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07 Jul 2005 - 02:49
A coda from Catherine and Barry to kick off comments: Catherine: Barry, I've forgotten theorems & postulates. Do you want to add a quick definition? (Isn't one of them supposed to be a kind of 'given,' and the other the logical deduction from the given?) BG: (Offstage voice in the funhouse) Yes, that's a good way of putting it. It is a proposition that is accepted without proof. What is logically deduced from postulates and definitions are theorems, which because they can be deduced, can be proven. Catherine (in front of crazy mirrors): I think I've got the two mixed up..... Also, do you know how popular Core Plus is? BG: (enters, walking on ceiling): Fairly prevalent throughout Michigan and Minnesota. Used in other states too, but those are the main ones. Google on "Bachelis; Core Plus" You'll find a paper he did on it. He did a survey of students in two high schools outside of Detroit; one used Core Plus, the other a normal program. Students using Core Plus did poorly in math in the university. Chris Hirsch, the PI for Core Plus threatened Bachelis with legal action. Tom Parker of MSU did a paper on Core Plus as well using statistical data showing performance in freshman year mathematics; similar to what Bachelis did. Also criticized by Hirsch. Back to main page.
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I'm LOLing!!!!!! I'm definitely standing in front of a crazy mirror--help! help! What's a postulate! What's a theorem! Which is which! Plus the image of Barry walking on the ceiling--yikes! Does Barry look anything like Jeff Goldblum? Speaking of what people look like, I'm gonna scan my favorite family photo & post it one of these days..... Another Jakob Nielsen tip! -- CatherineJohnson - 07 Jul 2005
Now that I'm seriously thinking about POSTULATE versus THEOREM, it makes sense a postulate would be the thing assumed to be true without proof.....it's confusing because in FILM STUDIES (I just have to hope reincarnation is a possibility) theories are the things-assumed-to-be-true-without-proof. -- CatherineJohnson - 07 Jul 2005
Barry, Since you talked to Jim Milgram, I am sure he told you about the study he did on Core Plus vs traditional math program in my school district in Michigan. I think KTM would be interested in the paper or article about it. The gist is that students from the same school district who take the Core Plus vs traditional math get statistically significantly lower SAT scores and approximately one letter grade lower in their first college math course. Some students have to take remedial math courses at local community colleges to get their math up to a level where they can take calculus in college. And still our administrators defend the program!! -- AnneDwyer - 07 Jul 2005
Theories and theorems are different. And the word "theory" takes on different meaning depending on the discipline. In law, legal theory means a particular line of reasoning (from what I can glean from listening to lawyers talk). In science, a theory is a conjecture based on empirical data. The sun will rise every day is a theory based on scientific induction; i.e., because it rises every day, we assume it will rise again tomorrow, but allow for the (remote) possibility that it may not. Theorems, generally, (a term used to cover myself, just in case) are not derived empirically, but are deduced using logical rules of inference. In reform math classes, however, empiricism seems to be the order of the day, with students making endless "lists" of data and interpreting such data. It's math taught as statistics. Measure 1,000 circles to get circumference and radius, take the ratio, and we get a probabilistic derivation of pi. Take a dixie cup of a specific height and base, fill it with water, and pour the water into a glass with same base area and same height as the dixie cup. Keep doing this until the glass is filled. The empirical data tell us 3 dixie cups = 1 glass of water, with equal base areas and equal height, so we get the empricially derived formula of the volume of a cone: 1/3 Base area times height. (In Larson Boswell Stiff's Geometry book, 1995 version, this is how they introduced the concept of volume of a cone, and this is a high school geom book. Glad to see they took that out in the 2000 edition). A bit of an off point discussion, but I'm still a bit dizzy from walking on the ceiling. -- BarryGarelick - 07 Jul 2005
-- BarryGarelick - 07 Jul 2005
Anne: I'm familiar with the Milgram study (and Greg Bachelis' study, which started it all). Also, Tom Parker of MSU did a study in 03 similar to Milgram's but very rigorous. I've attached it here. Catherine: I suppose I look like a skinny Jeff Goldblum, though I tell strangers that I look like Fabio. I should stop doing that because I don't think Fabio is all that good looking; the Viking look is definitely not a plus. -- BarryGarelick - 07 Jul 2005
Barry, I fixed up your attachment link a little. I did it because I am anal, I guess. Does Jeff Goldblum walk on ceilings? Does Barry? (I thought Jeff Goldblum WAS a skinny Jeff Goldblum). -- CarolynJohnston - 07 Jul 2005
Barry, If anyone has a case for education malpractice, this CorePlus is it. In the MSU study, very few CorePlus students could actually complete enough Calculus to major in engineering or science. I live in that school district in Michigan. My children are slated to go to high school with the traditional math program. But most parents don't understand the issue. I have found that many parents don't understand the issue of Everyday Math and Connected Math. You can tell people, but they don't really believe unless they have experienced a child who fails because they just cannot get the math. -- AnneDwyer - 08 Jul 2005
EVERYONE needs to read this report of the students in Andover, Michigan. Be sure to scroll far enough down to see their SAT and ACT scores. These are smart kids. In their own words, read their unfavorable report of the math education they got in high school They know they were ripped off and mince no words saying so. We must start listening to the students who sat through this "fuzzy math". Some feel they will never recover from their loss. GO TO THIS SIGHT AND READ BACHELIS' STUDY. Show it to everyone who teaches high school math anywhere! -- CarolynMorgan - 08 Jul 2005
Barry--Did you write the line about walking on the ceiling??? That was BRILLIANT! -- CatherineJohnson - 08 Jul 2005
Great minds think alike I, too, was under the impression that Jeff Goldblum was a skinny Jeff Goldblum. I once ran into Jeff Goldblum and Laura Dern in the Armani store in Beverly Hills. (This was the one and only time I was inside the Armani store in Beverly Hills....I'm still wearing the suit I bought that day.) They were tall. -- CatherineJohnson - 08 Jul 2005
And I mean really, truly, severely tall. -- CatherineJohnson - 08 Jul 2005
And btw, when I say tall I know whereof I speak. I once ran into Gena Rowlands in the restroom at.....TOTAL MEMORY LOSS, SORRY!
