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With all three kids, we've slowed to a crawl. It's going smoothly without disrupting our lives. It's downright relaxing! We wonder, "What's the catch?" Then we remember, "Oh yes, we're the taxpayers, our kids go to public school, and we're teaching our kids arithmetic."But that's because I'm a smart alec.
The Eyes of Honesty
By CLIVE THOMPSON
Published: December 10, 2006
In the psychology department at Newcastle University, there is a coffee station where people can help themselves, so long as they leave money in the tray — 50 pence (about $1) for a coffee and 30 for tea. It operates on an honor system.
Alas, not everyone is honorable. “The woman running the station was a little disappointed at the level of contributions,” says Gilbert Roberts, a professor in the department. Psychologists have long been aware of this dismal aspect of human behavior: people are more honest if they know they’re being observed — so when nobody’s watching, they feel they can get away with murder, or at least with a free cup of coffee.
This problem gave Roberts and two colleagues an idea for an experiment. For 10 weeks this spring, they alternately taped two posters over the coffee station. During one week, it was a picture of flowers; during the other, it was a pair of staring eyes. Then they sat back to watch what would happen.
A remarkable pattern emerged. During the weeks when the eyes poster stared down at the coffee station, coffee and tea drinkers contributed 2.76 times as much money as in the weeks when flowers graced the wall. Apparently, the mere feeling of being watched — even by eyes that were patently not real — was enough to encourage people to behave honestly. Roberts says he was stunned: “We kind of thought there might be a subtle effect. We weren’t expecting such a large impact.”
The paper prompted a British police department in Birmingham to slap posters of eyes around the city as part of a campaign called “We’ve Got Our Eyes on Criminals.” The researchers are studying the campaign to see if the posters have an effect on things like car crime and vandalism.
Mastery is essential for lower performers. Unless the practice children receive occurs over several lessons, lower performers will not retain information the way children from affluent backgrounds do. Prevailing misconceptions were (and are) that children benefit from instruction that exposes them to ideas without assuring that children actually learn what is being taught. If you present something new to advantaged children and they respond correctly on about 80 percent of the tasks or questions you present, their performance will almost always be above 80 percent at the beginning of the next session. In contrast, if you bring lower performers to an 80 percent level of mastery, they will almost always perform lower than 80 percent at the beginning of the next session.
The reason for this difference is that higher performers are able to remember what you told them and showed them. The material is less familiar to the lower performers, which means they can’t retain the details with the fidelity needed to successfully rehearse it. After at-risk children have had a lot of practice with the learning game, they become far more facile at remembering the details of what you showed them. When they reach this stage, they no longer need to be brought to such a rigid criterion of mastery. At first, however, their learning will be greatly retarded if they are not taught to a high level of mastery.
This trend was obvious in the teaching of formal operations. At first, the low- and high-performing groups were close in learning rate. Later, there were huge differences. Group 2 was able to learn at a much higher rate, largely because it was not necessary to bring them to a high level of mastery. On several occasions, I purposely taught the children in Group 2 to a low level of mastery (around 60 percent). I closed the work on the topic with one model of doing it the right way, and I assured the children that this was very difficult material. At the beginning of the next lesson, almost all of them had perfect mastery.
Maybe one reason why students need more advanced courses to become successful in college is because so many things have been taken out of the basic courses because of the addition of topics like data analysis. I can't understand why data analysis would be a part of a geometry couse. American students are extremely weak in geometry. In many cases, that is the only proof-based course, or at least it used to be a proof-based course, that students get. So, of all places, why sould data analysis be included in geometry?The day ends with this basic dispute hanging.
Superintendent of Public Instruction Terry Bergeson has agreed to an independent review of state math standards that critics have called at least partly responsible for Washington students' poor math achievement....
Mukilteo parent Hugh Taylor, a member of the state "Where's the Math?" group, called U.S. math instruction "uniquely unsuccessful." He said that since the state developed the original math standards, allowing the Office of the Superintendent of Public Instruction to conduct the standards review "would be like the fox guarding the henhouse."As Catherine alluded to earlier, a parent revolution is difficult to pull off, but with a little persistence it seems it is possible to make headway.
He said he welcomed an independent review, "as long as it's conducted by a mathematician."
If you have 40% of the cookies, what percentage does Mary have?About which Ricky asked:
Are Mary and I the only ones with cookies?Bravo, son! Bravo!
The Bell Curve (1994) by Richard Herrnstein and Charles Murray, which argued that IQ is destiny, was the most IQ-glorifying book since . . . well, ever. Now Mr. Murray has taken a big step away from his position in that book, yet he continues to glorify IQ.
