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June2005
AboutLongDivision 01 Jun 2005 - 01:17 CarolynJohnston
(I actually wrote this post a couple of days ago, when my internet connection was down!). Ben's half-brother is visiting for Memorial Day Weekend. It's always wonderful when Colin comes; in spite of their size difference (Colin, who is 16 and about 6'2", is more than a foot taller than Ben) there is a lot that they can do together; watch movies, play Nintendo, play basketball. But, of course, learning still has to go on, and last night I insisted that Ben had to get some long division practice in. He knows the long division algorithm, and a few months ago I taught him how to divide by decimals. So now I am trying to get Ben to overlearn decimal long division, and the best way to do that is to get him to practice it. So I handed him a sheet of paper with some long division problems on it and asked him to do them. He did them too fast -- too eager to get back to Colin and the Nintendo game -- and got most of them wrong. Not surprising, perhaps, but I'm looking for his long division skills to be so automatic that he can do them when most of his conscious attention is elsewhere. I want long division to be a no-brainer for him, literally. It should be in his fingers. He did the problems over again this morning; I stood looking over his shoulder to try to figure out what had gone wrong the night before. I was surprised at how good he actually is at the long division algorithm. He is, in fact, working out the few bugs left before he achieves mastery, and the distraction of Colin's presence had driven them out into the light. If your kid is at or near the mastery point in long division, here are a few problems to look out for, and some sample problems that might help diagnose them.
- Uncertainty about what to do if the divisor does not divide the current number, after you bring the next digit down. For example, this occurs in the second step of dividing 92.0 by 9. The answer to this problem is 10.2222... a child who does not have this down cold will typically get 12.222222 for an answer, skipping over that lone zero.
- Uncertainty about what to do with a problem where the dividend has fewer decimal places than the divisor. One example of this is the problem 34/.21. In setting up this long division algorithm, the divisor and dividend should both be multiplied by 100: i.e., the decimal should move to the right by two places for both values, and the division problem should become 3400/21. A kid who does not completely have this nailed may get confused about what to do with the 34.
- Uncertainty about where to stop the long division process. Division problems that do not terminate should read, in general, something like "find the value of 213/14 to the nearest tenth (or hundredth, or whole number) ". A kid needs to be taught explicitly how to handle answering these questions. For example, suppose a problem reads: find 92.17 divided by 13 to the nearest tenth. Then the child should actually calculate the quotient out to the hundredth place, and round the answer to the nearest tenth. In the case of this problem, the child will get 7.09 as an answer through long division, and should round this answer to 7.1.
StrugglesWithLongDivision
MathInTheBlood
ForgivingDivision
ForgivingDivisionPart2
TryThisWithForgivingDivision
TeacherGuideEverydayMath
EverydayMathEpilogue
ThirteenQuartersInTerc
HowNotToTeachMath
WhoSaysLongDivisionIsHard
comments...
PaperFractions 01 Jun 2005 - 15:39 CatherineJohnson
Success! I'd been trying to find one of my favorite Math Wars quotes, without luck. Then this morning it popped up unannounced in the middle of a different quest altogether. Here is David Klein, speaking at a 2002 AEI seminar called DOES TWO PLUS TWO STILL EQUAL FOUR? WHAT SHOULD OUR CHILDREN KNOW ABOUT MATH?:
DR. KLEIN: The NCTM standards actually have deep mathematical flaws. The 1989 version was worse than the present one, but the present one does have some serious problems. For one thing, the quadratic formula, a major topic in eighth grade algebra, isn't even mentioned in the document.
But when the NCTM standards attempt to explain how to divide fractions for middle school, they don't even do it correctly. The method that they give there is they suggest repeated subtraction and analogy with whole numbers. Try that with 5/8 divided by 3/4 using the NCTM methods, and you'll be cutting paper all day and all night.
I don't think 5/8 is a very friendly fraction.
DontRelyOnStateTests
PenfieldParents
NewYorkStateMathCurricula
CompareAndContrastPart3
FriendlyFractions
PaperFractions
ADifficultChild
ADifficultChildPart2
WorksheetsForSummer
AssessYourChildForFree
AssessYourChildForFreePart2
BonusOnlineAssessmentQuestions
comments...
FriendlyFractions 01 Jun 2005 - 16:20 CatherineJohnson
Want to know what comes up when you Google friendly fractions?
Visit Fraction Town and meet Friendly Fractions and Fractions Not So Friendly, even see a Fraction Frenzy as students learn about fractional parts. Dividing and multiplying by one and two digits and determining the probability of events occurring finish up the school year. Have a great summer!
Day 151 sounds especially fun!
Fraction lesson created for day 152 of the 180 day sequence of lesson plans. Students will use their knowledge of fractions to create a map of Fraction Town and decorate their map using what they've learned about fractions.
See also:
DontRelyOnStateTests
PenfieldParents
NewYorkStateMathCurricula
CompareAndContrastPart3
PaperFractions
ADifficultChild
ADifficultChildPart2
WorksheetsForSummer
AssessYourChildForFree
AssessYourChildForFreePart2
BonusOnlineAssessmentQuestions
comments...
SlowOnTheUptake 01 Jun 2005 - 18:31 CatherineJohnson
It's 2:30, and I've managed to miss the big news of the day 'til now. Joanne Jacobs has links to Jay Mathews' 10 Myths (Maybe) About Learning Math as well as to NYC HOLD's response.
ILikeMathPart2
ILikeMath
comments...
CulturalEvolution 01 Jun 2005 - 20:09 CatherineJohnson
NYC HOLD has posted a talk by Fred Greenleaf, Professor of Mathematics at NYU, called High School Programs That Work (pdf file). This passage jumped out at me, because Temple and I talked about this in Animals in Translation:
Since prehistoric times, human beings have survived and prospered by being
able to pass on the accumulated knowledge of our species to our children. In the
present era we have vast bodies of information to deal with; some areas (medicine,
mathematics) have taken hundreds or even thousands of years of patient exper-
iment, observation, and false starts to evolve into their present forms. Passing
all this knowledge from one generation to the next requires efficient and effective
methods, namely flexible and innovative direct instruction by teachers who are
highly competent in their subjects. Having students sit around re-inventing the
wheel in endless trial-and-error “discovery projects” is not an option.
Professor Greenleaf is talking about cultural evolution. Temple and I spent some time on this subject because, at the time we were writing, no one had seen cultural evolution in nonhuman animals. (Since we finished the book, cultural evolution may have been demonstrated in the New Caledonian crow -- and, for what it's worth, I personally won't be surprised if we find cultural evolution in other nonhuman animals. But that's beside the point. Cultural evolution is the hallmark of the 'human animal,' and is certainly the hallmark of our own culture.) Here is M. Tomasello on cultural evolution:
Cumulative cultural evolution is thus the explanation for many of human beings' most
impressive cognitive achievements. . . . Most importantly, cumulative cultural evolution ensures that human cognitive ontogeny
takes place in an environment of ever-new artifacts and social practices which, at any one time,
represent something resembling the entire collective wisdom of the entire social group throughout its
entire cultural history. Each child who understands [other people] as intentional/mental beings like
herself . . . can now participate in the collectivity known as human
cognition, and so say (following Isaac Newton) that she sees as far as she does because she "stands on
the shoulders of giants."
