kitchen table math, the sequel

In Waterloo, Iowa, Investigations in Number, Data and Space, is being used and getting rave reviews, according to this article.


Here's a quote taken right from the article. Stop me if you've heard it before:

"Administrators describe the curriculum, published by Pearson Education, as providing rich, problem-based, student-centered lessons that foster inquiry and develop critical thinking skills. They believe the result of developing those skills will be increasing student achievement."

at Out in Left Field

Two memories of this math controversy in SCASD never fail to make me chuckle when I think back on them.  The first was a comment posted on the CDT site after the Ed Mahon wrote his first article on the subject, entitled “The Great Math Debate”.  The commenter wrote, “If you say ‘math debate’ over and over again, it sounds kind of funny.”

The second one happened at a math information session for parents last spring.  The district curriculum staff were telling the parents how much fun Investigations was for their children, and a parent raised his hand and said, “You know, it’s okay if my kids don’t have so much fun if they learn some more math.  They have plenty of fun at home.”

Parents for Quality Math Education

Here!

For all the talking points that Reform Math proponents deploy in response to the general criticisms, I haven't yet seen any talking points that respond to concerns about children on the autistic spectrum. Has anyone else?

Since it's well-documented--and generally agreed--that AS children require structure, direct instruction, and discrete tasks, and that many of them have the potential to excel in math, and since the education establishment's purported missions include (1) mainstreaming and (2) catering to different learning needs, I believe this is a fruitful message to keep plugging.

Barry Garelick:

Investigations and EM both boast about how their programs emphasize mental math. Though they don't seem receptive to the idea of teaching long division. I wonder why not? Long division is an ideal way to hone mental math skills. A problem like 56,098 divided by 84 requires a lot in the way of number sense and mental math. The first step is looking at the maximum number you can have to multiply by 84 and stay under 560. Rounding, 560 divided by 80 would be 7, but a quick glance will tell you that 7 x 84 will be greater than 560, which quickly leads you to "6" for a choice. And so on and so forth. But reformers don't want to hear about all that. It's drill and kill, has no value, and anyway, calculators have made long division obsolete.

Constructivist Learning and Teaching
Douglas H. Clements
State University of New York at Buffalo, Buffalo, NY 14260
Michael T. Battista
Kent State University, Kent, OH 44242



CT Coalition for World Class Math
NJ Coalition for World Class Math
PA coalition for World Class Math
United States Coalition for World Class Math
Parents' Group Wants to Shape Math Standards
Common Core Standards: Who Made the List?

No one would deny that establishing the validity of ideas is critical to mathematics, both for professional mathematicians and for students. But how do people establish "truth"; how can they prove things? According to Martin and Harel (1989), in everyday life, people consider "proof" to be "what convinces me." Most mathematics instruction and textbooks, however, lead us to believe that mathematicians make use only of formal proof -- logical, deductive reasoning based on axioms.

But mathematicians most often "find" truth by methods that are intuitive or empirical in nature (Eves 1972). In fact, the process by which new mathematics is created is belied by the deductive format in which it is recorded (Lakatos 1976). In creating mathematics, problems are posed, examples analyzed, conjectures made, counterexamples offered, and conjectures revised; a theorem results when this refinement and validation of ideas answers a significant question. Hanna (1989) argues that because mathematical results are presented formally by mathematicians in the form of theorems and proofs, this rigorous practice is mistakenly seen by many as the core of mathematical practice. It is then assumed that "learning mathematics must involve training in the ability to create this form" (pp.22-23). The presentation obscures the mental activity that produced the results.

In fact, according to Bell (1976), personal conviction grows out of internal testing and forming a judgment about whether to accept or reject a conjecture. Later, one subjects this judgment to criticism by others, presenting not only the generalization formed but evidence for its validity in the form of a proof. For a mathematician, often this internal testing can take the form of proof as one attempts to perform the socially accepted criticism of one's argument.

In sum, formally presenting the results of mathematical thought in terms of proofs is meaningful to mathematicians as a method for establishing the validity of ideas. However, does proof convince students? Do they see it as a way to establish the validity of their ideas or, as Hanna (1989) suggests, as a set of formal rules unconnected to their personal mathematical activity?

Let me guess.

No?

No, students do not see proof as a way to establish the validity of their ideas?

Is that it?

Conclusion

Ironically, the most effective path to engendering meaningful use of proof in secondary school geometry is to avoid formal proof for much of students' work.

I had a feeling.

By focusing instead on justifying ideas while helping students build the visual and empirical foundations for higher levels of geometric thought, we can lead students to appreciate the need for formal proof. Only then will they be able to use it meaningfully as a mechanism for justifying ideas.
Geometry and Truth
by Michael T. Battista and Douglas Clements

Only then, after sophomore year has come to an end and so has geometry.

Here's a question.

How many sophomores in high school have mathematical ideas?

Following the Palo Alto, I find this comment from "5th grade teachers":

At the 1st Committee meeting: 5th grade teachers preferred SRA and Harcourt over the others (neither book was selected for piloting)

2nd Committee meeting: 5th grade teachers still preferred SRA and had nothing positive to say about Everyday Math ("lacking depth" "hard to figure out" "illogical connection to resources" "disconnect between teaching concepts and student practice")

4th Committee meeting (after piloting): 5th grade teachers continued to dislike Everyday Math by a wide margin grading EDM inferior in all categories (long list of reasons including "not much practice," "extremely hard to navigate," "has a lot of stuff that is not addressed in our standards," "teacher-unfriendly," "hard transition to 6th grade," and "spiraling was too broad and too much for kids.")