In today’s Wall Street Journal, Mr. Murray wrote an op-ed piece (“What’s wrong with vocational school?”) with which I mostly agree. His main point is that for most students, college is a waste of time. As a college teacher (at Berkeley), I have seen that all too clearly. Mr. Murray has an unfortunate way of stating his position. “A four-year college education teaches advanced analytic skills and information at a level that exceeds the intellectual capacity of most people.” I’d put it differently: A four-year college education teaches analytic skills and information at a level that exceeds the interest of most people. I am sure that if my students or anyone’s students were more interested in the material, they would learn it better. That most college students are not interested in the same things as most college professors is a good thing, economically speaking. A healthy economy is a diverse economy; a diverse economy requires a wide range of skills and knowledge, much wider than the narrow skills and knowledge possessed and taught by college teachers. But it is a bad thing for the students and teachers, who are trapped. They have to be there. I feel worse for the students, of course — they are paying to be there.
It isn’t complicated: IQ tests were designed to predict school performance. They do. People with higher IQs do better in school. To believe in the value of IQ is to believe in the school system it reflects. To glorify one is to glorify the other. Now Mr. Murray has taken a step away from one (the school system) but not the other (IQ). Well, nobody’s perfect.
[snip]
In The Nature of Economies, Jane Jacobs pointed to the stultifying effects of discrimination. “Macho cultures typically have pitiful, weak economies,” she wrote. “Half their population, doing economically important types of work, such as cooking and food processing . . . are excluded from taking initiatives to develop all that work [e.g., open a restaurant] — and nobody else does it, either.” IQ discrimination is also stultifying. If our society did a better job of helping students who are not good at college — helping them find jobs where their abilities shine, instead of wasting four precious years of their lives — the entire economy would benefit.
The Flynn Effect implies that there are one or more powerful environmental effects on IQ. They can raise or lower IQ on the order of 20 points. For simplicity, let’s say there’s just one factor, Factor X. If you are high on Factor X, your IQ will be 20 points higher than if you are low on Factor X. Herrnstein and Murray speculated on the possible genetic cause of Black/White differences and other group differences without knowing (a) what Factor X is and (b) where Whites, Blacks, and other groups fall on this factor. Once those two pieces of info were known, there might be nothing left to explain. Differences in Factor X might entirely account for the observed group differences.
Nineteen eighty-nine is, in mathematics education, indelibly tied to the National Council of Teachers of Mathematics’ publication, Curriculum and Evaluation Standards for School Mathematics (1989), which downplayed pencil and paper computations and strongly suggested that calculators play an important role in K-12 mathematics education. My 2006 students would have been about two years old at the time of this very influential publication, and it could easily have affected the mathematical education many of them received. Certainly, one possibility is that mathematics preparation is down across the country, thus limiting the pool of well prepared college applicants.
There is nothing that universities can do to correct the lack of preparation of their applicants. However, it is difficult to believe that there are not enough students to fill our classes with 1989 quality students. One of the major gate-keepers, the SATM test, is oblivious to this significant shift in preparation. Universities can certainly demand a more effective SATM test.
To misquote Bob Dylan's Ballad of a Thin Man: "Something is happening, but you don't know what it is; do you, Mr. Fennell?"
January 24, 2007 Edition > Section: New York
Do Social Issues Belong in Math Class?
BY GARY SHAPIRO - Staff Reporter of the Sun
January 24, 2007
Can social and economic justice issues be integrated into mathematics curricula?
Radical Math, Long Island University, and Math for America, a nonprofit founded by a Wall Street titan, James Simons, who is president of Renaissance Technologies, are sponsoring such a conference in April to explore such issues called "Creating Balance in an Unjust World."
The conference will feature both a Harvard-trained civil rights leader named Bob Moses and a former Weather Underground member turned educator, Cathlyn Wilkerson, whose father owned the West 11th Street townhouse where she and Kathy Boudin survived a 1970 explosion of a bomb intended for others.
A research professor of education at New York University, Diane Ravitch, believes combining math and social justice is ill-advised. She said students may learn the political opinions without learning the math. Ms. Ravitch said too much of combining social justice and mathematics was propagandizing and introducing politically partisan positions into the teaching of mathematics. "It doesn't belong in the math classroom. Leave that for social studies," she said.
A professor of education at the University of Illinois at Chicago, Eric Gutstein replied, "Where is the presumption that exposing youth to real questions of social justice in their world is either ideological or propagandistic?"
The communications director for one of the sponsors, Math for America, Lee Umphrey, said the group had contributed a small amount of money to the conference more in support of one of their fellows than of the content of the conference. He said Math for America supports the idea that everybody should have access to quality math.
That organization, whose board includes a former director of the Institute of Advanced Study at Princeton and a former managing director of Salomon Brothers, has a mission of improving math education in public schools.
