kitchen table math, the sequel

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In The Economist:

Estonia’s government has commissioned Mr Wolfram’s consultancy in Oxfordshire to modernise maths courses for secondary-school pupils. Starting this month, it will pilot lessons built around open-ended problems which have no single solution. One example: “What’s the best algorithm for picking a romantic date?” (Possible answer: go on more dates with a lower quality threshold to maximise the chance of success.) Another: “Am I drunk?”, which leads into quantitative analysis involving body masses, rates of alcohol absorption and other variables.

Time for a Ceasefire | Feb 1st 2014 | SHANGHAI AND TEL AVIV

Fabulous post from a substitute teacher in Great Britain

There's a rather spirited discussion going on at the TheAtlantic.com regarding various questions raised by my article there. Some people are claiming that the demands of the 21st require students to work in groups and be graded on their presentation skills. Please weigh in if you have an opinion on this!

I added a chart to the post on group learning:


The blue bar represents the low performers, the red bar high performers. All have the same measured IQ (126), and at the beginning of the study all are performing well below the level their IQ would predict. The higher performers then recover, and their performance increases to a "126" level. The the low performers do not recover, and their performance remains suppressed.

re: group work lowers IQ

I've skimmed the article (free online).

Assuming the findings are confirmed in other studies (I suspect they will be), this is bad news.

Set-up

• Subjects had the same IQ: 126.
• They were put in small groups of 5 and introduced to each other.
• They took an IQ test with no feedback as to how they did.
• Then they took a second computer-administered IQ test.
• After each question, they were told whether they got the answer right or wrong.
• At the same time, they were also given their rank inside the group (rank determined by each person's # of correct answers).
• They were also given their rank vis a vis 1 particular member of the group, chosen "pseudorandomly."
• 2 people had brain scans during the test-with-feedback condition.

Results

• Everyone did worse in the beginning. Across the board. Everyone. Everyone did worse than his/her measured ability.
• As the test went on, some people recovered. Their performance went back up to the level predicted by their IQ scores.
• The others never improved. They started low, and they stayed low.
• Females were more likely to start low and stay low than males.
• For high performers, brain scans showed activity in the amygdala (likely fear), decreasing over time. (That is, they were likely feeling less fear, perhaps growing more confident.)
• For high performers, activity in the lateral PFC increases over time. Activity in lateral PFC is associated with IQ tasks, with working memory tasks, and with increased task difficulty.

So. All told, membership in a small group produced a net decrease in number of correct answers compared to what you would predict for the same 5 people working alone.

Everyone's performance dropped at the outset.

Some people recovered, others didn't.

The people who recovered simply went back up to where they had been going in, before experimenters assigned them to a small group.

Questions

• How small is small? Would group of 20 students in whole class instruction show the same pattern? 25 students? 30?
• If so ... yikes.
• In the wake of this study, mixed-ability groups strike me as an even worse idea than I've thought in the past. Lower ability children in a mixed-ability group are going to be getting constant negative feedback about their status vis a vis the higher ability children. On the other hand, the study did not include a condition that manipulated feedback in this manner. That would be interesting.
• Assuming this study picked up on a personality difference (which we don't know, of course), what would happen if you grouped the 'nervous' kids together, putting the 'confident' kids in their own group? Would two groups still separate out in this way?
• Would same-sex groups change the results?
• What does this tell us about grades and grading?

The blue bar represents the low performers, the red bar high performers. All have the same measured IQ (126), and at the beginning of the study all are performing well below the level their IQ would predict. The higher performers then recover, and their performance increases to a "126" level. The the low performers do not recover, and their performance remains suppressed.

Implicit signals in small group settings and their impact on the expression of cognitive capacity and associated brain responses

I was just telling Ed about the study on group projects & IQ, and he said that already, in the 1990s, when he headed the California History Social Science Project (under the umbrella of the California Subject Matter Project), group learning was drilled into him as the absolute best way to teach.

Ed also tells me that Phil Daro (B.A. in English), was head of the original math project, and Bill Honig got rid of him: kicked him upstairs & hired a real math professor from San Diego State to take charge. Ed doesn't remember his name now.

The point of the Subject Matter Project was to take professional development away from ed schools and consultants and put it in the hands of content specialists.

Phil Daro wasn't a content specialist.

