete his math homework alone, and gets very frustrated.

I went to math n stuff and bought the Spectrum series of math books. They cover the same material as EDM, but they show step by step how to solve a problem. They give the formula where appropriate and they always give a few practice problems. This works much better for my son than the conceptual approach, where he discovers the formula, but gets frustrated in the process, and forgets what he "discovered" by the time he gets home. And, when he forgets it, there is nothing for him to reference in his homework packet. No example problems, no formulas, not instructions. When he gets to this point he gets almost all of the problems wrong, and we have to go over them and re-teach him. It's very frustrating for him. He thinks he is "bad" at math, and hates it. How sad.

Next problem. Just when my son begins to feel a bit more confident about the work he is doing, but before he masters it, the class moves on to a new math topic. Again, very frustrating. He was almost there....

My older son who is now in 8th grade, is in honors math (INT I), doing well. But with the help of many private tutors throughout the years. Though he is in honors math, I can still ask him a simple question like how do you subtract two fractions, and he can't remember. Says I haven't done that in years.

All in all SPS math has not been a good experience for our children. I can only hope that a more straight forward approach to math will be better.

anonymous said...

I also wonder about EDM's "pre algebra" in 5th grade (which feels more like algebra than of pre-algebra). Is it appropriate at this age? Are kids brains ready for algebra at age 10?

Josh Hayes said...

adhoc writes:

"I also wonder about EDM's "pre algebra" in 5th grade (which feels more like algebra than of pre-algebra). Is it appropriate at this age? Are kids brains ready for algebra at age 10?"

Good question. Here's one data point: My son, in the fourth grade, took an elective in "algebra". What they wound up learning was what an equation is and how to do operations on an equation (multiplying both sides by a constant, subtracting the same thing from both sides, and so on). He was able, and is still able, to take something like:

4x - 12 = x + 24

and solve for x. I know, that's quite simple, but I think learning the basics of how to move stuff back and forth across the equals sign is a great first step.

He's good at math but hardly gifted, so I would say that, sure, a lot of 5th-graders can handle beginning algebra. I didn't get full-fledged algebra until I was in 7th grade, myself -- simultaneous equations, that sort of thing. I kinda wish I HAD had the chance to start it earlier.

anonymous said...

It's so cool to offer an "algebra" elective to the younger children!

A question for you Josh. Since it was an elective, and not required math, did the teacher have to use EDM and it's pacing guide? Or was s/he able to teach it with material that s/he saw fit and at the pace the class needed? Also, since it was an elective was it a small class? I am very intrigued at the thought of offering math as an elective. It seems like it would be a great supplement to the district mandated math curriclum, and I wonder if it would give teachers a bit more freedom?

dan dempsey said...

Let me discuss my only year in the SPS because it is very relevant to this discussion.

I was hired as a Pathways Math teacher for the 2006-2007 school year. This was a program for students who had failed the 10th grade math WASL at level 1 (one student was level 2).
At that time the passing of the math WASL was to be a graduation requirement (the legislature abandon that idea in April 2007).

I was provided with the OSPI math modules, which were developed by OSPI with assistance from the Dana Center. {These modules were later found to be totally ineffective by Cole & Barnofsky of the WA Public Policy Institute, the research arm of the legislature}.

I was at West Seattle which had a four period day. The district provided the middle school materials from College Prep Math for pathways. In other schools with a 6 period day the class offered as pathways was in addition to a high school math class.

At West Seattle this was the High School math class. Keep in mind that my students were the products of Seattle Schools k-8 "de facto" social promotion policy that lists no necessary skills and provided no interventions, quite the opposite of written policies D44.00 and D45.00.

I eventually got permission from Central Admin's John Throp to use nothing that I was provided. College Prep Math middle school materials did not have enough content for a high school math class. The OSPI math modules were clearly not designed for my kids. The modules were supposed to take kids from mid-level two skill level to WASL Math passing. (Cole & Barnofsky showed they did not even do that).

Rich Mendes was teaching a Pathways class at Roosevelt. Rich's class was the in addition to regular math class. Rich gave up on the provided materials near the end of first semester.

What I did was to go pull out my debit card and head to Costco buying shelving and plastic tubs. I purchased materials from the Reform Math minded "Math Learning Center" in Oregon as well as lots of other manipulatives. I also purchased some Singapore Math texts.

Most class days centered around an activity.

Not a single one of my kids went from level 1 ( below 350 , often way below) to passing at level 3 400 or better.

When the district refuses to provide effective interventions k-8 and promotes unskilled students into high school, it really does not matter how much money is thrown into professional development (there was a bundle thrown at Pathways math) and how much they talk about the wonders of differentiated instruction, it is apparently too late for those things to have any significant effect.

Check results from Fife HS where I was part of a team of two that developed an activity based program in 2005-2006 for math. Algebra 1 had tenth graders in a year long class of 90 minutes. ( Fife is a grades 10,11,12 school and had a fairly straight forward algebra text) The following year this was abandoned in favor of the Math Module approach for one semester of math (1 credit because it is a 90 minute class).
Look at Spring WASL 2006 our year and compare with the previous year 2005 and 2007 & 2008 the administration's creation.

