This time from David Brooks of The New York Times.
Tuesday, March 30, 2010
Monday, March 29, 2010
Something's up with blogger today, and my own comments are only occasionally appearing below, so I'm reposting them here.
I hadn't consider the accountability angle on creativity and higher-level thinking. It also applies, I think, to "organizational skills."
Incredible story about reading level assessments. I've seen plenty of examples of this kind of Price is Right class participation affecting grades in general--but reading assessment???
I don't consider you the lone voice of dissent on this blog, and would be sorry to lose your voice here.
I agree with you that kids need more free time for creativity. Indeed, that free time is the number one ingredient. Let's get rid of the homework in early grades, and let's have schools stop pretending that they can teach creativity, and pretending that it's ethical of them to grade students on creativity. They can't. It isn't.
I hope you didn't think I was presenting the Chinese system as the panacea for everything. Please reread me. However, since you bring up "my kids with autism," I will say that I imagine that high functioning kids like my son probably do better academically under the Chinese system than under the American one because of the emphasis on math and lack of mandatory group work in China.
"In China, the group always trumps the individual."
This sounds like another one of those inaccurate stereotypes that Americans keep repeating about China. Chinese students can learn on their own; they are not forced into groups in the classroom. They are assessed as individuals, not as groups. I've taught in Hong Kong traveled extensively in China, and taught Chinese students here in the U.S., and while I do see some group effects in extracurricular socializing that are different from group effects in America, I never saw "the group always trumps the individual."
In the West "we celebrate the heroic individual who defies the group."
"for decades the US has been known for its creativity and innovation."
Sunday, March 28, 2010
Time and again you hear Americans claiming that East Asian education is all about rote learning, including East Asian math education. Where does the East Asian rote learning stereotype come from?
Friday, March 26, 2010
Introductory division problems:
From the end of 5th grade Investigations
From the beginning of 5th grade Singapore Math
Wednesday, March 24, 2010
Peg Tyre's book does a wonderful job exposing the ways in which reduced recess time, early literacy expectations, writing-intensive activities, the decline in penmanship instruction, excessive homework, zero tolerance for aggressive play, and lack of male role models have contributed to a marked decline in how well boys do in school.
Elementary school is a conveyor belt. It moves kids from the magical world of childhood toward a more complex universe where reading and writing, concrete reasoning, abstract thought, and time-management skills are the currency of the land. In the last ten years, that conveyor belt has been speeded up. Our children are being pushed to reach the milestones of literacy and arithmetic earlier and earlier.
If you doubt this is true, talk to any veteran kindergarten, first-grade, second-grade, or third-grade teacher. Fifteen years ago, kindergarten was a place or social and emotional development. Reading was reserved for first grade. First-graders were expected to learn their letters and slowly, over the year, master letter sounds, begin to recognize some words on sight, and read short sentences. Second grade was given over to developing math concepts and reading fluency. These days, in many schools principals urge parents to be sure that their incoming kindergartners already know the letters--uppercase and lowercase--and to make sure they have the corresponding letter sounds solidly under their Hello Kitty or Power Ranger belts. Many parents are warned that in order to stay at grade level, kindergartners should be able to read on their own by the end of the year. Today, first-graders are routinely pushed through a curriculum that fifteen years ago was considered standard for second or sometimes third grade.
A teacher who bucks current trends because she is "determined to prevent filling out worksheets and quiet desk work from taking away from active play and hands-on learning."
Monday, March 22, 2010
Saturday, March 20, 2010
Thursday, March 18, 2010
1. The final division practice session in the "Multiplication and Division" chapter of the 3rd grade Everyday Math Student Math Journal Volume I, p. 84:
|2. The final division practice session in the "Multiplication and Division" chapter in the 3rd grade Singapore Math Primary Mathematics 3A, p. 102:|
Should Singapore math students, like Everyday Math students, be solving 3rd grade division problems using counters?
Tuesday, March 16, 2010
It has recently occurred to me that one reason why Constructivist classrooms appeal to so many people--including so many newspaper reporters--is because of their inherent selection bias.
Sunday, March 14, 2010
That is, is it the case that when mathematicians collaborate, they do so by "divvying up the pieces, working independently, and only reconvening to present and tweak one another's solutions"?
