Friday, December 17, 2010

The Student Teacher said: ....
to which Mike said ...

and Dan supplied a bit of data

As a student teacher, I respectfully disagree.

K-5 in Seattle uses the Everyday Math curriculum, which has proven to be the most effective curriculum in the country.

Constructivist math helps students construct traditonal
[sic] algorithms rather ...than memorize them, thus creating a deeper, more conceptual understanding.

The problem is that veteran teachers don't get it, which in turn leads to parents freaking out. However, this type of math curriculum, if taught correctly, pushes students beyond memorizing formulas towards developing into little mathmaticians

Too many students learn algorithms for testing without having true number sense.

To which Mike replied

Wow… Where to begin?

Dear student teacher,

First, you are to be commended for choosing to be a teacher of children. I genuinely believe there is no higher calling or more noble a cause. Second, you are to be commended for your willingness to engage in respectful dialogue on a topic of paramount importance.

Respectfully, I adamantly disagree with each of your assertions. But I think I understand from where they come, as each of your unfounded contentions have been repeated over-and-over by champions of ed-reform for years. Incessant repetition of a falsehood does not make it true. I urge you, I beg you to subject what you’ve been told & taught by “the experts” to critical examination of your own. Ask for validating empirical data, evidence, and research; discriminate between genuine research and opinion pieces; and seek out and read referenced material.

As for my respectful dialogue, I’ll attempt to address your contentions one at a time.

“K-5 in Seattle uses the Everyday Math curriculum, which has proven to be the most effective curriculum in the country.”

Really? Where’s the evidence and empirical data to support such a statement of proven effectiveness? I suppose the truth of this statement could hinge on your definition of “effective.” If by effective, you mean that the EM curriculum boosts employment in the Seattle area, you may be able to build a case. The need for remedial mathematics at community colleges has skyrocketed, as have math tutoring boutiques in the private sector.

“Constructivist math helps students construct tradit[i]onal algorithms rather ...than memorize them, thus creating a deeper, more conceptual understanding.”


In the first place, EM does not emphasize traditional algorithms. Instead, it emphasizes “focus” or alternative algorithms that have proven less effective or totally inadequate for higher mathematics over time. Secondly, building any classroom on a framework approaching exclusive constructivist pedagogy is child abuse, as it denies the child the benefit of exposure to (direct instruction in) the accumulated wisdom and knowledge of generations over centuries. Thirdly, your statement implies a disdain for memorization (rote learning) in favor of the ed-reformist “holy grail” of conceptual understanding. Conceptual understanding in any particular domain cannot be taught in the absence of the accumulation of knowledge in that same domain. In mathematics, conceptual understanding develops over time as we gradually learn to efficiently manipulate numbers in the abstract, and in turn apply those manipulations to the concrete. It is both counter-intuitive and false to believe that this gradual learning, which due to time constraints must be efficient, can best occur in an environment where students are required to construct or discover for themselves the accumulated knowledge of generations.

“The problem is that veteran teachers don't get it, which in turn leads to parents freaking out.”

Hmmm… So your education has not only led you to a philosophical allegiance to the anti-intellectualism of constructivism, but also to a disdain for the temperance of actual experience (veteran teachers), as well as a contempt for the legitimate concerns of parents. I don’t know how to respond, except to implore you to remember this once you’ve advanced to the position of parent or veteran teacher. Such reflection may enable you to respond to youthful arrogance with patience. Ironically though, your quip does touch on one of the practical problems of these reform curricula. Because the “veteran teachers don't get it”, the adoption of these reform curricula are usually accompanied by requests for enormous amounts of “professional development.” Have you ever wondered who benefits from creating an environment in public education where perpetual “professional development” is the norm? Have you ever questioned why the increase in professional development requirements has run coincident with the decline in American public education?

“However, this type of math curriculum, if taught correctly, pushes students beyond memorizing formulas towards developing into little math[e]maticians.”

I don’t believe there is enough time to teach this type of curriculum correctly. I also don’t believe in mandating the required homogenization of pedagogical techniques, which would be the implication of the first part of your statement. The last part of your statement, again, reflects a disdain for memorization as a tool of learning. Yet, you’ve memorized the talking points of proponents of reform mathematics quite well. Left to your own devises, I wonder if you’d have “developed into a little student teacher” by personally discovering or constructing the philosophical underpinnings of constructivism? No… you were taught, weren’t you?