2003-04 44.6% 43.9%
2004-05 47.7% 47.5%
2005-06 56.8% 51.0%
2006-07 44.7% 50.4%
2007-08 45.6% 49.6%

I am an advocate for students and am hardly the long worksheet teacher (thanks for the unfounded accusation). A major problem of the SPS is the books they select are largely minimally guided inquiry and students need more structure in their text series.

My SPS Pathways students 2006-2007 did not have an appropriate book. Is there an appropriate book for that situation? Hard to tell. If the district had done their job k-8 that situation would not have existed.

Now you know why I spent one solid year "Whining" at the school board from Jan 2006 to Jan 2007 as well as why I joined the NAACP.

This year I am at Lummi Nations School teaching high school math to students who had Everyday Math and most do not know the Standard algorithms for either multiplication of division when I get them. Many can do the quite useless "Lattice Method" of multiplication.

This year Lummi Nations was the recipient of a grant from Indian Education to improve k-6 math. The grant requires the use of one of two k-6 math programs shown to have some promise with Indian kids.

They chose Saxon ... needless to say TERC and EDM were not among the choices. Lummi bought the useless as primary materials Connected Math Project 2 materials about the same time as Seattle. It was an administrative decision not a math teacher decision.

Proud to be a whiner.
If doing so produces a chance to liberate the kids from confusing poorly written Math materials.
Note the third printing of the CPM book had an incorrect definition of Quartile in the book, another defective reference product. Clearly proof readers and authors need to know more math.

Many of the teachers in this program did not know the definition of quartile ... so where does that leave the class?

The WASL is a poor test for High School Math but it is all we have for reference.
Fife HS 2006
Math - Grade 10

Number Percent
Meeting Standard 147 56.8%

Level 4 (exceeds standard)
69 26.6% (16.9% the previous year and 11.8% the following year)

Level 3 (met standard)
78 30.1%

Level 2 (below standard)
67 25.9%

Level 1 (well below standard)
42 16.2%(30.1% previous year and 25.4% the following year not including the 6.5% no score )

No Score 1.2%
As Charlie says .. it would be wonderful if decisions had to be backed up but that is not school decision making culture .. Everyone held accountable is nonsense.

Josh Hayes said...

good questions, adhoc. Unfortunately, that teacher was not comfortable in the AS1 environment, and left after only one year. :-(

My feeling is that it was not "standard" materials, but I do know another teacher at the school who helped set this class up. I'll check with her.

I think that "electives" can be very useful: they get kids comfortable with the lingo, without making the whole thing seem like some stressful "You Must Learn This NOW!" situation. I also think that young kids can find "advanced" topics really cool, before they learn that they're advanced.

I, for instance, was told in 4th grade that it was impossible to trisect an angle with a compass and straight-edge. Hah!, I said, and spent all my spare time working on it. (I cheated: if the angle is a right angle, you can construct 30 degree angles and in that way trisect it, but that's really not the same thing. Alas.)

It's that kind of gee-whiz, isn't that cool, sensibility that I'd like to see encouraged.

And, (WV), I'm serious: no punsings.

hschinske said...

I think quite a few modern math curricula (Saxon and Singapore among them) introduce some basic algebraic tasks very early on, by means of problems set up like this:

4 + __ = 6

rather than sticking with

4 + 2 = __


6 - 2 = __

For a student who's actually mastered such problems (yes, there are ninth graders who haven't, sigh), the use of a real variable by fifth grade or so is not too much of a step.

Helen Schinske

Dorothy Neville said...

I'm pretty sure problems like 4+_=6 have been around a long time in elementary school math. Turning the blank into a variable is considered a leap. Turning X+X into 2X or
X + 8 = 3X into 8 = 2X is further a leap.

Back when I was teaching algebra, there was a lot of discussion of kids' brain development around adolescence that allowed for more abstraction. That was seen as a barrier to teaching algebra earlier. This was Piaget sort of studies, I don't know more. I am not convinced there's a definitive study or answer though. Certainly the different paradigm of Singapore Math and Montessori have the students closer to such conceptual understanding of algebraic symbolic manipulation earlier.

I suspect that the 4th grade class Josh is talking about did Hands On Equations, a very good inquiry based method of teaching symbolic manipulation. It's highly regarded in home schooling circles, especially homeschooling gifted kids. My son had a unit of Hands On Equations in fifth grade and sure enough, the kids who were ready for it glommed on and loved it. The teacher said that a good number of the class was not *getting it* so she didn't keep it up. (This was APP)

In fact, I would say that Hands On Equations has been the only successful Inquiry Based mathematics my son ever had. Nothing from TERC or CM came close.

dan dempsey said...

Where is all the Math Funding going to come from???

The District is still looking at a large operating deficit.

