The latest things in our house to magically disappear are the champagne mangos and the latest Nextflix Mad Men CD.
Sunday, May 30, 2010
Friday, May 28, 2010
1. The first assignment on proving triangle similarity in Core Plus Mathematics, Contemporary Math in Context (a unified high school "core curriculum appropriate for all students") Course 2 (year 2), Part B, p. 395:
Imagine that you and a classmate each draw a triangle with three angles of one triangle congruent to three angles of the other triangle Do you think the two triangles will be similar? Make a conjecture.
a. Now conduct the following experiment. Have each member of your group draw a sement (no two with the same langth). Use a protractor to draw a 50o angle at one end of the segment. Then draw a 60o angle at the other end of the segment to form a triangle.
-What should be the measure of the third triangle? Check you answer.
-Are these two triangles similar to one another? What evidence can you give to support your view?
b. Repeat Part a with angles measuring 40o and 120o. Are these triangles similar? Give evidence to support your claim.
2. The first assignment on proving triangle similarity in Weeks & Atkins A Course in Geometry (a high school geometry text first published in 1961), p. 233:
P, Q are points on the sides AB, AC, respectively of the Δ ABC such that AP = 6 in. and AQ = 8 in. If AB = 16 in. and AC = 12 in., prove that the Δ APQ and ACB are similar. Is PQ parallel to BC?
[No accompanying diagram]
Wednesday, May 26, 2010
I've just written about how Applied Behavioral Analysis (ABA), one of the standard therapies for autism, neglects grammar instruction. Since then I've been reviewing for an online class I'm designing the language curriculum of ABA's main competitor, the D.I.R (Floor Time) approach of the late Stanley Greenspan. Greenspan's curriculum is called the Affect Based Language Curriculum, available on Amazon for $55, and it, too, neglects grammar.
We create purposeful affect by being a pain in the neck. [E.g. by standing in front of the door the child wants to open.]... We go away a step and come back saying “go, go?”… Once children have that purposeful affect and begin connecting it to the word “go,” guess what they do? They begin using words meaningfully and even using that verb and noun properly.A nonlinguist, Greenspan has no idea how complex grammar is. Neither verb conjugation nor noun phrase formation are trivial, and nowhere in the Affect-Based Language is there any discussion of how to teach this. Instead, as with ABA's Teach Me Language, the entire curriculum is organized around non-grammatical categories: requesting, using words to protest, talking about the past, adding to what the speaker just said.
Monday, May 24, 2010
An article in this month's Harvard Education Letter, just referenced by Catherine Johnson at kitchentablemath, argues for further expanding classroom group work. The article opens with the group-centered classroom of Rachel Otty, a 10th grade social studies teacher in Boston.
“I remember history in high school as just lecturing, and I didn’t enjoy it much,” recalls Otty, who has garnered a reputation at the school for her skillful use of group work. “In graduate school, we learned about differentiated instruction, and group work is a way to do that. It’s tough work and it requires a lot of brain power.”True to its genre as an education article, the article then moves on to what "research shows":
Research by educators, psychologists, and, increasingly, neuroscientists supports Otty’s personal experience. Done right, group work can harness the natural propensity of humans to interact, and—most important—make learning for a wide variety of students more engaging, memorable, and equitable. While it is more difficult to do than traditional lecturing, teachers say, most of the hard work is in the preparation, and the payoffs make the time invested well worth it.The article proceeds to invoke neurology, citing in particular a neurologist names Chris Frith:
Recent research by neuroscientists points to the existence of a “social brain” that enables humans to interact with each other. Summarizing the evidence gathered so far, Chris Frith, professor in neuropsychology at the Wellcome Trust Centre for NeuroImaging at University College London, has identified four regions of the brain associated with functions that allow humans to “read” others’ states of mind and predict what they will do (see sidebar “The Brain and Collaboration”).Chris Frith is the husband of renowned autism expert Uta Frith, who has conducted experiments showing that the "social brain" is highly impaired in autism. So I'm wondering if Chris has consulted Uta on how expanding group learning might affect autistic spectrum students who are mainstreamed into regular classrooms. Here's Frith's take on neurologists and group learning:
...Frith said there was “consensus that work on the social brain does argue for expanding the group learning and cooperative learning projects” in schools. “I certainly believe that the special feature of humans is that we can work together to achieve more than the sum of the individuals in the group. This is because we can share experiences,” he wrote in an e-mail, adding, “But we do have to learn how best to do this.”Well, yes, if a group consensus is so powerful that it can substitute for scientific evidence, than certainly we should worship the power of the group wherever possible.
But what about the many humans in whom this "special feature" is impaired--and whom Frith's wife has so thoughtfully written about?