That's the claim I make in my book, based on my observations growing up among mathematicians, and based on the affirmation of the mathematicians past whom I ran this hypothesis.
But for some reason I didn't run it past one of my closest mathematician friends, Dr. Stephanie Frank Singer, who just wrote a generous review of my book in which she observes that, "While many mathematicians do work that way, many others work collaboratively."
Friday, March 12, 2010
a. Compare the 1-3 step Everyday Math problems with the 4-6 step Singapore Math problems. Why does only the former request explanations for answers?
b. Relate your answer to (a) to the Everyday Math "Time to Reflect" questions that follow this section, in which pride, challenge, and learning are supposed to be made explicit:
Which activity in this unit do you believe is an example of your best work? Why do you think so?
Which activity in this unit did you find the most challenging? Why?
What is something new you learned about geometry in this unit?
Wednesday, March 10, 2010
Nobody gave The Treatment like Farquar. Palmer knew a kid who had his arm in a sling for a week after. Yet Farquar himself was maddeningly unpredictable. Some birthday boys he seemed to totally ignore, passing them on the street as he usually did, as if they were dog doo. On the other hand, he had been known to walk halfway across town, knock on a door and say sweetly to a surprised parent, "I hear there's a birthday boy in here."
Some kids turned into quivering zombies. They kept their birthdays as secrets as possible. In school, if their teacher announced their birthday, they denied it, claiming that it was a mistake. They refused to have parties. They stayed inside their house for a month so they would not bump into Farquar.
But there was another side to it. There was the honor. There was the respect you got from other kids, the kind of respect that comes to soldiers who survive great battles...(From The Wringer, by Jerry Spinelli.)
Instead of fighting with weapons, Ghandi and the Congress Party began to use other methods of resisting the British. They taught the Indians to resist with "noncooperation"--meaning that Indians simply refused to pay taxes to the British government. They encouraged Indians to "boycott" British goods (refuse to buy anything made in Great Britain). Gandhi told his followers to make their own handmade cloth for their clothes, rather than buying British cotton. When the British put a tax on salt, Gandhi led his followers on a march of 240 miles to go collect salt from the sea, rather than buying the taxed salt. He started with seventy-eight people. By the end of the march, thousands of people were following him.
(From The Story of the World, Volume IV, by Susan Wise Bauer).Gandhi told Indians to take their children out of British schools. He asked them to give up privileges given to them by the British. He himself sent back a medal that the British government had given him for his work in South Africa. When a factory refused to give its workers enough money to live on, Gandhi went on a hunger strike. He refused to eat until the factory owners agreed to the raise. It took too three days for the factory owners to give in and agree. They didn't want to be responsible for Gandhi starving to death!
Monday, March 8, 2010
ChemProf's comment about teachers bullying socially awkward children made me think of a recent post on the Math Investigations (TERC) website in which a teacher points out that a certain type of student is languishing under Reform Math, and, while pointing this out, uses an all-too-familiar negative caricature:
There is another population that I think we are in danger of leaving behind, a population that used to do well in school mathematics: tidy math fans.
What is tidy math? Worksheets containing orderly rows of computation problems, all essentially the same problem, but with different numbers. Textbooks or teachers that cleanly demonstrate a method step by step and then ask students to do thirty problems using that same method. These are examples of tidy math.
Who are tidy math fans? Students who are neat and well-organized. Students who may not be too creative, but who pay attention and follow directions well. Students who are satisfied with knowing how and who are not bothered by not knowing why. Students who grow up, meet math teachers like myself at parties, and say "Oh, I've always liked math. I love how there's always one right answer to a problem." These are tidy math fans.
Tidy math fans do well in what we now call "traditional" math programs. But as some schools adopt new programs like Investigations, some of these students face a sudden drop in status, from one of the best math students in the class to an average, sometimes struggling student. Their self-esteem about their math ability plummets. It's no wonder that some of their parents (who themselves grew up with tidy math) put up a fuss about the new program and teaching style that is causing their children's loss of confidence.I can't help detecting just a whiff of schadenfreude here. After all, what's more satisfying than bringing down the type who would have out-shined you back when you were a student?
The rules for success and the very definition of what it means to do math have changed on them. Math is much harder now.