The adoption cost is announced as $1.2 million. No instructional materials below “Discovering Algebra” are included. The instructional materials require that students below grade level in math will enroll in Algebra I and be served by additional interventions and in class small group instruction etc.

I spent the last two years futilely trying to get action on effective interventions for math k-8 {SPS board policies D44 & D45 are still not followed}. It is a fantasy that in a budget restricted environment, enormous expensive interventions are going to happen and that the district is prepared to pay for these annually. Many years of expensive interventions will be needed because k-8 keeps producing this fairly constant stream of math-disabled students. Interventions are needed long before grade 9. Were those teachers and principal John Boyd, from Sealth HS testifying (4-08-09) for this math recommendation, aware that Sealth 2008 WASL grade 10 math showed 40% of the students at level 1 and 12% with no score?

Ananda said...

Mr. Dempsey: Perhaps you should also mention that CSHS had the single highest gains on WASL scores statewide. But maybe you are not aware of that. Or maybe you missed the part where Mr. Boyd mentioned that ALL of the high school principals and program managers were in support of this recomendation. Perhaps you should not waste your time making this about a particular school when Mr. Boyd was clearly representing all of the high school administrators. But hey, I bet you can move on to bashing all of them.

Unknown said...

I think specific examples are illuminating. The devil is in the details.

I want to get back to the point that the only support for this adoption comes from the district. Math professionals, as opposed to education professionals, do not support this text adoption.

ds said...

I may be wrong, but my impression was that the principals had been at a meeting or retreat where Ms. de la Fuente presented the materials (can anyone confirm or deny?). She is very well-spoken and her presentations are pretty convincing, especially if you don't have a side-by-side comparison of the other options. It doesn't surprise me at all that the principals are supportive of the adoption.

The bottom line is that Seattle kids need to have a mathematically sound, coherent textbook that can be used as a reference. Not only will this give them a way to reaffirm what they've learned in class (or a back-up method of learning material if they didn't get the information in class), but it will give them practice with using textbooks as references, which is itself a critical skill to develop, whether a student goes on to college or the trades.

Unknown said...

"Math professionals, as opposed to education professionals." Call me crazy, but the opinon of EDUCATIONAL professionals is exactly the opinion I would defer to on EDUCATIONAL decisions.

dan dempsey said...

Ananda said:
Perhaps you should also mention that CSHS had the single highest gains on WASL scores statewide.

Here is CSHS WASL Math data:
Year ...... school ..district ..state
2005-06 .... 40.1% 55.7% 51.0%
2006-07 .... 29.3% 50.2% 50.4%
2007-08 .... 42.7% 50.4% 49.6%

Well certainly not the single highest gains for Math WASL scores statewide from Spring 2006 to Spring 2008.

How did you compute that Chief Sealth had the single highest gains on WASL scores statewide?

For what reasons do you believe that the "Discovering Series" will bring improvement?
Here is how valuable I find statements from Principals on issues like these unless they include specifics:
I am with Tom. I value those education professionals as much as NMAP's Dr. Sandra Stotsky.
The Negative Influence of Education Schools on the K-12 Curriculum

June 30, 2008 By Sandra Stotsky, University of Arkansas

The article refers to two general theories driving the pedagogy taught in education schools:

o Constructivism;
o Social justice theory
and their effects.

dan dempsey said...


I will call you crazy. Check the data on Math education USA over the last two decades. Check the achievement gap in Math over the last 12 years in Seattle Schools.

Check the performance of those NSF EHR produced curricula coming from Michigan State University, Western Michigan University, University of Chicago, etc.

Check the results of the UW's NSF funded professional development cubed project at Cleveland High School.

Investigate the depth of the mess here:

dan dempsey said...

Chief Sealth has had greatly improved WASL scores over the last decade in all subjects.

These hardly constitute a reason to adopt the "Discovering Series" or keep the inquiry based math direction of Seattle schools.


dan dempsey said...

Start looking for results instead of Edu-Fluff excuses...

Deferring to the opinion of EDUCATIONAL professionals is exactly why we have such poor math results as a nation.
In conversations with UW math professionals they expect the mathematical inadequacies of incoming freshman to increase. The Core-Plus crowd is on the way from Northshore and East of the Lake schools. 64% of middle schools use Connected Math and largely because of Dr. Bergeson's OSPI influence 85% of elementary schools are using reform math inquiry based materials. Little wonder WASL pass rates for grade 10 hover around 50%.

Try this letter if you missed it:

Hopefully the math improvement attempts by the legislature will have some effect on OSPI.

dan dempsey said...


Great idea trust the education professionals. Let me recommend E.D. Hirsch of Harvard with the Core Knowledge movement and Dr. Sandra Stotsky.

Here is a link to more about the education professionals at the UW etc.

Dorothy Neville said...

What if we were looking at science text adoption and the UW Education department supported a series but the UW science professors said that it was unsound, that it contained bad science, wrong use of science terminology, misrepresented the scientific method?

