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select another subject area Entries from IrvingtonMathHowIGotHerePart1 23 Jun 2006 - 13:15 CatherineJohnson For me, Kitchen Table Math—Picnic Table Math, in our case—began last June (2005) when our fourth grader, Christopher, came home with a 39 on his Unit 6 test in SRA Math. A 39. How does a person get a 39 in 4th grade math, I kept asking myself. An 80 or a 70, OK. Or, if you really learned nothing, maybe a 68 or a 66. But 39? I'd never even seen a 39 on a test; it's not even listed as a possibility on any of the grading rubrics, all of which stop at 65, or maybe a 60 at worst. A 39 is off the charts, only in the wrong direction. That’s when I bought a used copy of SRA Math Explorations and Applications, Level 4 and set up shop on our picnic table outside the kitchen. I figured, OK, I’ll teach him the stuff he missed. -- CatherineJohnson - 30 Apr 2005 MathInTheBlood 23 Jun 2006 - 13:16 CarolynJohnston Carolyn's side of the story of this website My husband and I have always worked with our kid on his math homework at home. We're both Ph.D. mathematicians, and he never had much of a chance to be anything other than wonderful at math. Every night he would either do his math in front of us, or we would check his work to make sure that he understood what had been covered. In fourth grade, last year, his school switched from the curriculum they had been using, Saxon Math, to a new math curriculum, Everyday Math. I knew the change was coming -- it was announced the previous year, and copies of the new book were left out for parents to review and comment on (and did I review it? ... actually, I didn't, because I was too introverted to Get Involved). Math, formerly my son's strongest subject, became an everyday struggle for him and for us. Our biggest problem was the frequent appearance of problems involving skills he hadn't been introduced to yet. First it was multidigit multiplication, a topic that practically all kids learn in the fourth grade anyway; but its first appearance was in a problem set that came early in the year, before the topic was taught. I don't think the Everyday Math guys intended the kids to approach those problems with the standard algorithms. The problems were always of the sort that you could hope to figure out with common sense. For example, the first multidigit multiplication problems were of the 51 times 3 sort... if you were a bright fourth grader with an adventurous attitude, and some energy left over from the day, you could hack around for a bit and discover for yourself that you could get the right answer by multiplying 50 by 3, and then adding another 3 to your answer. But then, in the next night's homework, there was 23 times 4 to be similarly discovered. Some night soon, I feared, there would be 324 times 5, and then 324 times 54. He would be like Archimedes, rediscovering math from first principles every night. Enough, I thought, and I taught the multidigit multiplication algorithm on the spot. Later that year, I taught my son long division... and drilled him on it every night for a couple of months, since it was a sticking point for him. When problems such as 4 times 1/2 appeared, I sighed and taught him how to do fraction multiplication calculations. Somewhere during the year, I realized that I was teaching him a lot of basic mathematics, but in a completely reactive way; I was allowing the Everyday Math curriculum to dictate the order and the style in which I taught math. If I had to teach my child math myself, I wanted to be doing it on my own terms, in the manner that I thought was best -- and I was sure, at the time, that I knew what that was. MathInTheBlood ReactiveTeaching NowThatWereBothHere AboutLongDivision StrugglesWithLongDivision ForgivingDivision ForgivingDivisionPart2 TryThisWithForgivingDivision TeacherGuideEverydayMath EverydayMathEpilogue ThirteenQuartersInTerc HowNotToTeachMath WhoSaysLongDivisionIsHard NowThatWereBothHere 23 Jun 2006 - 13:24 CatherineJohnson Carolyn wrote: Somewhere during the year, I realized that I was teaching him a lot of basic mathematics, but in a completely reactive way; I was allowing the Everyday Math curriculum to dictate the order and the style in which I taught math. I like that word reactively. I’m closing in on my 1 Year Anniversary, formally teaching math to Christopher here at home. At some point along the way I had the exact same feeling about the home-tutoring going on around me here in my own town, but I didn’t have the word for it. Now I do. It’s reactive. Reactive teaching. Everyone is scrambling to keep up with the content being taught at school. If a child comes home from school not understanding the distributive property, then mom or dad or Paid Tutor scrambles to explain it in time for the test. If he comes home not remembering how to change a fraction into a decimal (We learned it last year, but I forgot), then mom or dad or Paid Tutor scrambles to explain it again, hoping this time it will stick. There’s no rhyme or reason. MathInTheBlood ReactiveTeaching ThingsWeHaveLearned ImGoingToPlayland -- CatherineJohnson - 01 May 2005 SwoopAndSwoopPart2 23 Jun 2006 - 13:24 CatherineJohnson This is probably the time to mention that I’m re-teaching myself elementary mathematics, start to finish. I’m doing all of the lessons in Saxon Math Homeschool Edition, beginning with book 6/5, which Christopher and I finished a few weeks ago. I’m also (in theory) working my way through the entire Singapore Math series, beginning with 1st grade. UPDATE 10-8-2006: I am not working my way through the entire Singapore Math series. I am working my way through the entire Saxon oeuvre, which is all I can manage at the moment. I am, however, for reasons unknown to me, creating a hand-drawn solution manual for Singapore Math's Challenging Word Problems Book 4. I was always pretty good in math, though I stopped taking it after Algebra II, then hit the wall when I tried to take calculus freshman year in college. I flunked the first test and dropped the course. But up til then I was fine, I liked math, scored well on my SATs, etc. I don't have any math anxiety and I love statistics. I took one statistics course in college. Correlation coefficients, standard deviations, regression analysis: to me, these things sound like the key to palace. So, given my general level of math-friendliness, I didn’t think it would be too hard to teach Christopher the math he'd missed in 4th grade. However, I pretty quickly had the same experience the teacher quoted in the American Institutes for Research report did: “I never realized that I do not understand math until I had to teach mathematics from the Singapore textbooks.” This time around I’m trying to acquire conceptual understanding of elementary mathematics, and hook it up to my procedural understanding. It’s not easy. UPDATE 10-8-2006: Twenty-three lessons into Saxon Algebra 2 the mystery of my Wellesley calculus failure has been solved. Algebra 1 & 2 in my high school in Lincoln, IL correspond to Algebra 1 in Saxon. I went to college thinking I'd taken two years of algebra. I hadn't. I'd only taken one. Apparently Wellesley College wasn't big on placement exams in those days. HowIGotHerePart2 23 Jun 2006 - 13:27 CatherineJohnson So there we were, Christopher and I, installed at our picnic table, thrashing our way through SRA Math Unit 6: Fractions and Decimals. Two weeks later, there was blood on the floor. HowIGotHerePart1 MathInSalinaKansas 23 Jun 2006 - 13:28 CarolynJohnston From a forum I sometimes visit, I followed a link today to an urban legends website with a page on an internet claim about an 8th grade final exam supposedly given in Salina, Kansas, in 1895. Here are a few of the test questions in the arithmetic section:
Arithmetic
(Time, 1.25 hours)
When I looked at the Urban Legends page about this 1895 test I found that, contrary to my expectation, they weren't debunking the claim that it was a genuine final test from 1895. They were taking issue with the claim that it showed that educational standards had fallen since 1895:
What nearly all these pundits fail to grasp is "I can't answer
these questions" is not the same thing as "These questions
demonstrate that students in earlier days were better educated
than today's students." Just about any test looks difficult to
those who haven't recently been steeped in the material it covers.