“Too many students learn algorithms for testing without having true number sense.”

“Number sense” has been defined several different ways. The two most common interpretations have to do with “fluidity & competence” and the personal “dispositions” (confidence) that occur as a result of said competence. I assume, because of how you phrased your statement, that you’re applying the “personal dispositions” definition/interpretation to your use of “number sense.” These two interpretations must be addressed separately, because one is objective and the other subjective.

Fluidity & competence can be accurately & objectively measured (or tested, if you prefer) based on performance.

Personal disposition can only be subjectively assessed; it cannot be objectively measured. Additionally, any subjective assessment of personal disposition must be weighed against an objective measure of performance in order to gauge whether the personal disposition is warranted based upon the objective performance of the student. (It’s just as illegitimate for a student to think he’s good at something if he’s not, as it is for a student to lack confidence but exhibit superior performance.) Students must “learn algorithms for testing” because actual performance is the only objective measure we have to ascertain a student’s development.

In this way, this argument is related to the argument of procedural fluency versus conceptual understanding. Of the two, only procedural fluency can be objectively measured.

-- mike


Seattle adopted Everyday Math on May 30, 2007. EM was put into service September 2007 after professional development of most if not all elementary school teachers. In May 2007, CAO Carla Santorno told the Board that fidelity of implementation was necessary for the EM program to bring good results and said within four to five years the Achievement Gaps for groups of educationally disadvantaged learners would be gone as measured by annual OSPI testing at grade 4.

Such OSPI testing in Spring 2008 showed increased achievement GAPS for Blacks, Hispanics, Asians, American Indians, low income students, and limited English speaking students. Gaps became even larger in Spring 2009.

The Seattle School District since EM adoption required Math to be taught 75 minutes a day everyday. It seems that Mike is correct. Apparently, there is not enough time to teach Everyday Math correctly.

The District adopted Key Curriculum Press' "Discovering Algebra", "Discovering Geometry", and "Discovering Advanced Algebra", on May 6, 2009. Spending $800,000 on books and $400,000 on professional development. The Bethel School District had adopted "EM" and "Discovering" in Spring 2007 and has seen declining achievement. Seattle's grade 10 math OSPI HSPE results in Spring 2010 were disappointing.

"To improve a system requires the intelligent application of relevant data"
-- W. Edwards Deming (1900-1993)

The 2010 OSPI Math tests showed a pass rate for Black students in Seattle schools of

28.2% grade 4 (note the scores during the last three years and this after previous widespread use of TERC/Investigations)

12.5% grade 10 and Sophomore credit standing required to test.

4th Grade Math Black Students

Year ................. District : State
1997-98 WASL : 14.2% : 13.0%
1998-99 WASL : 12.0% : 15.3%
1999-00 WASL : 17.2% : 18.7%
2000-01 WASL : 15.0% : 19.5%
2001-02 WASL : 22.3% : 28.6%
2002-03 WASL : 31.1% : 35.5%
2003-04 WASL : 36.4% : 37.5%
2004-05 WASL : 33.1% : 37.7%
2005-06 WASL : 31.3% : 36.4%
2006-07 WASL : 32.0% : 35.1%
2007-08 WASL :27.6% : 31.3% <== EM begins in Seattle
2008-09 WASL :29.1% : 30.2%
2009-10 MSP .:28.2% : 32.5%

10th Grade Math Black Students

Year ................. District : State
1998-99 WASL .:. 5.4% : 9.5%
1999-00 WASL .:. 8.3% : 11.7%
2000-01 WASL .:. 6.1% : 11.9%
2001-02 WASL .:. 8.1% : 13.0%
2002-03 WASL .:. 7.0% : 14.2%
2003-04 WASL : 11.3% : 16.1%
2004-05 WASL : 12.9% : 20.4%
2005-06 WASL : 21.7% : 23.2% <= Seattle begins
2006-07 WASL : 19.6% : 22.5% .. requiring
2007-08 WASL : 16.0% : 22.2% .. Sophomore
2008-09 WASL : 16.3% : 20.9% .. Credits to Test
2009-10 HSPE : 12.5% : 19.0% <= "Discovering" begins

Bethel School District All students:

10th Grade Math All Students

Year ................. District : State
1998-99 WASL : 21.1% : 33.0%
1999-00 WASL : 26.7% : 35.0%
2000-01 WASL : 26.3% : 38.9%
2001-02 WASL : 23.2% : 37.3%
2002-03 WASL : 28.9% : 39.4%
2003-04 WASL : 31.6% : 43.9%
2004-05 WASL : 39.9% : 47.5%
2005-06 WASL : 39.2% : 51.0%
2006-07 WASL : 36.1% : 50.4%
2007-08 WASL : 35.0% : 49.6% <= BSD adopts Discovering
2008-09 WASL : 30.3% : 45.4%
2009-10 HSPE : 26.5% : 41.7%

10th Grade Math Black Students

Year ................. District : State
1998-99 WASL : 10.1% : 9.5%
1999-00 WASL : 13.4% : 11.7%
2000-01 WASL : 10.2% : 11.9%
2001-02 WASL : 13.5% : 13.0%
2002-03 WASL : 17.8% : 14.2%
2003-04 WASL : 19.7% : 16.1%
2004-05 WASL : 21.4% : 20.4%
2005-06 WASL : 23.3% : 23.2%
2006-07 WASL : 26.6% : 22.5%
2007-08 WASL : 22.5% : 22.2% <= BSD adopts Discovering
2008-09 WASL : 17.6% : 20.9%
2009-10 HSPE : 15.8% : 19.0%

Data obtained from OSPI Report Cards

I have removed two comments below, which were abusive and contained NO Constructive thoughts.

I would like this blog to be not just a source for information but a place for constructive civilized discussion of issues. My thanks to Mr. McCall for his contributions. I apologize to him for the responses of several of those posting comments. Others might wish to read their own comments and consider if they contribute anything to the discussion.

Let me say that my opposition to EDM remains firm. Prior to the EDM adoption by Seattle in May 2007, I analyzed data from all districts using EDM at the time of the 2005 Spring ITBS. What I saw were reasonable scores on ITBS grade three that dropped by grade 6 in every district except 1.

The drops were of 10 points in districts with below 10% Black and Hispanic populations.
In districts between 10% and 20% Black and Hispanic populations the drop was the same 10 points from grades 3 to grade 6.
For Districts above 20% Black and Hispanic populations the drop was 15.5 points.

This is the highly standardized ITBS not the flaky WASL.

The first two years of EDM use in Seattle the math achievement Gaps increased for every subgroup of disadvantaged learner. At the African American Academy at grades 3rd and 4th the WASL math scores fell off the map those two years.


I've removed two comments.
If someone wishes to discuss avenues to improvement great, if not no name calling etc. just read but do not write.

I have always believed that a strong program includes some constructivist activities but delivered in moderation and in a guided way. I remain a strong proponent of Singapore Math.

As Mr. McCall points out below, arithmetic fluency is required for math success. I do not believe from what I have seen that the continual spiraling without emphasizing mastery is delivering the goods for most educationally disadvantaged learners. I have encountered no data to convince me otherwise. Perhaps Mr. McCall, who uses his name (unlike those who had their comments removed), could provide some.


dan dempsey said...

Laura said this:

My response, the neighbor needs to get the facts straight.

1) Everyday Math has not been proven to be the most effective curriculum in the country. In fact, Math Expressions and Saxon have been shown to significantly improve student performance in mathematics according to "What Works Clearinghouse", a unit of the Department of Education. In contrast, Everyday Mathematics has shown insignificant improvement in math scores, and only compared to other constructivist curriculum. This information can be found at "What Work's Clearinghouse" website.

2) Direct Instruction is not just about memorizing algorithms blindly. Teachers are expected to instruct students in the standard and most effective methods of solving math problems in traditional math programs. That includes teaching the students why the math works, using a combination of proofs, examples, practice problems and visual aids to ensure the students understand what they are learning. The memorization comes with the desire to ensure students are fluent with their math facts so that they can more skillful as the math becomes more difficult.

3) Everyday Math does not ensure students construct traditional algorithms, in fact many of the Everyday Math algorithms are non-traditional and confuse students as they try to build math skills from methods that do not work well in algebra.

Your neighbor needs to understand that students are expected to learn mathematics that was developed over thousands of years of "discovery". There is a famous saying, "We stand on the shoulders of giants." Our students need to be carefully taught the discoveries of the past so that they can continue to build on those discoveries in their future. Just as a master contractor teaches an apprentice how to properly construct a home, master math teachers need to teach their apprentices (students) how to properly solve math problems so they will be well trained and effective in the future.