For the sake of argument, let's agree that we want our children to develop 21st century skills. What does this mean? It means we want them to go beyond us, to discover knowledge we have not discovered ourselves. We want them to stand on our shoulders. If our children spend their childhoods re-discovering the wheel, it is possible they will not be able to discover what comes after. We need to pass our knowledge on to them now, while they are young, and their minds are like little sponges. We need to do this now, because time is always short. Childhood is fleeting, and one day we will be gone.
(I'll upload the complete article shortly.)
comments...
FreshHorses 01 Jun 2005 - 21:00 CatherineJohnson
I had never seen this before:
It is a profoundly erroneous truism repeated by all copybooks, and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of operations which we can perform without thinking about them. Operations of thought are like cavalry charges in battle - they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.
- Alfred North Whitehead, Introduction to Mathematics
quoted by Ethan Akin, In Defense of 'Mindless Rote'
I love it! 'Fresh horses' and 'cavalry charges' are much more fun to think about than working memory and automaticity!
comments...
HowCouldIForget 02 Jun 2005 - 00:41 CatherineJohnson
I just remembered. I haven't posted anything about the fact that I have two kids with autism. Christopher isn't the only child around here who needs Serious Intervention. There are 3 of them! Jimmy, Andrew, and Christopher. Jimmy and Andrew are autistic. Andrew is Christopher's twin, and he's just started to learn some math this year. I'm going to Have At Him this summer. (So if anyone has any ideas, or knows anyone who has any ideas, please. Chime in.)
comments...
TheBomb 02 Jun 2005 - 00:48 CatherineJohnson
There. I've done it. I've dropped the autism bomb.
MoreAutismBomb
comments...
TheBombPart2 02 Jun 2005 - 01:07 CatherineJohnson
So yesterday, some of the moms on the aqueduct were debating whether anyone from our school ever gets into Harvard. One of them said, "The only reason to go there is so you can spend the rest of your life dropping the Harvard bomb."
MoreHarvardBomb
comments...
SpotTheFallacy 02 Jun 2005 - 01:09 CarolynJohnston
There's a new book out called "National Differences, Global Similarities: World Culture and the Future of Schooling", by two education professors at Penn State, and published by Stanford University Press. It was discussed in yesterday's PhysOrg.com newsletter (hat tip: bernie). They analyzed data from the Third International Study of Mathematics and Sciences, which in 1994 and 1999 collected a lot of data on educational effectiveness in 41 countries. From the article:
Their findings indicated a frequent lack of positive correlation between the average amount of homework assigned in a nation and corresponding level of academic achievement. For example, many countries with the highest scoring students, such as Japan, the Czech Republic and Denmark, have teachers who give little homework. "At the other end of the spectrum, countries with very low average scores -- Thailand, Greece, Iran -- have teachers who assign a great deal of homework," [author] Baker noted.
Their conclusion is that homework is actually bad for learning, proving that even education researchers can be tripped up by the correlation implies causation fallacy.
But worse than that, homework is not politically correct:
If schools expect every family to reinforce the child's learning process at home, they need to realize that, when families are unequal to the task, students will not receive the same quality of education. The addition of homework will only exacerbate existing inequities within a nation's student population and pull down overall scores, said Baker.
"Those families that are better able to marshal resources to support outside school learning will likely gain disproportionate advantage," he added.
Fixing this problem will put us one step closer to the year when everyone will finally be equal.
comments...
SuitablyHorrified 02 Jun 2005 - 01:28 CatherineJohnson
That's me. Suitably horrified:
The addition of homework will only exacerbate existing inequities within a nation's student population and pull down overall scores, said Baker.
"Those families that are better able to marshal resources to support outside school learning will likely gain disproportionate advantage," he added.
While we're playing Spot the Fallacy, how about a round of Identify the Logical Inconsistency? I'll go first. a) homework has no effect on learning b) homework will increase educational inequality because white children will do it, and black children will not Both statements cannot be true.
comments...
SuitablyHorrifiedPart2 02 Jun 2005 - 01:45 CatherineJohnson
OK, this is maybe not the best criticism for me to be raising after my 50% of 10 is one-half of 5 fiasco, but isn't there a problem with the math here?
The addition of homework will only exacerbate existing inequities within a nation's student population and pull down overall scores, said Baker.
So the way this works is . . . homework unfairly raises the scores of kids in high-functioning families, while the scores of kids in low-functioning families remain in the cellar, thus increasing Grade Inequality. So how exactly do you get decreased overall scores in that scenario? Doesn't the mean go up when the top scores go up? Isn't that the whole point of disaggregating the data?
MoreDisaggregatedData
comments...
FromAReader 02 Jun 2005 - 13:48 CatherineJohnson
My daughter was tutored for six months at the Sylvan Learning Center in [name of town omitted]. The . . . owners of the Center . . . said that Everyday Mathematics was great for their business. The program being used in several communities near the Center. [Name of town omitted] now has a Kumon! Of course this data never shows, because they dont want to know! My daughter went from two grades below grade level to two grades above grade level in the six months she was tutored. When she took the Stanford 9 she scored in the 90 percentile. No credit to Chicago Math but to her tutoring. She also did Saxon at home.
spaced repetition:
My daughter went from two grades below grade level to two grades above grade level in the six months she was tutored. When she took the Stanford 9 she scored in the 90 percentile.
ATeachersStory
CompareAndContrast
FromAReader
PracticePracticePractice
BarModelingVsGraphing (interesting comments from a KTM reader)
comments...
IHaveAPlanAndImStickingToIt 02 Jun 2005 - 14:47 CatherineJohnson
I'm going to clean off my desk today.
ImNotKidding
comments...
ADifficultChild 02 Jun 2005 - 15:24 CatherineJohnson
Barry Garelick told me to go find Ralph Raimi's web site and read his articles.
This is an excerpt from the one I started with:
If I were asked what seriously could be done to teach something
useful in the name of math to this kid, I would advise starting with the
arithmetic of fractions, i.e. what she failed to learn in the 5th and 6th
grades and since, and their applications and meaning of course. I believe
this could be made interesting to her once she knew she didn't have to
learn all those symbol manipulations she has been plagued with these last
five years. But there is nobody to do this for her, and there is no clear
incentive, since all she thinks she needs is to pass the next few exams.
Even with time and a knowledgeable teacher as private tutor,
fractions might not make it past the starting gate, since she has been
persuaded that her calculator has rendered them unnecessary.
Read the whole thing.
ADifficultChildPart2
TeachUsMath
PenfieldParents
DontRelyOnStateTests
NewYorkStateMathCurricula
CompareAndContrastPart3
FriendlyFractions
PaperFractions
WorksheetsForSummer
AssessYourChildForFree
AssessYourChildForFreePart2
BonusOnlineAssessmentQuestions
comments...