He still isn't a content specialist but he's chairing the Mathematics College and Career Readiness Standards Work Group for the new Common Core standards.

AND SEE:
Calculators? Don't Answer

Chris came into the bedroom this morning to announce that group projects make you dumber. He read it on cracked.com. (Only dimly aware of the existence of cracked.com. Now I'm a fan.)

Sure enough.

AND SEE:
Implicit signals in small group settings and their impact on the expression of cognitive capacity and associated brain responses
Attending meetings lowers IQ: research
Neuroscientists Find That Status within Groups Can Affect IQ
Group Settings Can Diminish Expressions of Intelligence, Especially Among Women, Study Finds
Warning: Meetings May be Bad for Your IQ

If you're concerned about achievement gaps of the sort recently reported on by the Times , you could either (re)instate rigorous, structured, direct instruction in line with the latest findings in cognitive science research, teaching each child in his or her Zone of Proximal Development, i.e., at his or her instructional level, with proper scaffolding, and furnishing each classroom with teachers who've mastered both their content areas and these best practices. Or you could:


I. Eliminate the ability of academically advanced students to get ahead in the classroom by:

1. implementing low level, one-size-fits-all instruction (for which there's no better model than Investigations math)

2. eliminating grade acceleration and individualized instruction

3. eliminating gifted programming or making it about time-consuming projects that supplement existing assignments rather about academic challenges that replace these assignments.

II. Reduce the ability of students to get ahead on their own time by:

1. assigning tons of homework of the low-ratio-of-learning-to-effort variety

2. including massive summer projects and one-size-fits all reading lists.

III. Reduce the ability of grades to reflect achievement differences via"grade compression" and inflexible "rubrics" that:

1. employ subjective grading standards (elevating "creativity" and "engagement" over correct answers, clarity, articulateness, and solid analysis)

2. take points off for unexplained answers, however correct

3. give partial credit for "explained" incorrect answers

4. keep the purely academic demands/expectations of assessments and assignments as low as possible

4. minimize the opportunity for students to demonstrate work that exceeds those demands/expectations

5. even if students find a way to demonstrably exceed expectations or go above and beyond academically, don't give them any extra points for it

6. deploy "wild card" variables that partially randomize who gets what grade (e.g., trick questions; unclear directions; trivial requirements like including today's date on the title page of your report or using the word "I" in your science project abstract; rather than collecting homework, leaving it up to the students to turn it in and giving out zeroes for things not turned in on time)

7. assign heterogeneous-ability group projects and give everyone in the group the same grade

IV. Reduce the ability of NCLB tests to reflect achievement differences, via:

1. low academic ceilings

2. partial credit for explained incorrect answers; points off for unexplained correct answers (as above)

3. wild card variables (as above)

V. Lobby colleges to pay less attention to high-ceiling standardized tests like the SATs and the Achievement Tests, and more attention to grades and "leadership" activities.



But then the next question becomes how to eliminate the growing achievement gap between U.S. students and those from other developed countries.

(Cross-posted at Out In Left Field)

Wonderful letter:

Excluding the higher functioning [autistic] children [from the autism diagnosis] means that schools will have to do more to make regular classrooms hospitable to them without the early intervention based accommodations mandated by the Individuals With Disabilities Education Act.

In particular, teachers will have to stop requiring children to work in groups, share personal reflections and do organizationally demanding interdisciplinary projects — all of which are challenging for the sort of child who, rightly or wrongly, has sometimes received a diagnosis of mild autism/Asperger.

The new American Reform Math is also problematic for this population, since it waters down the actual math and teaches it less systematically.

KATHARINE BEALS
Philadelphia, Jan. 23, 2012

The writer is a lecturer at the University of Pennsylvania Graduate School of Education and the author of “Raising a Left-Brain Child in a Right-Brain World.”

Susan Cain's op-ed in today's Times reminds me of Katharine's book:

But shyness and introversion share an undervalued status in a world that prizes extroversion. Children’s classroom desks are now often arranged in pods, because group participation supposedly leads to better learning; in one school I visited, a sign announcing “Rules for Group Work” included, “You can’t ask a teacher for help unless everyone in your group has the same question.” Many adults work for organizations that now assign work in teams, in offices without walls, for supervisors who value “people skills” above all. As a society, we prefer action to contemplation, risk-taking to heed-taking, certainty to doubt. Studies show that we rank fast and frequent talkers as more competent, likable and even smarter than slow ones. As the psychologists William Hart and Dolores Albarracin point out, phrases like “get active,” “get moving,” “do something” and similar calls to action surface repeatedly in recent books.

