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Entries from ConnectedMath

TitlesOfConstructivistMathCurricula 19 Jul 2005 - 01:46 CatherineJohnson

Jo Anne Cobasko has taken the time to construct a complete list of NCTM standards based math programs.

update: Department of Corrections

This list is David Klein's handiwork, not Jo Anne's.

Thank you, David! (For everything you do.)

All of us should keep this handy, because none of these programs ever calls itself constructivist, and schools don't seem to advertise this piece of information, either.

When I first raised the issue of TRAILBLAZERS being a constructivist curriculum with a teacher on the textbook selection committee, she looked at me blankly. I got a number of those blank looks before I discovered that everyone in the school knows what the word constructivism means, and knows what a constructivist curriculum is.

The reason I know this is that I finally read the original committee report, which states explicitly that the new curricula must have a constructivist approach with modeling. I was a little behind the curve there.

Elementary school

Everyday Mathematics (K-6)
TERC's Investigations in Number, Data, and Space (K-5)
Math Trailblazers (TIMS) (K-5)

Middle school

Connected Mathematics (6-8)
Mathematics in Context (5-8)
MathScape: Seeing and Thinking Mathematically (6-8)
MATHThematics (STEM) (6-8)
Pathways to Algebra and Geometry (MMAP) (6-7, or 7-8)

High school

Contemporary Mathematics in Context (Core-Plus Mathematics Project) (9-12)
Interactive Mathematics Program (9-12)
MATH Connections: A Secondary Mathematics Core Curriculum (9-11)
Mathematics: Modeling Our World (ARISE) (9-12)
SIMMS Integrated Mathematics: A Modeling Approach Using Technology (9-12)

Programs explicitly denounced by over 220 Mathematicians and Scientists:

Cognitive Tutor Algebra
College Preparatory Mathematics (CPM)
Connected Mathematics Program (CMP)
Core-Plus Mathematics Project
Interactive Mathematics Program (IMP)
Everyday Mathematics
MathLand
Middle-school Mathematics through Applications Project (MMAP)
Number Power
The University of Chicago School Mathematics Project (UCSMP)

printable page

Thanks, Jo Anne, for taking the time to do this!

key words:
DavidKlein
listofconstructivisttextbooks
constructivist textbooktitles
NSFfundedcurricula

ItsAlwaysWorseThanYouThink 16 Sep 2006 - 14:43 CarolynJohnston

(a hat tip to Catherine, whose family motto is the title of this post)

Today was Ben's first regular day at his new middle school (yesterday was officially Transition Day, for 6th-graders only). He came home pretty happy; they are helping him with his organizational stuff, he is coping with his locker, and he doesn't have any homework yet. He is enjoying feeling like a big kid. Life is pretty good.

I went to pick him up at the end of school; he wanted to give me the grand tour of his teachers and classes, but we didn't have enough time to do the whole thing. I did ask him to take me to his math teacher, so I could shake her hand and tell her that I'd chosen this middle school because I thought it had made a good choice in math curriculum (having chosen Prentice Hall's Math Courses 1 through 3), and that I'd fought like heck to get Ben into their school for just that reason, and was commuting for a half hour in the morning in order to get him there.

So Ben and I went into his math class, and I introduced myself, and stuck out my hand and smiled, and got about halfway through my spiel when I noticed that in back of her there is a stack on the floor of Connected Mathematics pamphlets. So my final sentence actually came out something like--

"... I really approve of the curricular choice you've made and -- what curriculum are you using ???"

It turns out they are using a hybrid curriculum: every unit will be taught using both Prentice-Hall and Connected Mathematics.

A little background first: Connected Mathematics is an extreme example of a constructivist mathematics curriculum that our school district has adopted (in fact, our SD was an early adopter of Connected Mathematics). I battled long and hard last year to get Ben into a middle school that used a traditional mathematics curriculum instead of Connected Math. I had tearful phone conversations and hot-tempered meetings over this issue.

Whether or not I think Connected Math is a reasonable math curriculum has not been an issue in my fight to have Ben learn math from a traditional curriculum. Ben has special needs, and won't have a lot of employment options; he will need a strong math background in order to have a trade as an adult.

In grade school, Ben did extremely well in Saxon math for the first 3 years; but for the last two, the school switched to a semi-constructivist curriculum (Everyday Math), and Ben ceased to thrive. He didn't cope well with the emphasis on verbal explanations, the games and group exercises, multiple methods for doing calculations, and constant jumping from topic to topic. He went from being completely independent in math class to requiring an aide on a daily basis (our story was mentioned in Linda Seebach's recent article on KTM in the Rocky Mountain News).

When we were discussing Ben's options for middle school, everyone agreed that he needed a traditional curriculum. I open-enrolled him into this school in order to ensure that he would get one, and battled the school district when it looked as though he would not get into it.

Now I find that the school I thought -- was in fact assured -- had a traditional math curriculum actually has a hybrid curriculum which incorporates Connected Math. Connected Math is so purely constructivist that it makes Everyday Math look tame.

Here is the Mathematically Correct review of 7th grade Connected Math (and the many reasons why it received an F).

Here are descriptions of the units in 6th grade Connected Math and 7th grade Connected Math. Read these to get a feel for what kids spend their time doing in Connected Math.