What if we were looking at History text adoption, and education departments supported a series but history professors were alarmed at the number of factual errors and misleading biases running through it?

Why should we accept a mathematics series with significant mathematical flaws? Oh, I forgot, we already did that; it's called Connected Mathematics. I would be much happier to support Discovering Algebra if I heard overwhelming support from parents of current high schoolers about their impressions of middle school math.

Rose M said...


I agree that education professionals should have a better understanding of teaching methods. They should know the best methods to get kids from counting to calculus.

I have 2 problems with the education professionals in this situation. One is that they have decided to change the final goal. Math. science & engineering depts at universities have set requirements for the math kids need to begin in their college studies. Yet SPS educators have decided they don't like those requirements & do not teach kids to get there.

The other problem I have with the credibility of education professionals is that even using the goals they decided are appropriate for math students, they still can not get most kids to the goal.

dan dempsey said...

It does not look like things are going to get better without more parent involvement.

Take a look at where the Transition Math Project phase 3 is headed.

Seems that Seattle TMP did not head this direction. Thank God.
But probably No Soup for Them.

anonymous said...

If the board adopts the Discovery Series, our students will 3 years of reform math (algebra, geometry, and algebra II).

I have a few questions:

1) Are HS kids that have taken 3 years of reform math prepared for pre-calc, calc and statistics?

2) What type of materials are used to teach these classes? Do they use traditional materials?

3) Are kids that have taken calc and statistics prepared for college level math?

Any info would be helpful...

reader said...

Look, I'm not saying TERC or EDM are the best possible thing. I'm sure there is better... and plenty of room for improvement. BUT, I'm also saying they're not that bad either. The teacher makes all the difference. We're just not going to get around the need for good teachers. We're not going to be able to get around the fact that good parents help too.

Michael Rice is correct in that students need practice. Yes, I want that in a text-book series. But he is wrong in lambasting the district's definition of math. The definition is fine... and fairly irrelevant, especially when you've only got 3 minutes to speak to the board on relevant issues.

Yes, Dan is indeed saying that minorities, in particular, can not learn constructivist math. Please don't make him "publish" the fact that Bellevue hasn't closed the achievement gap yet... then point out a single very very very small case (and at this point, very very very old data) where some direct instruction worked for the poor minorities that were subjected to it. There's no magic bullet.

The fact that Dan taught, *gasp*, one whole year in SPS... kinda says it all.

I'm just saying that university professors ALL have an axe to grind. Math profs, Ed profs, all of them. And as long as I can remember, they've been grinding those axes... even when we had the good ol' math of yore. Lots of people weren't learning that math then either.

dan dempsey said...

In regard to minorities and the achievement gap....

it was said:
The fact that Dan taught, *gasp*, one whole year in SPS... kinda says it all.Among other places since 1968 ...
I taught in South Central LA, Hispanics in Eastern WA, and currently on the Lummi Rez.

The old data you refer to was the largest study in Education History.
http://www.mathematicallycorrect.com/honestft.htmBellevue opened a large achievement gap during the last decade with the use of TERC, CMP, and Core-Plus.

Singapore Math written in English serves native speakers of Tamil, Mandarin Chinese and Malay very effectively, but Ms. Santorno thought she would close the achievement gap with Everyday Math.

Sorry this makes no sense to me.

When was there good ol' days of math?

Take a look at Singapore Math k-10. It does not look like anything I had in school.

It seems that those making some progress with the current k-8 SPS materials have lots of additional non-SPS help. Check the fact that TOPS 8th graders over half of them take an after school algebra class paid for by parents and only use Connected Math in the classroom not in their tuition based after school classes.

Mr Mark Ellis testified at the board meeting and was on the adoption committee but does not teach the after school class. Dr John Lee who started the after school TOPS classes and was rejected when he applied to be on the adoption committee testified against the "Discovering Series".

Look at the results for our best graduates over the last decade at UW:
http://mathunderground.blogspot.com/2008/02/60-uw-faculty-critical-of-current.html Oh right all these UW profs teaching frosh in STEM classes have an axe to grind.

Reader.... have you failed to notice the SPS has enlarged the achievement gap over the last 12 years on an annual basis?
What is your point in defending these ineffective and inefficient materials?

dan dempsey said...

Interesting that the largest most expensive study in the history of education is referred to by Reader as:
then point out a single very very very small case .

In addition the Bureau of Indian Education has grant funding available for the only two math programs that have shown any promise for Indian kids. Lummi has received a grant and this year switched from Everyday Math to Saxon Math ... that kinda says it all...

Here are the Lummi School 4th grade math WASL results.
All years were with Everyday Math:
Year School
1999-00 5.0%
2000-01 6.3%
2002-03 0.0%
2003-04 0.0%
2004-05 0.0%
2005-06 5.9%
2006-07 6.1%
2007-08 9.5%

Get my drift ... maybe Project Follow Through had a clue.
Needless to say on the Lummi Rez., we had more problems than just very poor math books.

anonymous said...

