kitchen table math, the sequel: 9/5/10 - 9/12/10

Saturday, September 11, 2010

Articles you may have missed...

I did, while I was out of town.

From the New York Times:  Forget What You Know About Good Study Habits
 But individual learning is another matter, and psychologists have discovered that some of the most hallowed advice on study habits is flat wrong. For instance, many study skills courses insist that students find a specific place, a study room or a quiet corner of the library, to take their work. The research finds just the opposite.
And from the Washington Post, a little opinion on:  School reform's meager results
Standard theories don't explain this meager progress. Too few teachers? Not really. From 1970 to 2008, the student population increased 8 percent and the number of teachers rose 61 percent. The student-teacher ratio has fallen sharply, from 27-to-1 in 1955 to 15-to-1 in 2007. Are teachers paid too little? Perhaps, but that's not obvious. In 2008, the average teacher earned $53,230; two full-time teachers married to each other and making average pay would belong in the richest 20 percent of households (2008 qualifying income: $100,240).

Friday, September 10, 2010


It is probably the most important day of your life. Your mind is racing and your hands are trembling at the thought of the erudite questions you are about to be asked, which will determine your future education, career and indeed the rest of your life. Then a man leans forward towards you and says: "Tell me about a banana."

other questions:
"Why isn't this chair acting as a wave?"(Chemistry, Oxford).

"Estimate the number of pebbles on Brighton Beach. If a pebble was given to each person would there be enough for the entire population?" (Natural sciences, Cambridge).

"If you leave the fridge turned on in a thermally isolated room, what happens to the room?" (Physics, Oxford).

Knowledge of a banana may be the key to Oxbridge entry
By Richard Garner
Monday, 6 September 2010
So You Want to Go to Oxbridge?: Tell Me About a Banana

So You Want to Go to Oxbridge?: Tell Me About a Banana

Barry G on just-in-time learning

I think this is my favorite of Barry's articles -- he nails it.
Even worse than the book itself were the discussions in class that came out of it. One event in particular stands out. In a chapter that discussed the difference between "knowing" and "understanding," a chart presents examples of “Inauthentic versus Authentic Work.” In this chart “Practice decontextualized skills" is listed as inauthentic and "Interpret literature" as authentic. The black and white nature of the distinctions on the chart bothered me, so when the teacher asked if we had any comments, I said that calling certain practices “inauthentic” is not only pejorative but misleading. I asked the teacher “Do you really think that learning to read is an inauthentic skill?”

She replied that she didn’t really know about issues related to reading. Keeping it on the math level, I then referred to the chart's characterization of "Solve contrived problems" as inauthentic and “Solve ‘real world’ problems” as authentic and asked why the authors automatically assumed that a word problem that might be contrived didn’t involve “authentic” mathematical concepts. “Let’s move on,” she said.


The authors’ approach to how one teaches for understanding is through a process that they call “backward design,” in which educators plan their courses, units and lessons by starting from what they want the end result to be. That is, what should students know, understand and be able to do? The planning process then entails working backwards from there, identifying the content that goes into this, the big ideas, the questions to be explored and so on.

As the authors state, backward planning is not a new idea. In fact, I was a bit confused as to why it is even needed, given that such work has essentially been done in the writing of the textbooks that cover the course material.... But this brings us to another axiom which I have heard repeated in education school, which states that textbooks are a resource and not a curriculum. The authors pick up on this as well and regard using the textbook for planning as a “sin," stating that “The textbook may very well provide an important resource but it should not constitute the syllabus.”


In a paean to constructivism and the abandonment of textbooks, Tomlinson and McTighe dispose of the notion that sequence of topics and mastery of skills is important, calling such beliefs the “climbing the ladder” model of cognition. “Subscribers to this belief assume that students must learn the important facts before they can address the more abstract concepts of a subject,” the authors state, and then quote Lori Shepherd, a University of Colorado education professor to make their point:
“The notion that learning comes about by the accretion of little bits is outmoded learning theory. Current models of learning based on cognitive psychology contend that learners gain understanding when they construct their own knowledge and develop their own cognitive maps of the interconnections among facts and concepts.”
In fact, this is the crux of how they approach differentiated instruction. Sequence doesn’t matter. Each student constructs his or her own meaning at their own pace, by being immersed in what the authors term “contextualized grappling with ideas and processes.” What does this mean? There are many examples, but the prevalent pattern of instruction to emerge from the book seems to be one of giving students an assignment or problem which forces them to learn what they need to know in order to complete the task. Say it is quadratic equations. Rather than teach them the various methods of factoring first, with the attendant drills, they might start with a problem such as x^2 + 5x + 6 = 0. The teacher may then provide some activities that illustrate what factoring is, and then provide some exercises. The goal would be to factor the above equation into (x+3)(x+2) = 0 and, from there, lead the students to see that there are two values that satisfy the equation. This is what they mean by “contextualized grappling” as opposed to “decontextualized drill and practice.” It is a “just in time” approach to learning, (my choice of phrase, not theirs) in which the tools that students need to master are dictated by the problem itself by not burdening the student's mental inventory with “mind numbing” drills for mastery of a concept or skill until it is actually needed.