Anne--You live in that district???? And they're still defending the curriculum????? Yup, we've got to get all that stuff covered here (I've read quite a bit of it, I think.) Do you want to write something about it??? -- CatherineJohnson - 08 Jul 2005
I have found that many parents don't understand the issue of Everyday Math and Connected Math. You can tell people, but they don't really believe unless they have experienced a child who fails because they just cannot get the math. This is probably a topic we need to make into a perennial. How do you explain your OBSESSION to other parents who are actually living a life, as opposed to writing a MATH BLIKI 24 hours a day? I had a horrible experience where I embarrassed the living daylights out of myself trying to ask a hostile question of the candidates running for school board while the PTSA "moderator" told me to sit down, my time was up. I'm mortified all over again, just thinking about it. Then a couple of days ago one of Christopher's friends said HE SAW ME ON TV. PEOPLE SAW ME ON LOCAL ACCESS CABLE TV GETTING TOLD TO STOP TALKING ABOUT TRAILBLAZERS-IN-IRVINGTON BY THE PTSA! AYYYYYYY! This is the same PTSA to which I have donated countless thousands of hours volunteering & running the after-school program. Thanks, guys! -- CatherineJohnson - 08 Jul 2005
I don't know why I didn't CONSULT WITH MY HUSBAND before attempting to ask a question in public. He's good at academic politics. I tried to ask whether the candidates thought it was OK for Irvington to bring in a curriculum that was rated Abominable or Wretched-beyond-belief or whatever it was by the state of CA, and their answer was, 'The administration looked at all the different curricula.' In point of fact, the school district looked at TERC, TRAILBLAZERS, & EVERYDAY MATH. Their stated 'Areas of Focus for Pilot' included 'Constructivist approach with modeling,' 'everyday applications of math,' 'consistent with NCTM standards,' 'developmental approach,' and yadda, yadda, yadda. In other words, the mission was to figure out which fuzzy-math curriculum to implement, not whether to go fuzzy in the first place. When I asked whether the administration had a duty to disclose the fact that they were choosing a controversial curriculum that has been formally rejected by the CA Board of Ed they said.... I don't remember what they said. Afterwards Ed told me I asked the question all wrong, which I demonstrably did. Then he told me how I should have asked it. I think he said I should have said, VERY BRIEFLY, something like, 'Do you approve of the Irvington administration adopting Math Trailblazers, which CA ranks unacceptable? Instead I managed to frame my question in such a way that the candidates could answer it by telling me I'd had an opportunity to voice my concerns at the school board meeting when TRAILBLAZERS was adopted. AND THE WHOLE THING WAS CAUGHT ON TAPE! -- CatherineJohnson - 08 Jul 2005
I've just consumed most of a kir. It doesn't show, does it? -- CatherineJohnson - 08 Jul 2005
Time to go watch my BATTLESTAR GALACTICA CD set. -- CatherineJohnson - 08 Jul 2005
"How do you explain your OBSESSION to other parents who are actually living a life, as opposed to writing a MATH BLIKI 24 hours a day?" I'm not going to compare my obsession to yours (I would probably lose.), but I know what you mean. How do you discuss these problems without overwhelming the person you're talking to? You want to do a brain dump or a mind meld, but it just can't happen. I like Ed's approach and have tried it myself. 1. I mention to people that our school uses MathLand, a math curricula so bad it is banned in California and even dropped by it's own publisher. Even people who like fuzzy math think it's bad. Why does our school use it? 2. I have mentioned to people on our school committee that they should hand out E.D. Hirsch's Core Knowledge series of books: "What your First (Second, Third, etc.) Grader needs to know" and tell parents that this is NOT(!) the education their children will receive. Why not? 3. I tell other parents about a fourth grade standardized math question (New Standards Reference Exam) that has the kids look at a bar graph with four bars showing the number of votes 4 kids received in a student election. All bars are less than 20. Two questions have to be answered: Who won the election?, and What is the total number of votes cast? Allotted time: 15 minutes. 4. I tell other parents that their kids will not be properly prepared for college prep math unless they get outside help. Parents want to know, but they don't want to be overwhelmed. Less is sometimes more. I told one parent that MathLand was horrible and was hurting our kids. In an almost conspiratorial voice, she says: "That's what someone else told me." This led to a discussion where she asked me questions. As for public officials, they have to be put on the defensive with questions like what Ed proposed. I also think it's best to stay away from arguments over constructivism. It's hard to argue over generalities and vague terms. I prefer the compare and contrast approach, especially if it is specific. Everything is quite clear when you compare two text/work books side by side. I would like to hear the NCTM math types explain how a CMP problem leads to better math "understanding" than a same grade Singapore Math problem. Show them to parents and ask them which problem they would like their child to be able to do. Let me just say that this is not about winning an argument. It's about letting people know about our complaints and concerns. The NCTM crowd throws out a lot of propaganda about understanding versus rote knowledge. We are not going to get very far if they dictate the terms of the discussion. We should start a new section of one liners. Conversation starters with barbs, if you wish. -- SteveH - 08 Jul 2005
I have just written an op-ed which I hope will be published, but looks at the circumvention that NCTM does in defending its approach. If you were to ask the question of them that Steve H does about comparing CMP to Singapore, they respond along the lines "It's not the text, it's the teacher" and then do their typical admonishments of "In the US they say here's the rule, now do the problem" and "There's too much teacher instruction". You will not be able to win an argument with these people anymore than you can catch a greased pig. What you will be able to do is convince others who may be on the fence, of the validity of your points. The PTSA that Catherine talked about has their minds made up. Most school boards do. So they looked at 3 bad math programs and picked the least worst. The question that perhaps should have been asked is "Why didn't you consider Saxon, or Singapore?" But they would have answered: 3 isn't enough for you? And so on. Doesn't matter. Come with your guns loaded, not to convince them, but the people in the room and the press (if they bother to show). In Washington DC, the school board just adopted Everyday Math, Math Trailblazers and Connected Math. I've written about this elsewhere. Their minds are made up. And the illustrious Washington Post asked Bas Braams a few questions about the issue and then never did a story. (I call the Post the Compost these days). In terms of Core Plus, Anne is correct. The program is abominable, and the harm to the students deplorable. But they fought back hard, and said things like "Who cares what students say in a survey; students can't be trusted. They're always going to bad mouth the programs, teachers, etc". Which is what motivated Tom Parker to do a more thorough review which also was lambasted by Core Plus on its web site. And, by the way, when the NAS did its study on the research base for the NSF funded programs (concluding the research doesn't show effectiveness nor ineffectiveness), Parker's study was not used. Politics. Chris Hirsch and his thugs are quite effective at what they do. I could go on. Uh, by the way, I look like a skinnier Jeff Goldblum and yes, I wrote the line about walking on the ceiling. -- BarryGarelick - 08 Jul 2005
There is an article still on the web (as of 6/10/05) titled "How a New Math Program Rose to the Top" which was published in the Christian Science Monitor, May 23, 2000, about the CorePlus Andover, Michigan story. Of what good is a high school course if smart students have to take remedial math programs in college? Quoted in this CSM article:
Yes, that's a good article. It mentions the survey that Bachelis did. -- BarryGarelick - 08 Jul 2005
I truly believe that I totally need a way to talk to parents about the math programs. I am an engineer by training, so I tend to want to give as much info as possible. And I tend to talk about it way too much. Most elementary school parents realize instinctively that Everyday Math is not good for their children. But, because of all the propaganda, they think, "I must be wrong and they know what they are doing." I wish I had some well constructed short examples or evidence that would convince them they need to do something for their children. On the other hand, most children with a parent or parents who work in a technical field know, for a fact, that the math program is bad. Instead of complaining, they send them to Kumon or something like it. The Chinese, Japanese and Indian children are also sent to Indus Academy. This is an independent math school taught on the weekends. It is taught by PhD? mathematicians. It's not fuzzy and it is not 'fun'. Most parents sit in with their kids so they can help them with their homework. As for the other high school in our district, they teach traditional math. I have very little data from which to form an opinion, but I am not impressed. How do you defend an Honors AlegebraII?/Trig class that never gets to trigonometry? BTW, I have been investigating the ACT test. The math part is all content knowledge and covers pre algebra through trig. So if you have not had trig, well, there are some problems that you just can't do. In that rigorous study of the CorePlus program at MSU, the author states that you have to have a 28 on the math part of the ACT or take AP Calculus to qualify for the first semester of Calculus. So students who take algebra in 8th grade and have already finished AlgebraII?/Trig and some precalculus by the time they take the exam in the 11th grade have a huge advantage. -- AnneDwyer - 08 Jul 2005 most children with a parent or parents who work in a technical field know, for a fact, that the math program is bad. Instead of complaining, they send them to Kumon or something like it. The Chinese, Japanese and Indian children are also sent to Indus Academy. That's what I see, too. 'Math' parents take one look at the stuff and reject it. Everyone else is either confused, or actively supportive, or defensively supportive. (Too long to go into at the moment.) I'll have to give this some thought, but the thing that works best for me is drawing the comparison to Singapore Math. At least one KTM commenter has said that all anyone needs to see is a comparison of a fuzzy-math problem side by side with a Singapore problem. I continually push the 'global-world-economy' angle. -- CatherineJohnson - 08 Jul 2005