Anonymous said...

Mike and Dan,
Had I known that my short, simple post would have been deconstructed, I would have been more careful. I feel that you’ve made some false assumptions.
Let me rephrase my original post to better show my point….
I am trained in elementary school math instruction, so my comments reflect on this only.
I've experienced both types of instruction and I am learning that effective math pedagogy incorporates math discovery using a cooperative learning model with direct instruction of traditional algorithms. Moreover, I have taught many math lessons using Everyday Math to large elementary level classes in a diverse, urban public school. I feel that EM incorporates this two-pronged approach – and reaches more students to develop better number sense than the way I learned math in the 70's, which was by traditional, direct instruction alone. There are a lot of studies - and meta-analysis of these studies - which back up my assertion, as posted by others on this page. Everyday Math is far from perfect, but I feel it is a positive step in the evolution of math instruction.
I’ve met and observed veteran teachers using EM poorly, and I assume that this is because they have had inadequate training. When I first looked at Everyday Math, I thought, “what the hell is this crap?”. However, since then I’ve taken courses on teaching new math, and now that I have a good understanding of how to implement lessons, I like EM. That being said, I also use a lot of supplementary material to make learning more authentic. In retrospect, my comment from my initial post about veteran teachers is based on limited observations and is unfounded.
I have no disdain for memorization. I taught in South Korea and Indonesia in the early 90’s and I have seen how effective memorization can be. I observed students being drilled on algorithms relentlessly in these countries. Korean students, for example, are given a lot more math practice than in our schools. Furthermore, Korean parents supplement instruction with additional lessons either at home or in after school programs - at a much higher rate than parents in the U.S. The best math students in my class receive supplementary instruction of some form. My problem with memorization as used in U.S. schools is that too many students forget a lot over the summer break - and thus require re-teaching. I think that memorization needs to be combined with discovery – to create a sense of “ownership” of the learning – which increases retention.
I agree that we stand on the shoulders of giants, which I tell my students frequently. I also like your analogy of the master contractor training their apprentice - because it implies that math should be taught with integrity and patience. Using this analogy of the master contractor, should the contractor take advice on how to build from the novice homeowner? That's sort of how this argument makes me feel.
Finally, I would love to know of any resources I can pass on to parents to become more proactive about math instruction. For example, do you know of clubs or groups that provide a framework for supplementary math instruction?
Please read “Elementary and Middle School Mathmatics, Teaching Developmentally” by Van De Walle, J. for detailed information about the effectiveness of discovering algorithms.
Note: to the administrator of this blog, please post as written.

Anonymous said...

Replacing experienced teachers in Title I schools with 5-week wonders and a textbook as bad as Everyday Math only makes sense to racists and billionaire developers.

If public school finally sold itself to the devil, then people will have to find other ways to receive a better education.

I see little purpose in standards based testing except to encourage more failure and violence in school.

If you want chaos, then begin with making your falsehoods look like the truth and finish by making truth itself appear like a falsehood.

Despite dire predictions that fewer students would attend school this year, it never materialized. Instead, our Broad-based curriculum office at the district increased its spending this year by $4 million. How does a district do that and still have a conscience.

Anonymous said...
This comment has been removed by a blog administrator.
Anonymous said...

I've seen the effectiveness of Everyday Math. You can't take physics or chemistry unless you know algebra. Not only do we have a 40% dropout rate, most of the students have been taking extended algebra for 3-4 years. Your typical senior can get past earth science without going to adult school and learning 'traditional' algorithms. Most 'college' students won't finish college, unless they know 'traditional' algorithms. McCall doesn't know what he's talking about.

Anonymous said...
This comment has been removed by a blog administrator.
Anonymous said...

You don't know whether to cry or laugh when you see your best high school student is a junior, from special education, and he's the only person in the classroom that can multiply two digit numbers using Napier's algorithm. That's how I measure the effectiveness of Everyday Math. An education that makes idiots. You couldn't employ these people to work, except for rubbing two sticks together.

Anonymous said...

A student can't multiply, divide, add, or subtract and Everyday Math says they can still be taught how to think.

But how does that serve our society. There is no practical application for educating students to be idiots, except give them money to spend and they will spend it. Tell them to vote and they will vote for the person with the most money and the biggest mouth.

Anonymous said...

What would public education look like if Dicken's Scrooge ran our schools? We've arrived haven't we.