LiveBloggingTheSpellingBee 02 Jun 2005 - 15:32 CatherineJohnson
Joanne Jacobs says Throwing Things is liveblogging the Spelling Bee. Spelling is our other big obsession around here.
BeingYourChildsFrontalLobes
GreatMomentsInWorldHistory
comments...
ProgressReportPart2 02 Jun 2005 - 15:37 CatherineJohnson
I can't say my desk is looking a whole lot better.
comments...
NewAndImproved 02 Jun 2005 - 16:41 CatherineJohnson
OK, progress. I have stacked, and I have dusted. Stacking is good.
The area beneath my desk, however, looks NothingLikeThis. Nor do I envision a day when it will.
comments...
DavidKleinAtAEI 02 Jun 2005 - 16:56 CatherineJohnson
I've learned from David Klein that the American Enterprise Institute posted his hand-out materials, not the speech he gave. go here to read it
excerpt:
While he was president of the NCTM, Jack Price said that minority groups and women do not learn math the same way as white males. He stated:
"... women have a tendency to learn better in a collaborative effort when they are doing inductive reasoning."
This was in contrast to the way white males learn math. According to Jack Price,
"males ... learn better deductively in a competitive environment."
This attitude toward women and minorities is consistent with the NSF funded math books. They rely heavily on superficial repetitive patterns, a form of inductive reasoning, rather than logical deduction, which is the core of mathematics.
The NCTM has attempted to redefine mathematics itself in order to support a notion of learning styles in math associated with skin color and gender.
This is misguided in the extreme.
I'll say.
comments...
CanAnyonePlayThisGame 02 Jun 2005 - 17:18 CatherineJohnson
re: DavidKleinAtAEI
I'm interested in the subject of sex differences in math learning & achievement. (I think the whole idea that Blacks, Hispanics, and Women all Learn The Same Way is ludicrous on the face of it.) I don't personally have a problem with the idea that men may have a biological advantage when it comes to learning math (or to very high achievement in math, I should probably say). Nor do I have a problem with the idea that if they do have an advantage, it has to do with spatial ability. I find this notion pretty interesting, as a matter of fact, and have now spoken to two women with degrees in mathematics who went out and learned how to draw specifically to increase their spatial ability. (When I finally learned to draw last summer, something I had wanted to do all my life, I was in the class for about 5 seconds before I realized: this is math. More on that another day.) Anyway, it may or may not be true that spatial reasoning has something to do with high achievement in mathematics, and it may or may not be true that men tend to be better at spatial tasks. As far as I can tell, the evidence for these two propositions is reasonably strong at this point, though I could be wrong. I'm not doing a review of the literature here. What I do know is that: I want to learn real math whether I'm good at rotating figures inside my head or not. (I stink at rotating figures inside my head.) I certainly do not want the NCTM to decide, on my behalf, that I need to learn a kind of math that isn't really math, because I'm a woman, so therefore I'm out of the running for the standard deductive math (white) boys and (white) men get to know. Furthermore, if the ability to solve certain spatial tasks is useful to learning and understanding math, then I want to develop spatial ability. I want to learn deductive math, and I want to 'remediate' anything in my own way of thinking and learning that will help me to do that.
comments...
DolcianiStructureAndMethod 02 Jun 2005 - 19:52 CatherineJohnson
Yay! My copy of Algebra Structure and Method Book 1, by Brown, Dolciani, Sorgenfrey, & Cole, just came. I discovered Dolciani in Barry Garelick's article on math ed:
Accomplished mathematicians wrote many of the texts used in that earlier era , and the math—though misguided and inappropriate for the lower grades and too formal for the high school grades—was at least mathematically correct. Some of the high school texts were absolutely first-rate, and new-math–era textbooks like Mary Dolciani’s “Structure and Method” series for algebra and geometry continue to be used by math teachers who understand mathematics and how it is to be taught.
I obsessively tracked down an edition from 1994, because that is the edition The Principal's Guide to Raising Math Achievement cites, but I have no idea whether the 1994 matters if the title and all four authors are the same.
I just came across a site that sells the teacher's edition as well. At least, it does today (click on the book):
comments...
TeachUsMath 02 Jun 2005 - 20:34 CatherineJohnson
Eventually Carolyn and I will get links to all the parents' sites & education blogs. Here is Penfield, NY's parent group, Teach Us Math. Be sure to check their blog. Commenters have left links to terrific sites.
PenfieldParents
ADifficultChild
ADifficultChildPart2
comments...
ParentAtTeachUsMath 02 Jun 2005 - 20:41 CatherineJohnson
Oh my goodness. I'm reading through the comments at Teach Us Math.
Our 7th grade, straight A math student, came home approximately five weeks ago and very proudly informed me that she finally got it. The fraction 1/4 equals .25 which equals 25%. I told her I was very proud of her, and when she left the room I cried. Of all the school districts we have had our children in, only Penfield has allowed children to pass math without knowing any math.
comments...
SayItAgain 02 Jun 2005 - 20:46 CatherineJohnson
Another commenter at Teach Us Math.
I teach math now at a university. The most significant barrier to students mastering calculus is poor symbol manipulation skills - especially with respect to fractions. These skills are acquired over many years with practice. First with paper and pencil calculations, then with operations with fractions, then with the first year of algebra. I have never met a student who was skilled at symbol manipulation who had any difficulty digesting the basic concepts of calculus. Students who stumble all over themselves doing basic algebra never really grasp the fundamental ideas. Unfortunately, at the university level they will never get enough practice to make up for the deficits they bring from K-12.
This is a universal perception. I have yet to meet a college-level mathematics professor who did not immediately bring up students' inability to handle fractions as a barrier to all future achievement.
comments...
TakingABreakPart2 02 Jun 2005 - 22:15 CatherineJohnson
comments...
WebmasterApologizes 03 Jun 2005 - 01:12 CarolynJohnston
To Catherine, who couldn't change the name on one of her posts; and to all who tried and were unable to comment today: I'm sorry. It was my fault. Pick an excuse:
a. I gotta stop webmastering when I'm drowsy.
b. I'm a novice at this, so sue me!
Anyway, the problem is all fixed now.
Please note our new 'anonymous login' feature! Enter a comment, and when the system prompts you for a username, give:
username: KtmGuest
password: guest
So if you're shy, now you can leave us a comment anyway, and we hope you will!
comments...
HappyFaceMath 03 Jun 2005 - 02:11 CatherineJohnson
See? I told you math is fun.
comments...