What is Indus? I've never heard of it. And why has the Comments box disappeared from this page? -- CatherineJohnson - 08 Jul 2005 SteveH How do you discuss these problems without overwhelming the person you're talking to? You want to do a brain dump or a mind meld, but it just can't happen. Exactly, and this isn't a new insight for me--plus I don't like to have people 'brain-dump' on me, and I don't want to brain-dump on them, either. So it's important to have talking points. -- CatherineJohnson - 08 Jul 2005
As for public officials, they have to be put on the defensive with questions like what Ed proposed. I also think it's best to stay away from arguments over constructivism. It's hard to argue over generalities and vague terms. I prefer the compare and contrast approach, especially if it is specific. Yes, absolutely. Strangely, although I'm a writer, the formulation of good questions (rhetorically good, I mean) doesn't automatically come to me. I guess that's not so strange; it's another skill, and it takes practice. We should definitely have a page of conversation starters & talking points. It's critically important, in part because we aren't going to 'win' this battle (IMO). It's been going on for a hundred years, and no one seems even close to pulling out the white flag. I have a slightly different POV on the question of arguing 'constructivism.' My sense is that the word 'constructivism' is experienced by many parents as having a 'negative valence.' You'll notice that the marketing people for NSF curricula never use it, and there's a reason for that. It's also quite difficult to find the term on the NSF site (I should check the NCTM site...) I see microexpressions of alarm and perhaps even disgust on people's faces when I spring the word 'constructivist' on them. (Definitely alarm.) Most people have either never heard the word, or have heard it a couple of times but have no idea what it means. So when they hear that their school district has selected a constructivist text ..... that raises more questions than simply saying that the district has selected a text that's too easy. The fact that the district has chosen a constructivist text without mentioning this fact to the community also registers. So I always use the word 'constructivist' and then move on to talking about the fact that my own child tested into Singapore 3rd grade at the end of U.S. 4th grade. END OF CATHERINE'S COMMENT START OF NEW COMMENT I can't find the comment box, so I'll just walk on the ceiling and barge my way in, if you don't mind. No, you won't see "constructivism" in NSF documents, nor anywhere on NCTM's web site. What you'll find on NCTM's website are admonitions from Cathy Seeley that there is too much "teacher instruction" in the U.S. No, don't bother asking her what she means, she'll wiggle out of that one easily. But you know what she means. As far as Anne's problem of succinctly stating what are the problems with Everyday Mathematics and other bad programs, it's good to have sound bites prepared. I like to quote the blurb from the EM Teacher's Reference manual how long division isn't worth the effort to teach because of the advent of calculators. That's a good ice breaker. Then I point out that when students stick to the EM curriculum, their kids are going to learn 4 inefficient ways to multiply two-digit numbers, and if they're lucky they'll be shown the traditional way. They won't be shown the traditional method for long division (not in the 4th grade anyway), and you will have bright students complaining that they don't really understand math because their confused over what method to use to solve a multiplication problem. (Yes, I heard this from a bright student). You can point to the Student Reference Manual (which is a glorified glossary) showing how equivalent fractions are handled. They will show how to convert 1/2, 1/4, 1/5 to decimals and percentages (since it's relatively easy to find ways to get the denominator to tenths or 100ths). For 3/8 (and students are presented with such problem frequently in the "Review boxes" that EM uses), the Student's Reference Manual provides detailed instructions of how to use a calculator to find the answer. If your response from the parent is "What's wrong with that?" change the subject and talk about the war in Iraq. I mean, if you have to get into a brawl, make it worth everyone's while. Barry G. NEW COMMENT--WOO HOO, I'M A WIKI MANIAC! Barry, Sorry to barge in like this, but you really do help when you give us specifics like the two-digit multiplication problems. When I used the Trailblazer letter concerning long division and mentioned it to fellow parents, that was when I actually got a response. It is very hard for the "layman" to understand all of this, particularly when teachers and administrators are using the jargon the NCTM wants them to use Catherine, Since you have Trailblazers, could you occasionally post some of their gems for us? Especially since I know you have so much free time.;-) Whatever you run across for us in Trailblazerland would be greatly appreciated. I don't see as much specifics on that one. Is it newer than the others? End of message--SusanS
Barry! Get off the ceiling! You're scaring people! Catherine 10:17pm est Friday
If your response from the parent is "What's wrong with that?" change the subject and talk about the war in Iraq. I mean, if you have to get into a brawl, make it worth everyone's while. ok, now you've been hitting the sauce. good idea, though Catherine 10:17 (still) Friday
SusanS Believe you me, I intend to post MANY problems from TRAILBLAZERS. Not that there are many to post.... Lots of TRAILBLAZERS PLAYLETS, thought. You don't see too much on the horrors of TRAILBLAZERS, it's true. EVERYDAY MATH seems to soak up all the bad publicity. Catherine 10:19 pm Friday July 8, 2005
What was it that worked for you again?
The fuzzies are smooth customers, that's for sure.
Can you be fuzzy and smooth?
Why don't I go enjoy my kir some place away from my laptop?
Seriously, though, I'm hearing from a pro-Trailblazers friend, whose child is in...2nd grade, i think...that he is acquiring conceptual knowledge of math, and that the math he's doing is much more challenging than any math she ever did. She is a 'math-friendly' mom; she took calculus in college, and has an MBA. Does TRAILBLAZERS do a good job in the very early grades? I only have the 5th grade text. The 5th grade text is ludicrous; the TRAILBLAZERS kids spend the whole book collecting data, and then adding it up. Basically, it's an entire 5th grade book about counting. (For people who don't know this, TRAILBLAZERS was originally called TIMS, which was 'integrated math and science.' The point is for all of math to be taught as a branch of statistics.) Catherine
"It's not the text, it's the teacher" and then do their typical admonishments of "In the US they say here's the rule, now do the problem" and "There's too much teacher instruction". You will not be able to win an argument with these people anymore than you can catch a greased pig. The first time I heard this I was dumbfounded. My neighbor raised her hand at the infamous 6th grade Phase 4 math meeting and said she'd be happy to put her child in Phase 3 if Phase 3 didn't have a constructivist math text. (Phase 4 has Prentice Hall). The principal, another smooth customer, swatted that one away. 'The book isn't the curriculum, the teacher is the curriculum.' This is a universal belief, I find. The teacher is the curriculum. Meanwhile, I WRITE BOOKS FOR A LIVING. WRITING BOOKS IS HARD. No teacher can teach full-time and also CREATE, out of whole cloth, A COHERENT CURRICULUM. You're right about speaking for the benefit of the parents, not for the sake of persuading the committed. At our small-group, going-to-middle-school meeting the principal told us that parents in the other meetings had asked him whether their Phase 3 kids would be able to take calculus in high school. He had been caught off-guard by that question and still, two weeks later, did not know the answer. Or, rather, he had one answer (no, Phase 3 kids wouldn't be able to take calculus in high school, but that situation would eventually be rectified, after it was too late for our kids) and the assistant principal had another (yes, Phase 3 kids can take calculus in high school). Well, 'Can Phase 3 kids take calculus in high school?' was a talking point I'd been putting out there at every opportunity. I had been telling parents, truthfully, that the slow track closes off options in high school. Obviously, parents had picked up on it. Steve's right. We need a page of talking points and advice. Barry, do you want to set one up? Steve? Anne? Susan? It needs to be set up by someone besides Carolyn or me, so everyone can edit. (Carolyn just spent hours doing the threads; eventually we'll have the user pages located up front--) Catherine
Greetings, ceiling walkers!!! I've put the comments box back below. There is a little bit of text at the bottom of every comments page that looks like this: %COMMENT{mode="above"}% Apparently someone wiped it out; that's why the comments box disappeared. Catherine, you and I can also create web pages from the comments page that are editable by everybody. It's only the blog pages that are protected. Here, I'll do it now: here is our new TalkingPointsDiscussion page. Catherine here: I know. This morning I woke up and thought: Carolyn and I can create web pages from the comments page that are editable by everybody.