If a 40-year-old can't score as well on a geography test as a high
school student who just spent several weeks memorizing the names of
all the rivers in South America in preparation for an exam, that
doesn't mean the 40-year-old's education was woefully deficient --
it means he simply didn't retain information for which
he had no use, no matter how thoroughly it was drilled into his
brain through rote memory some twenty-odd years earlier.
Lame, lame, lame. If you can't prove that this is not an authentic graduate exam from 1895, then complaining about it just makes you sound like a whiner (and notice the dig about 'rote memory' -- memorization is in very bad odor these days).
Besides, it's not about us (and what we retained) anymore: it's about our kids. And I am afraid it does imply that we've dumbed down the junior high curriculum. Only a tiny minority of kids graduating 8th grade these days could handle sophisticated word problems like these, even if we gave them the bushel-conversion formulas for free. Apart from the emphasis on farming applications, which is kind of funny and endearing, the application area of problems 6 and 8 (just for an example) is as alive, or more so, in 2005 as it was in 1895, and we simply do not teach it. In the late 1980s, I taught an elective course at LSU on the material covered in these problems. The entering students were completely ignorant of that material, mastery of which I claim is necessary to living adult life competently (and they were very glad to finally learn it, too). Many students who were stronger mathematically, and didn't take that elective math course, are no doubt still ignorant of it, because it is not taught in public schools anymore.
The second thing that leaps out at me is that these are mostly application problems -- word problems -- not problems testing either basic computation or deep understanding of the beauty of mathematics (with the exception of problem 1). It was just assumed that these kids could do the computations necessary to solve these problems, without calculators. What they needed to do was to solve those problems, and get the right answer, and that hasn't changed a bit. And I'll bet there was no partial credit given for having the right idea, either. CompareAndContrast CompareAndContrastPart2 CompareAndContrastPart3 CompareAndContrastPart4 CompareAndContrastPart5 CompareAndContrastPart6 CompareAndContrastPart7 MathInSalinaKansasPart2 23 Jun 2006 - 13:28 CatherineJohnson re: MathInSalinaKansas Wow. I spoke yesterday to a mathematics professor at a university here in New York state. When I asked him what level of mathematical knowledge entering freshmen bring to their course work, he said, "We can't assume that a student knows anything we would want him to know." Specifically, his students can't do algebra. They can't set up a two-variable word problem and solve it. These are college freshmen. Posted on May 07, 2005 @ 11:21 MathInSalinaKansasPart3 23 Jun 2006 - 13:28 CatherineJohnson re: MathInSalinaKansas Three sample problems from the PRAXIS 1 Content Assessment college students entering the field of education are frequently required to take:
1. Which of the following is equal to a quarter of a million?
The Educational Testing Service (ETS) describes these problems thus:
The Pre-Professional Skills Test in Mathematics measures those
mathematical skills and concepts that an educated adult might
need. It focuses on the key concepts of mathematics and on the
ability to solve problems and to reason in a quantitative context.
Many of the problems require the integration of multiple skills to
achieve a solution.
[snip]
Computation is held to a minimum, and few technical words are used.
Terms such as area, perimeter, ratio, integer, factor, and prime number
are used, because it is assumed that these are commonly encountered
in the mathematics all examinees have studied. Figures are drawn as
accurately as possible and lie in a plane unless otherwise noted.
see also:
MathInSalinaKansasPart2
PracticeAndOverlearningPart1 23 Jun 2006 - 13:29 CatherineJohnson Carolyn and I have both been using Saxon Math Homeschool Edition with our kids. Here is Saxon's explanation of the curriculum:
Saxon Math . . . systematically distributes instruction and
practice and assessment throughout the academic year
as opposed to concentrating, or massing, the instruction,
practice and assessment of related concepts into a short
period of time -- usually within a unit or chapter.
I can vouch for this.
SAXON 6/5 has 120 lessons in all, plus 12 'Investigations' & 3 Appendix lessons, and when you get to Lesson 120 you're still practicing the stuff you learned back in Lesson 1.
There are 100 or more problems and computations in each of the 120 lessons: Fast Facts, Mental Math, Problem Solving, Lesson Practice, and, finally, Mixed Practice.
This is what we call drill and kill.
Cognitive psychologists call it automaticity:
Practice Makes Perfect But Only If You Overlearn Ask the Cognitive Scientist: How We Learn by Daniel T. Willingham
review
GoodReadingPart1 23 Jun 2006 - 13:29 CatherineJohnson Just posted to Our Favorite Math Ed Articles: Daniel T. Willingham's 'Ask the Cognitive Scientist' columns for AMERICAN EDUCATOR (wonderful) William Schmidt, et al's phenomenally helpful 'A Coherent Curriculum: The Case of Mathematics' (Schmidt headed the Third International Mathematics and Science Study (TIMSS), and summarizes his findings here.) Specific Learning Disabilities: Finding Common Ground. A Report Developed by the Ten Organizations Participating in the Learning Disabilities Roundtable. This is the American Institutes of Research 2002 consensus report: what findings, hypotheses, and theories do 10 different organizations and insitutions, including the Department of Education and the Learning Disabilities Association of American, agree to be true of 'specific learning disabilities.' (I haven't read this yet.) See also: PracticeAndOverlearningPart1 NotTheWholeStoryPart2 23 Jun 2006 - 13:29 CatherineJohnson So just how far back does the U.S. fraction deficiency go, you ask. Answer: really far. In 1923, the NEW YORK TIMES reported that fewer than half of seventh grade students could convert the fraction 1/5 into a decimal. The Columbia Teachers College had a plan.