SummerSupplement 03 Jun 2005 - 03:52 CarolynJohnston
Ive been looking around a bit for an alternative to Saxon 76 for summer math practice. This was mainly because we only have 3 months, and Saxon homeschool books have well over a hundred lessons in them -- I would have had to go through it, picking what lessons to skip, and I'd rather not. I decided to take the opportunity to introduce the math series Ben is going to be using in his middle school math classes: Prentice-Hall Mathematics. Our school district has widely adopted Connected Math for grades 6-8, and I fought hard to get Ben into one of the two remaining schools in our district that use a standard curriculum. But it occurred to me the other day that I know very little about this school's curriculum choice: subconsciously, I guess I'd decided that any school with the sense not to jump on the CMP bandwagon could be trusted to choose a decent math curriculum. But of course, there's no being sure about that. The world isn't black and white, and there's more than one way to mess up a math curriculum. But I did as well as I could do within this district, and now I need to find out what we're in for. So I ordered a copy today of Prentice-Hall Mathematics, Course 1.
I must say, the table of contents is right up my alley:
1. Decimals
2. Algebra: Patterns and Variables
3. Number Theory and Fractions
4. Adding and Subtracting Fractions
5. Multiplying and Dividing Fractions
6. Ratios, Proportions, and Percents
7. Data and Graphs
8. Tools of Geometry
9. Geometry and Measurement
10. Algebra: Integers
11. Exploring Probablilty
12. Algebra: Equations and Inequalities
Short and to the point, with an early emphasis on the critical topic, fractions. Though we could probably do with a break of a year or two from Exploring any more Probability, but that's just too much to hope for. FreeWorksheets
TreadingWater
SummerSupplementTime
SummerSupplementTimePart2
SummerSupplementTimePart3
SummerSupplementTimePart4 (resources for kids who have fallen behind)
SummerSupplementTimePart5 (resources for preventing summer regression)
SaxonPlacementTestsAndGuides
SingaporeMathPlacementTest
TeachYourChildToTypeThisSummer
comments...
NoComment 03 Jun 2005 - 13:35 CatherineJohnson
Increasingly, the nation's richest are spending their money on personal services or exclusive experiences and isolating themselves from the masses in ways that go beyond building gated walls.When the Joneses Wear Jeans
These Americans employ about 9,000 personal chefs, up from about 400 just 10 years ago, according to the American Personal Chef Association. They are taking ever more exotic vacations, often in private planes. They visit plastic surgeons and dermatologists for costly and frequent cosmetic procedures. And they are sending their children to $400-an-hour math tutors, summer camps at French chateaus and crash courses on managing money.
also see:
MoneyTalks
SpecialEdReferralsEverydayMath
comments...
BrianLehrerOnNYCScoresNow 03 Jun 2005 - 14:20 CatherineJohnson
The Brian Lehrer show is covering the NYC score increase now Definitely worth listening; they're giving the Mayor's guy a lot of trouble at this point. He's giving them the run-around, IMO. His point: it's sad that, instead of celebrating all the hard work and great scores, people are looking for Bad Stuff. Brian Lehrer's response: we're journalists. We look for Bad Stuff.
Ed just called with something I missed; apparently the mayor's guy said that there is a widening gap between high and low scorers. The kids who were already at 3 or 4 scored higher; the kids at 1 and 2 scored lower. [IIRC, scores of 1 and 2 are 'below proficiency'; 3 is 'proficient'; 4 means the student scored above proficiency.] The mayor's guy (sorry, I didn't catch his name) said this pattern was seen across the board, at both high- and low-performing schools. He also says they didn't take a 'significant' number of non-English speakers out of the testing pool. OK, just caught his name: Dennis Walcott, Deputy Mayor for Policy
Now they've got Eva Moskowitz on. I can't say she's doing too well. She's not going to be 'pushed into an analysis' . . . something like that.
Bob Tobias from NYU (yay Hometeam) is up next, expert on testing. 'much more in-depth analysis of the data before we can' say what's what etc. etc.
Brian Lehrer: what do you really think? [Thank you, Brian Lehrer.] 'To me that says that something other than the policies in . . . [NYC] is responsible . . ' 'I don't see evidence for the efficacy of the reforms . . . ' UPDATE 9-30-2006: Bob Tobias was right. 'We have nothing to compare the city data to.' State scores went up everywhere. He's firm on this: if scores went up everywhere, then the rise we see in NYC scores isn't attributable to Bloomberg reforms. [I don't understand the ins and outs of NYC testing. City students apparently take two sets of tests: the state tets, and a unique set of tests only NYC takes. Apparently next year, because of NCLB, these tests will be given across the state, not just in the city.] Back to Tobias; I think it's fair to say he thinks the scores are flukey. 'I've been looking at scores for 30 years and I've never seen rises like this; These rises are really incredible, etc.'
The folks at Everyday Math must be writing up their press releases right this minute.
Now they're onto political analysis: Mayor Bloomberg told voters he'd do for education what Rudy did for crime, and now he can say he did it. I hope Diane Ravitch is surrounded by Good Friends and Soothing Music, seeing as how her view of Mayor Bloomberg can pretty much be summarized as:
(click on the Mayor for the article)
'It looks nit-pickey to the public to be raising questions.' Are we teaching to the test? Parents worry. We are as a society so solely focused on the tests that there are schools not teaching art as much as they used to. [this is not a concern for me now that math has become a branch of English Language Arts]
NYC HOLD on 'Children First', which seems to be the all-constructivist-all-the-time program Bloomberg & Klein instituted top-down
Next up on the Brian Lehrer show: chick lit . . . 'I am proud to admit I write chick lit . . . I try to empower myself to write chick lit . . .It's about being a single woman and owning that . . . '
Etc.
hoo boy. wait til you've got a coupla kids in the public school system, honey. ok, back to math.
Here's Bob Tobias in the Post: UPDATE 10-1-2006: sorry, link no longer working; NY Sun link good
Robert Tobias, director of the Center for Research on Teaching and Learning at NYU, wasn't certain how much credit to assign to Bloomberg's reforms.
He noted that districts with the highest fourth-grade gains had the highest number of third-graders held back last year.
In District 9, which posted a huge 17.5-point gain, more than 430 kids were held back, and roughly 12 percent fewer pupils took the tests this year.
"I'm not saying that the policies aren't working — however, I think we've got to put it in perspective," Tobias said.
"I would expect that [retention] would have an impact on the achievement gap."
Brian Lehrer Show on NYC scores 2005
stupid mayor trick
Thank you, whole language
guess and check reading
stupid mayor trick part 3: the good news
The Spin Doctors reading scores 2006
National Reading Panel (official website)
The Partnership for Reading
(govt website: "bringing scientific evidence to learning")
National Reading Panel report full text (pdf file)
comments...
TakingABreakPart3 03 Jun 2005 - 17:37 CatherineJohnson
(click on the painting for artist info)
comments...