Dan, since you are well informed, can you tell me what material is used for pre-calc, calc and statistics? Is it traditional? If so, how do kids who have taken 3 years of reform math (algebra I, geometry and algebra II) do in these classes? And finally, are kids who take calc and statistics prepared for college level math? Thanks.

reader said...
This comment has been removed by the author.
dan dempsey said...


I do not have all the answers for this.

Here is what I know. In a recent study published by Profs at U Minnesota some of these authors pushed NSF reform materials over the last decade+ into Minnesota schools.

http://mathunderground.blogspot.com/2009/03/aera-research-journal-findings-mach-1.html Finding is NSF funded programs (ie. reform) do not prepare students as well for collegiate math as commercially prepared programs (ie. traditional non-reform).
At Ballard which has by far the best AP Calc test results in the district Nutting uses the traditional Calculus by Larson. Ballard also uses largely traditional texts for pre-Calc to get students ready to succeed.

The District has pushed more kids into AP Calc ready or not. This was because US News and Newsweek were using % of kids taking AP classes as an indicator of quality .. no regard for passing AP test by those magazines.

AP calc test is scored from 1 to 5. With 5 being the highest. At West Seattle A few years ago the average AP Calc test score was below 2.

I have heard the Central Admin wants more kids pushed into AP classes, paying no attention to whether these kids are prepared. The district rationale is harder coarse of study will be good for every student.

The reality is that Central Admin still fails to realize that much of mathematics is hierarchical and that without previous effort and skill development students should not be in AP Calc. I view the pack as many into AP Calc as possible as simply a logical conclusion to the SPS k-8 social promotion policy and the differentiated instruction nonsense.

The word from UW STEM teachers is high school preparation of the incoming freshman continues to decline year by year and with crops of k-12 reform math taught students soon entering it does not look good.
Northshore and many schools east of the lake used and continue to use Core-Plus. CorePlus has been an incredible failure as those hoping to pursue STEM fields in college, are usually unable to do so because of inadequate preparation.

Bobby Knight said:
Many have the will to win but
few have the will to prepare to win.
It seems that the SPS finds preparation over-rated.

reader said...

Dan, I'm not "defending EDM". Are you able to read?

Look, I'm not saying TERC or EDM are the best possible thing. I'm sure there is better... and plenty of room for improvement.
If Saxon is great. Great! But you aren't going to get around the teachers. The curriculum doesn't teach itself. The constructivists have made all those same claims about the "Indians" too. In fact, that was their big reason for starting constructivism in the first place. "We tried this on the Indians, and they got really good at math." Now you're saying the same thing.

At some point, constantly switching from one thing to another is worse than sticking with a less than perfect solution. Teachers will learn how to teach it... if only, we don't switch to something else... and something else... and then something different over here, but not over there, oh I hope you don't transfer there from here.

Do they teach studets with disabilities is Singapore? No, they do not. Do they teach lots of cultures, many of whom do not value education in Singapore? No, they do not. Education is a core value in Asian cultures (mostly Chinese variants in Singapore).

dan dempsey said...


Great Job!!! I get it. I get what you are saying. Thanks for your patience. It will take me a few days to craft an adequate response that explains my thinking.

I do not value what is said from all parties in this Math Conflagration equally.

My reasoning has a lot to do with where the money comes from and how it is used. In addition to those who fake the truth.

If I thought the materials were close enough in quality to each other I would agree with you. For God sakes stick with something.. Have some consistency please.

But I do not think these materials are close in quality. I've spent a few years now gazing at spreadsheets of Seattle, Bellevue, and lots of other district's results and TERC and EDM are very poor and should not be used. I have experience teaching kids this year who are EDM products. EDM should not be used. I've read the NCTM focal points and looked at the EDM goals and the State Math Performance expectations. EDM should not be used. I looked at the TERC text, it should not be used.

Another big reason is the dynamic of funding and the failure to accurately report the real results.

Like I said give me a few days for that.

Thanks for your patience,


dan dempsey said...

Looks like the Roosevelt PTSA will have a presentation on the HS Math adoption 7PM on 4-15-2009.

If anyone attended, was this a discussion? or a its a done deal let us explain the materials to you?

The up down vote on the materials is on April 22, 2009 ...
I think tonight's meeting may be a lobbying effort from DownTown.

Mr Christensen will be the presenter and I do not believe any other RHS faculty knew that math was to be part of the PTSA meeting.

dan dempsey said...

In regard to middle school teacher Mr Mark Ellis and his speaking as the teacher at the presentation of the high school adoption, consider how committees are picked.

Do you find it odd that a middle school teacher was the teacher presenting at the high school adoption?

The really strange part is that Mr Ellis was on the Middle School Committee that picked CMP2.
He was one the Elementary committee that initially picked TERC/Investigations but then went with Santorno's EverdayMath. Now he is on the High School Committee that is picking the "Discovering Series".