You might argue that this change is for the students' good. What tidy math fans were successful at before really wasn't mathematics anyway, and we do all students a favor by showing them what doing mathematics is really about. "Doing math has to do with thinking and reasoning about problems or situations that call for applying mathematical ideas and skills . . . Skills should be learned in the context of problems and situations and should not exist isolated from the problems and situations that give them their purpose." (Burns, p. 69.)The mathematicians I know consider Traditional Math far more mathematical than Reform Math, but why ask them? After all, they are all tidy math fans. Surely math educator and children's book author Marilyn Burns has a much better handle on what mathematics is really about.
In Beyond Arithmetic, Investigations authors advocate that students work on nonroutine mathematical problems. "With nonroutine problems, students should expect "messiness." There may be different paths to a solution, and there may be several different good solutions to a problem . . . Doing mathematics often means rough drafts, tentativeness, challenge, and hard work." (Mokros et al., p. 53.)And surely math education specialist Jan Mokros is a much better source on what doing mathematics involves than tidy, correct-answer-obsessed mathematicians are.
Our teacher goes on to express concern about the mixed blessings that Investigations has brought (which apparently include making math more enjoyable to most students--a constituency of students whom I have yet to meet):
Most students LOVE Investigations, messiness and all. I am excited about the many students who are turned on by Investigations, students who used to think math is boring. I'm thrilled to hear the stories of students who would rather continue with math time than go to recess. But I am also troubled by the few students who liked math better the old way.I have a few suggestions, but I'm afraid they may be a bit too tidy for the Powers that Be.
We need to recognize how hard the adaptation to "messy math" is for a few children. To achieve our vision of equity, we must support these children too, but how?
Saturday, March 6, 2010
I just came across an online article by a Singaporean named Justin Lee, the founder of two education businesses in Singapore. In reaction to many articles "fussing about Singapore Math on the Internet," Lee writes:
While many authors bemoaned or even whined about the difficulty American kids had with Math, it made me at times sympathetic or even amused. You see, Math in Singapore was highly enjoyable in my time and we dreaded other subjects like English and Science instead. Why is this so?One reason, Lee points out, is that, for about 50% of the Singaporean population, English is not the native language. As a result:
Math in primary school (for 7-12 year olds) was one of the easiest subjects to ace. It did not involve language application as extensively as Science. Although the word problems in Math papers still involved the English language, it required us only to write one-liners as conclusions. Many friends of my age then scored above 80 marks out of a 100 in Math on a regular basis. Being able to score so highly in Math (as opposed to barely passing English or Science) easily made Math our favourite subject in school!This, of course, makes me think of all the language impaired math buffs who suffer under Reform Math's much more language-intensive "story problems" and verbal explanations requirements.
Lee goes on to lament a development in Singapore that is taking math standards in Singapore in the opposite direction as that which American math standards have followed. Apparently, "there has been a rising trend of schools setting impossible-to-pass Math tests and examinations in the late 2000s." Instead of parents being upset that standards are too low, Singapore parents are upset that standards, which have long been higher than ours, have now risen too high.
Lee proceeds to describe how he and his classmates found Singapore math to be easy and enjoyable, with plenty of time left over for fun:
It is true that the Mathematical concepts are built year upon year and concepts that have been taught are not taught again, but merely revisited briefly. This is as opposed to the slightly incoherent system in the US, where kids can sometimes wonder why they are doing the same things again. While this arrangement may appear to be harder on Singapore students, I actually felt it was very easy on us. In fact, we felt that it was a gift from heaven to be able to do fractions at primary 6 again, right after we learnt something similar the year before.
It might appear as though a Singapore student would have had to spend many hours poring their beady eyes other Math textbooks and Math problems to acquire such ‘astounding’ proficiency in the subject. The truth is, the pace of learning was rather fine. I could do quite well in school without having to attend extra lessons (tuitions), and school only lasted from 730am to 1pm, Monday to Friday. There was still ample time for monkey business after 1pm.
To sum up, I am positive that Math in primary school was enjoyable for most students in the 1990s. This may not be so after internal Math examination standards were revised upwards in the late 2000s, but we shall address this issue in another article.I look forward to more! In our self-absorbed, American-exceptionalist country, the Singaporean perspective, which should be a key element in the debate over math reform, is all too often overlooked.
Thursday, March 4, 2010
I. The last 4 fractions problems in the 4th grade Everyday Math Student Math Journal, volume 2 fractions unit, "Fractions and Their Uses: Chance and Probability," pp. 227-8.