I attended a new parents session at our neighborhood middle school in which Connected Math was discussed. We were told that Connected Math was generally not well liked by parents, who found it impossible to help their kids do the problems because "the style in which it is taught is so different from the rote way in which parents have typically learned math". I have a Ph.D. in math, and taught and tutored math at the college level for ten years; this kind of prevarication doesn't impress me. I know what Connected Mathematics and similar curricula do; they leave college students weak, and utterly without math skills.

We have not yet decided what to do; fortunately we have the weekend to think this over.

worsethanyouthink

ObjectingToConnectedMath 30 Aug 2005 - 16:01 CarolynJohnston

Ben came home today with a Connected Math 'assignment' that said only the following:

"List all first moves that allow your opponent to score only 1 point: 1 to 99."

There was no explanation of the underlying game, and Ben couldn't clearly explain what the game was about, although he seemed to feel that he understood it.

The assignment, it turns out, is from the first pamphlet in the Connected Math 6th grade series. Here's what Dr. Betty Tsang (doctorate in high-energy physics, by the way) has to say about that pamphlet:

1. Prime Time: Factors and Multiples
Mainly a game book but unfortunately, a boring game book with factors. The material is very boring for a regular 6th grader who learn most of these materials in 5th grade. For a curriculum that stresses on real world problems, most of the problems are not real life problems. For example, there are exercises to discover abundant, deficit and perfect number which are interesting numbers but have no application in life -- most scientists and mathematicians have not heard about them. This is also the unit where students are asked to make posters about numbers (including my favorite number). Points are given for creativity such as writing a poem. The last chapter on the locker problem is interesting. However, if the student is smart, he/she will realize that without working hard there is a 50% to be correct just by guessing.

(Click here to get reviews of the rest of the pamphlets).

Apparently, in Connected Math, each pamphlet is supposed to take 4 weeks to cover: that's 4 weeks of some factor game, the nature of which is apparently to be kept a secret from parents.

I don't know exactly what I'm going to do yet, but I'm going to do something. There is no way that, after all I did last year to try to get Ben into a decent math program, I'm going to stop trying now.

A buddy of mine came across this parent letter about Connected Math tonight when he went hunting for information about it. It's a valuable document, because it includes line-by-line rebuttals by a presumably knowledgeable Director of the progressive math project.

If you want to take your objections about a fuzzy math curriculum to your school, these are the arguments you have to be able to address. Don't be knocked out of the running by some show-stopper about research supporting a constructivist math curriculum.

For example, here's a parent concern about Connected Math:

The reading level and lack of examples is very difficult for some of the children. The children are not given the concrete foundation that many of them need to be successful with math.

and here is the expert's rebuttal:

The lack of "worked examples" is part of the CMP instructional philosophy that aims to get students more responsible for their own learning and thinking. It is not wrong unless results of student achievement studies were to show that students taught from this approach learn less than students taught from a traditional demonstration and practice approach. There will undoubtedly be some school situations where test scores decline after CMP adoption (though even in those reported situations one has to be careful to check that no plausible alternate explanations for decline are present). However, the experiences in many school district across the country do not in any way support the claim that a decline in test scores is the normal or even common consequence of CMP adoption).

Note how the author of the rebuttal places the burden of proof of inadequacy on the questioners. Connected Math is to be allowed to fail our kids unless someone can prove that all the environmental conditions under which it was used were perfect. CMP is innocent until proven guilty.

Here is another parent objection:

In summary, North Penn has decided to replace the 8th grade Pre-Algebra program with a program called Connected Math. Traditional Pre-Algebra will not be an option for our 8th grade students.

and another rebuttal:

This decision is well-supported by research, expert panel reviews and international studies. The Third International Mathematics and Science Study amply documented that American eight grade mathematics students were not competitive internationally -- even the better students werea not as competitive when matched with other industrialized countries's better students, See: http://www.rbs.org/mathsci/timss/index.shtml. This gap in performance has been a long standing concern. See "A Nation at Risk" report in 1983 http://www.gphillymath.org/NationalResearchStudies/NationRisk.pdf.
The National Council of Teacher of Mathematics (NCTM) first published their Curriculum and Evaluation Standards in 1989 in response to these international studies. The standards call for more algebra, geometry, statistics and probability in the middle grades focused on students performing complex problem solving and developing mathematical reasoning. These NCTM standards were updated in 2000. See http://standards.nctm.org.
In January 1999, Pennsylvania State Board of Education adopted state mathematic standards similar to those of NCTM. See http://www.pde.state.pa.us/k12/cwp/view.asp?a=85&Q=74000#CHAP4.
An expert panel review commissioned by the American Association for the Advancement of Science (AAAS) performed and exhaustive review of middle school mathematics text books. Only four were rated highly. Connected Mathematics was the top rated. See. http://www.project2061.org/tools/textbook/matheval/default.htm.

Note that this statement implies that the results of the TIMSS study support Connected Math, but they offer no evidence that this is so. In addition, although they state that CMP is supported by research, they offer no citation; only a report of a panel review. The What Works Clearinghouse does not report any research done on CMP that fully meets its evidence standards.

In fact, one might reasonably ask why we don't adopt the curriculum that was used by the country that was top-performing on the TIMSS, which was Singapore. We could do it: the curriculum is marketed in the U.S. as Singapore Math.

Talk about a research-based, proven winner.

ConnectedMathProjects 14 Sep 2005 - 09:20 CarolynJohnston

While trolling around tonight (having googled "My Special Number"), I came across the Connected Math Project curriculum site. One of its pages has descriptions of all of the Connected Math projects.

