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Entries from ImpCurriculum
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 CorrectionsThis list is David Klein's handiwork, not Jo Anne's.
Thank you, David! (For everything you do.) 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 schoolEveryday Mathematics (K6)TERC's Investigations in Number, Data, and Space (K5) Math Trailblazers (TIMS) (K5) Middle schoolConnected Mathematics (68)Mathematics in Context (58) MathScape: Seeing and Thinking Mathematically (68) MATHThematics (STEM) (68) Pathways to Algebra and Geometry (MMAP) (67, or 78) High schoolContemporary Mathematics in Context (CorePlus Mathematics Project) (912)Interactive Mathematics Program (912) MATH Connections: A Secondary Mathematics Core Curriculum (911) Mathematics: Modeling Our World (ARISE) (912) SIMMS Integrated Mathematics: A Modeling Approach Using Technology (912) Programs explicitly denounced by over 220 Mathematicians and Scientists:Cognitive Tutor AlgebraCollege Preparatory Mathematics (CPM) Connected Mathematics Program (CMP) CorePlus Mathematics Project Interactive Mathematics Program (IMP) Everyday Mathematics MathLand Middleschool 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
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 Amazeing 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. So how does this finesounding 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. 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 CatherineI 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.
TwoWaysOfTeachingMath 19 May 2006  21:12 CatherineJohnson
HowToGetParentBuyInPart2 27 May 2006  02:30 CatherineJohnson source: Getting Your Math Message Out to Parents how to get parent buy in, part 1
newsletter excerpt
NctmReformsAgain 14 Sep 2006  16:52 CatherineJohnson In today's Wall Street Journal ($):
Arithmetic Problem 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.
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. lowincome students
This is very exciting. The AIR report (pdf file) led me to believe that Singapore Math had been a flop in lowincome 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. Threequarters 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. Cuisinaire rods for bar models!
That's so cool!
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. 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 gradelevel 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.
If it weren't for the parents, teaching would be a great job.
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. wow
I bet things are hopping over at mathteach & mathlearn.
[pause] hmm No action thus far. Once Wayne Bishop posts this baby, we'll be in a shooting war.
let the fun begin  CatherineJohnson  12 Sep 2006
NationalMathAdvisoryPanelLinks 21 Nov 2006  18:07 CatherineJohnson meetings
email updates
homepage I'm posting links to the Math Panel homepage, transcripts, & ktm posts here:
You can find both pages on the menu to the left. If all else fails you can search posts using the keyword nationalmathematicsadvisorypanel with no spaces between words. (Works pretty well with spaces, too.) I'm thinking this is about as findable and redundant as I can make the links now...unfortunately, you will have to remember some constellation of the words "national mathematics advisory panel" to find these links (that could be iffy for me these days....)
But I think I've just raised the odds of refinding the transcript links considerably.
nationalmathematicsadvisorypanel
LindaMoranListserv 11 Dec 2006  19:25 CatherineJohnson I think everyone here knows about Linda Moran's Teens and Tweens blog. I've recently (re)discovered that she has a listserv attached to the blog. I joined last week, and I think some of you might like to join as well. There have been some very interesting posts to the listserv that I don't believe have been posted to the blog itself — and that I don't expect to see posted to the blog itself.
 CatherineJohnson  09 Dec 2006
 