You don't see too much on the horrors of TRAILBLAZERS, it's true. EVERYDAY MATH seems to soak up all the bad publicity. -- Catherine I think the only reason for that is that Everyday math is a lot more popular. Everyday Math is EVERYWHERE, but you're the only person I know that's afflicted with Trailblazers. -- CarolynJohnston - 09 Jul 2005
Trailblazers has just been adopted in DC. Their day is coming, unfortunately. -- BarryGarelick - 09 Jul 2005
Catherine, My neighbor will be dealing with the 5th grade Trailblazers text so whatever you say about it I'm relaying it back to her. I have been doing that all along. I've said about as much as one can say on the subject. She is concerned, but I can tell still waffling a bit. What cracks me up is how these curriculums are always described (by parents and teachers) as the only courses that reveal conceptual logic behind the basic math algorhythms, like no other math text deals with concept. I'm pretty sure I, too, would have totally fallen for the pretty texts and pictures myself, along with all the long-winded explanations on why my kid doesn't need that nasty "kill-and- drill" since he will just pick these skills up naturally. If math was hard for you and you never learned why then this just washes all that discomfort away. By the time the kid has trouble down the road I imagine the parent is still going to be unable to figure out who to pin the blame on. Also, it seems that parents (who may also have a faulty math education) whose kids don't appear to be very good at math (for who knows what reason) are seriously lulled by the feel-good quality of the courses. From some of my conversations with different friends of mine they seem to love the "real world" aspect of it, along all that cool data collecting. To some adults this looks practical. BTW, Illinois Loop has a lot of testimonials from parents. I read a great one that is actually a couple of years old, by a very well-educated and active parent who totally missed the signs of what was happening with her daughter in math class. One interesting point was that she wrongly associated any resistance to math reform as being a conservative thing. She was truly horrified by her error in judgement and wanted eveyone to know her story since she couldn't go back and change her daughters experience (although I think she did a Kumon rescue attempt that helped quite a bit.) -- SusanS - 09 Jul 2005
My neighbor will be dealing with the 5th grade Trailblazers text so whatever you say about it I'm relaying it back to her. I have been doing that all along. I've said about as much as one can say on the subject. That reminds me, we have to continue our 'how to correct fuzzy math at home' topic..... We probably need a separate page for that. I'm just reading some fantastic articles by a Russian mathematician who emigrated to the U.S. that are making me feel that the simplest way to handle a fuzzy math curriculum at school may be:
The amazing thing about TRAILBLAZERS is all the playlets. Do the other fuzzy curricula have endless playlets? -- CatherineJohnson - 09 Jul 2005
The other amazing thing is that in many of the TRAILBLAZERS playlets the kids are expressing abject doubt. One of these days I'm going to do a COMPARE AND CONTRAST on the visuals in TRAILBLAZERS versus SINGAPORE. Most of the pages in PRIMARY MATHEMATICS have drawings of little 'student helpers' who know the answer, and how to get it. TRAILBLAZERS is filled with drawings of students who have no clue what the answer is. -- CatherineJohnson - 09 Jul 2005
There's one huge drawing of a TRAILBLAZERS kid whose face is filled with MATH ANXIETY. How does this square with 'modeling'? -- CatherineJohnson - 09 Jul 2005
btw, this is something I never got around to blogging about way back when. Carolyn found evidence that group learning works, and we were wondering why that would be. Bernie thought some of it had to do with competition, which is probably true. It also struck me that groups allow for observational learning. Kids & animals do huge amounts of observational learning. In a group, children are going to see other children doing math & solving problems. This is why educators always tell parents to read in front of their kids--and it's why we should 'do math' in front of our kids, too. Back to TRAILBLAZERS: the book is filled with kids who are perplexed, confused, and struggling. Singapore is filled with kids successfully & efficiently doing math inside their heads. No child in Primary Mathematics is shown collecting data. Of course, that's what Steve Leinwand objects to. -- CatherineJohnson - 09 Jul 2005
I have also found a couple of "math-smart" people who like the ideas in Trailblazers, also. It should be interesting to see how that develops. Catherine, I'm not good at linking, so I'll just tell you where to find the article. Go to Illinois Loop site's main menu. Click on Personal Stories. About three links down is a story called "My Conversion." That is it. The other stories are quite good, also. In the book Knowing and Teaching Elementary Mathematics (is that Liping Ma?) there is a lot of discussion about group learning and manipulatives but I see one big difference: The Chinese teachers are not "facilitators" in the least. They control the discussion and clearly lead at all times. Plus, I imagine teaching half of the subjects that Americans teach means they have more time for such activities anyway. -- SusanS - 09 Jul 2005
By the way, with linking all you have to do is paste the URL into the comments box. Like this: http://www.illinoisloop.org/conversion.html -- CatherineJohnson - 09 Jul 2005
That's the story, right? -- CatherineJohnson - 09 Jul 2005
If somebody wants to pretty up a 'naked' html link, he can. But it's not necessary to do all the html-ing. Just copy the link from the URL & paste it in the edit window! If you want to look at the html for a standard-format link, hit 'edit' at the top of this page and scroll down until you find this comment: My 'Conversion' -- CatherineJohnson - 09 Jul 2005
I am not a good writer. I would love it if I could send a well written letter to the editor of my local paper explaining why people should be concerned about Everyday Math. Could KTM have a section containing letters like this that people like me could copy? -- LoneRanger - 10 Jul 2005
Could KTM have a section containing letters like this that people like me could copy? YES KTM COULD! Ed and I headed up an unbelievably successful pro-Lynn and Bob Koegel campaign at the NIH a few years ago by doing exactly this. I spent hours and hours writing a letter about their research; Ed edited; then we put it out on the web and told everyone: This is your letter. Cut and paste the whole thing, use parts of it, edit it, change it; do whatever you like. Huge numbers of parents flooded the NIMH with letters based on ours (or were sparked to write their own). We heard later, from a good source, that people at the NIMH were 'literally running through the halls.' We were all kind of curious about why exactly a staffer at the NIMH would run through the hall under any circumstances. -- CatherineJohnson - 10 Jul 2005
Catherine, the visual of people running through the halls at the NIMH cracks me up. It's sort of like West Wing combined with the halls-and-doors scene from Yellow Submarine. Prentice Hall Course 1 has a lot of photos of kids too, but I'm honestly not sure why. They aren't doing math in their heads, and they aren't struggling either; they are propping up posters with text on them, describing the different ways that they came to the same answers. Their main purpose seems to be to teach a subtle side lesson on diversity; they are Asian, black, white, Hispanic, walking on crutches, sitting in wheelchairs. No Down Syndrome kids, though. -- CarolynJohnston - 10 Jul 2005
Barry Garelick guest blogs on Core Plus
I've been wearing my KitchenTableMath System Administrator hat the last couple of days, and one of the things I've done is to create a whole new set of topic pages, to make indexing KTM content a bit easier (to see the new topics, click on the Archives organized by thread menu at the upper right of the main page; but most of them are empty, because we don't have the existing posts indexed yet). One thing we tried to do was to create topics for all the major contenders in the curriculum game, constructivist and not, so that people searching for information about some new curriculum they've been handed could find information about it easily (hat tip to David Klein for the suggestion!). As a result, I've created topics for curricula that I personally know nothing about, and CorePlus is one of those. But BarryGarelick is very familiar with CorePlus, and here is his input on it. Thanks again, Barry -- and you'll see this post back on the page that I took it from! -- Main.CarolynJohnston - 07 Jul 2005The CorePlus program