The new aim of the progressive arithmetricians is to abandon
drilling in artificial problems and to bring mathematics close
to every-day life.
from: 'New Teaching Puts Life into Dreary Arithmetic',
NYTIMES December 9, 1923
Apparently, the plan was working.
The new method is so successful, according to its sponsors,
that one school has playfully threatened to abandon it for the
reason that the pupils are so enthusiastic over arithmetic that
their teachers can scarcely interest them in other subjects.
This was the start of progressive education in America. So flash forward to 1989, and we find NAEP reporting that 60 percent of seventh grade students can 'express simple fractions' as decimals. A mere 70 years of progress, and 10% of American seventh graders who wouldn't have known that 1/5 is the same thing as 20% back in 1923 do know in 1989. That was my first thought. My second thought was, OK, I'll take it. 10% is 10%. Then I noticed Chris Correa's second post on the subject.
I browsed through the publicly released NAEP questions
and found the most comparable question to be from 1992:
Of the following, which is closest in value to 0.52?
This is my beef with constructivism. It's not like constructivism hasn't been given a fair shake. Constructivists have had a good hundred years to show us what they can do. I say it's time to move on. [Thank you, Chris Correa.] NotTheWholeStory GoodReadingPart2 23 Jun 2006 - 13:29 CatherineJohnson Posted to Our Favorite Math Ed Research Articles: The A-Maze-ing Approach to Math by Barry Garelick. NotTheWholeStoryPart3 23 Jun 2006 - 13:30 CatherineJohnson re: NotTheWholeStory & NotTheWholeStoryPart2 Carolyn's right that Everyday Math can't be blamed for the sorry state of college freshmen's ability to add fractions. I haven't been able to track down the first printing, but EVERYDAY MATH seems to date back to around 1993 or thereabouts. Garelick reports that approximately 10% of U.S. schools have now adopted E-Math, and I read just this week that another 10% of U.S. schools have adopted one of the other constructivist math curricula. (I've forgotten the source, or I'd link -- sorry.) Of kids entering college this year, only a small percentage will have spent much time using the latest crop of constructivist mathematics programs. Of course, that's leaving aside the fact that constructivism has been part of ed school philosophy for a century. CarolynIsGobsmacked 23 Jun 2006 - 13:33 CarolynJohnston Did you see this chart in Garelick's article that showed the grants that ed departments were given to come up with new math curricula? Man, did I ever go into the wrong branch of academia. Five million dollars for Everyday Math! Six for Trailblazers! Fourteen for Contemporary Math in Context!!!! The path I should have taken is now clear:
MoreBigNumbers BigNumbers CatherineIsGobsmackedPart3 16 Sep 2006 - 19:58 CatherineJohnson re: CarolynIsGobsmacked No question, Carolyn. When it came time to choose a response, you blew it. (Sorry. Inside joke. I am WAY ready for summer vacation.) * OK, that's not fair. We had a publicist - a free lancer - before we had Trailblazers. keywords: choose a response no putdowns bullying character education lost instructional time BooksPart1 23 Jun 2006 - 14:00 CatherineJohnson
two fantastic books Elaine McEwan's website CurricularGamePlayingPart2 23 Jun 2006 - 21:21 CatherineJohnson About a month after Christopher and I began working with Saxon Math 6/5, he told me,
Multiplication and division are the big brothers,
Then he said,
And multiplication and division are cousins.
+ + + This is a 9-year who, just 6 weeks earlier, had been flunking math. Any way you slice it, that's conceptual knowledge. In just a few weeks he'd absorbed the idea that addition & subtraction, multiplication & division, are inverse operations, and that multiplication was repeated addition, while division can be seen as repeated subtraction. I should add that Christopher doesn't consciously know that division can be described as repeated subtraction (I don't think). He probably couldn't put it into words, though he could tell you that multiplication is repeated addition. But a few weeks into Saxon he had intuited the relationship. This is exactly the goal constructivist math programs have set for themselves: they are trying to help students connect the dots. Addition, subtraction, multiplication, & division aren't Four Separate Things, as they were for me until I read and studied Saxon Math! I haven't worked with a constructivist text. But I know for a fact that Saxon gives children conceptual understanding. Curricular Game Playing Curricular Game Playing, part 2 number bonds vs. 4-fact families Numicom Dominoes CalBoardOfEdStudyPart2 16 Sep 2006 - 19:59 CatherineJohnson Carolyn wrote:
I thought I would do a 'mini-series' [on the California Board of Education study]
What a great idea! I've been wanting to know more about the famous California Board of Ed study. Here's a terrific factoid about Dixon et al, from The Principal's Guide to Raising Math Achievement by Elaine K. Mc Ewan:
From a total 8,727 published studies of mathematics in
8,727 "studies."
Of which, 231 were scientifically valid.
231
Parents, teachers, administrators, and Concerned Citizens everywhere should have this figure tattooed to their foreheads.
When textbook publishers and ed school types use the words "research shows," you're looking at maybe a 3% chance they're right about that.
Given the fact that, by law, all research findings have to be replicated before they can be certified as facts, the odds are probably closer to zero.
(OK, I'm kidding. There's no law. Anyone can call anything a fact if they want to. It's a free country.)