Yet shy and introverted people have been part of our species for a very long time, often in leadership positions. We find them in the Bible (“Who am I, that I should go unto Pharaoh?" asked Moses, whom the Book of Numbers describes as “very meek, above all the men which were upon the face of the earth.”) We find them in recent history, in figures like Charles Darwin, Marcel Proust and Albert Einstein, and, in contemporary times: think of Google’s Larry Page, or Harry Potter’s creator, J. K. Rowling.

In the science journalist Winifred Gallagher’s words: “The glory of the disposition that stops to consider stimuli rather than rushing to engage with them is its long association with intellectual and artistic achievement. Neither E=mc2 nor ‘Paradise Lost’ was dashed off by a party animal.”

We even find “introverts” in the animal kingdom, where 15 percent to 20 percent of many species are watchful, slow-to-warm-up types who stick to the sidelines (sometimes called “sitters”) while the other 80 percent are “rovers” who sally forth without paying much attention to their surroundings. Sitters and rovers favor different survival strategies, which could be summed up as the sitter’s “Look before you leap” versus the rover’s inclination to “Just do it!” Each strategy reaps different rewards.

IN an illustrative experiment, David Sloan Wilson, a Binghamton evolutionary biologist, dropped metal traps into a pond of pumpkinseed sunfish. The “rover” fish couldn’t help but investigate — and were immediately caught. But the “sitter” fish stayed back, making it impossible for Professor Wilson to capture them.

[snip]

Next, Professor Wilson used fishing nets to catch both types of fish; when he carried them back to his lab, he noted that the rovers quickly acclimated to their new environment and started eating a full five days earlier than their sitter brethren. In this situation, the rovers were the likely survivors. “There is no single best ... [animal] personality,” Professor Wilson concludes in his book, “Evolution for Everyone,” “but rather a diversity of personalities maintained by natural selection.”

[snip]

...sitter children are careful and astute, and tend to learn by observing instead of by acting. They notice scary things more than other children do, but they also notice more things in general. Studies dating all the way back to the 1960’s by the psychologists Jerome Kagan and Ellen Siegelman found that cautious, solitary children playing matching games spent more time considering all the alternatives than impulsive children did, actually using more eye movements to make decisions. Recent studies by a group of scientists at Stony Brook University and at Chinese universities using functional M.R.I. technology echoed this research, finding that adults with sitter-like temperaments looked longer at pairs of photos with subtle differences and showed more activity in brain regions that make associations between the photos and other stored information in the brain.
Once they reach school age, many sitter children use such traits to great effect. Introverts, who tend to digest information thoroughly, stay on task, and work accurately, earn disproportionate numbers of National Merit Scholarship finalist positions and Phi Beta Kappa keys, according to the Center for Applications of Psychological Type, a research arm for the Myers-Briggs personality type indicator — even though their I.Q. scores are no higher than those of extroverts. Another study, by the psychologists Eric Rolfhus and Philip Ackerman, tested 141 college students’ knowledge of 20 different subjects, from art to astronomy to statistics, and found that the introverts knew more than the extroverts about 19 subjects — presumably, the researchers concluded, because the more time people spend socializing, the less time they have for learning.

THE psychologist Gregory Feist found that many of the most creative people in a range of fields are introverts who are comfortable working in solitary conditions in which they can focus attention inward. Steve Wozniak, the engineer who founded Apple with Steve Jobs, is a prime example: Mr. Wozniak describes his creative process as an exercise in solitude. “Most inventors and engineers I’ve met are like me,” he writes in “iWoz,” his autobiography. “They’re shy and they live in their heads. They’re almost like artists. In fact, the very best of them are artists. And artists work best alone ... Not on a committee. Not on a team.”
Shyness: Evolutionary Tactic?
By SUSAN CAIN
Published: June 25, 2011

Quiet: The Power of Introverts in a World That Can't Stop Talking

Quiet: The Power of Introverts in a World That Can't Stop Talking

Raising a Left-Brain Child in a Right-Brain World: Strategies for Helping Bright, Quirky, Socially Awkward Children to Thrive at Home and at School


Raising a Left-Brain Child in a Right-Brain World: Strategies for Helping Bright, Quirky, Socially Awkward Children to Thrive at Home and at School

Susan Cain's blog

re: crowds vs herds, jtidwell writes:

I worked at Google. I was based in the Cambridge (Mass.) office, but its architecture is comparable to the NYC office. I spent my share of time working as a visitor in the NYC office, too, and also in Mountain View.