If you're a parent of a Connected Math kid, just starting to get concerned, a thorough perusal of just this one page would be an excellent education.

I'll be in Washington the next couple of days, but will check in as often as I can (hopefully every evening)!

My Special Number page - hand in assignments here
complete list of Connected Math projects
My Special Number, part 2
All Vlorbik All the Time
Brenda's special number

ConnectedMathProjectList 14 Sep 2005 - 16:58 CatherineJohnson

I'm going to have to pace myself.

One week into the new school year and I'm already fuming. The Connected Math page Carolyn found hasn't helped.

It's worth reading the whole thing.

Here's a project that caught my eye:

Bits and Pieces II
Ordering from a Catalog
Students select items from a catalog and fill out an order form, calculating shipping, tax, and discounts.

That's special.

Susan S says....

Boy, they seriously need to update to more 21st century skills. A better world application might be to go to Amazon.com and click on your own special one-click button. Why should life be so complicated?

BenAndSaxon 24 Sep 2005 - 20:49 CatherineJohnson

way to go--

I'm relieved, I have to say. I've been semi-sanguine about the possibility of having two math curricula in your child's life, a fuzzy one at school & a non-fuzzy one at home.....but the fact is, I haven't (really) had to face that situation.

Last year, in 5th grade, Christopher had SRA Math at school, and Saxon Math 6/5 at home. SRA Math is a very tough textbook to teach from (impossible for me, and experienced teachers have told me the same). But it's not hardcore fuzzy.

David Klein points out that most U.S. textbooks are fuzzy to some degree. That was certainly the case with SRA. Time and again I'd read a passage--this was when I was just setting out to reacquaint myself with math--and not have a clue what it meant. Invariably this was because the text would lay out a couple of observations and then pose a question to the student, who was supposed to draw the appropriate conclusion.

I remember one day I was trying to figure out how to find the equation for the slope of a line, and there was just no way. Finally my neighbor came over, read the passage, and said, 'You'd have to know how to do it to understand this explanation.' Then she showed me how.

Still and all, SRA Math wasn't a b*s book. Not at all. The math was real, and Christopher had two good teachers who'd had plenty of experience getting math into kids' heads in spite of the problems.

I'm pretty sure that in Christopher's case it was a net plus that he had two separate math curricula. He had far more time-on-task, and he had the benefit of seeing the same subjects from slightly different vantage points (which always helps me, and is probably good for everyone).

But I wasn't having that feeling about Ben at all. SRA & Saxon, OK. Connected Math & Saxon? Blech.

So, long story short, I was getting worried about Ben. I'm glad Connected Math is gone.

Saxon into the breach

I keep coming back to Saxon Math.

I've now read quite a few negative assessments of Saxon, by people whose judgment I respect. These are folks on the web--a couple of obviously intelligent homeschoolers, as well as Robert, who writes the brightMystery blog. Robert told me he wants to like Saxon, but just does not--and that students who come to his college courses having been homeschooled in Saxon aren't ready. (That's a paraphrase, so take it with a grain of salt.)

I have misgivings myself. Sometimes I worry Saxon is TOO 'structured'; I worry about pattern training--that Christopher is going to be a Saxon Boy who can only do Saxon Problems typed in Saxon Font.

Thus far that has not been the case. As far as I can tell, all of Christopher's Saxon knowledge has transferred to SRA (and, now, to Prentice Hall).

Other times I've felt the Saxon books are too scattered & fragmented. The fragmentation of topics is a deliberate strategy on Saxon's part, the intention being to use the principles of spaced repetition and distributed practice. That makes sense, but when I taught the Primary Mathematics Grade 3 chapter on fractions to Christopher and his friend Greg it was so much more satisfying and rich, or seemed so.

So.....I've been a heavy-duty Saxon user; I owe Christopher's move to Phase 4 math to Saxon 6/5. And I know the knowledge he's gained from Saxon is conceptual as well as procedural.

But in spite of all these good things, I have Nagging Doubts.

Usually I pay attention to Nagging Doubts. But in this case I think my doubts are either wrong or, more likely, misdirected. Because I keep coming back to Saxon every time I'm in trouble, and Saxon keeps bailing me out.

Saxon vs Dolciani

Take this week.

Christopher has another quiz today, on algebraic expressions.

I was reading along in Prentice Hall, which said that in an expression like x + 7 the x and the 7 are terms.

In an expression like 2x + 7, 2x and 7 are terms, and 2 is the coefficient.

Well, right away I was confused.

Does a term mean you're either adding or subtracting?

Does multiplication mean you don't have a term, you have a coefficient?

That seemed wrong.

So I got out my copy of Mary Dolciani's Pre-Algebra: An Accelerated Course.

I'd been thinking, OK, I'm done with Saxon. There are just too many negative opinions out there, Mary Dolciani's a genius, my neighbor's son liked Dolciani's book, it's shorter than Saxon & we're pressed for time......this year I'm going with Dolciani.

She was no help at all:

In the expression 9 + a, 9 and a are called the terms of the expression because they are the parts that are separated by the +. In an expression such as 3ab, the number 3 is called the numerical coefficient of ab.

Saxon on coefficients

Back to Saxon.

Saxon 8/7 has an entire lesson on algebraic terms. Lesson 84, page 571. I haven't read it yet--I've skimmed--but it's obvious that when I do, my question will be answered.

Here's how he opens:

We have used the word term in arithmetic to refer to the numerator or denominator of a fraction.