TeenageBrain 03 Jun 2005 - 21:40 CatherineJohnson
Jerry Becker has posted TIME MAGAZINE's article on the teenage brain over at The Math Forum. I'm especially interested in this subject, because, last I checked, researcher Jay Giedd seemed to have found a second window of very active brain growth in adolescence -- a discovery I interpret to mean that 'Birth to 3' is not the only period in a child's life that can benefit from intensive intervention. (I could be wrong; this is what I remember of the first coverage of his research a few years ago.) One of these days I'll get around to reading The Myth of the First 3 Years: A New Understanding of Early Brain Development and Lifelong Learning, and while I'm at it I'll re-read Malcolm Gladwell's review. I've seen special ed programs that simply give up on middle schoolers, because the window has closed. I'm against that.
update 1-19-2006 FRONTLINE interview with Giedd:
The most surprising thing has been how much the teen brain is changing. By age six, the brain is already 95 percent of its adult size. But the gray matter, or thinking part of the brain, continues to thicken throughout childhood as the brain cells get extra connections, much like a tree growing extra branches, twigs and roots. In the frontal part of the brain, the part of the brain involved in judgment, organization, planning, strategizing -- those very skills that teens get better and better at -- this process of thickening of the gray matter peaks at about age 11 in girls and age 12 in boys, roughly about the same time as puberty. After that peak, the gray matter thins as the excess connections are eliminated or pruned. So much of our research is focusing on trying to understand what influences or guides the building-up stage when the gray matter is growing extra branches and connections and what guides the thinning or pruning phase when the excess connections are eliminated.
comments...
PatternLearning 04 Jun 2005 - 01:14 CarolynJohnston
see also: SummerSupplement. Another reason I want to supplement from the Prentice Hall text this summer is to familiarize Ben with the style of his middle school math series, so we can skip the format shock period at the beginning of the school year. This is the period when the style of the book seems so new and strange, and he can't find the problems he's supposed to do, and he can't focus on the topic just because of the strangeness of the book. This is definitely something that has to be taken into account in Ben's learning. He copes better with transitions of all sorts over time, but there is still a cost to making changes. Besides, he is starting middle school this fall. He doesn't know what's about to hit him, and his teachers keep assuring me that my concerns about his managing lockers, his homework, the transitions between classes, are all pointless. I hope they're right about that; I think they're crazy, but I hope I'm wrong. At least, if all goes well this summer, Prentice-Hall Mathematics will be a familiar friend in the fall. Catherine and I both have a lot of familiarity with 'format shock', because it's a characteristic that everyone has to one degree or another, and people on the autism spectrum have extreme cases. Transitions of any sort are just hard for people with autism disorders, even mild ones. One of the things that autism affects is the ability to extract the main idea from something. This is why transitions are difficult; because in the prior learning experience, the person may have focused on, and felt supported by, something that wasn't central to the topic. When the support vanishes -- which it may at any time, if it's not central to the topic -- it's disruptive. The support itself can be something very insignificant, like the color or font of a 'highlights' box on the corner of a page. But we all rely on incidental supports to some extent, when learning something new. Non-central props help support us as we move to the next stage in our learning. At the other extreme, imagine how frustrating it would be if you were trying to learn something really new and difficult -- like Mandarin, say -- and the font, style, and problem set layout were dramatically different from day to day. When Ben was taking Saxon Math in grades 1-3, he became very comfortable with the predictable format of its worksheets: a word problem at the top (usually with a rectangle to do little drawings in), followed by problems attacking the central feature of the lesson from different angles, all laid out similarly from day to day, and always with the same font. As long as it is actually helping Ben's learning instead of derailing it, I'm fine with Ben's depending on a predictable format. I want the book itself to be out of the way of his learning, not to hinder it by providing continual little shocks. Still, pattern learning can really derail real learning, by preventing a kid from generalizing what he knows. Consider, for example, a kid who always does subtraction problems oriented vertically, and when introduced to a subtraction problem that's oriented horizontally, can't do the problem. It could happen; but most math books take great care to avoid introducing fixed patterns like that. A little variation nudges a student toward full mastery, by whittling away what's unessential. Most textbook writers know this. It's a much more common problem these days for the format, and the desired response, to be unpredictable.
PatternLearningPart2
PatternTraining
comments...
PatternTraining 04 Jun 2005 - 16:05 CatherineJohnson
I think I first learned about pattern training from Temple. Pattern training is a big problem with animals, and also with autistic people . . . but now that I’m trying to teach my son math I realize it’s a huge problem for me, too. I just didn’t know it. The best way to understand pattern training is to think about dogs. Pattern training happens when you always train your dog in the same place at the same time using the same sequence of commands. The dog learns the pattern, not the individual commands, so he can’t generalize what he knows about sit in the training situation to a whole new situation. If you ask him to ‘sit’ outside of a training session, he doesn’t know what you’re talking about. The same thing happens training service dogs. You can’t just train a dog to cross a corner. You have to train him to cross lots of different corners, in lots of different places. Otherwise he only knows how to cross the one corner, and that’s it. Take him to another corner a block away and he’s stumped. He doesn’t generalize. This is a huge problem in autism, and it’s the heart of Temple’s & my book, Animals in Translation. Autistic kids don’t generalize well, and neither do animals, and Temple and I argued that this gives autistic people like her unique insight into the behavior of animals. I believe this is true, but since we wrote the book I think I overestimated just how great we ‘typicals’ are at generalizing. TO BE CONTINUED
PatternLearning (format shock)
PatternLearningPart2
SummerSupplement
comments...
RussianMathPart2 04 Jun 2005 - 18:39 CatherineJohnson
My copy of Mathematics 6 came yesterday, and it is incredible. A beautiful, beautiful book. The design is exquisite (in my next life I'm going to be a graphic designer) and I've learned things just reading the first 5 pages. I'm pretty attached to the Saxon books, but I actually feel love for this one. [Now I'm thinking . . . do I sound completely nuts? Well, if I do, the beauty of a Bliki is that I can DELETE THIS POST later on today, after I've come to my senses.] I'm going outside right now to do the problems in Chapter 1.1 Factors and Multiples.
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RussianMath
RussianMathPart3
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Mike McKeown comment
IndusAcademy
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BasBraams 04 Jun 2005 - 18:49 CatherineJohnson
I'm a big fan of Bas Braams. I'm just realizing I haven't read all of his posted works, so I'm getting started.
update: oh my gosh! I've just discovered Bas Braams has a blog! It's called Scientifically Correct.
update 2: He is writing Scientifically Correct with Ze'ev Wurman.
comments...
HowToGetParentBuyIn 05 Jun 2005 - 02:48 CatherineJohnson
The TRAILBLAZERS teachers' guide devotes a number of sections to strategies for neutralizing incensed parents. I had planned to quote some of these passages, and then, tonight, found an online TRAILBLAZERS document (PDF file) that's chock-ful of them:
Be pro-active with parents. Don’t wait until complaints hit. People have done a lot of things to involve parents, from math nights to big math carnivals, where the kids teach the activities to the parents. There are letters in the program that go home to parents.