How many votes does this guy get?

Lets just say he is really good at filling out those application forms that are blind scored. I am beginning to think there may be a reform math bias.

Of course it may be that he is always picked to be on the committee because he always supports the predetermined outcome. If possible when community volunteers are needed Charlie Mas and Melissa Westbrook are avoided by the district ... Mr Ellis it seems is always picked for math adoptions.
Speaking of Bias.
Ms de la Fuente thinks the mathematicians opinions on the "Discovering Series" is a draw.
Three real mathematicians that have PhD's in math find Discovering mathematically unsound.

George Bright no PhD in mathematics but rather Math Ed who was hired by OSPI to be Dr Bergeson's special math gopher suddenly became an independent mathematician (????)

The UW's Dr Jim King, who has published a book through Key Curriculum Press, finds their materials mathematically sound. Dr King has been the recipient of enough NSF grants to push NSF profession development programs for reform math that anyone who labels him an independent mathematician is just not paying attention.
Independent would be UW Dr John Lee
John Hopkin's Math Dept head Dr W. Stephen Wilson, and Dr Guershon Harel.

You can read what Wilson and Harel had to say here:
http://www.sbe.wa.gov/ in the right hand column under what's new.

Dorothy Neville said...

Dan, don't assume too much. Presupposing such a negative tone makes you look, um, less professional.

The RHS PTSA has been asking different departments to come to a meeting and say hi, what's up, and discuss current issues. So far LA and Foreign Language have come (and both have current issues) and tonight was Math's turn.

Mr Christensen did come and while he was for the adoption, I don't think he was being a tool for the district at all. He seemed earnest and open and admitted that there's controversy. I don't see eye to eye with him on the issue, but he is an experienced, well-regarded teacher and I do take what he said seriously.

His take on it is that Discovering is not that bad, as far as Inquiry texts go. He does see it as a compromise, and that the issue is so polarizing, strict constructivists that do not want any "answers" in the book and traditionalists who want cut and dried math, that it seemed he didn't think another solution was possible.

The thing he added which I haven't heard elsewhere is that IF the adoption doesn't happen, then the money disappears. He seems genuinely worried about losing the opportunity to have an adoption at all, given that there is absolutely no other source of funding.

But I do feel he is confident that RHS can make this work, and that it would be good for the district to have a single text series. I am also confident that RHS will make it work. They will do as he said, work together with the state standards, emphasize some things, de-emphasize others. The teacher is ultimately more important than the text. (and again, there was Ms de la Fuente at the last board meeting, saying that but also saying we don't have enough good math teachers. It's a problem everywhere.)

I wish I could feel confident for the district as a whole. I wish I could feel confident for schools without such a concentration of advanced students. I wish I felt as confident that the Discovering Series can be used as a reference. The little that I have seen seems like it would be a challenge to use it as a reference, but the on-line supplementation isn't bad (although what percent of households have internet access?). And the little that I have seen has some mathematically unsound language. I don't like that, but I don't know if I am being too picky. Mr Christensen and others have spent way more time with the book than I have. I know I am biased because of my ongoing frustrations with Connected Math.

But the teacher's notes at the beginning of the Discovering Alegbra (2, I think) says a lot about inquiry, how it "puts the students in the role of researchers." I just get queasy about that. Doing research well means first learning the language and structure, learning how to argue logically to prove something. If I were in charge of creating an Inquiry based math text, it would look very different.

I don't know if you stayed for the whole meeting last week, but Cheryl Chow did announce that she would be out of town. And there's no proxy vote, so her definite yes vote is gone. Mr Christensen seemed to think the rest of the board was split 3-3 on the adoption.

Dorothy Neville said...

Dan just linked to a website with a
review of the mathematical soundness of a number of high school texts.

an interesting read. Here's a quote from the section on Discovering:

"consistently the text generalizes from empirical observations without attention to mathematical structure and justifications. This empirical-without-proof approach is not unique to the unit on linear function; rather, it is prevalent throughout all the units that have been examined."

This is what I was afraid of. This is what I see in Connected Math. Learning by generalizing examples, without logic. I see students often forming the wrong conclusion with this empirical approach.

dan dempsey said...


Having watch the Elementary school math adoption shenanigans ... I am often times presupposing similar underlying tactics at work here.

I do think that Royce Christensen is top notch, but disagree on his views about reform texts and the impact they have on student learning.

I believe he found TERC acceptable and I do not.

In the Elementary adoption of 2007, Ms Santorno had encouraged me to meet with her rather than sending emails. I sent her an email of questions that needed answering during our coming meeting that she suggested and a meeting date. Then at the IMC meeting she came over to me and said she would never meet with me because I was mistreating her, perhaps because she was a Black Woman.

She would never respond to real serious questions about Everyday Math performance and what the data really showed.

Interesting how she was very cordial one day and then when questions are posed refused to meet.

If playing these kinds of games the way she did in 2007 is professional, please view me as unprofessional.