Right off the bat, he's made the smart metacognitive move. We have used the word 'term' to refer to numerators and denominators, and it's a good thing to point this out to the student, because otherwise, at some point (probably not now, but later on, when it will really ball things up) the student is going to think, Wait! Doesn't TERM mean DIVISION? Does it mean FRACTION? Does it mean NUMERATOR & DENOMINATOR?

OR WHATTTTTTT?????????

I'm going to go out on a limb and say that Saxon Math is the most metacognitively aware textbook I've encountered to date. Constantly, the books remind you of what you have learned, and point out to you that you are now learning an extension of that concept or you are learning a new and possibly quite different meaning of the same word.

Back to Lesson 84.

Next the book has a table of monomial, binomial, and trinomial algebraic expressions. Wonderful.

THEN the text says:

Terms are separated from one another in an expression by plus or minus signs that are not within symbols of inclusion.

Thank you, John Saxon. I needed that.

More examples follow, and eventually we get to this:

Each term contains a signed number and may contain one or more variables (letters). Sometimes the signed-number part is understood and not written. For instance, the understood signed-number part of a^2 is +1 since a^2 = +1a^2. When a term is written without a number, it is understood that the number is 1. When a term is written without a sign, it is understood that the sign if positive.

Perfect.

At least, perfect for me. What do you think?

deer in the grass

Martine (nanny) just said, 'That one is dark.' She was looking out the window.

So I looked out, too, and sure enough: the young deer grazing in our lawn is darker than the young deer who was living here a month ago.

But Martine thinks it's the same one. She thinks they get dark in the fall.

It's probably time to give him a name.

(a^2 means a squared - right?)

update

Just had an email from Barry re: Saxon Math.

The story problems!

Barry reminded me: they're dreadful. They're just wildly too-easy.

I had meant to put that in the original post, and forgot.

However, the story problems aren't the reason for my 'nagging doubts'.....the story problems are an obvious problem you can remediate easily through supplementation.

It's the other stuff.....

MySpecialNumberPart2 21 Dec 2005 - 01:38 CarolynJohnston

For those of you who've been wondering, as I did, what the Connected Mathematics curriculum's My Special Number project could possibly be trying to get at, I've posted a sample essay at the Official KTM My Special Number webpage. It's Ben's essay; he had it for a class project last week.

I still don't know what the point of the project was, but now at least I know what the result looks like.

Ben's exactly right; at the time he wrote the essay, it was exactly 48 months to his 16th birthday and the first legal opportunity he'll have to get his driver's license. I'm a bit alarmed that he's tracking it so precisely.

My Special Number page - hand in assignments here
complete list of Connected Math projects
My Special Number, part 2
All Vlorbik All the Time
Brenda's special number

MySpecialNumberPart3 27 Sep 2005 - 16:08 CatherineJohnson

My special number
by VlorbikDotCom

6 = 1 + 2 + 3.
6 = 1 * 2 * 3.
6 connects me to my world.
i like clipper ships.

Carolyn and I are waiting for the rest of you to hand in your assignment.

My Special Number page - hand in assignments here
complete list of Connected Math projects
My Special Number, part 2
All Vlorbik All the Time
Brenda's special number

MySpecialNumberPart4 25 Oct 2005 - 16:33 CatherineJohnson

Brenda has handed in her project:

Well, it's not my special number, but I hear that "three... is a magic number." Sorry, couldn't resist -- I was raised on Schoolhouse Rock.

yay Brenda!

Although Brenda did not fulfill the assignment, I am awarding full credit for her demonstrated ability to communicate and make connections.

My Special Number page - hand in assignments here
complete list of Connected Math projects
My Special Number, part 2
All Vlorbik All the Time
Brenda's special number

WhatIsConstructivism 14 May 2006 - 17:18 CarolynJohnston

AndyJoy asked on this thread: Can someone explain extreme constructivism to me? Is the problem that proponents never want to introduce the standard algorithm for a problem or make children memorize facts?

The short answer is yes, but for the record, here is a fuller explanation. I think the best quick introduction to constructivism and its recent history in U.S. educational practice is Barry Garelick's An A-maze-ing Approach To Math, which appeared in Education Next this year. I'll excerpt a little piece of it to answer Andy's question, entirely without Barry's permission (but hopefully with his blessing).

Discovery learning has always been a powerful teaching tool. But constructivists take it a step beyond mere tool, believing that only knowledge that one discovers for oneself is truly learned. There is little argument that learning is ultimately a discovery. Traditionalists also believe that information transfer via direct instruction is necessary, so constructivism taken to extremes can result in students' not knowing what they have discovered, not knowing how to apply it, or, in the worst case, discovering (and taking ownership of) the wrong answer. Additionally, by working in groups and talking with other students (which is promoted by the educationists), one student may indeed discover something, while the others come along for the ride.
Texts that are based on NCTM's standards focus on concepts and problem solving, but provide a minimum of exercises to build the skills necessary to understand concepts or solve the problems. Thus students are presented with real-life problems in the belief that they will learn what is needed to solve them. While adherents believe that such an approach teaches "mathematical thinking" rather than dull routine skills, some mathematicians have likened it to teaching someone to play water polo without first teaching him to swim.
The Standards were revised in 2000, due in large part to the complaints and criticisms expressed about them. Mathematicians felt that the revised standards, called The Principles and Standards for School Mathematics (PSSM 2000), were an improvement over the 1989 version, but they had reservations. The revised standards still emphasize learning strategies over mathematical facts, for example, and discovery over drill and kill.