When this teacher says 'there are letters in the program that go home to parents,' she doesn't mean that her school writes letters to parents once a month. She means that her school has purchased, as part of the TRAILBLAZERS 'package' (which is enormous, I've seen it; worse yet, I've lifted it) a set of special TRAILBLAZERS Dear-Parent letters to be photocopied and sent home in the backpack at regular, designated intervals. What the parent sees is a friendly letter from the school about her child’s math program. What the school sees is a professionally-developed public relations campaign targeted to dissenting moms & dads. The TRAILBLAZERS Dear Parent letters are not intended to serve an educational purpose. At least, no educational purpose is mentioned in any of the supporting materials I've seen as yet. The explicit and openly stated purpose of the TRAILBLAZERS Dear Parent letters is to promote parent buy-in. All of which means that not only am I paying for a program I don't like and don't want, I am paying for the press kit to persuade me I'm wrong. Maybe this isn't exactly the kind of thing the Boston Tea Party was about, but it's getting there.
+ + +
And here is another strategy for dealing with parents! This strategy was developed by one Barbara Martin, principal of the Holmes Elementary School in Chicago:
[For parents] we do also have a math day, and on that math day, we invite parents to be in the room. The kids do math all day. In order to get the parents in the room, I offer them a little stipend. I only offer the stipend to the parents who can stay in the room all day—they’re helping the teacher, because they’re doing math all day, with Trailblazers and all the manipulatives. At the same time, they’re also getting to see what kids do. There are other parents that visit math day and leave because they can’t stay all day. We have a good turnout.
Ms. Martin has had fantastic success with TRAILBLAZERS ---
"For some of my children, our feeder schools are saying, “Please, please send us more like these.”
+ + +
So let's see how Holmes Elementary School children are faring in the high-stakes world of standardized testing.
+ + +
Oh dear. Third grade: 30% of the kids meet state standards.
Fifth grade: down to maybe 27%.
Eighth grade: down to 5% meeting state standards.
This is an all-black, poor school, so they've got a lot to contend with. Maybe they'd have a 95% fail rate in 8th grade no matter what curriculum you gave them. But look at their reading scores. 3rd grade: maybe 17 or 18% meet standards.
5th grade: up to 36 or 37%meeting standards.
8th grade: they're up to around 44% meeting standards.
Math goes down, reading goes up. Same kids, same school, same period of time.
EverydayMathDoesItToo
ILoveTheWorldWideWeb
ATeacherUsingTrailblazers
NoCommentPart2
CarolynFisksBook
AnotherGemFromMathForum
BigNumbers
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ADifficultChildPart2 05 Jun 2005 - 04:20 CarolynJohnston
In ADifficultChild, Catherine linked to a story that Ralph Raimi told about a high school girl he evaluated, on behalf of her mother, who was becoming concerned about her problems in math class. He talks about specific problems with her math education, which begin with her great confusion about basic fraction manipulation and the operations of algebra, but in the end are dwarfed by her resentment of math.
She had never heard of "the number line", and when I suggested a yardstick she said she had never used one. She didn't know what numbers appeared on a yardstick, or what I was talking about when I wanted to know the position of the markings between inch or foot labels. So I drew a picture and got a reluctant agreement that there must be such things.
His conclusion about her future vis a vis mathematics is pretty dismal.
She is scheduled to take a non pre-college math next year (some-
thing like statistics one term and business math the other, but I've
forgotten what she told me on that), and she could probably pass that one
now. It is cruel and inhuman to push algebra and trig on her, and truth
tables forsooth, this year, given her background and her school's attitude
towards textbooks and other such unnecessary explanations. Can I recommend
she spend extra time on math, besides the torture of a meaningless class
every day? But I haven't found out if it is even legal for her to stop
her present course at all. I'll have to ask around.
If I were asked what seriously could be done to teach something
useful in the name of math to this kid, I would advise starting with the
arithmetic of fractions, i.e. what she failed to learn in the 5th and 6th
grades and since, and their applications and meaning of course. I believe
this could be made interesting to her once she knew she didn't have to
learn all those symbol manipulations she has been plagued with these last
five years. But there is nobody to do this for her, and there is no clear
incentive, since all she thinks she needs is to pass the next few exams.
Now here is the part I find desperately sad.
She livened up considerably when we talked about things which were
not mathematics. She wants to grow up to be an emergency room nurse.
She likes her biology class and her "history and music" class, where she
learns about "classical" and "baroque" music. She says she can't take
chemistry, which I had suggested as useful for a nurse, because she wasn't
going to take Math III. There was lots of math needed for the chem course,
she said, more than for the physics. (Yet she asked irritably several
times during our interview "what good was all this math" for her.)
She didn't know, and apparently Ralph didn't either, that the certification examination for a registered nurse in most if not all states (and certainly in New York, where 'Sarah' lives) contains algebra questions, and nursing school requires students to be able to pass a college algebra course. They like RNs to be able to do basic calculations of dosages and mixtures and the like; careless errors by an RN can be dangerous.
I've had nursing students who hated math as much as 'Sarah' did, who suddenly found that they had to take a college algebra class in hand and try to get a passing grade in order to get a job in their chosen career path. All of them suffered hugely; some of them couldn't do it at all. I knew one student who, having long since finished most of the coursework required to graduate from her nursing program, had been working for several years as an aide in a nursing home while taking college algebra over and over, trying vainly to get a passing grade.
In order to avoid any more mathematics, this girl has already shut the door on chemistry. Will she shut the door on her chosen career just as casually?
[ Afterword: I may have to eat my words. After I wrote this, I went looking online for information about nursing licensure requirements and nursing programs. The national licensure test for RNs is the NCLEX-RN. On a brief review of some practice questions from the NCLEX, I did not find any specifically relating to math (although I did find some relating to chemistry). Most of the nursing schools I found did have some kind of algebra requirement, although often high school algebra was sufficient. It may be that requirements were once stiffer at Binghamton University's nursing school, where I encountered my struggling students; it may be that requirements have been relaxed. If anyone can fill me in on the status of math in nursing education, I'd like to know more about it. -- CarolynJohnston ]
ADifficultChild
TeachUsMath
PenfieldParents
DontRelyOnStateTests
NewYorkStateMathCurricula
CompareAndContrastPart3
FriendlyFractions
PaperFractions
WorksheetsForSummer
AssessYourChildForFree
AssessYourChildForFreePart2
BonusOnlineAssessmentQuestions
comments...
ATeacherUsingTrailblazers 05 Jun 2005 - 16:12 CatherineJohnson
One of the things that I’ve learned is what homeworks are good homeworks to send home and what homeworks we really need to do in class because of parent frustration. Last year, not yet knowing this, I sent a homework home and got back such venomous mail: “What is this? Why are you asking my 3rd grader to do this? If you ever send another magic square home, I am pulling my child out of the school. I can’t do this, and neither can he.” So now I’m just making better choices on what to send home.
I think we can all agree that it's important for teachers to make good choices (pdf file). But why any parent would object to an 8-year old child being asked to construct a magic square for homework is beyond me. After all, think how much conceptual knowledge that child will have after his mom has looked up Magic Squares on the internet and helped him draw one.