A professor at the Courant Institute at New York University, Sylvain Cappell, cautioned that combining social justice and math elided a reasonable concern with a potentially very damaging one. He said there was legitimate concern about society providing disadvantaged children with a full opportunity to get high-quality mathematics training. But he said the substitution of teaching of concrete mathematical skills with ideology threatens those very children.
Mr. Gutstein has found that youth in Chicago public school were often disengaged and did not learn mathematics — "high-quality or otherwise." A high school teacher and co-organizer of the conference, Jonathan Osler, said studying issues relevant to students' lives is one way of engaging them in the mathematics material.
An advocate for mathematics education, Elizabeth Carson, said student engagement is only the beginning of the process of effectively teaching, not the end or goal.
Mr. Gutstein said the purpose of schooling was to create opportunities for young people to simultaneously develop academic competencies and to understand real issues in their world.
Mr. Cappell said that in combining social justice and mathematics, the math might get short shrift. Mr. Gutstein turned the question around by saying that when a social studies teacher puts a graph on the board and takes the time to explain the mathematics involved, few would say the teacher was giving short shrift to social studies.
Ms. Ravitch, said one of the things children learn in mathematics is how to review evidence and come at questions with a nonpartisan, dispassionate perspective.
Ms. Ravitch said it was better if children were free to reach their own opinions and politics. Mr. Gutstein again responded, "Where is the presumption that we are substituting students views with our own?" He said students in his classroom consider multiple perspectives and make up their own minds and have to back up their opinions with mathematical evidence.
Messrs. Osler and Gutstein acknowledged that it would take much work balance math and social justice in an effective way.
Ms. Ravitch was less sanguine. "What they really need is to work on is teaching mathematics and equipping students for careers in the 21st century — that would be the most radical thing of all."
January 24, 2007 Edition > Section: New York
Read Engelmann. He's not a naive observer of education. Once you understand what Engelmann is talking about, you have the antidote to all the education nonsense you'll encounter on a daily basis. If chapter one is any inducation, this book will be an easily accessible introduction for the layman.You will have to click over to get the link to the book, but I recommend you read D-EdReckonings observations.
"The NCTM Focal points are issued at a time when many parents are appalled by the lack of quality and content in their children's math programs. The Focal Points in grades 6 to 8 seem reasonable. But in earlier grades, they fail to disqualify very weak programs, still in use, that derive inspiration from and are consistent with the 1989 Standards.
"In Grades 1 to 5, the Focal Points fail to explain that sustained experience with nontrivial multi-digit arithmetic problems is critical to success in algebra and higher mathematics. They omit all reference to memorization. They do not admit the interpretation that skills can be developed first and understanding filled in later. Some content material is vague or weak. Indeed, the description of whole number division activities with multi-digit dividends suggests that the hardest problem that students need to handle is 99 divided by 9, while the description of place value fails to name numbers above 1000. That is unacceptable. The NCTM authors should have incorporated existing documents, most notably the State of California's Mathematics Content Standards, which provide a crystal clear grade by grade delineation of computational and symbolic skills appropriate to a content-rich elementary math program."
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. In one district, the coordinator ran a six-week course for parents and taught them mathematics, essentially. It depends on what will work with your audience. Teachers need to communicate with parents, making sure that the parents see the math facts practice and that the arithmetic they value is visible.
The math nights have helped [with parent complaints] a lot. I took one of my math nights and just addressed Trailblazers. I actually took them through the steps of how they teach addition and subtraction, using all the base-ten blocks and the manipulatives and how it flowed into the algorithm. After that, I did not have another negative letter. There are still a lot of parents who are worried that, at the end of 3rd grade, kids haven’t memorized all of their multiplication facts. The focus of the math night that I just had was on games that parents and children could play at home to work on math facts, just using decks of cards and things. These are things they can work on with their kids that are fun and easy to do. I don’t want to spend a half hour in class memorizing multiplication. We have far greater things, bigger things to think about.
We invite parents to an orientation where we talk about all our programs early on in the year. Our math coordinator speaks to the group about math lessons. Math Trailblazers has parent letters that go home all the time telling about what’s going on in the math program. 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.
Wherever students go into in the middle grades, if they’ve had a sound foundation in the primary grades, they will be prepared..... For some of my children, our feeder schools are saying, “Please, please send us more like these.”
January 6, 2007
Dear K-5 Parents,
As you know, the mathematics Trailblazers program was adopted by the Board of Education in 2004 and is in its final phase of implementation this year in Grade 5. The District has provided strong support to teachers to ensure excellent initial training and ongoing professional development, and the results to date, are very positive. As with any new initiative, however, it is imperative that we continue to monitor children’s progress and to provide ongoing opportunities to keep parents informed as well as to continually evaluate the program’s effectiveness.