CalStateStudyIntro
California study intro California state study of group learning California Board of Ed study part 2 education research - peer reviewed studies - chart RoyalRoadToGeometry 24 Jun 2006 - 17:23 CatherineJohnson I had never read this story before today: When Ptolemy I, the king of Egypt, said he wanted to learn geometry, Euclid explained that he would have to study long hours and memorize the contents of a fat math book. The pharaoh complained that that would be unseemly and demanded a shortcut. Euclid replied, “There is no royal road to geometry.”I'm sorry to hear that, because a royal road to geometry is exactly what I need today. I just checked out the next lesson in Christopher's SRA Level 6 book, which turns out to be about finding the equation for a line that's been plotted on a graph. I could do the easy, obvious problems, but the graph where 'one step to the right' seemed to be followed by '1/3 step up' stopped me cold. I don't remember ever being taught how to find a formula from a line on a graph. I also don't remember ever being taught a formula for making a line on a graph in the first place, although I do remember plotting out lots of coordinated pairs. That's got to be be worth something, right? Unfortunately, while I remember plotting out lots of coordinated pairs, I have no idea when in my mathematics education this occurred, or why. Exactly what Subject Matter Area does finding-an-equation-from-a-graph fall under? Since the formula-finding problems in Christopher's book are in the unit on 'Algebra Readiness,' I figured this must be algebra, so I went to get my copy of Algebra to Go (buy this book, you'll need it) from the dining room-cum-math-&-spelling-zone. This is where I feel God Wants Me To Learn Math, or at least not suffer hideously while I try to make sure Christopher Learns Math, because an Unseen Force led me to pull out Geometry to Go instead (buy this book, too), open it up, and land smack dab in the middle of the page explaining the formula for charting linear functions on a graph — all of this before realizing I had the wrong book, glory Hallelujah. Leading to my first Math Revelation of the day: it's not algebra! It's coordinate geometry! * I had no idea! Thank you! Then my neighbor, the statistician, came over and showed me how to do it. * UPDATE 10-8-2006: It's algebra. Algebra and coordinate geometry, I guess. I don't know. I will press on and report back. ![]() source: Bitter Single Guy see also: BuyThisBookToo EnglishLanguageArtsBookRecommendation MathRefs MoneyClassSizeMathAchievement 16 Sep 2006 - 20:00 CatherineJohnson This item made my day. After our school board announced that budgetary constraints had left them no choice but to increase class size in the 4th and 5th grades (from 19 or 20 students per room up to 23 or 24) parents voted in our second double-digit tax increase in a row. Our fourth and fifth grade classes will remain small. I was skeptical. For one thing, I was aware that Asian math classes are far larger than our own. For another, I was aware that comparative education researcher James Stigler* actually recommends increasing class size as a means of improving math achievement in America. Larger class size would allow American teachers to meet with colleagues in the lesson study groups that are standard practice in high-achieving countries. But while I knew all this, I hadn’t quite allowed myself to draw the obvious conclusion. I hadn’t grokked the possibility that if you’re living in a school district where everyone’s clamoring for small class size, and no one’s clamoring for teacher release time, . . . that might be a problem. So this afternoon I found this analysis of TIMSS data in Education Next: When other factors are taken into account, higher Well, all I’ve got to say is, thank heavens there’s only a small correspondence between high spending, small class size, and inferior mathematics and science results. Because if there were a large correspondence we’d be in trouble. + + + I like this chart, too: ![]() soucre: * James Stigler was one of the investigators in the 1999 TIMSS study and is coauthor of The Teaching Gap: Best Ideas from the World's Teachers for Improving Education in the Classroom by James W. Stigler, James Hiebert and The Learning Gap: Why Our Schools Are Failing and What We Can Learn from Japanese and Chinese Education by Harold W. Stevenson, James W. Stigler. HowToRespond 16 Sep 2006 - 20:00 CarolynJohnston Although this ship has already sailed for me and Catherine, here's instructions on what to do when your school district announces a switch to a new-new math curriculum. I'd love to know if anyone is able to use this information to their advantage. My experience is that this stuff is like the flu... once you've caught it, there's little you can do but let it run its course. ClandestineTeaching 16 Sep 2006 - 19:52 CatherineJohnson Following up on an observation made by Jo Anne Cobasko: Parents who teach their children math at home help raise the apparent success rates of constructivist math curricula. If Carolyn's son does better in school because he has a Ph.D. mathematician for a mom who's teaching him Saxon Math, his success doesn't get chalked up to Saxon. It gets chalked up to Everyday Math. All I can say is, she's right. I think I first encountered the term clandestine teaching in something Elizabeth Carson wrote. Carolyn and I are engaged in clandestine teaching, teaching that goes undocumented and unmeasured. Teachers do clandestine teaching, too, when they close their doors and teach the way they want to. I should add that my son's teachers and our principal know all about my home-teaching, and have been terrifically supportive. My efforts are clandestine only in the sense that they don't show up in official statistics. + + + This got me to thinking: why shouldn't we know how many children are being tutored at home? Do we have survey data on this? Anecdotally, I can tell you that I'm constantly meeting parents who've hired math tutors for their kids, or who are doing a huge amount of 're-teaching' themselves. I also have the impression that in my district it's the parents of average and above-average kids who are hiring tutors. (I could certainly be wrong about this, so take it with a grain of salt.) + + + I was actually told by one teacher that she preferred teaching kids with special needs, because they have I.E.P.s (Individualized Education Plans) that the school has to stick to, and does stick to. (That is a feather in my school's cap. There are plenty of schools out there not complying with IEPs, and I'm in a postition to know.) Regular kids don't have IEPs, and if they're not learning math the school has the option, and probably the temptation, of assuming that the problem lies in the child, not in the curriculum or the teaching. The teacher who filled me in on all this felt that the IEP was a 'protection' for the teacher, not just the child. The IEP empowers her to do whatever she needs to do to make sure this child learns math. + + + Of course, this is one of the standard criticisms of public schools today: a child can't get quality direct instruction until he's been classified as having special needs. If he's average or above average, forget it. He's gonna be discovering his algorithms. Nobody expects a child with learning problems to discover long division. CompareAndContrast 10 Oct 2006 - 01:52 CatherineJohnson problems in three grade 5 textbooks from the last page of Primary Mathematics 5B (U.S. Edition): 18. A fish tank is 2/5 full after Sara poured 14 gal of water into it. What is the full capacity of the tank in gallons? final problem in Saxon Homeschool Math 6/5 3rd Edition: Change each of these base 10 numbers to base 5: a. 31 b. 51 c. 10 d. 100 e. 38 f. 86 from the last page of Math Trailblazers Grade 5: 4. Write a paragraph comparing two pieces of work in your portfolio that are alike in some way. For example, you can compare two labs or your solutions to two problems you solved. One piece should be new and one should be from the beginning of the year. Use these questions to help you write your paragraph: Which two pieces did you choose to compare? How are they alike? How are they different? Do you see any improvement in the newest piece of work as compared to the older work? Explain. If you could redo the older piece of work, how would you improve it? How could you improve the newer piece of work? CompareAndContrastPart2 CompareAndContrastPart3 CompareAndContrastPart4 CompareAndContrastPart5 CompareAndContrastPart6 CompareAndContrastPart7 MathInSalinaKansas ATeachersStory FromAReader PracticePracticePractice BarModelingVsGraphing (interesting comments from a KTM reader) HowToGetParentBuyIn ATeacherUsingTrailblazers BigNumbers ProfoundUnderstandingFundamentalMathematics 16 Sep 2006 - 19:54 CatherineJohnson
Carolyn mentioned Liping Ma's concept of 'profound understanding of fundamental mathematics' (PUFM). This chart is Ma's map of the 'knowledge package' Chinese teachers possess for the topic of subtraction. This is what Chinese mathematics teachers know and understand about subtraction. I don't happen to have this knowledge package inside my own head, and neither does any other parent I know. This is why it won't do to say:
One way to understand a math program like EM is to read through and do the exercises in the curriculum consecutively, openmindedly as a learner, not as an assessor. Play with the manipulatives, perhaps even borrow a teaching guide. These programs are much different, and much more exciting than the way we were taught. They are also very hard to describe. With some study, you might find yourself a great parent contributor to something your children's school is attempting to perfect.
