kitchen table math, the sequel: 5/22/11 - 5/29/11

Friday, May 27, 2011

Barry Garelick on mini lessons and inequality

The history of tracking students in public education goes back to the early part of the 1900′s. By the 20′s and 30′s, curricula in high schools had evolved into four different types: college-preparatory, vocational (e.g., plumbing, metal work, electrical, auto), trade-oriented (e.g., accounting, secretarial), and general. Students were tracked into the various curricula based on IQ and other standardized test scores as well as other criteria. By the mid-60’s, Mirel (1993) documents that most of the predominantly black high schools in Detroit had become “general track” institutions that consisted of watered down curricula and “needs based” courses that catered to student interests and life relevance. Social promotion had become the norm within the general track, in which the philosophy was to demand as little as possible of the students.


By the early 80’s, the “Back to Basics” movement formed to turn back the educational fads and extremes of the late 60’s and the 70’s and reinstitute traditional subjects and curricula. The underlying ideas of the progressives did not go away, however, and the watchword has continued to be equal education for all. While such a goal is laudable, the attempt to bring equity to education by eliminating tracking had the unintended consequence of replacing it with another form of inequity: the elimination of grouping of students according to ability. Thus, students who were poor at reading were placed in classes with students who were advanced readers; students who were not proficient in basic arithmetic were placed in algebra classes. Ability grouping was viewed as a vestige of tracking and many in the education establishment consider the two concepts to be synonymous.

The elimination of ability grouping occurs mostly in the lower grades but also extends to early courses in high school. The practice of such full inclusion is now so commonplace that theories have emerged to justify its practice and to address the problems it brings. “Learning styles” and “multiple intelligences” are now commonplace terms that are taught in schools of education, along with the technique known as “differentiated instruction” to address how to teach students with diverse backgrounds and ability in the subject matter. Teachers are expected to “differentiate instruction” to each student, and to keep whole-group instruction to a minimum. To do this, the teacher gives a “mini-lesson” that lasts 10 to 15 minutes; then students work in small groups and told to work together. The prevailing belief is that by forcing students to solve problems in groups, to rely on each other rather than the teacher, the techniques and concepts needed to solve the problem will emerge through discovery, and students will be forced to learn what is needed in a “just in time” basis. This amounts to giving students easy problems, but with hard and sometimes impossible approaches since they have been given little to no effective instruction to the mathematics that results in effective mathematics problem solvers.


Brighter students are seated with students of lower ability in the belief that the brighter students will teach the slower ones what is needed. And frequently this occurs, though the fact that the brighter students are often obtaining their knowledge via parents, tutors or learning centers is an inconvenient truth that is rarely if ever acknowledged. The result is that brighter students are bored, and slower students are either lost, or seek explanations from those students in the know. Another inconvenient truth is that in lower income communities, there are unlikely to be students who have obtained their knowledge through outside sources; they are entirely dependent on their schools.


Through the efforts and philosophies of otherwise well-meaning individuals, full inclusion and equality for all has served as a form of tracking.

Protecting Students from Learning: Raymond
by Barry Garelick
In my experience, when a school opts for "differentiated instruction," parents have no way to know whether their children are being taught the same curriculum as other children -- especially since differentiated instruction tends to go hand-in-hand with a reduction in quizzes and tests and the introduction of "standards-based" report cards parents don't know how to interpret.

A less-able child is treated equally in the sense of being placed in a classroom with more-able children.

But is the less-able child taught the same curriculum?

Is the less-able child given the same problems to do?

And, if he is given the same problems but can't do them, what then?

In Singapore, somewhere around 4th or 5th grade, less able children are given more time in the day to master the curriculum. Equality means that all children are taught the same curriculum.

Thursday, May 26, 2011

the children of immigrants

One surprising characteristic unites the majority of America’s top high school science and math students – their parents are immigrants. While only 12 percent of the U.S. population is foreign-born, 70 percent of the finalists in the 2011 Intel Science Talent Search competition were the children of immigrants, according to a National Foundation for American Policy analysis. Just 12 of the 40 finalists at this year’s competition of the nation’s top high school science students had native-born parents. While former H-1B visa holders comprise less than 1 percent of the U.S. population, 60 percent of the finalists had parents who entered the U.S. on H-1B visas, which are generally the only practical way to hire skilled foreign nationals. Finalists’ parents sponsored through a family preference category represented 7.5 percent of the total, about four times higher than their proportion in the U.S.


Today's Mantra: Learn to Mastery, Then Add 20% More Study Time

Willingham's advice has been incredibly useful as my son heads into finals this season.

Interestingly, my son seems as intrigued by the study advice as I am, and wants to read the articles and book for himself when school ends.