I filed a complaint with the SEA union and wrote to Raj Manhas, and Seattle got Everyday Math with no Singapore ... (professional??)

ds said...

A couple more bits of info about the Wilson/Harel & King/Bright reviews...

King & Bright's reviews are found in the OSPI report that assessed degree of alignment with WA state standards (a few other things were considered...but 70% of these ratings were based on alignment). Only those textbooks that were found to be in the top 4 for each category (algebra & geometry) were reviewed by K & B. Discovering Geometry was NOT in the top 4 geometry books,
so no one that I know of has written a formal positive review of Discovering Geometry.
The State Board of Ed commissioned a report on the top 4 textbook SERIES from Wilson & Harel. The "top 4" were determined by the overall OSPI rankings (combining algebra & geometry); it actually ended up being the top 3 (which were all algebra-geometry-algebra series) plus the top integrated series. This is the report that criticizes all 3 Discovering texts as being mathematically unsound.

Rose M said...

Elementary school teachers thought they could work with EDM too. Because they thought they would be able to use the text to support their own teaching of the standards. They thought they would be able to do their own calculation practice, use different materials for children who were struggling or who were far ahead, skip parts of the text they found unhelpful.

But then came the pacing guides & fidelity of implementation.

That will be the same for high school teachers.

dan dempsey said...

Rose M,

The fidelity of Implementation talk was very prevalent in May 2007.
Both DeBell and Santorno had great hope for fidelity of Implementation because it was going to make all the difference.

The fact is that "Fidelity of Implementation" means precisely that elementary teachers have limited flexibilty to make student based decisions.

One teacher said if I get a poor evaluation because my kids are not achieving in math ... that will be ridiculous. I need to be allowed to make appropriate decisions for students ... the district does not allow that ... any failure is theirs not mine.

On the way to extending a failure even further if "Discovering" is approved.

Here is where EDM and CMP2 came from: http://mathunderground.blogspot.com/2009/04/is-this-ponzie-scheme.html Dan

hschinske said...

You know, isn't the WHOLE POINT of these inquiry-based methods to be able to work with kids' own input and ideas and such? And isn't that DIAMETRICALLY OPPOSED to using ultra-rigid pacing guides (if this is Thursday, April 16, we must be on page 147)?

This reminds me so much of how bad preschools teach children to be "creative" and "use all their senses in learning" by telling them exactly where to glue the cotton ball on the rabbit.

Helen Schinske

hschinske said...

You know, isn't the WHOLE POINT of these inquiry-based methods to be able to work with kids' own input and ideas and such? And isn't that DIAMETRICALLY OPPOSED to using ultra-rigid pacing guides (if this is Thursday, April 16, we must be on page 147)?

This reminds me so much of how bad preschools teach children to be "creative" and "use all their senses in learning" by telling them exactly where to glue the cotton ball on the rabbit.

(Word verification: ousia, which happens to be Greek for "substance" or "essence.")

Helen Schinske

Dorothy Neville said...

[Hey Dan, about professionalism, you are a little confused. Regardless of the district's behavior, you ought to act professional. So if/when they lapse into the nasty acting, you'll look even better in comparison. A simple little "Hey, anyone go to the RHS PTSA meeting with the math teachers, what happened?" would have sufficed. Remember, just because Socrates was mortal, doesn't make him a man. :) ]

I am not sure all readers appreciate this talk of "empirical observations" and what we mean by "not mathematically sound." Let me try to explain a little. See, there are three different sorts of things one can prove mathematically. A statement can be true Always, Sometimes or Never. There are lots of different ways to argue (ie, prove) one type of statement or another. When you generalize by examples however, one can only prove Sometimes sorts of statements, not Always or Never sorts. So when inquiry based mathematics for K12 spends all (or most) of its time generalizing from example, kids do not learn logical thinking, they do not learn the nature of proof or the structure of mathematics. In fact, it can end up confusing them and leading to false ideas. They are asked to find patterns (a really good thing) but then they are not trained how to evaluate those patterns and prove (or disprove) that one can generalize them. Finding patterns and then figuring out when they generalize is a key mathematician behavior.

But finding patterns and jumping to conclusions is very very bad, it only serves to perplex students who then don't learn when to generalize and when not to, and can make them feel stupid. It's what I see all too often, because simultaneous to this "finding patterns and forming conclusions without proof," kids are taught to guess, guess, guess. Guessing is considered helpful for their self-esteem but what it ends up doing is both obscuring patterns and short circuiting any growth of understanding logic. Look at Sudoku or Kenken. Beautiful puzzles that can and should be solved totally by logical deduction. Guessing will only frustrate and hurt success. These sorts of activities are wonderful for exploring (inquiry based!) how to improve logical thinking. Where do they come from? Japanese math teachers. 'nuff said.