+ + + Chinese math teachers develop pedagogical content knowledge over the course of many years teaching and studying elementary mathematics. There are no shortcuts. How long does it take to acquire a profound understanding of fundamental mathematics? I'm guessing 10:
Some evidence that a great deal of practice, and not just talent, is a prerequisite for expertise is the "ten year rule," which states that individuals must practice intensively for at least 10 years before they are ready to make a substantive contribution to their field. What about prodigies like Mozart, who began composing at the age of six? Prodigies are very advanced for their age, but their contributions to their respective fields as children are widely considered to be ordinary. It is not until they are older (and have practiced more) that they achieve the works for which they are known.
+ + + No parent is going to pick up a copy of Everyday Math, read through the book, work the exercises, and be ready to teach or tutor the curriculum effectively. That's not the way it works. Parents have a fighting chance of teaching or tutoring effectively with a direct-instruction curriculum like Saxon Math. We have that chance because the books are written so that anyone who's been through grade school can understand what the lessons are about. None of us is going to do a brilliant job teaching math using Saxon. Becoming brilliant at anything takes 10 years. But we can help our children learn math. It's not just children who need direct instruction. Parents need it, too. We parents need to be able to pick up our child's mathematics textbook, read the lesson, and know what it's talking about. That school districts consciously select unproved mathematics curricula they know parents will not understand and will not be able to teach or tutor from is, to me, unconscionable. It's not up to us to go begging for a peek at the teacher's guide. It's up to our schools to bring us into the loop. TeacherGuideEverydayMath 07 Oct 2006 - 13:19 CatherineJohnson Wow. Speaking of sneaking a peak at the teacher's guide, it just so happens that I have open, on my desktop, a bunch of pdf files from the Everyday Mathematics Teacher's Reference Manual, Grades 4-6, The University of Chicago School Mathematics Project, Everyday Learning Corporation, Chicago, IL, 1999, ISBN 1-57039-515-2, pages 127-139, courtesy of one Tsewei Wang, Ph.D., Associate Professor, Department of Chemical Engineering, University of Tennessee and Concerned Parent. Have I mentioned how much I love the internet? Interesting to see that Everyday Math teaches the same Guess-and-Check algorithm for long division that's in Trailblazers. Only, Trailblazers calls it 'Forgiving Division' (pdf file; search for 'forgiving division'): Forgiving Division Method + + + So say you're dividing 239 by 3. Instead of using math facts to know that 3 goes into 23 seven times, you start by guessing how many times 3 goes into 239. + + + OK, let's divide 239 by 3 using forgiving division! 'I'm ready!'I'm going to start by guessing the number . . . 7! I guess 7! 3 x 7 is . . . 21! I write down 21 underneath 239, then I subtract, and I get . . . 218. Whoa. That's a lot. OK, I'm going to use a strategy. I'm going to guess . . . 10, because 10 is a friendly number. 10 x 3 is . . . 30! I write 30 underneath 218, then I subtract----188. Wow. 188 is big. OK. 188. I'm down to 188. . . . I'm going to try 10 again. 10 x 3 is 30, subtract 30 from 188, get . . . 158. 158?
Forgiving Division see: The Many Faces of the Bitter Single Guy and: BlameTheTeacher ProfoundUnderstandingFundamentalMathematics ForgivingDivision ForgivingDivisionPart2 TryThisWithForgivingDivision ILoveTheWorldWideWeb TeacherGuideEverydayMath EverydayMathEpilogue ThirteenQuartersInTerc HowNotToTeachMath AboutLongDivision StrugglesWithLongDivision MathInTheBlood WhoSaysLongDivisionIsHard Everyday Math alternate division algorithm keywords: Sponge Bob Bitter Single Guy ATeachersStory 16 Sep 2006 - 19:56 CatherineJohnson Carolyn (J) has just alerted me to the fact that there are comments under some of our posts . . . so apparently my Next Action vis a vis KTM is: ask Carolyn how to keep track of comments. ('Next Action' is Getting-Things-Done-speak. Carolyn and I are both fans of David Allen's Getting Things Done, and in fact last week Carolyn tipped me off to a whole Getting-Things-Done blog that I am hoping will change my life.)