So how does this fine-sounding idea play out in the classroom? Kids tend to spend too much deriving everything from first principles. What gets sacrificed is time spent learning advanced skills, as Barry shows:

Concept still trumps memorization. Textbooks often make sure students understand what multiplication means rather than offering exercises for learning multiplication facts. Some texts ask students to write down the addition that a problem like 4 x 3 represents. Most students do not have a difficult time understanding what multiplication means. But the necessity of memorizing the facts is still there. Rather than drill the facts, the texts have the students drill the concepts, and the student misses out on the basics of what she must ultimately know in order to do the problems. I've seen 4th and 5th graders, when stumped by a multiplication fact such as 8 x 7, actually sum up 8, 7 times. Constructivists would likely point to a student's going back to first principles as an indication that the student truly understood the concept. Mathematicians tend to see that as a waste of time.
Another case in point was illustrated in an article that appeared last fall in the New York Times. It described a 4th-grade class in Ossining, New York, that used a constructivist approach to teaching math and spent one entire class period circling the even numbers on a sheet containing the numbers 1 to 100. When a boy who had transferred from a Catholic school told the teacher that he knew his multiplication tables, she quizzed him by asking him what 23 x 16 equaled. Using the old-fashioned method (one that is held in disdain because it uses rote memorization and is not discovered by the student) the boy delivered the correct answer. He knew how to multiply while the rest of the class was still discovering what multiples of 2 were.

Now, consider the constructivists' argument for allowing this lack of 'domain knowledge' to persist -- kids develop deeper understanding, 21st century skills, bla bla bla -- after having read KDeRosa's "Terminator essay" on math education.

That essay just puts this nonsense to death, don't you think?

p.s. from Catherine

I found the smart constructivism post.

Here are the 2 best passages.

Smart constructivism says:

A common misconception regarding 'constructivist' theories of knowing (that existing knowledge is used to build new knowledge) is that teachers should never tell students anything directly but, instead, should always allow them to construct knowledge for themselves. This perspective confuses a theory of pedagogy (teaching) with a theory of knowing. Constructivists assume that all knowledge is constructed from previous knowledge, irrespective of how one is taught (e.g., Cobb, 1940)--even listening to a lecture involves active attempts to construct new knowledge.**

Radical constructivism says:

It is possible for students to construct for themselves the mathematical practices that, historically, took several thousand years to evolve.

MySpecialNumberPart5 25 Oct 2005 - 18:25 CatherineJohnson

Go here

I think I'll have my special number be 5

PenfieldInTheNewYorkTimes 17 Nov 2005 - 15:02 CatherineJohnson

Ken strikes gold:

'Innovative' Math, but Can You Count?

LAST spring, when he was only a sophomore, Jim Munch received a plaque honoring him as top scorer on the high school math team here. He went on to earn the highest mark possible, a 5, on an Advanced Placement exam in calculus. His ambition is to become a theoretical mathematician.
So Jim might have seemed the veritable symbol for the new math curriculum installed over the last seven years in this ambitious, educated suburb of Rochester. Since seventh grade, he had been taking the "constructivist" or "inquiry" program, so named because it emphasizes pupils' constructing their own knowledge through a process of reasoning.
Jim, however, placed the credit elsewhere. His parents, an engineer and an educator, covertly tutored him in traditional math. Several teachers, in the privacy of their own classrooms, contravened the official curriculum to teach the problem-solving formulas that constructivist math denigrates as mindless memorization.
"My whole experience in math the last few years has been a struggle against the program," Jim said recently. "Whatever I've achieved, I've achieved in spite of it. Kids do not do better learning math themselves. There's a reason we go to school, which is that there's someone smarter than us with something to teach us."
Such experiences and emotions have burst into public discussion and no small amount of rancor in the last eight months in Penfield. This community of 35,000 has become one of the most obvious fronts in the nationwide math wars, which have flared from California to Pittsburgh to the former District 2 on the Upper East Side of Manhattan, pitting progressives against traditionalists, with nothing less than America's educational and economic competitiveness at stake.
In these places and others, groups of parents have condemned constructivist math for playing down such basic computational tools as borrowing, carrying, place value, algorithms, multiplication tables and long division, while often introducing calculators into the classroom as early as first or second grade. Such criticism has run headlong into the celebration of constructivism by the National Council of Teachers of Mathematics and such leading teacher-training institutions as the Bank Street College of Education.
The strife has taken on a particular intensity here in Penfield, perhaps, because the town includes an unusually large share of engineers and scientists, because of the proximity of companies like Xerox, Kodak and Bausch & Lomb. Skilled themselves in math, they have refused to accept the premise that innovation means improvement, and in their own households they have seen evidence to the contrary.

This is about the worst I've ever seen school officials come off in a news article.

Susan Gray, the superintendent, attributed the criticism of the math program to "helicopter parents" who are accustomed to being deeply involved in all aspects of their children's lives. "Because the pedagogy has changed, the parents who knew the old ways didn't know how to help their children," she said. "They didn't have the knowledge and skills to support their children at home. There's a security in memorization of math facts, and that security is gone now."

helicopter parents

unbelievable

She opened her mouth and said helicopter parents to a reporter.

Helicopter parents and a whole lot more; every word is hostile, belittling, and contemptuous—and she got busted for it.

