Monday, April 27, 2015

Homeschooling update

The homeschooling schedule need not have any clear-cut beginnings or endings. Every once in a while, however, a bunch of things conclude at more or less the same time, and a bunch of new things begin. And then it's time for a homeschooling update.

In Literature, we recently moved on from Arthur Lang's King Arthur to Bullfinch's The Age of Fable; from assorted works of Washington Irving (Tale of Old New York, Rip Van Winkle, Sleepy Hollow) and Poe (The Cask of Amontillado; The Masque of the Red Death; the Black Cat) to To Kill a Mockingbird and Animal Farm; from Little Women to Good Wives; from The Hound of the Baskervilles, The Strange Tale of Dr. Jekyll and Mr. Hyde, and Macbeth to Frankenstein; and from Kings to Chronicles.

In history she recently finished Gombrich's A little History of the World and is now reading Outlines of European History.

In science we recently finished a McGraw Hill earth science text and The Way Life Works and are now working our way through our various science experiment kits.

In French she recently moved on from Level II to Level III in A-LM French, and from Astérix le Gaulois to Astérix et la serpe d'or.

Sadly, the three after-school art classes she takes at the Pennsylvania Academy of the Fine Arts are about to conclude this coming week.

Finally, in what is her biggest academic accomplishment this year, she just finished Wentworth's New School Algebra (which has made numerous appearances on this blog), doing nearly every problem in the book (skipping some of the really messy problems at the end), and is about to embark on an alternation of Weeks & Adkins Geometry (my husband's high school text) and A Second Course in Algebra (my mother's high school text), which includes some trig and pre-calc.

Not everything is new: I have her scanning the New York Times every morning, reading a poem once a week, working her way through a long American History text (Glencoe), Wheelock’s Latin, and music theory. Music lessons and ensembles continue, and this summer she looks forward to doing the six-week piano program at the Interlochen Center for the Arts.

Saturday, April 25, 2015

“Asian” collectivism vs. “Western” individualism: what does the fish tank experiment really show?

If you show an American an image of a fish tank, the American will usually describe the biggest fish in the tank and what it is doing. If you ask a Chinese person to describe a fish tank, the Chinese will usually describe the context in which the fish swam.
Skeptical about whether modern Chinese culture really is less individualistic than modern American culture, I was going to offer an alternative explanation for the results of the fish tank experiment, as discussed, for example, by David Brooks. What I like about this explanation, besides the fact that I can claim it as my own, is that the variable it targets also accounts for that other common stereotype about Chinese culture: that the education system is based mostly on rote memorization.

The variable I have in mind is the Chinese writing system.

In my earlier post, I wrote that the rote memorization in Chinese schools stems mostly from the logographic system of written Chinese. The thousands of characters prerequisite for literacy in written Chinese require many thousands more hours of memorization than the few dozen sound-symbol correspondences of written English.

But learning the Chinese vs. the English writing systems doesn’t just involve quantitative differences in time spent memorizing things. Also at play are qualitative differences in the memorization process. Learning an alphabet means attending to the symbols’ most salient features: the big lines and curves rather than the little serifs (or lack thereof) around the edges. Learning Chinese characters means attending to everything: the big lines and curves, but also the patterns of smaller lines and dots all around them. If Chinese people are more aware of the context of a fish tank, perhaps it’s because learning the Chinese writing system trains you in a certain attention to visual detail; in particular, to the details that surround the larger, more visually salient elements.

I liked this explanation so much that I was sorry to find out just now that, along with all the other experiments that supposedly show today’s Chinese to be less individualistic than their Western counterparts, the fish tank experiment fails, across many dimensions, to support not only the broader claims that I’m skeptical of, but the proximal claims about who reports what about the fish tank. The details are found in a 2008 post by Mark Liberman on the Language Log—a post so delightful and interesting that, for me at least, it more than makes up for my sorrow at having to abandon something I really, really wanted to believe.