HowToGetParentBuyIn
EverydayMathDoesItToo
ILoveTheWorldWideWeb
CarolynFisksBook
AnotherGemFromMathForum
BigNumbers
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TeacherAppreciationWeek 05 Jun 2005 - 19:48 CatherineJohnson
This is obviously the time to say that Christopher's math teacher for the second half of the year, Nancy Woeckener, told one of the other moms way back in September: "I don't believe in giving kids homework their parents are going to have to do." Mrs. Woeckener has been a terrific teacher for Christopher, and for me. Not only did she not assign homework for Christopher's parents to do, but when she taught a unit that stumped the moms (on figuring compound interest, and, yes, I am embarrassed)—she wrote out a precise mathematical explanation of what she was teaching and sent it home to all of us. I now know how to figure compound interest the easy way, using the commutative property, thanks to Mrs. Woeckener! (I know that I know how to figure compound interest the easy way, because another friend of mine, whose son is in a different math class, had to ask me the other day how to do it. She'd forgotten, probably because she hadn't quite gotten the concept back when her son's teacher was going over it. Not only did I remember how to do it, I could explain why the formula worked. Thanks to Mrs. Woeckener, I have Gained Conceptual Knowledge!) Mrs. Woeckener answered emails instantly, telling me exactly when tests would be given & what would be on them. Last but not least, she kept an eye out for Christopher when he joined her class mid-year. It's rare for a child in this district to move up a level in the middle of the year. The district is looking to cut children from the Phase 4 class, not add. Christopher was the only child who made the jump (as far as I know) and I've already mentioned more than once that, going into the fall, he wasn't the kid anyone would have pegged to be 'the one.' He had to come from behind. Not long after Christopher had moved to Phase 4, Mrs. Woeckener sought me out on a field trip and introduced herself. She told me she was keeping track of Christopher, that he was doing fine, and that she'd get hold of me right away if she had concerns. She also gave me the feeling that her plan was to see to it there wouldn't be any concerns. And that's exactly the way things worked out. Christopher was a lucky boy to have Mrs. Woeckener as his math teacher this year.
ILikeMath
comments...
EverydayMathDoesItToo 05 Jun 2005 - 21:15 CarolynJohnston
Regarding Catherine's awesome post, HowToGetParentBuyIn: It's just occurred to me that for two years now, since our school started using Everyday Math, little math pamphlets about the Everyday Math units have been coming home on Xerox copy paper, like everything else coming from the school. And come to think of it, there are always little helpful hints for parents on how to do the homework. I should have realized I was being public relationed. The school never sent home little parent hints on how to help with Saxon homework. So that's three points of reference: Trailblazers and Everyday Math are actively trying to manage their relationships with parents. Saxon is not. My question is: why would school districts turn themselves inside out to adopt these programs, when the publishers acknowledge that they are potentially putting themselves at odds with parents? What's in it for them? I have my theory about why reform math programs roll through the educational world. More to come: stay tuned.
HowToGetParentBuyIn
ILoveTheWorldWideWeb
ATeacherUsingTrailblazers
NoCommentPart2
AnotherGemFromMathForum
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ILoveTheWorldWideWeb 05 Jun 2005 - 22:13 CatherineJohnson
I knew if I just kept looking I'd find them. Somebody would have made helpful pdf files of all the TRAILBLAZERS PARENT LETTERS and posted them on the web. Sure enough, somebody did.
HowToGetParentBuyIn
ILoveTheWorldWideWeb
ATeacherUsingTrailblazers
EverydayMathDoesItToo
CarolynFisksBook
AnotherGemFromMathForum
BigNumbers
CompareAndContrast
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ForgivingDivision 05 Jun 2005 - 22:33 CatherineJohnson
It's official. TRAILBLAZERS does not teach the standard algorithm for long division at all:
The paper-and-pencil method that Math TrailblazersTM
uses to do long division is somewhat different from the
way long division is traditionally taught in the United
States. This method, called the forgiving division
method, is often easier for students to learn. They do
not have to erase as much, and they learn more about
division and estimation.
from:
Letter Home (pdf file)
page 6
Division and Data
+ + +
If you were wanting to see what forgiving division looks like, page six shows a forgiving division of 644 by 7. I'm surprised they actually tell parents this is what they're doing. Of course, by the time you get the Division and Data letter you've been receiving TRAILBLAZERS PARENT LETTERS for years and you're still in the school. They probably figure they've worn you down.
AboutLongDivision
StrugglesWithLongDivision
MathInTheBlood
ForgivingDivisionPart2
TryThisWithForgivingDivision
TeacherGuideEverydayMath
ILoveTheWorldWideWeb
EverydayMathEpilogue
ThirteenQuartersInTerc
HowNotToTeachMath
WhoSaysLongDivisionIsHard
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ForgivingDivisionPart2 05 Jun 2005 - 22:54 CatherineJohnson
This is pretty droll. Here's a parent asking Math Forum for help on his son's forgiving division homework:
From: Dan Bruce
Subject: Solving division problems using the "forgiving" method
My son has been asked to solve his division problems using the
forgiving method, but he doesn't recall what this process is, and
judging by the answers he's arriving at, he's way off base. Have you
ever heard of this method and could you demonstrate it using the
example 100/6?
Thanks.
And here's the answer:
Date: 05/15/2002 at 09:49:17
From: Doctor Mitteldorf
Subject: Re: Solving division problems using the "forgiving" method
I'd never heard of the forgiving method, and couldn't find references
to it in our archives. From a reference that I found in a discussion
group on the net, I gather that it's about piecing together whatever
multiplication facts you are comfortable with to solve the problem at
hand.
Suppose you want to know how many 6's there are in 100. You
can remember that 7*6=42, so you write down the 7 as part of your
answer, then take the 42 away from 100 and have 58 left.
Next step: you might say the same thing. There's another 42 in
there, so there's another 7 sixes. Write down another 7 under the
first one, and subtract 42 from 58.
Now you've got 16 left, and you know you can squeeze 2 sixes out of
16, but not 3. So you write down the 2 under your 7's and add them
up: 7+7+2=16.
You've pulled 16 sixes out of 100 (with 4 left over that wasn't enough
to make another 6). You did it in groups of 7, 7 and 2, but someone
else might have done 5 and 5 and 5 and 1, and the "standard" method
would have been to do 10 + 6. The method is forgiving in the sense
that your partial guesses don't have to be anything in particular, as
long as you don't overshoot.
- Doctor Mitteldorf, The Math Forum
+ + +
Yup. I can just see all the extra learning about division and estimation that's going on here. And so much less erasing, too!
ForgivingDivision
TryThisWithForgivingDivision
TeacherGuideEverydayMath
EverydayMathEpilogue
ILoveTheWorldWideWeb
HowNotToTeachMath
ThirteenQuartersInTerc
MathInTheBlood
StrugglesWithLongDivision
AboutLongDivision
WhoSaysLongDivisionIsHard
comments...
TryThisWithForgivingDivision 06 Jun 2005 - 00:25 CatherineJohnson
Go ahead. Try it.