Next paragraph:

YET many of the dissident parents have extensive math backgrounds and thus the ability to criticize the curriculum. It is also true that most of them tolerated the constructivist program for its first several years, until bitter experience drove them into rebellion.

The article closes on this note:

Still, in the math wars, tweaking around the edges does not settle the issue. The dispute is fundamental. To its advocates, constructivist math applies the subject to the real world, builds critical thinking and rescues classes from numbing repetition.
But to those parents in Penfield and elsewhere - who have children in junior high unable to do long division or multiply two-column numbers, who pay for private tutors or sessions at traditionalist learning centers like Kumon, who wonder why there are so many calculators and so few textbooks - the words of a recent graduate to the Board of Education ring tragically true.
"My biggest fear about going to college," Samantha Meek said at a meeting last spring, "is attending introductory math courses How am I going to be able to explain to my professors that I do not understand what they are talking about, that I do not have the same math background as the rest of the students, and that I cannot do mental math and can barely do it with pencil and paper?"

Wipeout.

Susan Gray is probably trying to remember how to walk and talk right about now.

one more thing
So Ed was going on about how Nicolas Sarkozy had no business calling the rioting beurs "thugs," and how destructive that is, throws gas on the fire, etc.

OK, he's right. When you've got urban riots happening, it's almost certainly not the best strategy to call the rioters thugs.

Ditto for school superintendents.

Memo to Susan Gray.

When you're in the middle of the Math Wars, helicopter parents is the wrong choice of words.

International Red Cross Symbol for Guess and Check

update
There's a link to the Penfield web site on the sidebar: Teach Us Math

Letter to the Editor

AnotherCMPStory 14 Nov 2005 - 14:22 CarolynJohnston

This was posted on the PenfieldInTheNewYorkTimes thread today by CharlesH.

In the spectrum of mistakes made in the Connected Math series, this is at the other end from MySpecialNumber: projects that are so difficult and time-consuming that, in the end, the child learns nothing from having done them.

Here's Charles:

Giving people a choice is the democratic thing to do and is also a good political strategy. It should satisfy everyone. It's an inoffensive offensive. But I doubt that zealous educationists in a position of power will go along. Being responsive to reasonable popular wishes is not their thing. I also suspect that many parents are not conversant with the math issues and won't know what to do with choice.
Just yesterday I talked to a parent of a sixth grader I am tutoring in math who had no clue of fuzzy math. (I tutor disadvantaged kids after hours in addition to my regular classes.)
I was helping the kid do homework. Part of the homework required the kid to cut a sheet of paper into strips to make various fractions. The parent was aghast and thought it was a time-waster. I had to explain the purpose of the exercise. It was all news to her.
The school the kid is in uses the fuzzy series Connected Math. The homework assignment was quite demanding and way beyond the kids abilities. She had neither a conceptual understanding of the task nor the requisite tools (computational skills, procedural knowledge, math facts) to accomplish the task had she had a conceptual understanding of the problem. This is a key problem with fuzzy math. It is quite pretentious on the one hand, and refuses to teach the necessary skills on the other. The result: the kid was hopelessly drowning and getting straight F's.
Now what was the task? It was a real-world problem.
A class was holding a fundraiser to raise $300.00 in ten days. The progress was shown in the form of thermometers showing progress in two-day increments. The thermometers were all 8 1/2 inches long and showed the money raised so far on the various days in red. The fraction strips were to be used to determine the amount of money raised so far on the various days and then to plot the progress in a coordinate plane. The kid was to make the strips and mark fractions from 1/2 to 1/12 on the various strips.
Making fractions strips of 1/2, 1/4 and 1/8 is of course easy. It's not so easy to come up with 1/3, 1/5, 1/12. You could do time-consuming trial-and-error folding. Or you could divide 8 1/2 by the INVERSE of the various fractions. This adds another layer of complexity far beyond the capabilities of the mathematically crippled kid.
Dividing by the fractions tells you how many fractions should be on the strip, e.g. 8 1/2 divided by 1/5 gives you 42.5
Dividing by the inverse gives you the length of the fraction (1.7). Now convert 1.7 to 1/16's so you can use the inch ruler!!!
Now try doing this with the remaining fractions up to 1/12's as required by the CMP task used as a homework assignment!
Even if you can get the numbers they don't work well with an inch ruler. You could approximate. Suppose you (meaning the kid) could accomplish all that. Then what? She was supposed to find the strip with the right fractions and measure the red thermometer bar (money raised). Then she had to add the fractions and know how to calculate the decimal from the red bar to total thermometer length ratio to finally determine the amount raised to begin plotting. All this without instructions in CMP and without computational skills and procedural knowledge.
No wonder the kid is drowning. What a tragedy.

ConnectedMathForParents 22 Dec 2005 - 19:55 CatherineJohnson

Becky C tracked down an important website for parents of children using Connected Math: Connected Math for Parents.

I was trying to dig up information on Investigations this weekend to assist me in connecting the boys' curriculum at school with our Singapore curriculum at home. The parent letters given out with each Investigations unit, and the game rules for each homework activity, are inadequate to explain the point of each activity. The desirable, final, procedural, and conceptual point of each activity. Lacking a Teacher's Guide, I have to rely on my Superior Reasoning Skills to figure out the point. Until January, when I may get up the courage to ask for my own copy of the Teacher's Guide, to keep. Which is probably illegal.
But for you, you can check out this parent guide for Connected Math. Go through the Concepts and Connections link for any unit, and then download a PDF of the C and C document.
I was AMAZED and favorably IMPRESSED that these folks have the courage of their convictions to put this out for parents to see and to work with. It must be the same as what's in the Teacher's Guide for Connected Math.