(cross-posted on Perfect Score Project)

And speaking of books, I am currently obsessed with brain/how we learn books. In the past month I have read:

Moonwalking with Einstein (about memory -- but includes brain research)

The Shallows (I'm about 3/4 done. Well worth the read. I'm identifying strongly.)

About to read:

Wednesday, May 25, 2011

another Chinese mom

Caught this line in a Wall Street Journal review of The Woman Who Could Not Forget:
..."As my mother used to say to me, the success in one's life was dependent on 70% hard work and only 30% talent or genetic makeup."
Stigler and Stevenson found that "American children, teachers, and parents emphasize innate abilites as a component of success more strongly than their Japanese and Chinese counterparts do."

I'd be interested to know what percentages American parents would slot into Ying-Ying's statement on the subject of math and math learning.

I'd really be interested to know what percentages American math teachers would pick - !

The Woman Who Could Not Forget: Iris Chang Before and Beyond the Rape of Nanking- A Memoir

The Woman Who Could Not Forget: Iris Chang Before and Beyond the Rape of Nanking- A Memoir

Learning Gap: Why Our Schools Are Failing and What We Can Learn from Japanese and Chinese Education

Learning Gap: Why Our Schools Are Failing and What We Can Learn from Japanese and Chinese Education

Engineering Professor: Out of 18 Ph.D's I advised, 16 were from China

Interesting comment from Engineering professor in post about Chinese students taking SATs:
As a professor in Engineering, I see that the Chinese students who study in the US are just incredible. Out of 18 Ph.D's I advised, 16 were from China and we don't get any Americans into the doctoral program with nearly their qualifications. When they go back home, they will just leap-frog the US within the next 10 years.

The Benign Cousin to Rote Knowledge

I'm savoring these Willingham articles. Just one more to go, then I will read his book.

It's not only helping me with my own learning process, but I feel armed to help my kids study with specifics about what works best.

(cross-posted on Perfect Score Project)

Tuesday, May 24, 2011

lsquared on what you must know to take calculus

(lsquared couldn't get this comment to post on Blogger):
Yes, you need to be very good at algebra. Think factoring, equation solving and complex fractions.

You also need to be quite good at trigonometry: knowing right triangle trigonometry is sufficient for almost everything except calculus--for calculus you need to know how to solve equations that have trig functions in them, and you need to know your trig formulas (the double angle formulas are particularly useful). You don't actually do any of the "verify this trig formula" stuff in calculus, but those "verify the trig formula" problems are very useful for teaching the algebraic trigonometry you use in calculus. Oh--and radians. I'm morally convinced that radians were invented to make trig functions work for calculus. Degrees are better for everything else, but in calculus, you have to have radians.

You also need to know logs: solving exponential equations with logs, solving log equations with exponents, and manipulating logarithms.

Back to rational functions. Be able to solve rational equations, simplify rational expressions that are not equations, and graph (by hand, not by calculator) rational functions (using properties of the rational function to graph, not by plotting points) (I may be unusually picky about this).

Sequences and series, including finding sums using the formulas for arithmetic and geometric sequences. Also the binomial theorem.

You don't need matrices, though you do need to be able to solve simultaneous linear equations. If there's a section in the pre-calc book on find partial fraction decompositions, that's directly a calc algorithm.

I think that might be everything you need for pre-calc.

This was an excellent exercise for me. I’m going to have to keep a copy of this to use when counseling students about whether they are ready for calculus or not. Indeed, the homeschooled kid next door wants to get into my calc class in the fall, and I shall be handing this to him I expect. Good luck finding a good class--I think the community college might be a good choice (assuming that they have a pre-calc course).

help desk - precalculus

This year's math course has been a disaster. Beyond disaster, actually. Where math is concerned, this year has been epically* bad.

Some kind of emergency repair has to happen this summer - but what?

Any suggestions?

I could conceivably sign C. up for an algebra 2/precalculus course at the local community college - but are the teachers there going to be any better? At this point, we desperately need an actual math teacher: a person who can teach math to a student who doesn't teach math to himself.

We could do ALEKS, but ALEKS is super-slow and overwhelmingly procedural; the 1 1/2 courses I took on ALEKS taught me one disembodied procedure after another. At this point disembodied procedures might be better than nothing -- but then again to the extent C. learned anything this year he learned disembodied procedures.

I could insist that the two of us work through Foerster (I own the teacher's edition).

We could work our way through Saxon.

I could advertise for a math teacher or check out the various tutoring companies....

We also have to do serious SAT prep (though that's not going to be onerous & time-consuming).

I'm thinking this wasn't the summer to sign up for the precision teaching institute at Morningside.

* My neighbor's son, who is a terrific writer, is constantly inventing words he says ought to exist, and having watched him do this a few times, I think he's right. Epic is an excellent word, and its non-existent cousin epically is the word I need today.