Tuesday, March 2, 2010
I've been researching this question for an online class I'm designing on High Functioning Autism/Asperger's, and found what I've learned to be applicable to bright, quirky, socially awkward children in general--and their parents. Here's what I've written up.
Studies suggest that sensitive, socially awkward children are particularly vulnerable to persistent teasing--of the sort that people now classify as bullying. Being academically gifted, further setting the child apart from his classmates, may make matters even worse.
Encourage your child to talk about the situation; just talking and being heard may help him feel better. It will also build trust between the two of you, and give you a sense of the issues.
In advising your child, you can avoid making him more self-conscious about his differences by shifting the spotlight from him to his bullies. Explain to him what motivates them: bullies thrive on getting a reaction; those who tease him are trying to make him cry.
Then empower your child. Explain that while we can’t control bullies, we can control our reactions to them and how often we cross their paths.
Help your child brainstorm ways to avoid the bullies. Perhaps there are particular places at school where bullies hang out, or specific groups of kids that he could avoid spending time with. It may turn out that some of the children he considers his friends are among those who tease him. In this case, you need to convince him that friends don’t make their friends feel bad, and that if his friends won’t stop teasing, or stand up for him when other friends tease him, he needs to start looking for new friends.
Advise you child, as well, on how to best to react to teasing. As bullying researchers have repeatedly found, ignoring the perpetrator doesn’t work; it will just make him try harder to get a reaction. Instead, advise you child to give a different reaction from that which the bully is seeking.
Effective responses include the direct, honest, retort: “Why are you saying cruel things about me when you know it upsets me?” or “It hurts my feelings when you tell people that I suck my thumb when I don’t.” Alternatively one can direct the insult back at the bully: “I know, it must really bother you that I dress this way,” or “Does making me feel terrible about myself make you feel better?"
After presenting these options to your child, help him brainstorm a handful of ready responses that he is comfortable delivering. Whichever ones he chooses, it’s crucial that he speak his lines with confidence. He should enunciate them clearly in a sufficiently loud voice, standing up straight and looking directly into the eyes of the bully. Message delivered, he shouldn’t wait around for a reaction, but calmly walk away.
Many socially awkward children will find it difficult to deliver their lines with sufficient confidence. Role playing the interaction at home will help them tremendously. Start by having your child play the bully, modeling his chosen response yourself. Then change roles and practice until your child shows the requisite confidence.
Some victims of bullying may be too self-consciousness to share their plight with their parents. If you suspect that your child is a victim and are unable to encourage him to talk about it, it’s still important to act: persistent teasing and bullying can have profound, long-term effects on mood and self-esteem. Many reluctant children are ultimately relieved when things are brought out into the open; the more so, of course, once they’re actually dealt with.
If your child is reluctant to admit to being bullied, present your advice in general terms. You might say that all children have to deal with teasing, and here are some things you learned to say when you yourself were teased.
Besides advising your child, there is much you can do without involving him directly. Telling the teacher and principal right away is crucial; don’t assume that school officials are necessarily aware of the situation. Request ways to minimize the opportunities for bullying—e.g., by having recess or cafeteria aides keep a close eye on your child, or by changing his classroom seating arrangements, assigning him to a different group during group activities, or allowing him to work independently instead of in a group.
You can also request that school officials convene meetings with the bullies and their parents. Many schools have official anti-bullying protocols. Many parents have no idea that their children have bullied others and are eager to do what they can to set things right.
Finally, it’s important to address the root causes of your child’s victimization. Some awkward children unwittingly irritate others in ways that invite teasing. Discretely observe your child during play dates or other interactions and see if he provokes others through behaviors that are under his control to alter. If so, give him constructive feedback later on, perhaps role playing specific interactions.
The most effective antidote to bullying, however, is building self confidence. Show your child love and understanding. Help him develop his talents and focus on his positive qualities. Help him improve his social skills through regular play dates, carefully chosen extra-curricular activities, and/or social skills classes. Help him find true friends by inviting over like-minded peers who share his quirks, or kind, socially responsible classmates who will stand up for him when others tease him. By helping your child develop his social self-confidence, you not only reduce his susceptibility to bullying, but strengthen his ability to cope with all sorts of other social challenges that life eventually presents.