I thought the first 3 pages of the fractions homework were pretty good. After that the lesson seems to unravel a bit, with numerous references to 'different ways students may do this,' etc.

I'm curious what others think.

TakeTheKtmChallenge 23 Dec 2005 - 17:33 CarolynJohnston

Here's a sample problem from the Connected Math for parents material that BeckyC found:

Dario made 3 pizzas which he sliced into quarters. After considering how many people he would be sharing with, he thought to himself, 'each person can have a half.'
a. Is it possible that there was only one person to share with? How?
b. Is it possible that there were 5 other people to share with? How?
c. Is it possible that there were 11 other people to share with? How?

I imagine that as a sixth grader myself, I would have stared at this problem for a while, trying to figure out not what the answer to the problem was, but what the question could possibly be getting at with the 3 pizzas and the cutting them into quarters and Dario and his thoughts about a half of something.

Here's the answer (bold-faces are all Connected Math's):

This question illustrates how the actual amount can vary, but still be called a 'half', depending on the size of the 'whole'.
a. If there was only one other person to share with then Dario's comment means that Dario will have half of the total amount of pizza, and so will the other person. (This would mean one and a half pizzas each).
b. If there were 5 other people to share with than Dario's comment would mean that each person could have half of a pizza. (6 people each getting half of a pizza would use a total of 3 pizzas).
c. If there were 11 other people than each person would get a quarter of a pizza. Dario's comment would have to mean that each person gets half of a half-pizza. (12 quarters would be the same as 3 pizzas).

There's just something so awkward and convoluted about this problem, one has the sense that the same point could have been gotten at in a much more effective and straightforward way. Maybe this is because I learned mathematics all the wrong way in the bad old days and need to relearn it, but you know what? I don't think so.

And therefore I offer the following

KTM challenge: construct a problem that achieves the desired end without being misleading or convoluted.

NctmReformsAgain 14 Sep 2006 - 16:52 CatherineJohnson

In today's Wall Street Journal ($):

Arithmetic Problem
New Report Urges Return to Basics In Teaching Math
Critics of 'Fuzzy' Methods Cheer Educators' Findings;
Drills Without Calculators Taking Cues From Singapore
By JOHN HECHINGER
September 12, 2006; Page A1

The nation's math teachers, on the front lines of a 17-year curriculum war, are getting some new marching orders: Make sure students learn the basics.
In a report to be released today, the National Council of Teachers of Mathematics, which represents 100,000 educators from prekindergarten through college, will give ammunition to traditionalists who believe schools should focus heavily and early on teaching such fundamentals as multiplication tables and long division.
The council's advice is striking because in 1989 it touched off the so-called math wars by promoting open-ended problem solving over drilling. Back then, it recommended that students as young as those in kindergarten use calculators in class.
Those recommendations horrified many educators, especially college math professors alarmed by a rising tide of freshmen needing remediation. The council's 1989 report influenced textbooks and led to what are commonly called "reform math" programs, which are used in school systems across the country.
The new approach puzzled many parents. For example, to solve a basic division problem, 120 divided by 40, students might cross off groups of circles to "discover" that the answer was three.
Infuriated parents dubbed it "fuzzy math" and launched a countermovement. The council says its earlier views had been widely misunderstood and were never intended to excuse students from learning multiplication tables and other fundamentals.
Nevertheless, the council's new guidelines constitute "a remarkable reversal, and it's about time," says Ralph Raimi, a University of Rochester math professor.
Francis Fennell, the council's president, says the latest guidelines move closer to the curriculum of Asian countries such as Singapore, whose students tend to perform better on international tests.

So maybe it wasn't such a great idea after all for IUFSD to ban my Singapore Math course.

new timeline

According to their report, "Curriculum Focal Points," which is subtitled "A Quest for Coherence," students, by second grade, should "develop quick recall of basic addition facts and related subtraction facts." By fourth grade, the report says, students should be fluent with "multiplication and division facts" and should start working with decimals and fractions. By fifth, they should know the "standard algorithm" for division -- in other words, long division -- and should start adding and subtracting decimals and fractions. By sixth grade, students should be moving on to multiplication and division of fractions and decimals. By seventh and eighth grades, they should use algebra to solve linear equations.

Here's the Singapore sequence.

Lutherans turning into Catholics

A recent study by the Thomas B. Fordham Foundation, a Washington nonprofit group, found that only two dozen states specified that students needed to know the multiplication tables. Many allowed calculators in early grades.
Chester E. Finn Jr., the foundation's president and a former top official at the U.S. Department of Education, blamed the earlier math-council guidelines for state standards that neglect the basics. He described the new advice as a "sea change," saying that "it's a little bit like Lutherans deciding to become Catholics after the Reformation."
Understanding math, rather than parroting answers to poorly understood equations, was the goal of the council's controversial 1989 standards. Those guidelines called on teachers to promote estimation, rather than precise answers. For example, an elementary-school student tackling the problem 4,783 divided by 13 should instead divide 4,800 by 12 to arrive at "about 400," the 1989 report said. The council said this approach would enable children using calculators to "decide whether the correct keys were pressed and whether the calculator result is reasonable."
"The calculator renders obsolete much of the complex pencil-and-paper proficiency traditionally emphasized in mathematics courses," the council said then. In 2000, in another report, the council backed away somewhat from that position.
Still, in response to the earlier recommendations, many school systems required children to describe in writing the reasoning behind their answers. Some parents complained that students ended up writing about math, rather than doing it.
As the debate heated up, concern grew about U.S. students' math competence. In 2003, Trends in International Mathematics and Science Study, a test that compares student achievement in many countries, ranked U.S. students just 15th in eighth-grade math skills, behind both Australia and the Slovak Republic. Singapore ranked No. 1, followed by South Korea and Hong Kong. Fueling concern about the quality of elementary and high-school instruction: one in five U.S. college freshmen now need a remedial math course, according to the National Science Board.