Anyway, this is a comment from a teacher who has a fascinating situation with Saxon Math. (I've inserted extra paragraph breaks to make this easier to read): I teach in a private Christian School. My 5th graders continue to score above all other grades on SAT's. I am now the only teacher who teaches Saxon, although when I came 11 years ago, all grades used Saxon. It was felt that there were gaps in the Saxon program for lower grades, so they changed to another program for K-3. That program didn't work, so they are now trying another curriculum. They also felt there were gaps in Saxon for high school, so that has changed. Then they changed 7-8 grades to Mc Dougal-Littell's Passport to Algebra and Geometry, leaving only 4,5,6 using Saxon. Then, they added Passport to Mathematics in 6th. Now, this year they have changing 4th grade to the K-3 curriculum. After three years of complaints from parents and after losing many families, they realized they were going to have to do something about the problems between 5th and 6th grades. But because of my success in Saxon, they are allowing me to remain with the curriculum. I know this is a long story, but I find this incredible: one grade in the school continues to be at the top on SAT's, year after year, no matter the class's Math abilities and strengths -- it's my 5th grade class and I use Saxon. Now, I do use Saxon as it is designed to be used (students make corrections and corrections until they get it right) and that's very important. And I require all the proof, rather than merely answers. Students who have hated math for years learn to love math. Even if they don't understand the total concept, an algorithm allows them to get the right answer and they feel successful for the first time. Their self esteem jumps because they are successful. The bottom line is: Saxon, when used properly and as designed, works. Then, the students go into Passport and good students make F's. I'm trying to determine if Passport is considered to be "constructivist" but can find no informatiion on that. I've read the reports from Mathematically Correct's seventh grade review. Passport to Algebra/Geometry is given an A, Passport to Mathematics is given a C. That's all I have found. I see no reference to its being constructivist. All I know is this: students fall apart, parents ask me to help tutor them, yet it does little good. Our new secondary principal describes the two programs (Saxon and Passport) as being very different, so I'm guessing that our students are having to go from a very traditional, incremental approach that is successful to a very non-traditional approach. I'm very glad that I found your blog site. I'm going to refer parents to you. Perhaps, they can get insights that I can't yet offer them because I can only teach the "old fashioned, traditional (and successful) way". Thanks for listening and God bless.
I'm pulling these lines out for emphasis: Students who have hated math for years learn to love math. Even if they don't understand the total concept, an algorithm allows them to get the right answer and they feel successful for the first time. Their self esteem jumps because they are successful. This is absolutely my own experience. When I started teaching Christopher math, in the wake of his two failed Unit exams, I was hearing 'math is for geeks,' 'math is for nerds,' 'I hate math,' 'math stinks,' and 'I'm not from Singapore.' A few weeks into the program all that went away. He was getting As on his tests, he understood the lessons, and suddenly math wasn't for geeks after all. Self-esteem comes from being able to do something. If a child can do math, he feels good about math. It's that simple. The other day Christopher actually said to me, spontaneously, in the midst of doing his Saxon homework when he could have been outside shooting baskets or upstairs playing WWE Here Comes the Pain on his PlayStation, "I like math, I just don't like doing math problems." I had to stop what I was doing and check this out. "You like math?" "I like the idea of math." He's not ready to Commit, but he sounded happy. ILikeMathPart2 CompareAndContrast FromAReader PracticePracticePractice BarModelingVsGraphing (interesting comments from a KTM reader) BeingYourChildsFrontalLobes GreatMomentsInWorldHistory ProgressReport BonusPreTeenPost SummerSupplementTimePart2 SundaySchool ILikeMath TheGoodNewsFromHere GoodNewsBadNews ImGoingToPlayland ImportantQuestionFromJoanneCobaskoOfSocmm ImportantQuestionPart2 OutsmartingTheTests ConversationsWithKids HowToGetParentBuyIn 10 Oct 2006 - 02:01 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 ATeacherUsingTrailblazers 10 Oct 2006 - 02:01 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 ForgivingDivision 10 Oct 2006 - 01:55 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 ForgivingDivisionPart2 10 Oct 2006 - 02:30 CatherineJohnson This is pretty droll. Here's a parent asking Math Forum for help on his son's forgiving division homework:
From: Dan Bruce
And here's the answer:
Date: 05/15/2002 at 09:49:17
+ + + 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 TryThisWithForgivingDivision 10 Oct 2006 - 02:30 CatherineJohnson Go ahead. Try it.
ForgivingDivision ForgivingDivisionPart2 TeacherGuideEverydayMath EverydayMathEpilogue ILoveTheWorldWideWeb ThirteenQuartersInTerc HowNotToTeachMath AboutLongDivision StrugglesWithLongDivision MathInTheBlood WhoSaysLongDivisionIsHard CompareAndContrastPart3 10 Oct 2006 - 01:52 CatherineJohnson This page is from the Grade 6, second semester workbook for Primary Mathematics. Children in Singapore do not use calculators to work these problems. update 7-5-06: the page I linked to in June 2005 has disappeared, and I don't remember what was on it. The page shown here now is different... ![]() This answer sheet is no longer relevant: AnswerSheetFractions6B CompareAndContrast CompareAndContrastPart2 CompareAndContrastPart4 CompareAndContrastPart5 CompareAndContrastPart6 CompareAndContrastPart7 MathInSalinaKansas See also: DontRelyOnStateTests PenfieldParents NewYorkStateMathCurricula FriendlyFractions PaperFractions ADifficultChild ADifficultChildPart2 WorksheetsForSummer AssessYourChildForFree AssessYourChildForFreePart2 BonusOnlineAssessmentQuestions CompareAndContrastPart4 10 Oct 2006 - 01:54 CatherineJohnson