(As Mr Christensen pointed out, strict constructivists want kids to discover on their own a "whole body of knowledge that's already been discovered and proved valid." How much of that is worthwhile, how much a waste of time, how much of it simply confuses things, especially when the teacher is not that well trained on the nature of proof? And the strict constructivists do not want the kids to have access to the knowledge unless and until they discover it themselves. Isn't that like LA teachers refusing to allow kids to use a dictionary? Shouldn't all kids be able to learn new words from context and group discussion? Because of course, once you have discovered the meaning yourself, you are much more likely to remember it than if someone told you what the word meant. Right?)

Historically, K12 math did not demonstrate much in the nature of proof, except in Geometry. Whether or not it is useful for adults to know all the properties of perpendicular bisectors, Geometry has been a useful topic for exploring proof, deductive, rigorous proof of Always and Never statements. Now Geometry has been a love/hate sort of subject. I think it's partly due to different people's learning styles, but also how it's taught. Two column proofs do not have to be a drudge. And proofs do not have to follow a two-column format either. It's just a handy way of representation, making a table. For students who are just learning how to be clear and logical, it can be a useful organizing tool. After high school Geometry, one rarely sees proofs written that way.

So, at the RHS PTSA meeting, I asked about Geometry. Jack Lee had pointed out at the School Board meeting that the Discovering Geometry book does not teach deductive proof until chapter 13. I was concerned, but haven't looked at that text myself. Mr Christensen replied that there are lots of ways of proving things, he recently discovered that himself, a revelation watching a mathematics talk on MIT video. (What he didn't know is that with a BS and MA in math, I knew that already.) What I think he was saying is that while it doesn't look like what we ordinary parents think of as proof --- because it isn't two column --- it is still fine and logical. So, OK, that's a reassuring statement. I haven't looked at the text myself, but if it's true, it's good. Then I get on the internet and find Dan's link to the review of Discovering and find that it's not good. If the non-deductive 12 chapters in Geometry are empirical observation without logical justification --- that's bad. Really bad.

So, this Discovering Geometry seems to maintain the goal of having everyone learn about angles and bisectors, but with mostly observation and generalization. So they focus on the unimportant (the actual geometry facts) and blow off the real reason we teach geometry (the logical reasoning skills).

An example (empirical observation!): I was observing an Integrated 2 class at Eckstein. These were all smart advanced students. The teacher started each class with a challenge problem. One day the problem boiled down to: What's the smallest positive integer satisfying certain constraints? Well, these smart advanced kids all found an integer that satisfied the constraints. They did not use logic; they all guessed. The number worked, bingo, they are done. None of them had actually read carefully enough the "smallest positive" criteria. Well, they had found the smallest one though, by luck. So a student was chosen to demonstrate the solution. And he did. He showed that the number solved all the constraints. Everyone was happy. But, then I raised my hand and asked "The question wanted the smallest answer, is this the smallest?" Some were stymied, but at least one student had some ideas, and after some discussion, they proved that sure enough it had to be the smallest. No two column proof, it was a very useful sort of proof by contradiction . (assume there's a smaller integer that works. Then ______ must be true. However, that cannot be true, therefore the assumption was wrong.) The first half of the exercise -- guessing the answer, observing that it worked -- was simply some practice with factoring. It was only the second half, the discussion leading to a proof, where real learning happened. (Inquiry based! no one told them the proof, they figured it out.)

dan dempsey said...


Thanks for the advice and nice job with the explanation. Geometry should be about Geometry for there is a whole lot going on in Geometry. The idea of number sense is important in Arithmetic so shape sense is important in Geometry.

Geometry is much more than proofs but with no proofs there is only a shell of a geometry class. It is the thinking that is important and beautiful.

Reform Math has been a cash cow for the Universities... this fleecing of the public needs to end. Math k-8 needs fixing, extending its defects to high school would indicate a failure of logical thinking. Hopefully the board members had good Geometry courses.


anonymous said...

Dorothy, can you recommend a really good math tutor that could work with a 9th grade student long term? Or do you recommend a tutoring center (I'm not crazy about Kumon)?

If the district adopts Discovering, I will have to supplement (it beats paying for private school).

We live near Nathan Hale HS.

Rose M said...

Where in Seattle can a middle school student get a good solid high school geometry class over the summer?

Charlie Mas said...

I took Geometry as a freshman in high school. I still think back fondly on the class and the teacher, Mr. Mooko. The class was almost entirely proofs with some calculations of area, volume, and surface area. He was very clear about why we were there. He told us that we may never in our lives ever have to bisect an angle, but that doing proofs would teach us on how to make a multi-step logical argument.

That's the only time a math teacher ever gave me a fully satisfying answer to the eternal question "Why do we have to learn this?"

I also remember that by the 9th grade I was already a de-motivated student and rarely did the reading. As a result, I had to discover nearly all of the theorems for myself (often while standing at the board solving a problem in front of the class). Mr. Mooko would say "Good job, Charlie, but if you had done the reading you could have replaced steps 2 through 8 by just writing 'Theorem 4.2'. Thanks for proving the Theorem for us." Then he would throw a piece of chalk at me.