What they are doing at Google is TOTALLY different from guess-the-number problems. :-)

But, first, the architecture. There are large rooms with an open layout, but these aren't generally huge. Most that I visited only held about 20-30 people, and the people working in them were respectful about a quiet environment. There are countless meeting rooms, both large and tiny, that one can retreat to when necessary. And truth be told, I never spent much time at my desk! I was frequently working in one of these meeting rooms, either in F2F meetings, or on videoconferences, or some hybrid thereof, or by myself when I needed serious quiet.

Plus, everyone is issued laptops instead of (or in addition to) one's desktop computer. Googlers are encouraged to take their work anywhere they please, as long as it's secure. Working from home is fine, too.

The nature of the work there is quite collaborative, as all good software product teams are. But once decisions are made, or questions formulated, everyone scurries off and does individual work. Very intense individual work. (In my case, it was UX design, with occasional programming or online research to figure something out.) And let me tell you, if you weren't extremely competent at self-directed work and individual achievement, you didn't last long in that environment. :-)

Following the crowd's opinion, just because you don't have the nerve to state your own differing opinion, isn't looked well upon either.

In my book I draw a distinction between "cooperation" and "collaboration," defining the former as people working while interacting, and the latter as people working on joint projects, but not necessarily in one another's presence or with much productive interaction. In collaborations, after the work is divvied up, participants might spend the majority of their time working independently. 

Speaking of group work:

PAUL M. MASON does not give his business students the same exams he gave 10 or 15 years ago. “Not many of them would pass,” he says.

[snip]

Business majors spend less time preparing for class than do students in any other broad field, according to the most recent National Survey of Student Engagement: nearly half of seniors majoring in business say they spend fewer than 11 hours a week studying outside class. In their new book “Academically Adrift: Limited Learning on College Campuses,” the sociologists Richard Arum and Josipa Roksa report that business majors had the weakest gains during the first two years of college on a national test of writing and reasoning skills. And when business students take the GMAT, the entry examination for M.B.A. programs, they score lower than students in every other major.

This is not a small corner of academe. The family of majors under the business umbrella — including finance, accounting, marketing, management and “general business” — accounts for just over 20 percent, or more than 325,000, of all bachelor’s degrees awarded annually in the United States, making it the most popular field of study.

[snip]

IN “Academically Adrift,” Dr. Arum and Dr. Roksa looked at the performance of students at 24 colleges and universities. At the beginning of freshman year and end of sophomore year, students in the study took the Collegiate Learning Assessment, a national essay test that assesses students’ writing and reasoning skills. During those first two years of college, business students’ scores improved less than any other group’s. Communication, education and social-work majors had slightly better gains; humanities, social science, and science and engineering students saw much stronger improvement.

What accounts for those gaps? Dr. Arum and Dr. Roksa point to sheer time on task. Gains on the C.L.A. closely parallel the amount of time students reported spending on homework. Another explanation is the heavy prevalence of group assignments in business courses: the more time students spent studying in groups, the weaker their gains in the kinds of skills the C.L.A. measures.

The Default Major Skating Through B-School
By DAVID GLENN
Published: April 14, 2011

Academically Adrift: Limited Learning on College Campuses

I talked to a high school teacher last weekend who told me teachers are being evaluated on:

• arrangement of furniture in the classroom (desks not in rows)
• presence of group work
• students sharing personal details of their lives with the teacher

I didn't get the sense that 'personal details' meant inappropriately personal. It seemed to mean students sharing biographical detail with the teacher during class time.

I think that is a dreadful criterion - and I would bet a modest sum that students sharing biographical detail with the teacher during class time would be associated with lower achievement, not higher.