Thursday, April 23, 2015

Common Core-inspired high school exam questions vs. Chinese and Finnish counterparts

From America's PARCC (The Partnership for Assessment and Readiness for College and Careers, a consortium of 23 states involved in developing Common Core tests):


From the Chinese Gao Kao



From Finland's National Matriculation exam:

Extra Credit:

Perhaps I'm cherry picking. Prove it by finding Common Core-inspired high school test questions as mathematically challenging as the ones above from China and Finland.

Tuesday, April 21, 2015

The stereotype of rote learning in East-Asian classrooms, III

(Third in what's become a series.)

This installment begins with a few more thoughts on Fareed Zakaria’s recent Why America’s obsession with STEM education is dangerous--which, for all its problems, is certainly thought-provoking:

Americans should be careful before they try to mimic Asian educational systems, which are oriented around memorization and test-taking. I went through that kind of system. It has its strengths, but it’s not conducive to thinking, problem solving or creativity. That’s why most Asian countries, from Singapore to South Korea to India, are trying to add features of a liberal education to their systems. Jack Ma, the founder of China’s Internet behemoth Alibaba, recently hypothesized in a speech that the Chinese are not as innovative as Westerners because China’s educational system, which teaches the basics very well, does not nourish a student’s complete intelligence, allowing her to range freely, experiment and enjoy herself while learning.
Jack Ma was born and educated in China and lives there now; thus creatively undernourished, how is he qualified to talk about creativity? For that matter, how qualified is the Indian-educated Zakaria, who, as he himself claims, went through a system oriented around “memorization and text-taking.”?

The fact that there are plenty of creative individuals educated in India and China should make us wonder whether the claims of these two particular Chinese and Indian-educated individuals--not to mention so many of us native-born Americans--are actually true.

When it comes to China in particular, Americans have hopelessly incoherent opinions. On the one hand, with our stereotype-confirming fish tank experiments, we think the Chinese (along with Asians in general) are more into group harmony than we Westerners are; on the other hand, with their competitive exams and tiger moms, we think they are more into competition and individual success. We carry on about how steeped in memorization the Chinese education system is, ignorant of how most of this is an artifact of a logographic writing system that demands thousands more hours of memorization than what our alphabetic system demands. Those hours do limit how much time Chinese K12 schools spend on a broader curriculum—e.g., on history, science and art—but, when it comes to math, their curriculum is akin to the highly conceptual Singapore Math.

Americans carry on about China’s college entrance (Gao Kao) exams, conflating stiff competition with rote memorization. Yes, the exams are highly competitive, and students study very hard for them, and, like most exams the world over, they favor the wealthy. And, by the time they take these exams, exhausted, sleep-deprived students may feel like mindless zombies.

But the exams aren’t rote. Both the Chinese and English sections include essay questions, and the problems on the math sections are highly conceptual. In many ways the Chinese Gao Kao exams are more demanding of conceptual understanding and creativity than America’s Common Core exams.

Sample essay question for the Chinese section of the Gao Kao can be found here and include questions like:
"You can choose your own road and method to make it across the desert, which means you are free; you have no choice but finding a way to make it across the desert, which makes you not free. Choose your own angle and title to write an article that is not less than 800 words."
Sample essay questions for the English section, found here, include:
A pencil laughs at a shorter pencil, which is almost used up, saying: "You're nearing the end!" You are discussing a picture with an English friend. Describe your understanding of the illustration, and the reason why.
And sample math questions, found on the slideshow on this site, include:



Critical thinking and conceptual understanding, anyone?

It took me only an ounce of skepticism and a handful of clicks to track down this information. But most Americans (including, apparently, naturalized Americans like Zakaria) are so sure that the Chinese system amounts to mindless rote learning that it hasn’t occurred to them to spend a few seconds verifying what their own mindless rote learning has taught them to take on faith.