Core Plus is a so-called "integrated math" program. It has undergone one set of revisions so far, and I believe is undergoing another one. So far, Western Michigan University which develops the program has received $11 million in grant money from NSF-EHR to do this. At last glance, Core Plus doesn't introduce the quadratic equation until the 11th grade, thereby rendering many problems difficult or unsolveable until then. (It generally is presented in a first year algebra course). Also, their treatment of geometry is a bit unusual. In most texts, the congruence relationship between triangles that depends on SIDE ANGLE SIDE (SAS) is stated as a postulate. Core Plus states it as a theorem, and proves it using the law of cosines. Since the law of cosines is dependent on similar triangles and the SAS congruence theorem itself, some might say this is circular. I wrote Dr. Hirsch (the PI for Core Plus at Western Michigan University) about this, and he responded as follows:"With respect to our approach to sufficient conditions for similarity and congruence, it would be helpful for you to carefully examine the development in our texts. See Course 1 Unit 5 for initial work with the Pythagorean Theorem; Course 2 Unit 2 for initial work with similarity via size transformations; Course 2 Unit 6 for development of the trigonometric ratios; Course 3 Units 1 and 3 for development of the Law of Sines and the Law of Cosines; and Course 3 for the proofs of sufficient conditions for similarity and congruence. "The geometry work has been reviewed by two research geometers: James King and Doris Schattschneider. Professor Schattschneider is working closely with us on the revision of the geometry units. "Hope this helps. There is really no substitute for a careful examination of the texts themselves."Disregarding the haughtiness of his answer, I asked for the opinions of three mathematicians on his approach: Hung-Hsi Wu of Berkeley, Jim Milgram of Stanford and Richard Askey of U of Wisconsin. Jim Milgram pointed out that postulates are not God given. One can assume any number of propositions to be a postulate and then the theorems and corollaries follow logically from it. There is a way in which the SAS congruence relationship between triangles can be proven, but it is an advanced approach to geometry, and one which Core Plus does not rely on in its proof. Dr. Milgram could not be sure that Core Plus was mistaken in its approach without a thorough examination of the text, but said that in any event, such an approach for a high school course was not advisable. (Actually his words were a bit stronger than that). Dr. Wu is himself a geometer who teaches at U.C. Berkeley. He stated outright that Core Plus' approach to "proving" the SAS congruence relationship using the law of cosines was circular:
"You cannot define sine and cosine, in the usual sense of leg of right triangle to hypotenuse, WITHOUT knowing similarity of triangles. Otherwise the sine and cosine functions would be function of angles OF A PARTICULAR RIGHT TRIANGLE rather than a function of the angle itself. This being the case, using sine and cosine to prove SAS is circular reasoning. So CORE-PLUS teaches INCORRECT mathematics, but what else is new?"Dick Askey from U. of Wisconsin concurred. (Also Larry Gray of U of Minnesota in his own comments about Core Plus on his website; he is head of undergraduate dept of Mathematics). Whether Core Plus corrects this in their next version will be "interesting". In any event, even if they succeeded in a proof of a proposition that is normally presented as a postulate, this raises the question of why on earth you would subject a high school student, being exposed to formal mathematical proof for the first time, to something like that? It would be like teaching second graders that it doesn't matter whether the earth goes around the sun or vice versa, because all motion is relative per Einstein's theory of relativity. In early grades, it makes sense to teach kids that the planets revolve around the sun. Later, maybe high school but usually college, discussion of relative motion is introduced and students understand that viewing the sun as center of the solar system is for utilitarian reasons but that all reference frames hold. Core Plus' approach of proving SAS for high school students is inappropriate. And the way they have done it is incorrect, to boot. BarryGarelick 7/6/05
A coda from Catherine and Barry to kick off comments: Catherine: Barry, I've forgotten theorems & postulates. Do you want to add a quick definition? (Isn't one of them supposed to be a kind of 'given,' and the other the logical deduction from the given?) BG: (Offstage voice in the funhouse) Yes, that's a good way of putting it. It is a proposition that is accepted without proof. What is logically deduced from postulates and definitions are theorems, which because they can be deduced, can be proven. Catherine (in front of crazy mirrors): I think I've got the two mixed up..... Also, do you know how popular Core Plus is? BG: (enters, walking on ceiling): Fairly prevalent throughout Michigan and Minnesota. Used in other states too, but those are the main ones. Google on "Bachelis; Core Plus" You'll find a paper he did on it. He did a survey of students in two high schools outside of Detroit; one used Core Plus, the other a normal program. Students using Core Plus did poorly in math in the university. Chris Hirsch, the PI for Core Plus threatened Bachelis with legal action. Tom Parker of MSU did a paper on Core Plus as well using statistical data showing performance in freshman year mathematics; similar to what Bachelis did. Also criticized by Hirsch. Back to main page.
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I'm LOLing!!!!!! I'm definitely standing in front of a crazy mirror--help! help! What's a postulate! What's a theorem! Which is which! Plus the image of Barry walking on the ceiling--yikes! Does Barry look anything like Jeff Goldblum? Speaking of what people look like, I'm gonna scan my favorite family photo & post it one of these days..... Another Jakob Nielsen tip! -- CatherineJohnson - 07 Jul 2005
Now that I'm seriously thinking about POSTULATE versus THEOREM, it makes sense a postulate would be the thing assumed to be true without proof.....it's confusing because in FILM STUDIES (I just have to hope reincarnation is a possibility) theories are the things-assumed-to-be-true-without-proof. -- CatherineJohnson - 07 Jul 2005
Barry, Since you talked to Jim Milgram, I am sure he told you about the study he did on Core Plus vs traditional math program in my school district in Michigan. I think KTM would be interested in the paper or article about it. The gist is that students from the same school district who take the Core Plus vs traditional math get statistically significantly lower SAT scores and approximately one letter grade lower in their first college math course. Some students have to take remedial math courses at local community colleges to get their math up to a level where they can take calculus in college. And still our administrators defend the program!! -- AnneDwyer - 07 Jul 2005
Theories and theorems are different. And the word "theory" takes on different meaning depending on the discipline. In law, legal theory means a particular line of reasoning (from what I can glean from listening to lawyers talk). In science, a theory is a conjecture based on empirical data. The sun will rise every day is a theory based on scientific induction; i.e., because it rises every day, we assume it will rise again tomorrow, but allow for the (remote) possibility that it may not. Theorems, generally, (a term used to cover myself, just in case) are not derived empirically, but are deduced using logical rules of inference. In reform math classes, however, empiricism seems to be the order of the day, with students making endless "lists" of data and interpreting such data. It's math taught as statistics. Measure 1,000 circles to get circumference and radius, take the ratio, and we get a probabilistic derivation of pi. Take a dixie cup of a specific height and base, fill it with water, and pour the water into a glass with same base area and same height as the dixie cup. Keep doing this until the glass is filled. The empirical data tell us 3 dixie cups = 1 glass of water, with equal base areas and equal height, so we get the empricially derived formula of the volume of a cone: 1/3 Base area times height. (In Larson Boswell Stiff's Geometry book, 1995 version, this is how they introduced the concept of volume of a cone, and this is a high school geom book. Glad to see they took that out in the 2000 edition). A bit of an off point discussion, but I'm still a bit dizzy from walking on the ceiling. -- BarryGarelick - 07 Jul 2005
-- BarryGarelick - 07 Jul 2005
Anne: I'm familiar with the Milgram study (and Greg Bachelis' study, which started it all). Also, Tom Parker of MSU did a study in 03 similar to Milgram's but very rigorous. I've attached it here. Catherine: I suppose I look like a skinny Jeff Goldblum, though I tell strangers that I look like Fabio. I should stop doing that because I don't think Fabio is all that good looking; the Viking look is definitely not a plus. -- BarryGarelick - 07 Jul 2005
Barry, I fixed up your attachment link a little. I did it because I am anal, I guess. Does Jeff Goldblum walk on ceilings? Does Barry? (I thought Jeff Goldblum WAS a skinny Jeff Goldblum). -- CarolynJohnston - 07 Jul 2005
Barry, If anyone has a case for education malpractice, this CorePlus is it. In the MSU study, very few CorePlus students could actually complete enough Calculus to major in engineering or science. I live in that school district in Michigan. My children are slated to go to high school with the traditional math program. But most parents don't understand the issue. I have found that many parents don't understand the issue of Everyday Math and Connected Math. You can tell people, but they don't really believe unless they have experienced a child who fails because they just cannot get the math. -- AnneDwyer - 08 Jul 2005
EVERYONE needs to read this report of the students in Andover, Michigan. Be sure to scroll far enough down to see their SAT and ACT scores. These are smart kids. In their own words, read their unfavorable report of the math education they got in high school They know they were ripped off and mince no words saying so. We must start listening to the students who sat through this "fuzzy math". Some feel they will never recover from their loss. GO TO THIS SIGHT AND READ BACHELIS' STUDY. Show it to everyone who teaches high school math anywhere! -- CarolynMorgan - 08 Jul 2005
Barry--Did you write the line about walking on the ceiling??? That was BRILLIANT! -- CatherineJohnson - 08 Jul 2005
Great minds think alike I, too, was under the impression that Jeff Goldblum was a skinny Jeff Goldblum. I once ran into Jeff Goldblum and Laura Dern in the Armani store in Beverly Hills. (This was the one and only time I was inside the Armani store in Beverly Hills....I'm still wearing the suit I bought that day.) They were tall. -- CatherineJohnson - 08 Jul 2005
And I mean really, truly, severely tall. -- CatherineJohnson - 08 Jul 2005
And btw, when I say tall I know whereof I speak. I once ran into Gena Rowlands in the restroom at.....TOTAL MEMORY LOSS, SORRY!