And here is a later comment by "reality":

[T]he teachers didn't vote overwhelmingly for EDM in a vacuum. They voted overwhelmingly for EDM instead of EnVisions, which is the TERC offering, isn't it? So given those two choices, and not being allowed to vote for the programs they asked for that were cut out for some reason, they voted for EDM. Not really much of a choice, if you think about it.

Could we please just step back and get some answers about why the fifth grade teachers' input was so resoundingly ignored when the committee narrowed down the choices to a vote? This is not disrespect for teachers. This is asking to be given a rational explanation (and one may exist for all we know) for why those two were the curricula in the final cut.

ignoring parents in Palo Alto
welcome to the Grand Canyon
a teacher-mom on Everyday Math
the plot thickens
enlightenment
Steven H on Everyday Math in Palo Alto
where parents get their information
"reality" in Palo Alto

Parents frustrated over math texts
Teacher committee recommends new math text
Ed Week on the ed wars

interview with my cousin re: her experience with EM

Sad news from PWC, VA. The school board voted to keep Investigations, though that's not how they phrased it. They voted for a "blended approach". Which means Investigations. An excellent summary of the night's events can be found here.

The parents have not given up, however, and school board elections are not far away. There are many disgruntled parents there.

I posted something earlier about Prince William County, Virginia, refuting Pearson's "Evidence of Success" of Investigations. A person in PWC says it better than I did:

"We were told that MI was research proven. Well the research the school board was citing was a document called “Investigations in Number Data and Space: Evidence for Success”. A very diligent parent called every school district in that marketing brochure and most have dropped or are dropping MI. The rest are either heavily funded with large numbers of title 1 schools or very small school districts."

This document is an incredibly important indictment; not only against Investigations but against the marketers selling this snake oil.

A blogger named Black Velvet Bruce Li has been making YouTube videos serving as a documentary of the proceedings of the Prince William County School Board. His latest addresses the above mentioned document.

The parents against "Investigations in Number, Data and Space" in Prince William County, Virginia, have been busy lately. Some of them put together a well written report refuting the "success stories" about Investigations touted by Pearson Publishing. The report has been posted on the Teach Math Right web site, and can be downloaded here.

Towards the end of the report in the section called "Success Stories" there are emails and records of phone conversations with people in the school districts that were touted by Pearson as having success with Investigations. They were fairly candid in their emails--perhaps they didn't know just how public this report was going to be. One of my favorites is this one:


Fairfield City School District, OH - Elementary Curriculum Coordinator:

"I did ask teachers to keep their thoughts to themselves and not express their dislike of the program to the parents. And that actually worked. I told them they could have the parent call me or they could say whatever they wanted about the program when we had our PDs [professional development]. I asked them to do their venting any way but [not] with the parents and the children. Another thing in our favor was that the school that did the pilot was one of our lower achieving schools, but their test scores went up significantly."
[Email of 2/9/09]

Pay no attention to the man behind the curtain!

In a December 19, 2008 letter to the editor of the Frederick News Post, Steve Wilson, a math professor from Johns Hopkins University, issues a warning "not to the newspaper or to the board or the teachers, but to the parents. If your child goes to a school that uses TERC Investigations, you should understand that it means your child's school has abdicated its responsibility to teach your child mathematics. By doing so, the responsibility now rests with the parents. Good luck."

Such a letter has long been overdue. Hats off to Dr. Wilson.

Update: Independent of his letter to Frederick News Post, Dr. Wilson has been invited to be on a panel with other mathematicians and scientists to talk at Sidwell Friends School in mid January. The topic is on the mathematical skills, background and preparation necessary for success in mathematics and related mathematics fields in college. For those who don't know, Sidwell uses Investigations as well as Everyday Math. Most everyone knows, I think, that the Obama kids will attend Sidwell. And if you haven't seen it, I wrote about this here. And yes, Dr. Wilson intends to talk about Investigations during the panel discussion. Wish I could go but I think it's open only to parents of students who attend Sidwell.

A parent and I recently started up a Continental Math League team at our school, which uses Investigations math.

Commenter SteveH said in another thread:

We're all trying to find the right angle or leverage to create the most change. Perhaps [Prof. Wu] can change the thinking at the NCTM level, I don't know, but I don't think he will have much effect at the local level.

I find this an interesting point to elaborate on. I understand Steve's point, but I don't know if I agree: Steve, what do you think created the perspective at the local level?

Personally, from my outsider perspective, it looks to me like all of the local changes in our school board to disasters like Everyday Math or TERC came from the top level. They came from national boards. They came from national foundations, big things like Gates, etc. And overwhelmingly, the ideas came to them from ed schools' ideas having infiltrated the very top of the food chain, and that food chain is now pushing down down down to the local level.

I cannot IMAGINE a situation where a local public school board change is made without the national ethos changing first. That's why it takes privates or charters or any other structure to just get decent textbooks.

But maybe I'm wrong. What do you all think? I'm not a teacher in the schools. For those who are, where did these changes come from? Top down? Has ANY change come bottom up? What can an individual teacher or even principal do? What would it take to make a change at the local level if philosophies on the national level aren't changed?