Over 20,000 Students Took SAT Prep in China Last Year

According to the dean of admissions for the University of Virginia, 1200 applicants from China scored an average of 783 in math.

(Cross-Posted at Perfect Score Project)

Monday, May 23, 2011

Edgemont High School

Jay Mathews' Newsweek Challenge Index is now at the Washington Post (very glad to see it survive Newsweek's sale), where it is now called The High School Challenge.

How schools are ranked:
The formula is simple: Divide the number of Advanced Placement, International Baccalaureate or other college-level tests a school gave in 2010 by the number of graduating seniors.
Edgemont High School is ranked 197 in the country, which is not surprising given the high socioeconomic status of its students.

What is surprising - what is astonishing, really - is Edgemont's "Equity and Excellence" score, which gives the percent of graduating seniors who have scored a 3, 4, or 5 on at least one AP exam by graduation: 86.6% of Edgemont's graduating seniors passed at least one AP test.*

Can that possibly be true?

I assume it can, given that Rye and Chappaqua have reported similar scores now or in the recent past. 

Their figures over the past several years are very high compared to the percent most schools - including most affluent suburban schools - post.

*IB scores count, too, but I don't think Edgemont has IB courses.

Familiarity Fools the Mind

I *feel* like I'm getting better at SAT math.

Turns out that feelings aren't facts. Practice test scores not improving (yet), despite being able to solve formerly elusive slope and function problems.

I told my son this morning, Daniel Willingham says, when you think you know the material cold, study 20% more.

(cross-posted at Perfect Score Project)

Telling truth from fiction

One of these stories appeared as a front page, May 18th Philadelphia Inquirer article. The other one is made up. Which is which?

Story A:
Some teachers swear that the best way to establish their authority is to avoid smiling for the first two weeks of class.

David Hall takes a very different approach with his students at North Penn High School by cracking self-deprecating jokes and pretending to be the dude who thinks he is hip but so is not.

In the classroom, Hall brings social studies alive, bypassing textbooks in favor of original sources and creating his own lesson materials. Inside and outside the classroom, he spends time getting to know students, hoping to connect with them and inspire them.

Now in his 13th year of teaching, Hall, 37, recently received a "Teacher as Hero" award from the National Liberty Museum in Philadelphia, the latest in a long string of teaching laurels. The Liberty Museum cited Hall's field trips to courtrooms and prisons in Philadelphia and his work as an adviser for the school Gay-Straight Alliance. During summer vacations, Hall does corporate training on workplace diversity issues.

Lauren Ewaniuk, 28, who graduated from North Penn in 2001, called Hall her "all-time favorite teacher by far."

"The best thing about his class was we didn't use the textbook very often," said Ewaniuk, now a teacher in Cheltenham. "He taught us in different ways. The classroom was set up as a circle - it was all class discussion. We read court cases, we did interactive things, watched videos - it was very engaging."
Story B:
Some teachers swear that the best way to engage with students is to crack jokes and relate to them as peers.

David Hill takes a very different approach with his students at South Penn High School. He spends most of his time standing in front of the class and rarely goes off topic

Hill brings social studies alive by ensuring that students can make sense of it. His approach bucks what has become a common trend among award-winning teachers: creating lessons from scratch out of original source materials. Noting that students often find such materials confusing or overwhelming because they lack the necessary background knowledge, Hill makes teaching this knowledge his number one priority.

"My job is to get them ready for the kinds of serious, primary source research that occurs in college and graduate level courses," Hill explains.

Now in his 13th year of teaching, Hill, 37, recently received a "Teacher as Teacher" award from the National Liberty Museum in Philadelphia, the latest in a long string of teaching laurels. The Liberty Museum cited the well-informed essays that Hill's students wrote about the history of prison reform in Philadelphia and Hill's own original research on Gay-Straight relations in Philadelphia high schools. During summer vacations, Hill seeks out the most informative, interesting history texts and conducts workshops for teachers in what he calls "Textbook Resuscitation."

Evelyn Lemaniuk, 28, who graduated from South Penn in 2001, called Hill her "all-time favorite teacher by far."

"The best thing about his class was how he renewed my interest in reading history," said Lemaniuk, now a teacher in Cheltenberg. "Most of the approved textbooks are incredibly low-level and boring, and so the better teachers tend not to use them. The problem is that, without a textbook, we're really at a loss when it comes to understanding primary source materials and how they fit into the bigger picture."

(Cross-posted at Out In Left Field)

Sunday, May 22, 2011

Music While You Study?

My kids are always trying to convince me that they can study just as well while IMing and BBMing and video chatting and listening to music. In fact, they may have even said they study better while multitasking.

Turns out my gut was right.

(Cross-posted at Perfect Score Project)