update: Trump's
I think it was the restroom at Trump's. In West Hollywood. (What am I doing in Westchester?) --Main.CatherineJohnson-08 Jul2005Anne--You live in that district???? And they're still defending the curriculum????? Yup, we've got to get all that stuff covered here (I've read quite a bit of it, I think.) Do you want to write something about it??? -- CatherineJohnson - 08 Jul 2005
I have found that many parents don't understand the issue of Everyday Math and Connected Math. You can tell people, but they don't really believe unless they have experienced a child who fails because they just cannot get the math. This is probably a topic we need to make into a perennial. How do you explain your OBSESSION to other parents who are actually living a life, as opposed to writing a MATH BLIKI 24 hours a day? I had a horrible experience where I embarrassed the living daylights out of myself trying to ask a hostile question of the candidates running for school board while the PTSA "moderator" told me to sit down, my time was up. I'm mortified all over again, just thinking about it. Then a couple of days ago one of Christopher's friends said HE SAW ME ON TV. PEOPLE SAW ME ON LOCAL ACCESS CABLE TV GETTING TOLD TO STOP TALKING ABOUT TRAILBLAZERS-IN-IRVINGTON BY THE PTSA! AYYYYYYY! This is the same PTSA to which I have donated countless thousands of hours volunteering & running the after-school program. Thanks, guys! -- CatherineJohnson - 08 Jul 2005
I don't know why I didn't CONSULT WITH MY HUSBAND before attempting to ask a question in public. He's good at academic politics. I tried to ask whether the candidates thought it was OK for Irvington to bring in a curriculum that was rated Abominable or Wretched-beyond-belief or whatever it was by the state of CA, and their answer was, 'The administration looked at all the different curricula.' In point of fact, the school district looked at TERC, TRAILBLAZERS, & EVERYDAY MATH. Their stated 'Areas of Focus for Pilot' included 'Constructivist approach with modeling,' 'everyday applications of math,' 'consistent with NCTM standards,' 'developmental approach,' and yadda, yadda, yadda. In other words, the mission was to figure out which fuzzy-math curriculum to implement, not whether to go fuzzy in the first place. When I asked whether the administration had a duty to disclose the fact that they were choosing a controversial curriculum that has been formally rejected by the CA Board of Ed they said.... I don't remember what they said. Afterwards Ed told me I asked the question all wrong, which I demonstrably did. Then he told me how I should have asked it. I think he said I should have said, VERY BRIEFLY, something like, 'Do you approve of the Irvington administration adopting Math Trailblazers, which CA ranks unacceptable? Instead I managed to frame my question in such a way that the candidates could answer it by telling me I'd had an opportunity to voice my concerns at the school board meeting when TRAILBLAZERS was adopted. AND THE WHOLE THING WAS CAUGHT ON TAPE! -- CatherineJohnson - 08 Jul 2005
I've just consumed most of a kir. It doesn't show, does it? -- CatherineJohnson - 08 Jul 2005
Time to go watch my BATTLESTAR GALACTICA CD set. -- CatherineJohnson - 08 Jul 2005
"How do you explain your OBSESSION to other parents who are actually living a life, as opposed to writing a MATH BLIKI 24 hours a day?" I'm not going to compare my obsession to yours (I would probably lose.), but I know what you mean. How do you discuss these problems without overwhelming the person you're talking to? You want to do a brain dump or a mind meld, but it just can't happen. I like Ed's approach and have tried it myself. 1. I mention to people that our school uses MathLand, a math curricula so bad it is banned in California and even dropped by it's own publisher. Even people who like fuzzy math think it's bad. Why does our school use it? 2. I have mentioned to people on our school committee that they should hand out E.D. Hirsch's Core Knowledge series of books: "What your First (Second, Third, etc.) Grader needs to know" and tell parents that this is NOT(!) the education their children will receive. Why not? 3. I tell other parents about a fourth grade standardized math question (New Standards Reference Exam) that has the kids look at a bar graph with four bars showing the number of votes 4 kids received in a student election. All bars are less than 20. Two questions have to be answered: Who won the election?, and What is the total number of votes cast? Allotted time: 15 minutes. 4. I tell other parents that their kids will not be properly prepared for college prep math unless they get outside help. Parents want to know, but they don't want to be overwhelmed. Less is sometimes more. I told one parent that MathLand was horrible and was hurting our kids. In an almost conspiratorial voice, she says: "That's what someone else told me." This led to a discussion where she asked me questions. As for public officials, they have to be put on the defensive with questions like what Ed proposed. I also think it's best to stay away from arguments over constructivism. It's hard to argue over generalities and vague terms. I prefer the compare and contrast approach, especially if it is specific. Everything is quite clear when you compare two text/work books side by side. I would like to hear the NCTM math types explain how a CMP problem leads to better math "understanding" than a same grade Singapore Math problem. Show them to parents and ask them which problem they would like their child to be able to do. Let me just say that this is not about winning an argument. It's about letting people know about our complaints and concerns. The NCTM crowd throws out a lot of propaganda about understanding versus rote knowledge. We are not going to get very far if they dictate the terms of the discussion. We should start a new section of one liners. Conversation starters with barbs, if you wish. -- SteveH - 08 Jul 2005
I have just written an op-ed which I hope will be published, but looks at the circumvention that NCTM does in defending its approach. If you were to ask the question of them that Steve H does about comparing CMP to Singapore, they respond along the lines "It's not the text, it's the teacher" and then do their typical admonishments of "In the US they say here's the rule, now do the problem" and "There's too much teacher instruction". You will not be able to win an argument with these people anymore than you can catch a greased pig. What you will be able to do is convince others who may be on the fence, of the validity of your points. The PTSA that Catherine talked about has their minds made up. Most school boards do. So they looked at 3 bad math programs and picked the least worst. The question that perhaps should have been asked is "Why didn't you consider Saxon, or Singapore?" But they would have answered: 3 isn't enough for you? And so on. Doesn't matter. Come with your guns loaded, not to convince them, but the people in the room and the press (if they bother to show). In Washington DC, the school board just adopted Everyday Math, Math Trailblazers and Connected Math. I've written about this elsewhere. Their minds are made up. And the illustrious Washington Post asked Bas Braams a few questions about the issue and then never did a story. (I call the Post the Compost these days). In terms of Core Plus, Anne is correct. The program is abominable, and the harm to the students deplorable. But they fought back hard, and said things like "Who cares what students say in a survey; students can't be trusted. They're always going to bad mouth the programs, teachers, etc". Which is what motivated Tom Parker to do a more thorough review which also was lambasted by Core Plus on its web site. And, by the way, when the NAS did its study on the research base for the NSF funded programs (concluding the research doesn't show effectiveness nor ineffectiveness), Parker's study was not used. Politics. Chris Hirsch and his thugs are quite effective at what they do. I could go on. Uh, by the way, I look like a skinnier Jeff Goldblum and yes, I wrote the line about walking on the ceiling. -- BarryGarelick - 08 Jul 2005
There is an article still on the web (as of 6/10/05) titled "How a New Math Program Rose to the Top" which was published in the Christian Science Monitor, May 23, 2000, about the CorePlus Andover, Michigan story. Of what good is a high school course if smart students have to take remedial math programs in college? Quoted in this CSM article:
"Since I was a kid, I loved auto engineering," he says. "So I attended a session for those who wanted to go into engineering. When they asked how many of us took calculus, all the others raised their hands. I began to realize my dream was not going to happen." So Mr. Daitch took remedial math at the university - and became a communications major.The quote was referring to Robert Daitch, a student who took four years of Core-Plus before graduating from Andover in 1998. -- InterestedTeacher - 08 Jul 2005
Yes, that's a good article. It mentions the survey that Bachelis did. -- BarryGarelick - 08 Jul 2005
I truly believe that I totally need a way to talk to parents about the math programs. I am an engineer by training, so I tend to want to give as much info as possible. And I tend to talk about it way too much. Most elementary school parents realize instinctively that Everyday Math is not good for their children. But, because of all the propaganda, they think, "I must be wrong and they know what they are doing." I wish I had some well constructed short examples or evidence that would convince them they need to do something for their children. On the other hand, most children with a parent or parents who work in a technical field know, for a fact, that the math program is bad. Instead of complaining, they send them to Kumon or something like it. The Chinese, Japanese and Indian children are also sent to Indus Academy. This is an independent math school taught on the weekends. It is taught by PhD? mathematicians. It's not fuzzy and it is not 'fun'. Most parents sit in with their kids so they can help them with their homework. As for the other high school in our district, they teach traditional math. I have very little data from which to form an opinion, but I am not impressed. How do you defend an Honors AlegebraII?/Trig class that never gets to trigonometry? BTW, I have been investigating the ACT test. The math part is all content knowledge and covers pre algebra through trig. So if you have not had trig, well, there are some problems that you just can't do. In that rigorous study of the CorePlus program at MSU, the author states that you have to have a 28 on the math part of the ACT or take AP Calculus to qualify for the first semester of Calculus. So students who take algebra in 8th grade and have already finished AlgebraII?/Trig and some precalculus by the time they take the exam in the 11th grade have a huge advantage. -- AnneDwyer - 08 Jul 2005 most children with a parent or parents who work in a technical field know, for a fact, that the math program is bad. Instead of complaining, they send them to Kumon or something like it. The Chinese, Japanese and Indian children are also sent to Indus Academy. That's what I see, too. 'Math' parents take one look at the stuff and reject it. Everyone else is either confused, or actively supportive, or defensively supportive. (Too long to go into at the moment.) I'll have to give this some thought, but the thing that works best for me is drawing the comparison to Singapore Math. At least one KTM commenter has said that all anyone needs to see is a comparison of a fuzzy-math problem side by side with a Singapore problem. I continually push the 'global-world-economy' angle. -- CatherineJohnson - 08 Jul 2005