low-income students

This is very exciting. The AIR report (pdf file) led me to believe that Singapore Math had been a flop in low-income schools because the student mobility is so high (and see Hirsch on this subject, too):

If school systems adopt the math council's new approach, their classes might resemble those at Garfield Elementary School in Revere, Mass., just north of Boston. Three-quarters of Garfield's students receive free and reduced lunches, and many are the children of recent immigrants from such countries as Brazil, Cambodia and El Salvador.
Three years ago, Garfield started using Singapore Math, a curriculum modeled on that country's official program and now used in about 300 school systems in the U.S. Many school systems and parents regard Singapore Math as an antidote for "reform math" programs that arose from the math council's earlier recommendations.
According to preliminary results, the percentage of Garfield students failing the math portion of the fourth-grade state achievement test last year fell to 7% from 23% in 2005. Those rated advanced or proficient rose to 43% from 40%.
Last week, a fourth-grade class at Garfield opened its lesson with Singapore's "mental math," a 10-minute warm-up requiring students to recall facts and solve computation questions without pencil and paper. "In your heads, take the denominator of the fraction three-quarters, take the next odd number that follows that number. Add to that number, the number of ounces in a cup. What is nine less than that number?" asked teacher Janis Halloran. A sea of hands shot up. (The answer: four.)
Ms. Halloran then moved on to simple pencil-and-paper algebra problems. "The sum of two numbers is 63," one problem reads. "The smaller number is half the bigger number. What is the smaller number? What is the bigger number?" (The answers: 21 and 42.)
In this class, the students didn't use the lettered variables that are so prevalent in standard algebraic equations. Instead, they arrived at answers using Cuisenaire rods, sticks of varying colors and lengths that they manipulate into patterns on the tops of their desks. The children use the rods to learn about the relationship between multiplication and geometry. The goal: a visceral and deep understanding of math concepts.
"It just makes everything easier for you," says fifth-grader Jailene Paz, 10 years old.

Cuisinaire rods for bar models!

That's so cool!

TERC time

The Singapore Math curriculum differs sharply from reform math programs, which often ask students to "discover" on their own the way to perform multiplication and division and other operations, and have come to be known as "constructivist" math.
One reform math program, "Investigations in Number, Data and Space," is used in 800 school systems and has become a lightning rod for critics. TERC, a Cambridge, Mass., nonprofit organization, developed that program, and Pearson Scott Foresman, a unit of Pearson PLC, London, distributes it to schools.

parents don't get it part 1

Ken Mayer, a spokesman for TERC, says many parents have a "misconception" that Investigations doesn't value computation. He says many school systems, such as Boston's, have seen gains in test scores using the program. "Fluency with number facts is critical," he says.

parents don't get it part 2

Polle Zellweger and her husband, Jock Mackinlay, both computer scientists, moved to Bellevue, Wash., from Palo Alto, Calif., two years ago so their two children could attend its highly regarded public schools. She and her husband grew suspicious of the school's Investigations program. This summer, they had both children take a California grade-level achievement test, and both answered only about 70% of the questions correctly. Ms. Zellweger and her husband started tutoring their children an hour a day to catch up.
"It was a really weird feeling," says their daughter, Molly Mackinlay, 15. "I do really well in school. I am getting A-pluses in math classes. Then, I take a math test from a different state, and I'm not able to finish half the questions."
Eric McDowell, who oversees Bellevue's math curriculum, says parents misunderstand Investigations.

If it weren't for the parents, teaching would be a great job.

math wars and war wars

In the Alpine School District in Utah, parent Oak Norton, an accountant, has gathered petitions from 1,000 families to protest the use of Investigations. His complaints began more than two years ago, when he discovered at a parent conference that his oldest child, then in third grade, wasn't being taught the multiplication tables.
Barry Graff, a top Alpine school administrator, says the system has added more traditional computation exercises. Over the next year, Alpine plans to give each school a choice between Investigations or a more conventional approach. Mr. Graff, who says Alpine test scores tend to be at or above state averages, expects critics to keep up the attacks and welcomes the national math council's efforts to provide grade-by-grade guidance on what children should learn.
"Other than the war in Iraq, I don't think there's anything more controversial to bring up than math," he says. "The debate will drive us eventually to be in the right place."

wow

I bet things are hopping over at math-teach & math-learn.

[pause]

hmm

No action thus far.

Once Wayne Bishop posts this baby, we'll be in a shooting war.

update: Bishop's got it!

let the fun begin

what Singapore students can do at the end of 7th grade

-- CatherineJohnson - 12 Sep 2006

NationalMathAdvisoryPanelLinks 21 Nov 2006 - 18:07 CatherineJohnson

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