Sunday, April 19, 2015

...And to teach reading, study math instruction

In her recent Edweek commentary To Teach Math, Study Reading Instruction, Marilyn Burns asks:

How can we connect literacy and math, so that teachers bring the strengths they have with language arts instruction to their math teaching? How can teachers make links between mathematics and language arts pedagogy that will enable them to engage children with math in the same way they bring children to the wonder of reading?
One way, she proposes,
is for teachers to think about leading classroom discussions in mathematics as they often do when teaching language arts. Probing students' thinking during math lessons is valuable, so that the goal is not only getting correct answers, but also explaining why answers make sense.
Asking students why answers make sense: this idea is so novel that it apparently hasn’t occurred to most math teachers. Along these lines, Burns advises, it’s important
even when [students’] answers are correct to ask: "Why do you think that?" "How did you figure that out?" "Who has a different idea?" "How would you explain your answer to someone who disagreed?"
Naturally, Burns is also a fan of verbal explanations and peer tutoring:
It's useful to have students comment on their classmates' answers as well, asking them to explain what a peer said in their own words, or asking students if they have a different way to explain the answer. If students are stuck, it's sometimes useful to have them turn and discuss the problem with a partner and then return to a whole-class discussion.
Her takeaway?
There's much for us to think about to help teachers teach math more effectively. But I think we can make headway if we take the two most important areas of the curriculum—reading and math—and look at them side by side to analyze what's the same, what's different, and what we can learn from one to enhance the other.
I agree. And so here are some of my suggestions about how good math instruction (the kind done in countries that outperform us in math) can teach us about reading instruction (so as to make it more closely resemble that done in countries that outperform us in reading):

1. Basics first, learned to mastery: just as good math instruction teaches basic arithmetic facts and procedures to automaticity; reading instruction should teach phonics to automaticity. Since many students, even older ones, currently lack automatic symbol-to-sound decoding skills, this means much more time on phonics than is currently occurring.

2. Focus in depth on the one best method(s) rather than covering a bunch of less effective methods superficially. Just as the best math classes focus on standard arithmetic and algebraic algorithms rather than drawings of groups of objects, digit splitting, skip counting, number bonds, repeated addition, repeated subtraction, landmark numbers, and lattices, reading classes should focus on phonics, vocabulary acquisition, and close readings rather than on sight word recognition, context clues, text-to-world references, and text-to-self references.

3. Make sure students have sufficient background knowledge: just as good math instruction waits until students have mastered relevant concepts before having them do novel applications in novel problems, good reading instruction should provide relevant background knowledge to new books (e.g., for Pride and Prejudice, information about English hereditary law; for the Great Gatbsy, information about the Jazz Age).

4. Keep it content-focused: just as good math instruction doesn’t focus away from the actual math via verbose word problems, verbose explanations, and overly concrete, detailed, real life situations, reading instruction should focus on inferences within the text, rather than on inferences that take readers out of the world of the text--and, worse (in the case of “text-to-self” references), distract or annoy them with the task of having thoughts about themselves rather than about what they’re reading.

Friday, April 17, 2015

Math problems of the week: Common Core-inspired quadratic structure problems

A sample high school math problem from PARCC (The Partnership for Assessment and Readiness for College and Careers, a consortium of 23 states involved in developing Common Core tests):


PARCC's discussion of how this problem aligns with Common Core Standard MP.7:


A more challenging set of "seeing quadratic structure" problems from over a century ago (Wentworth's New School Algebra):


Extra Credit:

1. Are there other useful structures one could recognize the PARCC problem as having other than Q2 + 2Q = 0? For example, might recognizing it as having the form a*a = b*a be an alternative, non-brute-force way of seeing its solutions?

2. If "seeing structure in a quadratic equation" warrants a special Common Core standard (MP.7), why aren't students getting more challenging quadratic structure problems like those in Wentworth above?

3. Was "seeing structure in a quadratic equation" even more important a century ago, before we needed the Common Core authors to remind us of how important it is?