What is Indus? I've never heard of it. And why has the Comments box disappeared from this page? -- CatherineJohnson - 08 Jul 2005 SteveH How do you discuss these problems without overwhelming the person you're talking to? You want to do a brain dump or a mind meld, but it just can't happen. Exactly, and this isn't a new insight for me--plus I don't like to have people 'brain-dump' on me, and I don't want to brain-dump on them, either. So it's important to have talking points. -- CatherineJohnson - 08 Jul 2005
As for public officials, they have to be put on the defensive with questions like what Ed proposed. I also think it's best to stay away from arguments over constructivism. It's hard to argue over generalities and vague terms. I prefer the compare and contrast approach, especially if it is specific. Yes, absolutely. Strangely, although I'm a writer, the formulation of good questions (rhetorically good, I mean) doesn't automatically come to me. I guess that's not so strange; it's another skill, and it takes practice. We should definitely have a page of conversation starters & talking points. It's critically important, in part because we aren't going to 'win' this battle (IMO). It's been going on for a hundred years, and no one seems even close to pulling out the white flag. I have a slightly different POV on the question of arguing 'constructivism.' My sense is that the word 'constructivism' is experienced by many parents as having a 'negative valence.' You'll notice that the marketing people for NSF curricula never use it, and there's a reason for that. It's also quite difficult to find the term on the NSF site (I should check the NCTM site...) I see microexpressions of alarm and perhaps even disgust on people's faces when I spring the word 'constructivist' on them. (Definitely alarm.) Most people have either never heard the word, or have heard it a couple of times but have no idea what it means. So when they hear that their school district has selected a constructivist text ..... that raises more questions than simply saying that the district has selected a text that's too easy. The fact that the district has chosen a constructivist text without mentioning this fact to the community also registers. So I always use the word 'constructivist' and then move on to talking about the fact that my own child tested into Singapore 3rd grade at the end of U.S. 4th grade. END OF CATHERINE'S COMMENT START OF NEW COMMENT I can't find the comment box, so I'll just walk on the ceiling and barge my way in, if you don't mind. No, you won't see "constructivism" in NSF documents, nor anywhere on NCTM's web site. What you'll find on NCTM's website are admonitions from Cathy Seeley that there is too much "teacher instruction" in the U.S. No, don't bother asking her what she means, she'll wiggle out of that one easily. But you know what she means. As far as Anne's problem of succinctly stating what are the problems with Everyday Mathematics and other bad programs, it's good to have sound bites prepared. I like to quote the blurb from the EM Teacher's Reference manual how long division isn't worth the effort to teach because of the advent of calculators. That's a good ice breaker. Then I point out that when students stick to the EM curriculum, their kids are going to learn 4 inefficient ways to multiply two-digit numbers, and if they're lucky they'll be shown the traditional way. They won't be shown the traditional method for long division (not in the 4th grade anyway), and you will have bright students complaining that they don't really understand math because their confused over what method to use to solve a multiplication problem. (Yes, I heard this from a bright student). You can point to the Student Reference Manual (which is a glorified glossary) showing how equivalent fractions are handled. They will show how to convert 1/2, 1/4, 1/5 to decimals and percentages (since it's relatively easy to find ways to get the denominator to tenths or 100ths). For 3/8 (and students are presented with such problem frequently in the "Review boxes" that EM uses), the Student's Reference Manual provides detailed instructions of how to use a calculator to find the answer. If your response from the parent is "What's wrong with that?" change the subject and talk about the war in Iraq. I mean, if you have to get into a brawl, make it worth everyone's while. Barry G. NEW COMMENT--WOO HOO, I'M A WIKI MANIAC! Barry, Sorry to barge in like this, but you really do help when you give us specifics like the two-digit multiplication problems. When I used the Trailblazer letter concerning long division and mentioned it to fellow parents, that was when I actually got a response. It is very hard for the "layman" to understand all of this, particularly when teachers and administrators are using the jargon the NCTM wants them to use Catherine, Since you have Trailblazers, could you occasionally post some of their gems for us? Especially since I know you have so much free time.;-) Whatever you run across for us in Trailblazerland would be greatly appreciated. I don't see as much specifics on that one. Is it newer than the others? End of message--SusanS
Barry! Get off the ceiling! You're scaring people! Catherine 10:17pm est Friday
If your response from the parent is "What's wrong with that?" change the subject and talk about the war in Iraq. I mean, if you have to get into a brawl, make it worth everyone's while. ok, now you've been hitting the sauce. good idea, though Catherine 10:17 (still) Friday
SusanS Believe you me, I intend to post MANY problems from TRAILBLAZERS. Not that there are many to post.... Lots of TRAILBLAZERS PLAYLETS, thought. You don't see too much on the horrors of TRAILBLAZERS, it's true. EVERYDAY MATH seems to soak up all the bad publicity. Catherine 10:19 pm Friday July 8, 2005
What was it that worked for you again?
The fuzzies are smooth customers, that's for sure.
Can you be fuzzy and smooth?
Why don't I go enjoy my kir some place away from my laptop?
Seriously, though, I'm hearing from a pro-Trailblazers friend, whose child is in...2nd grade, i think...that he is acquiring conceptual knowledge of math, and that the math he's doing is much more challenging than any math she ever did. She is a 'math-friendly' mom; she took calculus in college, and has an MBA. Does TRAILBLAZERS do a good job in the very early grades? I only have the 5th grade text. The 5th grade text is ludicrous; the TRAILBLAZERS kids spend the whole book collecting data, and then adding it up. Basically, it's an entire 5th grade book about counting. (For people who don't know this, TRAILBLAZERS was originally called TIMS, which was 'integrated math and science.' The point is for all of math to be taught as a branch of statistics.) Catherine
"It's not the text, it's the teacher" and then do their typical admonishments of "In the US they say here's the rule, now do the problem" and "There's too much teacher instruction". You will not be able to win an argument with these people anymore than you can catch a greased pig. The first time I heard this I was dumbfounded. My neighbor raised her hand at the infamous 6th grade Phase 4 math meeting and said she'd be happy to put her child in Phase 3 if Phase 3 didn't have a constructivist math text. (Phase 4 has Prentice Hall). The principal, another smooth customer, swatted that one away. 'The book isn't the curriculum, the teacher is the curriculum.' This is a universal belief, I find. The teacher is the curriculum. Meanwhile, I WRITE BOOKS FOR A LIVING. WRITING BOOKS IS HARD. No teacher can teach full-time and also CREATE, out of whole cloth, A COHERENT CURRICULUM. You're right about speaking for the benefit of the parents, not for the sake of persuading the committed. At our small-group, going-to-middle-school meeting the principal told us that parents in the other meetings had asked him whether their Phase 3 kids would be able to take calculus in high school. He had been caught off-guard by that question and still, two weeks later, did not know the answer. Or, rather, he had one answer (no, Phase 3 kids wouldn't be able to take calculus in high school, but that situation would eventually be rectified, after it was too late for our kids) and the assistant principal had another (yes, Phase 3 kids can take calculus in high school). Well, 'Can Phase 3 kids take calculus in high school?' was a talking point I'd been putting out there at every opportunity. I had been telling parents, truthfully, that the slow track closes off options in high school. Obviously, parents had picked up on it. Steve's right. We need a page of talking points and advice. Barry, do you want to set one up? Steve? Anne? Susan? It needs to be set up by someone besides Carolyn or me, so everyone can edit. (Carolyn just spent hours doing the threads; eventually we'll have the user pages located up front--) Catherine
Greetings, ceiling walkers!!! I've put the comments box back below. There is a little bit of text at the bottom of every comments page that looks like this: %COMMENT{mode="above"}% Apparently someone wiped it out; that's why the comments box disappeared. Catherine, you and I can also create web pages from the comments page that are editable by everybody. It's only the blog pages that are protected. Here, I'll do it now: here is our new TalkingPointsDiscussion page. Catherine here: I know. This morning I woke up and thought: Carolyn and I can create web pages from the comments page that are editable by everybody.