Not to mention the many others who are hesitant about groups and their consensuses?
I suggest that Chris Frith get into a group with his wife and have a conversation with her about this.
Group work can also work against factors known to inhibit learning, such as the fear of making mistakes or becoming discouraged, says Judy Willis, a neurologist who has taught elementary and middle school in Santa Barbara for 10 years and often writes and speaks about how findings about the brain can inform teaching.And the shy, socially awkward child could play the part of the quiet guy who keeps to himself and is shunned by the rest of the community.
Group work can also increase engagement because individuals can be assigned roles that allow them to be “experts in something,” so that they can be challenged at a level appropriate to their understanding, she says. To discuss and present various theories for why the Jamestown settlement failed or why the dinosaurs became extinct, for example, more advanced students may be “producers” charged with stopping their group periodically to summarize what is being said; those with attention deficits might be assigned to be “prop directors” to keep track of supplies needed to make a chart for the final presentation.
And the child with Asperger's could play the role of "little professor", who spends the entire time lecturing his group mates. Unless that's somehow contrary to group-centered discovery learning...
Saturday, May 22, 2010
I've just discovered that Grammar Trainer has been listed as a resource on the Verbal Behavior website. This is good news, not just for me, but also for addressing what I've always considered a weak point in Applied Behavioral Analysis (ABA), one of the standard therapies for autism, which includes Verbal Behavior as its approach to language teaching.
Thursday, May 20, 2010
I. Final division problems in the first half of the 3rd grade Everyday Math curriculum, Student Math Journal, Volume 1, pp. 154-5 (final set of Math Boxes):
Tuesday, May 18, 2010
I'd always assumed that the extraordinary litigiousness of American society said something deep about our culture. It must be that we expect to have more control over the chance events in our lives than people from other cultures do; that we accept less readily that sometimes bad things simply happen and no one's at fault; that we're always looking for easy ways to make big bucks--if not through the state lottery, then through the lottery of the civil court.
Sunday, May 16, 2010
J's drive for mischief is tempered by his drive to construct new things with Snap Circuits. But mischief means longer waits for the next electronic part--provided you get caught. So J has figured out what all too many neurotypical individuals eventually figure out as well: to lie effectively, first convince yourself. We see this in J's increasingly passionate, indignant denials of responsibility for mishaps we're 99% sure he caused.
Friday, May 14, 2010
I. From Hamilton's Essentials of Arithmetic, Higher Grades (published in 1919), final problem set (for 7th grade) involving fractions, p. 154:
Make out sales slips for the following purchases in this form:
[A model sales slip including fields for Quantity, Article, Amount, Total, and Change Due]
1. Edith Mason bought 2 ¼ yd. lace @ 32 ¢; 2 5/8 yd. edging at 7 ¢; 1 ¼ yd. chiffon @ $2.50. Amount received, $5.00.
2. Cora Wise bought ½ doz. lienen towels @ $6.75; ¾ doz. linen napkins @ $5.94; 1 ½ doz. kitchen towels @ $2.95. Amount received, $13.
3. Ruth Wade bought 5 ¼ yd. serge @ $2.35; 4 7/8 yd. wool Jersey cloth @ $2.75. Amount received, $30.
4. Alice Miner bought 1 chiffon blouse @ $5.95; 5 5/8 yd. ribbon @ 29 ¢; 2 ¼ yd. braid @ 19 ¢. Amount received, $10.
5. Clara Hold bought ½ doz pencils @ $.3; 1 box writing paper @ $.59; ¼ gross pens @ $1.0; ½ doz pads @ $1.15; 1 founatin pen for $2.75. Amount received, $5.
6. Emma Stone bought 3/8 yd. damask @ 225; ¼ doz. napkins @ $5.90. Amount received, $3.
7. Maud Smith bought 13 /8 yd. cretonne @ 45 ¢; 12 3/8 pd. ribbon @ 12 ½ ¢; 6 5/8 yd. braid @ 19 ¢; 7 ¼ yd. lace @ 17 ¢; 2 5/8 yd. edging @ 9 ¢. Amount received, $15.
II. From Bits and Pieces 2, Using Fractions Operations booklet, final problem set, p. 64:
Use Your Understanding: Fraction Operations
1. The Scoop Shop sells many types of nuts. Jayne asks for this mix:
½ pound peanuts
½ pound almonds
1/6 pound hazelnuts
¾ pound cashews
¼ pound pecans
a. Nuts cost $5.00 per pound. What is Jayne’s bill?
b. What fraction of the mix does each kind of nut represent?
c. Diego does not like cashews, so he asks for Jayne’s mix without the cashews. What is his bill?
d. Kali is making small bowls of nuts for a party. Each bowl uses ¼ cup of nuts. Kalli has 3 3/8 cup of nuts. How many bowls can she make?