ForgivingDivision
ForgivingDivisionPart2
TeacherGuideEverydayMath
EverydayMathEpilogue
ILoveTheWorldWideWeb
ThirteenQuartersInTerc
HowNotToTeachMath
AboutLongDivision
StrugglesWithLongDivision
MathInTheBlood
WhoSaysLongDivisionIsHard
comments...
SingaporeMathPlacementTest 06 Jun 2005 - 10:41 CatherineJohnson
The placement test for Singapore Math is here, along with basic info about the curriculum. A very useful Quick Guide is here. Boiling it down:
- The series they recommend for grade school kids is Primary Mathematics US edition.
- Each grade uses two textbooks (and corresponding workbooks) per grade, labeled A & B. 'A' is used in the fall semester, 'B' in the spring semester.
There are a couple of other Singapore Math books for parents that I think are terrific. More on that later.
FreeWorksheets
TreadingWater
SummerSupplement
SummerSupplementTime
SummerSupplementTimePart2
SummerSupplementTimePart3
SummerSupplementTimePart4 (resources for kids who have fallen behind)
SummerSupplementTimePart5 (resources for preventing summer regression)
SaxonPlacementTestsAndGuides
TeachYourChildToTypeThisSummer
advice on Singapore Math 6-2005
Singapore Math book recommendations in a nutshell
comments...
TakingABreakPart4 06 Jun 2005 - 12:24 CatherineJohnson
Off to Playland today, where I will not be riding this.
comments...
DontRelyOnStateTests 06 Jun 2005 - 22:47 CatherineJohnson
A quick note on state tests. I'm sure both Carolyn and I will have more to say about this, but since Instructivist has raised the question of 'what's on the tests?' I wanted to post these links. I read fairly often that 'math scores have risen over the past decade, but reading scores have remained flat.' Assuming I understand Tom Loveless's research correctly, we should probably all drop what we're doing right this minute and send a letter to our respective newspapers urging the staff to delete the 'math scores have risen' macro from their word processors:
Despite sharply rising test scores on both the NAEP Math and most state math tests, the Brown Center's analysis of the difficulty of the math items at fourth and eighth grade demonstrates that the NAEP test fails to assess essential arithmetic skills that are required for success in algebra and higher mathematics. "The good news is that NAEP scores have risen dramatically in mathematics over the past decade," noted Tom Loveless, director of the Brown Center on Education Policy and author of the 2004 Brown Center Report on American Education. "But, given our findings, it is unclear whether this is a significant accomplishment in terms of substantial gains in mathematics skills and knowledge." The National Assessment of Educational Progress, or NAEP as it is commonly known, assesses fourth, eighth, and twelfth grade students in math and reading. Scores on the math assessments have risen dramatically over the last 10 years, indicating that U.S. students are becoming more adept at mathematics. But the Brown Center analysis shows that the NAEP math assessments rely on arithmetic skills that are far below the grade levels of the students being assessed. The analysis finds that almost all problem solving items use whole numbers and avoid fractions, decimals, and percentages – forms of numbers that students must know how to use to tackle higher order mathematics like algebra.
The press release from Brookings is here. The full study is here. (pdf file) David Klein's California standards assessment problems are an excellent way to assess your children yourself. I used them with Christopher this year. Carolyn says they're 'golden' and I agree. There are other good sources for assessment problems parents can use. We'll get to those as soon as we can. Another thought: you might want to give your child the very short Singapore Math 'placement exam'. The Singapore tests are an eye-opener, because you see exactly how far behind our kids really are. If we had moved to Singapore at the end of 4th grade, Christopher would have been placed in second semester 3rd grade. That's a gap of 18 months by the age of 10. Having seen the kinds of questions kids in Singapore are answering in 8th grade (we'll post those, too) I can tell you that the 'Singapore gap' gets bigger, not smaller.
+ + +
quick note:
The Singapore tests aren't upsetting; at least they weren't for Christopher. He'd never even seen some of the material, so he certainly didn't feel bad about not being able to do it.
BonusOnlineAssessmentQuestions
See also:
NewYorkStateMathCurricula
PenfieldParents
CompareAndContrastPart3
FriendlyFractions
PaperFractions
ADifficultChild
ADifficultChildPart2
WorksheetsForSummer
AssessYourChildForFree
AssessYourChildForFreePart2
BonusOnlineAssessmentQuestions
sample NAEP questions
comments...
BonusPreTeenPost 06 Jun 2005 - 23:06 CatherineJohnson
I just asked Christopher if he thought this joke was funny:
He said, "No." Then he said, "I just put down Who cares? for everything." I love this age.
BeingYourChildsFrontalLobes
GreatMomentsInWorldHistory
ProgressReport
ATeachersStory ("I like the idea of math")
SummerSupplementTimePart2
SundaySchool
ILikeMath
TheGoodNewsFromHere
GoodNewsBadNews
ImGoingToPlayland
ImportantQuestionFromJoanneCobaskoOfSocmm
ImportantQuestionPart2
OutsmartingTheTests
ConversationsWithKids
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ConcreteThinking 07 Jun 2005 - 01:58 CatherineJohnson
NCTM Standards-based curricula consistently claim to enhance students’ conceptual understanding, a goal typically touted as a revolutionary advance over traditional adherence to “blind rote manipulation.” This is nonsense. When NCTM curricula such as TERC’s Investigations use the term “understanding,” they often refer merely to the obvious and pedagogically useful technique of furnishing concrete models for simple arithmetical examples, e.g. by using fraction strips to picture fractions such as 3/4 and 2/3. Every competent parent or educator knows that this is a good way to start. Unfortunately, a principal failing of Standards-based curricula is that students never move beyond, and so are forced to rely on, simple models and representations. As a result, when students confront purely symbolic representations that are not attached to physical models, they simply freeze. Their reaction, perhaps best characterized as “symbol shock,” is, in my experience, a primary cause of students’ failure to succeed in college mathematics.
read the whole thing
comments...
WhyILoveCarolyn 07 Jun 2005 - 02:07 CatherineJohnson
Carolyn just told me she's known a few Russian mathematicians, and 'they have chops.'
Our Favorite Supplements
RussianMath
RussianMathPart2
RussianMathPart3
ItTakesChops
Mike McKeown comment
IndusAcademy
comments...
ItTakesChops 07 Jun 2005 - 02:13 CatherineJohnson
It takes chops to solve this when you're eleven:
Two cars leave simultaneously at 9 a.m. heading toward one another from different cities that are 210 km apart. The average speed of one car is 50 km/h while the other car averages 70 km/h. Come up with an appropriate question and answer it.
This problem appears on page 5, 'Review,' of Mathematics 6: an award-winning textbook from Russia, by Enn Nurk and Aksel Telgmaa. The 6 in the title stands for 6th grade.
+ + +
update: OK, I solved it.
But I couldn't think of a bar model.
Our Favorite Supplements
RussianMath
RussianMathPart2<