You don't see too much on the horrors of TRAILBLAZERS, it's true. EVERYDAY MATH seems to soak up all the bad publicity. -- Catherine I think the only reason for that is that Everyday math is a lot more popular. Everyday Math is EVERYWHERE, but you're the only person I know that's afflicted with Trailblazers. -- CarolynJohnston - 09 Jul 2005
Trailblazers has just been adopted in DC. Their day is coming, unfortunately. -- BarryGarelick - 09 Jul 2005
Catherine, My neighbor will be dealing with the 5th grade Trailblazers text so whatever you say about it I'm relaying it back to her. I have been doing that all along. I've said about as much as one can say on the subject. She is concerned, but I can tell still waffling a bit. What cracks me up is how these curriculums are always described (by parents and teachers) as the only courses that reveal conceptual logic behind the basic math algorhythms, like no other math text deals with concept. I'm pretty sure I, too, would have totally fallen for the pretty texts and pictures myself, along with all the long-winded explanations on why my kid doesn't need that nasty "kill-and- drill" since he will just pick these skills up naturally. If math was hard for you and you never learned why then this just washes all that discomfort away. By the time the kid has trouble down the road I imagine the parent is still going to be unable to figure out who to pin the blame on. Also, it seems that parents (who may also have a faulty math education) whose kids don't appear to be very good at math (for who knows what reason) are seriously lulled by the feel-good quality of the courses. From some of my conversations with different friends of mine they seem to love the "real world" aspect of it, along all that cool data collecting. To some adults this looks practical. BTW, Illinois Loop has a lot of testimonials from parents. I read a great one that is actually a couple of years old, by a very well-educated and active parent who totally missed the signs of what was happening with her daughter in math class. One interesting point was that she wrongly associated any resistance to math reform as being a conservative thing. She was truly horrified by her error in judgement and wanted eveyone to know her story since she couldn't go back and change her daughters experience (although I think she did a Kumon rescue attempt that helped quite a bit.) -- SusanS - 09 Jul 2005
My neighbor will be dealing with the 5th grade Trailblazers text so whatever you say about it I'm relaying it back to her. I have been doing that all along. I've said about as much as one can say on the subject. That reminds me, we have to continue our 'how to correct fuzzy math at home' topic..... We probably need a separate page for that. I'm just reading some fantastic articles by a Russian mathematician who emigrated to the U.S. that are making me feel that the simplest way to handle a fuzzy math curriculum at school may be:
- worksheets
- Singapore Math Challenging Word Problems books
The amazing thing about TRAILBLAZERS is all the playlets. Do the other fuzzy curricula have endless playlets? -- CatherineJohnson - 09 Jul 2005
The other amazing thing is that in many of the TRAILBLAZERS playlets the kids are expressing abject doubt. One of these days I'm going to do a COMPARE AND CONTRAST on the visuals in TRAILBLAZERS versus SINGAPORE. Most of the pages in PRIMARY MATHEMATICS have drawings of little 'student helpers' who know the answer, and how to get it. TRAILBLAZERS is filled with drawings of students who have no clue what the answer is. -- CatherineJohnson - 09 Jul 2005
There's one huge drawing of a TRAILBLAZERS kid whose face is filled with MATH ANXIETY. How does this square with 'modeling'? -- CatherineJohnson - 09 Jul 2005
btw, this is something I never got around to blogging about way back when. Carolyn found evidence that group learning works, and we were wondering why that would be. Bernie thought some of it had to do with competition, which is probably true. It also struck me that groups allow for observational learning. Kids & animals do huge amounts of observational learning. In a group, children are going to see other children doing math & solving problems. This is why educators always tell parents to read in front of their kids--and it's why we should 'do math' in front of our kids, too. Back to TRAILBLAZERS: the book is filled with kids who are perplexed, confused, and struggling. Singapore is filled with kids successfully & efficiently doing math inside their heads. No child in Primary Mathematics is shown collecting data. Of course, that's what Steve Leinwand objects to. -- CatherineJohnson - 09 Jul 2005
I have also found a couple of "math-smart" people who like the ideas in Trailblazers, also. It should be interesting to see how that develops. Catherine, I'm not good at linking, so I'll just tell you where to find the article. Go to Illinois Loop site's main menu. Click on Personal Stories. About three links down is a story called "My Conversion." That is it. The other stories are quite good, also. In the book Knowing and Teaching Elementary Mathematics (is that Liping Ma?) there is a lot of discussion about group learning and manipulatives but I see one big difference: The Chinese teachers are not "facilitators" in the least. They control the discussion and clearly lead at all times. Plus, I imagine teaching half of the subjects that Americans teach means they have more time for such activities anyway. -- SusanS - 09 Jul 2005
By the way, with linking all you have to do is paste the URL into the comments box. Like this: http://www.illinoisloop.org/conversion.html -- CatherineJohnson - 09 Jul 2005
That's the story, right? -- CatherineJohnson - 09 Jul 2005
If somebody wants to pretty up a 'naked' html link, he can. But it's not necessary to do all the html-ing. Just copy the link from the URL & paste it in the edit window! If you want to look at the html for a standard-format link, hit 'edit' at the top of this page and scroll down until you find this comment: My 'Conversion' -- CatherineJohnson - 09 Jul 2005
I am not a good writer. I would love it if I could send a well written letter to the editor of my local paper explaining why people should be concerned about Everyday Math. Could KTM have a section containing letters like this that people like me could copy? -- LoneRanger - 10 Jul 2005
Could KTM have a section containing letters like this that people like me could copy? YES KTM COULD! Ed and I headed up an unbelievably successful pro-Lynn and Bob Koegel campaign at the NIH a few years ago by doing exactly this. I spent hours and hours writing a letter about their research; Ed edited; then we put it out on the web and told everyone: This is your letter. Cut and paste the whole thing, use parts of it, edit it, change it; do whatever you like. Huge numbers of parents flooded the NIMH with letters based on ours (or were sparked to write their own). We heard later, from a good source, that people at the NIMH were 'literally running through the halls.' We were all kind of curious about why exactly a staffer at the NIMH would run through the hall under any circumstances. -- CatherineJohnson - 10 Jul 2005
Catherine, the visual of people running through the halls at the NIMH cracks me up. It's sort of like West Wing combined with the halls-and-doors scene from Yellow Submarine. Prentice Hall Course 1 has a lot of photos of kids too, but I'm honestly not sure why. They aren't doing math in their heads, and they aren't struggling either; they are propping up posters with text on them, describing the different ways that they came to the same answers. Their main purpose seems to be to teach a subtle side lesson on diversity; they are Asian, black, white, Hispanic, walking on crutches, sitting in wheelchairs. No Down Syndrome kids, though. -- CarolynJohnston - 10 Jul 2005
| WebLogForm | |
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| Title: | Barry Garelick guest blogs on Core Plus |
| TopicType: | WebLog |
| SubjectArea: | CorePlus, MathWars |
| LogDate: | 200507062248 |
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 HillParker5.pdf | manage | 208.9 K | 07 Jul 2005 - 13:36 | BarryGarelick |