I don't want to see students in, say, a U.S. history class talking about themselves.

I want to see students in a U.S. history class talking about U.S. history.

The cartoonist who does Mallard Fillmore either attended ed school at one point, or knows people who are in education:

from Barry Garelick:

Not only is the tissue box assignment real, but elsewhere in her book Katharine talks about how in language classes, kids have to make posters about their family. My daughter had to do a family tree chart with photos for her Spanish class. The teacher lost the poster, and called my daughter at home to ask her to do another one, and said it was important for her grade. (!!) My daughter, who didn't like the assignment to begin with was infuriated to have to do it again, and all because the teacher had lost the first one. The sadder aspect of all this is parents get drawn in to the "this project is worth a lot of points for your grade" type thinking, and are afraid to make waves by telling the teacher that the student is NOT going to do this; please give an alternative assignment.

For English class in 8th grade, the teacher gave the students a choice of projects for Lord of the Flies. One was a standard book report. Others included designing a T shirt about the book. My daughter hated the alternatives and chose writing the book report. And she is not fond of writing!

I'm reading Katharine's book right now and have nothing but praise for it. I am going to recommend it to several teachers I know at George Mason's ed school. I really think it should be required reading.

What most middle class parents in Chicago are seeking when they have their children apply for the magnet and selective schools is classmates that are not two grade levels or more behind. If the teachers are also good, all the better. But many would choose humdrum teachers, in a grade-level or better classroom, over high octane teachers trying to teach to a large number of children with serious remediation needs in the same room as children already on grade level.

Funny how parents just aren't getting with the program on differentiated instruction.

Or anything else, for that matter.


children should struggle
mixing fast and slow learners
constructivism solves classroom discipline problems
ed schools and you
palisadesk on recent graduates of ed schools

re: group learning

Let's see; it's very important to have a great/highly-qualified teacher, but somehow a few minutes per hour of that teacher's time (supervising groupwork in a full-inclusion classroom) is just as good as having 45+ minutes of her time (in a teacher-centered, homogeneous classroom)? Does the ed world have any idea how illogical that sounds? Impossible is probably closer to it.

I can say from anecdotal experience that putting kids in groups tends to reinforce the group issues they already had, even cement their anti-social tendencies rather than correct them.

For example, I was in my 4th grader's classroom awhile back when the kids were assigned to groups of four kids to work on a writing project. It was a pretty good idea and the kids came up with some very interesting ideas. BUT, the groups didn't seem to enhance the work product -- nothing came out of it that they wouldn't have been able to do individually. And, the kids with the most trouble academically sat on the edges, didn't contribute or were rebuffed by their more able peers. For them, it was a complete waste of time. For the "good" girls, they had a great time sitting with their friends, putting down the boys in their group, and doing their best to come up with something the teacher would like.

But with the kids divided into 5 or 6 groups, the teacher could not be everywhere. She was needed full-time in at least 3 of the groups, and her dropping in for a few minutes on each group was too little too late. One kid in my daughter's group is in dire need of social skills. He spent the entire time spinning circles on his butt, standing up and asking to go to the bathroom or wandering off to the windows, or telling the other groups members that this was "stupid" or complaining that no one listened to him. When the teacher hovered, he acted out less, but at no point did he contribute.

I think about that and wonder, how is the 21st CS movement helping him? When the theory hits the road, how do they really expect kids to learn anything useful? How are they going to get the kids that need the social and collaborative skill to gain them just by assigning them to a groups of social adept kids?

Speaking as a parent whose son is attending a boys' school, I read accounts like this one and shudder.

Public school officials need to ask themselves whether group work is hurting some (or many) kids more than helping.


report

In reading, girls outperformed boys in 2008 at the elementary, middle, and high school levels. Higher percentages of girls than boys scored at or above the proficient level on state reading tests at grade 4, grade 8, and high school; in some states, these gaps exceeded 10 percentage points.

Are There Differences in Achievement Between Boys and Girls?
Center on Education Policy
March 2010

Constructivist classrooms, Reform Math, Reform Foreign Language, group learning, writing across the curriculum, 21st century skills, 21st century grading, 21st century gifted programming, and other alarming trends in K12 education--particularly as they affect math buffs, shy/socially awkward children, and children on the autistic spectrum.

More information at Out In Left Field.