thank you: Elizabeth Carson, Co-Founder NYC HOLD update: I forgot to mention that this chart comes from an article circulated on the NY Math Forum list, The Curricular Smorgasbord by Williamson M. Evers & Paul Clopton. (pdf file) CompareAndContrast CompareAndContrastPart2 CompareAndContrastPart3 CompareAndContrastPart5 CompareAndContrastPart6 CompareAndContrastPart7 MathInSalinaKansas keywords: the f word the f-word bibliography greatest hits BigNumbers 10 Oct 2006 - 01:54 CatherineJohnson We lived in California for 18 years. For all 18 of those years, it was an article of faith in our household that California ranked 49th-in-the-nation on educational spending. Apparently Californians still believe California ranks 49th in the nation on educational spending. But it doesn't. California is nowhere near 49th-in-the-nation. Nope, it's exactly in the middle. So now I'm wondering if California ever ranked 49th in the nation, or if I spent almost two decades of my life believing an urban legend. Sigh. This part of the story was funny, though: Palmer, of the Department of Finance, explains: “People just do not get that when California adds billions each year to the schools---which we do---adding another $1 billion means you multiply $1 million by one thousand.”This reminds me of my favorite passage in the Math Trailblazers Grade 5 Student Guide. (A Math Trailblazers Grade 5 Student Guide is pictured here. We can see from the photograph that the Student Guide is what people who live on Planet Earth used to call a "textbook.") Now that we've cleared that up, my favorite Grade 5 Student Guide passage is a 5-page drama at the beginning of Unit 2 called 'Reading and Writing Big Numbers.' Here's how the play begins: Students in a fifth-grade class are learning about populations in their Social Studies class. Their teacher wrote some of the populations on the board for them to read and write. Some students had difficulty reading and writing the big numberes. The teacher gave these students a play to read. The play was about students who worked together to solve a problem about big numbers. Here is the play: The characters in the play are: N.S. (Not Sure)N.S. must be from California. thanks to Kausfiles check out the Comments thread CompareAndContrast HowToGetParentBuyIn ATeacherUsingTrailblazers CompareAndContrastPart6 10 Oct 2006 - 01:53 CatherineJohnson math facts in Singapore, grade 3:Studying Exhibit 3 in the big Singapore Math Report (pdf file), we learn that:Singapore students master multiplication tables up to 10 x 10 in grade 3 math facts in Math Trailblazers, grade 5:To be honest, it's difficult to say what, precisely, the MATH TRAILBLAZERS schedule actually is. It seems to vary from one document to another. I did find this TRAILBLAZERS playlet on page 260 of the 5th grade TIMS Tutor: Math Facts (pdf file).Suzanne: But the facts with nines are harder. I have to think about them, but I use the tens to make them easier. Teacher: How, Suzanne? Suzanne: Well, when I see 15 – 9, I think, “What do I need to get from 9 to 15?” I use counting up: from 9 to 10 is 1 and from 10 to 15 is five more. So, I get 6. That's 5th grade, folks. update 11-2005 I talked to a friend whose son is in second grade. He's a brainy kid who loves math, but he can't use the addition algorithm. Apparently, the algorithm hasn't been taught. If he's adding numbers smaller than 20, he counts on his fingers and toes. If the numbers are larger than 20, say 12 + 19, he draws 12 circles, then 19 circles, and finally counts them. Same process for subtraction, only in reverse. 63 - 19 means drawing 63 circles, then crossing out 19 of them. The kids have the triangular flash cards that portray number families, and her son is working on flashcards with numbers 1 - 10. A friend of hers whose child is in 3rd grade told her the children in her child's class are working on the exact same cards. CompareAndContrast CompareAndContrastPart2 CompareAndContrastPart3 CompareAndContrastPart4 CompareAndContrastPart5 CompareAndContrastPart7 MathInSalinaKansas MathInIrvington 10 Oct 2006 - 01:51 CatherineJohnson Just got back from picking up Christopher's other school supplies from the store at the Middle School. While there I debriefed a high school girl about the math track at Irvington High School. The Irvington math track is something parents know essentially nothing about unless they do things like debrief high school kids at the school store. There's no brochure; there's nothing on the web site. It's a secret. OK, it's not a secret. My problem is I don't see why I have to work to find out what the math track is in my own school district. I've mentioned more than once that for a variety of reasons Irvington grade school ended up with 4 math tracks starting in 3rd grade, a situation no one inside the school liked or ever intended to create. They started with the idea of an enrichment program for the best math kids, then one thing led to another, and they ended up with four math tracks. At the beginning of 3rd grade Christopher was placed in 'Phase 3,' one step down from Phase 4, the most advanced track. He was 8. We had no idea what Phase 3 meant, and we were never told. We just thought.....well, I don't know what we thought. At some point I realized they were hitting the Phase 4 kids with a lot of Math Olympiad problems the kids couldn't do. Often the parents couldn't do them, either. Apart from that, both phases were using the same textbook (SRA Math) and moving through it at basically the same rate. Giving kids a lot of Math Olympiad problems they couldn't do seemed like a waste of time (and in fact is a waste of time), so I didn't worry about it. At the end of 4th grade we were told, directly, by Christopher's 4th grade teacher: 'Don't worry about the phases. They don't make any difference. All the kids have the same ability.' Because of the funky way the Phases evolved in the first place, she was probably right that there wasn't a significant difference in ability level, so we took her word for it that there was 'no difference' between Phase 3 and Phase 4. Then, at the beginning of 5th grade, we showed up for school and discovered that, lo and behold, the Phase 4 kids were using the 6th grade book. Phase 3 kids were using the 5th grade book. All of a sudden this difference that was not a difference was a difference of one year. That's the back story. The point is: none of us parents knew, back in 3rd grade, that all but the Phase 4 kids had just been tracked out of calculus in high school. We had no idea. Zero. Christopher was 8; we were one year out from 9/11 and 10 months out from the anthrax attacks. (We lost our TONYSS tests that year because they went through one of the anthrax post offices. So we didn't know how he'd done on the state tests.) We weren't thinking about high school calculus. This is not the way a school district should work. Track a kid out of high school calculus in the 3rd grade and not tell the parents? That's not the social contract I thought I was signing when we moved here. So today I debriefed this girl. Like Christopher, she was placed in Phase 3. Then, at some point, she 'turned out to be good at math.' This was not discovered until her freshman year in high school, it seems. A week from now, when school starts, she'll be joining the honors track. To jump tracks, she had to spend her entire summer taking math at Rye Country Day School, which I'm sure cost an arm and a leg. She also had to get permission from the high school; she had to petition them to move her to the honors track this fall. When I got home and figured out exactly how much ground she had to make up in one summer, I was stunned. The advanced kids are about a year and a half ahead of everyone else, which means she had to take and master all the math those kids have been taking and mastering for the last 2 years. And she had to do it in 8 weeks. She said it was torture. She was up at 7 am every day doing math 'til she went to bed. I'm impressed as heck that she did it, but in my view it's pedagogically unsound, and she should not have been put in this position in the first place. Worse yet, my own experience is that you can't cram math. You need time for math to sink in. Unless you're a natural born whiz, you need to be doing math every day, and living with it. And, of course, we know