2. Shaquille likes dried fruit. He wants a mix of peaches cherries, pineapple chunks, an apple rings. The following chart shows how much The Scoop Shop has of each fruit and how much of each fruit Shaquille orders.
The Scoop Shop’s Stock: 1 ¼ pounds dried peaches.
Shaquille’s Order: ½ of the stock
The Scoop Shop’s Stock: 4/5 pound dried cherries
Shaquille’s Order: ½ of the stock
The Scoop Shop’s Stock: ¾ pound dired pineaaple chunks
Shaquille’s Order: 2/3 of the stock
The Scoop Shop’s Stock: 2 ¼ pounds dried apple rings
Shaquille’s Order: 3/5 of the stock
a. How many pounds of dried fruit does Shazuille order?
b. Dried fruit costs $5.00 per pound. What is Shaquille’s bill?
Explain Your Reasoning
When you use mathematical calculations to solve a problem or make a decision, it is important to be able to support each step in your reasoning.
3. What operations did you use to find the cost of the nuts in Jayne’s mix?
4. How did you find the fraction of the mix for each kind of nut?
5. 4 ÷ 1/3 = 12 and 4 ÷ 2/3 = 6. Why is the second answer half of the first?
6. Use the following problems to show the steps involved in algorithms for adding, subtracting, multiplying, and dividing fractions. Be prepared to explain your reasoning.
a. 5/6 + ¼
b. ¾ - 2/3
c. 2/5 × 3/8
d. 3/8 ÷ 3/4
III. Extra Credit
What is Diego's bill?
Wednesday, May 12, 2010
An article in last week's New York Times describes a teacher exchange program in which teachers from China work "for up to three years in American schools, with their salaries subsidized by the Chinese government." As the Times explains, "China wants to teach the world its language and culture."
Monday, May 10, 2010
Reading about the death of Dr. Stanley Greenspan in last week's New York Times, I wondered about the future of Floor Time. This was the approach that Greenspan, a well-known child psychologist, championed as the most effective therapeutic approach to autism--an approach I've critiqued first here and later in Raising a Left-Brain Child.
Saturday, May 8, 2010
An enthusiastic article in last week's Philadelphia Inquirer reports on a visit by Bill Gates to the Science and Leadership academy, a partnership high school between the School District of Philadelphia and The Franklin Institute. During his visit, Gates listened to students present their science projects and then asked them specific questions.
"It's great to see people doing hands-on science," said Bill Gates after the presentations were over. "Science is fun."
"Hopefully, many of you will go into these fields which are so cool, so interesting," Gates said.According to the article, Gates also discussed philanthropy, how he taught computer programming to his fellow students in high school, about being an overconfident math student at Harvard, and how the SLA students should learn as much as they could about science.
Frederic Bertley, a Vice President at the Franklin Institute, was also thrilled.An alternative litmus test would be one that measures how much scientific knowledge SLA students have acquired. As I've noted in a recent post, (1) there's reason to believe that scientific knowledge acquisition should be a higher priority in k12 science education than hands-on learning, and (2) on this measure, SLA has not tested well. According to the Philadelphia Inquirer's own Report Card on the Schools, which came out just two weeks ago, 59% of SLA's 11th graders weigh in at "below basic."
The museum takes the partnership with SLA very seriously, Bertley said. Watching the students - who were not prepped for the session - engage in such high-level dialogue with Gates was a thrill for him.
"I couldn't have asked for a better litmus test for the project," said Bertley. "This is why we do what we do."
Gates implored the students to take advantage of the wealth of knowledge available to them for free. For example, Gates wanted a refresher course on physics, so he followed an MIT course online available for anyone to take advantage at no cost.
Thursday, May 6, 2010
I. From Hamilton's Essentials of Arithmetic, Volume II (published in 1919), first four word problems involving rate (intended for students in "year 7"), p. 253:
How much will 30 dozen eggs cost when 70 dozen cost 42?
When Irish potatoes are 5 lb for 17 cets, how much should a bushel of 60 lb. cost?
If 25 men can build a bridge in 18 days, how long, at the same rate, will it take 15 men to build it. (Notice that fewer men require more time. 15: 25 = 18: ?).
It is estimated that 90 men are necessary to grade a certain street in 45 days. If only 81 men are hired to do the work, how long will it take them?