As part of our commitment, there will be a Math Information night for K-5 parents on January 22, 2007 at 7:00 PM in the Dows Lane Library hosted by staff from Dows Lane and Main Street Schools. Teachers will present information about the Trailblazers program, and parents will be able to ask questions to which they will receive responses that evening or soon after the session. As the date draws near, a separate flyer will be sent home by building principals requesting confirmation of your attendance.
In addition, since students in the current elementary program are not tracked and those in the current Middle School program are in leveled classes, the staff recognizes that the transition to 6th grade is a valid concern on the part of parents and one that will soon be addressed. Therefore, parents of current fifth graders will have an opportunity to attend a meeting in February 2007 to discuss this topic. Once again, information will be sent home later this month.
I hope that you will make every effort to attend these important parent meetings.
As always, we value the input of parents [ed.: no more input] and look forward to these opportunities to hear from you and to be able to respond and work collaboratively with you as we move forward.
Thank you for your ongoing support and cooperation and best wishes to you and your families for a healthy and Happy New Year.
Sincerely,
Superintendent of Schools
"Last year, Manual High was one of the worst schools in Colorado. Nine out of ten students failed the state writing test; ninety-seven of a hundred failed the math test; one in five freshmen graduated. This wretched showing belied the fact that, for a decade, Manual High had been the object of aggressive and thoughtful reforms. The most recent was a million-dollar intervention by the Bill & Melinda Gates Foundation, begun in 2001, which turned each of Manual's three floors into an intimate mini-school, with its own principal. In these environments, some students had a sense, for the first time, that their teachers knew and cared for them. But in many classrooms the mutual affection came at the expense of academic rigor. Discipline was weak, gang ties intensified, and in five years a student body of eleven hundred shrank by nearly half. The academic performance of the vestigial students --"the dregs," as one counsellor put it -- barely changed."
"Think about it," he said. "What other public institution would we let sink to this level? If the Mayor says, 'I'm going to pave one hundred and fifty alleys,' then comes back the next year and says, 'Well, I spent all the money and only got to two, I'll get to it next year,' we'd go crazy. But when we spend three quarters of a million dollars in a school ostensibly teaching a subject, and only two kids in that school learn anything, we think that's normal. And I think that's because we've allowed ourselves to confuse the sytem's lack of quality with the kind of kids who are in our district."Bennet appears to be trying to do everything at once, feed the kids, keep class size down, hire good teachers, improve the curriculum, keep the kids in the school . . . . He pushes for teacher merit pay; he adopts KIPP type policies; and performance begins to creep up.
"Out of panic, and of motivations that involved personal vanity as well as social justice, a safety net was being strung under a school system's hardest cases -- one involving parents, mentors, fast-food restaurant managers, United Airlines executives and city-council members who knocked on doors, an engrossed media, nonprofit organizations, and student leaders like Julissa."OK, this has gone on long enough. You get the idea. The article lays out a plan that looks like it might work in some of the worst schools in the country.
I was pleased to read your positive comments on how tutoring benefits the teacher because of my teenage son’s current paid job tutoring a classmate.
When he first proposed this tutoring job I had mixed emotions about it. For some of the reasons AndyJoy listed in his comments on Rory’s post on peer tutoring.
This week the high school kids are taking mid-term tests. My son, as usual, seems to be spending very little time “hitting the books”. However, he has been tutoring every day.
He keeps telling me that tutoring helps him with his tests. He loves it because he feels he’s being paid to study!
After reading your post, I have come to believe a big benefit is he’s “developing and refining his schema”. This is especially relevant because he is often viewed as a walking encyclopedia.
(Also, it doesn’t hurt that his tutee is a very cute female. This leads my husband to conclude that there is a whole other set of benefits to this arrangement. lol!)
I was fascinated to see a teenager being self-reflective enough to perceive the benefits of teaching to the teacher.
It'll be interesting living with a typical teen. (Typical as opposed to atypical for people new to the blog. Jimmy, who has autism, is 20.)
I'm starting to look forward to it.
Because power is inherently situational, it is potentially unstable. Force, violence, and coercion aside, voluntary compliance may fluctuate markedly over time, even reversing itself dramatically among the same set of actors.
...the more you know the more you have to lose. The rate from test-year to test-year at which the more educated participants lost their word-recall ability was proportionately faster, with both groups finishing with nearly identical word-recall capabilities at the study’s end.
[snip]
“Even though we find in this research that those with higher education do better on mental-status tests that look for dementia-like symptoms, education does not protect better against more normal, age-related declines, like those seen on memory tests,” said Dawn Alley of the University of Pennsylvania, a co-author of the study
Chronic stress appears to hasten the shriveling of the tips of the bundles of genes inside cells, which shortens their life span and speeds the body's deterioration, according to a small, first-of-its-kind study involving mothers caring for chronically ill children.
x2 + 2y = 10
What do you notice about the expression?