from years of research on learning & memory that crammed knowledge disappears rapidly. (See Practice Makes Perfect But Only If Your Practice Beyond the Point of Perfection.) I think it's extremely unlikely that her parents knew, when she was put in Phase 3 math, what kind of heroic effort it would take for their daughter to get back out of Phase 3 math. I know for a fact that none of the parents around me have any idea Phase 3 means no calculus in high school. The incredible thing is, they still don't know. I made noises about this all last year, to anyone who would listen, which apparently did some good, because some 5th-grade parents raised the question in get-together meetings with the Middle School principal. By the time Ed & I went to our own get-together, on the last available date, the principal told us that parents at the other meetings had been asking whether their Phase 3 kids would be able to take calculus in high school. He acted surprised anyone would ask such a thing. Then he said Phase 3 kids wouldn't be able to take calculus in high school, at which point the vice principal jumped in and said, Yes, they would be able to take calculus if they wished. And there we left it. That is not what I call Information. The principal says no & the vice principal says yes.....and that's an answer? That's it? They've had 3 weeks since the first get-together to figure it out and they still don't know? And if the principal & vice principal of the middle school don't know whether a Phase 3 kid is on track to take calculus in high school, how am I supposed to know? After the meeting, I was thinking the vice principal was more likely to be right, because she's been here awhile and the principal is new. But no. The principal was right. Phase 3 kids are not going to be taking calculus in high school unless their parents sign them up for a brutal summer of 12-hour a day algebra & geometry catch-up 4 years from now. Of course, now that Trailblazers is coming in and tracks are going out.....it'll be interesting. I own the 5th grade Trailblazers book, which is the final book in the series. I've read it. I don't see anyone coming out of Trailblazers on track to take calculus in high school. UPDATE 10-9-2006: Based on what I hear from other parents, the tracks seem to have been preserved. It's possible the administration finally looked at the calculus track and realized they'd abolished it. I surmise this because two years ago parents of mathematically gifted children were pressing Raph Napolitano, the Assistant Superintendent in charge of curriculum, for an answer to the question of whether their children would be able to take calculus in high school. He didn't know. That was his answer. He didn't know whether mathematically gifted 3rd graders taking Math Trailblazers would be able to take calculus in high school. That's typical of this district. Parents are given no syllabi, no scope and sequence, no topic matrix. Unless we debrief other parents and their children we have no idea what lies ahead, or what our children need to know today to be prepared for advanced high school courses tomorrow. It takes many weeks and many emails and telephone calls to get a simple answer to a simple question. So I could be wrong about the tracks. Maybe we have them; maybe we don't. UPDATE 10-24-2006: A friend whose child is in 4th grade says the tracks are gone. I have no idea what's going on. question about calculus and collegeThe girl I was talking to says her brother has the impression that colleges want to see 'BC calculus' on kids' high school transcripts. Is that true? (He's applying to the Ivies.) My close friend in CA says that all colleges now require kids to take calculus....(her son is a freshman at Occidental). So either you need to have taken it in high school, or you'll have to take it in college. Does anyone know anything more about this? Thanks—learning a year of math in 2 months overlearning remediating Los Angeles algebra students Terminator James Milgram on long division & time lag in math learning James Milgram statement to Congress key words: summer school cram cramming math cram math sophomore Irvington High School freshman VacationReport 08 Oct 2006 - 22:19 CatherineJohnson We have emerged from the first day of school unscathed. Christopher does have the math teacher who scandalized the entire Phase 4 Parent Body last year, so I'm expecting to see a massive packet of Math Olympiad problems later on today. Ed says every time they send home Math Olympiads I should send back my own Math Olympiads. Don't think I won't do it. otoh, Christopher was utterly charmed by Ms. Kahl (I think that's her name). He reported every single one of her rules to me in detail, a serious look on his face. 'I like Ms. Kahl,' he said. 'She's nice.' This reminds me of the goofy feminism of my youth. For a while there, everyone was talking about RAISING BOYS WHO LIKE STRONG WOMEN. Even though I was still childless & quite possibly husbandless at the time, I thought the whole thing was ridiculous. The implicit antagonism to boys got on my nerves. Then I turned out to be the kind of mother who raises boys who like strong women. When Christopher was 4 he came home from nursery school one day and said, 'Mommy, I like a girl. Jean.' I wasn't sure who Jean was, so I asked another mom. 'That Jean,' she said. 'She's a bossy one.' teach your son math and set him up for a happy marriage, too! It's probably just as well. A few years ago John Gottman came out with one of his Key Factors determining whether a marriage succeeds or fails, and it turns out the Key Factor is how much the husband is willing to be 'influenced' by his wife. 85% of the variance in whether a marriage succeeds or fails is based on the husband's actions and attitude. John Gottman, PhD, discovered that successful marriages involve husbands who resist immediate negative reactions to their wives' concerns. These men increase the odds of having a happy marriage by allowing themselves to accept the influence of their spouse.... Clarke, a 30-year veteran of marriage, demonstrates these principles in a contribution to SecretsofMarriedMen.com. "When my wife asks me to do something, almost anything, my initial reaction used to be annoyance because I have lots of work to do, lots of things to do around the house, and lots of other bullsh-t reasons why not. However, most of what she asks me to do is actually quite reasonable, usually my responsibility, and I probably will end up doing it anyway. So, now I've trained myself to say 'yes' or 'no problem' as my initial response. This has contributed to less arguing and a better relationship."By the time Ms. Kahl and I get done with him, Christopher will not only be Good At Math, he'll be excellent Future Husband Material to boot. Here is Gottman's The Mathematics of Marriage: Dynamic Nonlinear Models ![]() I'm afraid one of my Life Goals has become learning enough math to be able to read, understand, and form an educated opinion about the contents. my vacation wow Two days into the school year and I'm already so re-absorbed by Math-Math-Math I almost forgot the whole point of this post. My Vacation. It was great! It was the first fun family vacation we've had since Andrew was born! One word: Abilify If it doesn't work for your kid, it'll probably work for y |