They admit that there are times when direct instruction or ‘teaching by telling’ might work extremely well. “There is a need for balance between student construction of meaning and teacher guidance”, they proclaim. That direct instruction would work even better if topics were presented in a logical sequence is not the message of this particular book, however.


“Just in time” approaches that work as a model for business inventory work just as well in education, they believe. The result is an approach that is like teaching someone to swim by throwing them in the deep end of a pool and telling them to swim to the other side. For the students who may already know a bit about swimming, they may choose to take that opportunity to learn the butterfly. The teacher might advise the weaker students to learn the breast stroke and provide the much needed direct instruction which they may now choose to learn. Or not.

Let’s move on.

Integrating Differentiated Instruction & Understanding by Design: Connecting Content and Kids

Thursday, September 9, 2010

rule of 20

Surprisingly, the vast majority of skills which we try to teach appear to begin the passage from acquisition to fluency-building at roughly the same point —when correct frequencies are somewhere between 14 and 20 per minute, and an accuracy of between 67% and 83% has been achieved. That rule seems to apply to very basic behaviors like pointing to named objects, steps taken while walking, and completing parts of a dressing sequence. The same transition point also seems to apply to very complex behaviors like reading, speaking, and writing digits to solve advanced mathematics problems. Indeed, the rule appears so universal that when Sokolove (note 9) examined circa 3300 programs of children in grades 1 through 6, the “rule of 20” predicted progress in more than 97% of the cases.

Decisions, Decisions
Owen Roberts White
University of Washington
Fall 2000

unfriendly worksheets, part 2

from A Guide to Learning English:
Rule number 2: Be aware of the difficulties of cultural references!

The following text is the first part of the introductory paragraph to a question about car speed:
"The police used to measure the speed of cars on the road by having two PCs some distance apart using a stopwatch. One of them would stand and wave as a car reached him. When the wave was seen by the second PC a stopwatch was started. As the car passed the second PC, the stopwatch was stopped."
The question itself read:
"Is the car exceeding the maximum speed limit in Britain?"
The ESL student who asked for my help with this question was puzzled how a personal computer could stand and wave. He also had no idea what the maximum speed limit is in Britain.

I would like to know how two personal computers can stand some distance apart and use a stopwatch.

unfriendly worksheets

A Guide to Learning English

Monday, September 6, 2010


Examination dreams are reported to persist even into old age...
- Time magazine

You will never graduatefrom this dream
of blue books.
No matter how
you succeed awake,
asleep there is a test
waitinmg to be failed.
The dream beckons
with two dull pencils,
but you haven't even taken the course;
when you reach for a book--
it closes its door
in your face; when
you conjugate a verb--
it is in the wrong
Now the pillow becomes
a blank page. Turn it
to the cool side;
you will still smother
in all of the feathers
that have to be learned
by heart.

Linda Pastan

The Compact Bedford Introduction to Literature
Michael Meyer

Sunday, September 5, 2010

edu-fads at home

Found this comment on Jay Mathews' 2009 column about 21st century skills:
One of my friends holds advanced degrees in education, and she used cutting-edge methods to teach her own kids. What she forgot was the classic problem of the teacher being all fired up and motivated, and the student feeling left out of the picture. After all, fundamentals may be old-hat for teachers, but for students they're all new concepts. Her son was all but forgotten in her enthusiasm and fascination with the perpetually new. She has asked me a hundred times what I think is "wrong" with him (answer: "you").

She force-fed her son this and that fad over the years while he quietly turned off to learning. He recently dropped out of the marginal college he was able to squeak into with his middling test scores, yet it is obvious to anyone who talks with him for five minutes that he is very bright. I think he'll probably drop back in some day when he returns for his own reasons, but his mom's incessant buzz-speak about the latest pedagogical gewgaws of the day (I suspect 21st-century skills were part of it) really did a number on him. Poor kid.
1/5/2009 7:10:48

The Latest Doomed Pedagogical Fad: 21st-Century Skills
by Jay Mathews
Washington Post
Monday, January 5, 2009
I wonder if this boy was being homeschooled or afterschooled.