II. From the Core-Plus Mathematics ("a four-year curriculum that replaces the traditional Algebra-Geometry-Advanced Algebra/Trigonometry-Precalculus sequence") Course 1 Student Study Guide, first four word problems involving rate, p. 30:
Which is the better deal? $18 for 3 bracelets; $30 for 5 bracelets
Which has the fewer calories per serving? 120 calories in 2 servings; 360 calories in 6 servings
Which is the better pay? 4 hours worked for $12; 7 hours worked for $28
Which is the better deal? 15 blank CDs for $5; 45 blank CDs for $15
III. Extra Credit
Comment on the following:
Numerical calculations in the pre-calculator age.
Everyday math problems before "Everyday Math."
Rote patterns in word problems before and after the age of aversion to rote learning.
Tuesday, May 4, 2010
An article in last week's Education Week discusses how U.S. lawmakers are moving to revamp No Child Left Behind so that it focuses on "the whole child," and not just on academics:
As Congress gears up for renewal of the Elementary and Secondary Education Act, lawmakers and the Obama administration are seeking to address a perennial complaint: that the current version of the law, the No Child Left Behind Act, places too much emphasis on students’ test scores and pays little attention to their health and other needs.
And at a hearing of the Senate Health, Education, Labor, and Pensions Committee last week, lawmakers agreed that the idea of educating “the whole child” encompasses a wide range of support services, which advocates are hoping could be reflected in the rewrite of the ESEA.
Those include dental and mental health, as well as programs aimed at providing prekindergarten and library services, summer and after-school enrichment, mentoring, college counseling, and increased parent and community involvement. The whole-child concept can also refer to making sure schools attend to students’ nonacademic interests, through programs such as the arts and physical education.Some of this sounds innocuous enough, but to anyone familiar with current trends in education, the term "the whole child" carries a lot of baggage. Concerned about some of this baggage, I posted the following comment:
I'm concerned that the emphasis on "the whole child" will move beyond measures to ensure basic physical and psychological welfare to include measures that require students to spend even more of their time working in groups; writing about their personal feelings; making dioramas for language arts, posters for science, and illustrations for math problems; and doing large-scale, open-ended, interdisciplinary/multi-media projects.
There's altogether too much of this at those k12 schools that are considered models for other schools, and it alienates large numbers of what I call "left-brainers," who languish with groups and arts & crafts requirements as much as they thrive with independent work and academic challenge.
Also, nearly all American students need more rigorous math and science than they are currently getting (thanks in part to the bar-lowering that No Child Left Behind has inspired, as well as to Reform Math). "The whole child" should include these priorities; unfortunately, the analytical needs of children are not the first things that come to mind when we ponder terms like "the whole child."
Sunday, May 2, 2010
As the mother of a mainstreamed middle school child on the autistic spectrum, and as the designer of an online course on high functioning autistic students in mainstreaming environments, I spend much of my waking hours thinking about how best to accommodate students with autism in regular ed classrooms. So when an article featuring an Asperger/autism inclusion middle school teacher by the name of Cherie Fowler appeared in this week's Teacher Magazine, it caught my eye immediately.
According to the article, Ms. Fowler's goals are to teach her students to express themselves better so they are successful academically in general education classes in middle school and beyond. The article credits Ms. Fowler with five specific strategies:
4. Allowing them one class period that is designed just for them.
5. Educating each general-education class about what Asperger's/autism is.
These are good measures, but, I'm hoping, not the only things that Fowler is doing for her autistic spectrum students. When it comes to reading assignments, AS students often read at a lower level when the content is primarily social, emotional, or grounded in popular culture, and at a higher level when the content is more scientific, technical, and linearly organized, and/or removed from everyday culture (as are fantasy fiction and science fiction).
In writing, AS students often languish when asked to write about their personal lives and personal feelings, or to produce realistic fiction. When the topic is science or fantasy, on the other hand, they are often much more inspired and have much more to say.
In math, AS students often do complicated problems in their heads and aren't able to explain their answers verbally. They should be exempted from having to give such explanations, and should receive full credit for correct answers that lack verbal explanations.
When it comes to large, interdisciplinary/multimedia/ open-ended projects, AS students are often so overwhelmed by the breadth of material that they don't even know where to begin. In lieu of such projects, they should be given a larger number shorter, more structured assignments that offer the same degree of academic challenge.
AS students also flounder when required to work in groups. While group activities specifically targeted at improving their social skills, run by an expert in AS, are fruitful, group activities centering on learning tasks should be replaced by independent learning opportunities.
Finally, AS students are often way ahead of their peers in certain subjects and need to be allowed to progress at their own rates.
What AS children, in other words, are not just supports for, and modifications of existing assignments, but a wholesale replacement of many of these assignments by alternative assignments and learning opportunities that are specifically tailored to their strengths and weaknesses.