On one of our first days with Michael Paul Goldenberg in math, a student casually asserted that 'Zero is not a number'. We wondered about that assumption, and asked students to come in with arguments for and against zero's legitimacy as a number.
Here are a half-dozen of the best metaphors students used in the discussion.
Zero is a border.
Zero is nothing.
Zero is a hole that's been filled.
Zero is the foundation of a house.
Zero is the bottom.
Zero is the middle.
And I can't resist one of my favorite metaphors, courtesy of Saturday morning cartoons in the 1970s.
http://www.youtube.com/watch?v=3huvvxUHDmM
(There's also a terrific cover of this song by The Lemonheads.)
7-8
Sunday, November 11, 2012
True Math
A few words about middle school math at Summers-Knoll.
Our objective is to graduate students who are numerate. This is precisely analogous to literate. A literate person can read, but that isn't the whole picture. A truly literate person can use words precisely, practically, powerfully, and with an exciting sense of possibility.
A truly numerate person can do all that with numbers. This is a critically, even criminally undervalued skill. It is why Tom Magliozzi of Car Talk fame--he of the PhD in from MIT--wrote, chagrined:
The purpose of learning math . . . . . is only to prepare us for further math courses.
In 2011, journalist, author and social entrepreneur David Bornstein opined, in The New York Times:
It’s hard to imagine what society might look like if we could undermine the math hierarchies that get solidified in grade school. These patterns tend to play out across society, often in negative ways. Wasn’t it the whiz kids who invented financial derivatives and subprime mortgages? And how many adults got themselves into hot water with their mortgages because, at bottom, they didn’t really understand the risks?
How will we produce thoughtful, numerate graduates at SK? There are three corners to this program: math in the world; math on the page; and project-based math.
IN THE WORLD
Math in the world asks real questions. Why was the 2012 Presidential election primarily fought in seven states? Why is zero a revolutionary concept? How much money should an adult save per paycheck? How does one build a safe playground structure? How much mulch is enough mulch underneath a set of monkey bars? Michael Paul Goldenberg has been posing such questions with students of all ages for three decades, and we are fortunate to have him driving these questions in the SK middle school. Answering them requires hard-core, gory, flat-out arithmetical axioms, theorems, operations, and principles. But answering them also requires the ability to identify which skills and operations are relevant.
ON THE PAGE
Those skills have historically been practiced at SK via Singapore Math, an innovative approach to basic skills that gained global credibility and popularity approximately a decade ago, after it prompted rapid advances in test results from that Asian city-state's elementary students. Singapore has been joined in recent years by the uber-viral website Khan Academy.
Khan and Singapore are terrific practice, and we expect our students to spend fifteen minutes per day with their noses in the book or screen, because, in mathematics, as in second-language study, there is no substitute for exercise. Not for nothing do our students attend math on a regular basis, even in a project-based curriculum. Jason DePasquale is masterminding our students' work in these programs, and in a school the size of SK, we are able to individualize these work programs and goals to an unusual degree.
PROJECT-BASED
In keeping with the theme of Ancient Civilizations, students in my section of math have been divided into Mesopotamians and Egyptians. Each will build a pyramid in the style of its civilization. The math will emerge as necessary as each group decides what materials it will use, the dimensions of its building, the geometry required, the physics of architectural design. These projects should be on display at the performances of 'Gilgamesh' in mid-December. Other projects will evolve as our school service and theme-based work in Global Citizenship and Circle of Life develops over the course of the academic year.
NEXT STEPS
We have settled upon the work of an innovative scholar, teacher, mentor, and gamer, Henri Picciotto of Beirut and San Francisco, to help shape the direction of our seventh and eighth grade students. Henri is the author of a highly regarded algebra textbook--after whose publication, he founded a professional organization called Escape the Textbook. For more on his approach, and more of his plentiful materials, go to http://www.mathedpage.org/. Henri is also a former colleague of mine from the Urban School of San Francisco. His vision of math education, in part:
Mathematics education is not just about preparing students for "practical" matters and helping the economy. It is an important part of human culture of sense-making, and should be introduced as such to all students from a young age. In addition to being useful, math is fun and beautiful. We should not lose sight of this as we attempt to make the curriculum more relevant through greater reliance on applications.
Finally, another word from David Bornstein.
Even deeper, for children, math looms large; there’s something about doing well in math that makes kids feel they are smart in everything. In that sense, math can be a powerful tool to promote social justice. “When you have all the kids in a class succeeding in a subject, you see that they’re competing against the problem, not one another,” says [Canadian mathematician and teacher John] Mighton. “It’s like they’re climbing a mountain together. You see a very healthy kind of competition. And it makes kids more generous to one another. Math can save us.
Our objective is to graduate students who are numerate. This is precisely analogous to literate. A literate person can read, but that isn't the whole picture. A truly literate person can use words precisely, practically, powerfully, and with an exciting sense of possibility.
A truly numerate person can do all that with numbers. This is a critically, even criminally undervalued skill. It is why Tom Magliozzi of Car Talk fame--he of the PhD in from MIT--wrote, chagrined:
The purpose of learning math . . . . . is only to prepare us for further math courses.
Imagine if someone at a dinner party casually announced, “I’m illiterate.” It would never happen, of course; the shame would be too great. But it’s not unusual to hear a successful adult say, “I can’t do math.” That’s because we think of math ability as something we’re born with, as if there’s a “math gene” that you either inherit or you don’t.
How will we produce thoughtful, numerate graduates at SK? There are three corners to this program: math in the world; math on the page; and project-based math.
IN THE WORLD
Math in the world asks real questions. Why was the 2012 Presidential election primarily fought in seven states? Why is zero a revolutionary concept? How much money should an adult save per paycheck? How does one build a safe playground structure? How much mulch is enough mulch underneath a set of monkey bars? Michael Paul Goldenberg has been posing such questions with students of all ages for three decades, and we are fortunate to have him driving these questions in the SK middle school. Answering them requires hard-core, gory, flat-out arithmetical axioms, theorems, operations, and principles. But answering them also requires the ability to identify which skills and operations are relevant.
ON THE PAGE
Those skills have historically been practiced at SK via Singapore Math, an innovative approach to basic skills that gained global credibility and popularity approximately a decade ago, after it prompted rapid advances in test results from that Asian city-state's elementary students. Singapore has been joined in recent years by the uber-viral website Khan Academy.
Khan and Singapore are terrific practice, and we expect our students to spend fifteen minutes per day with their noses in the book or screen, because, in mathematics, as in second-language study, there is no substitute for exercise. Not for nothing do our students attend math on a regular basis, even in a project-based curriculum. Jason DePasquale is masterminding our students' work in these programs, and in a school the size of SK, we are able to individualize these work programs and goals to an unusual degree.
PROJECT-BASED
In keeping with the theme of Ancient Civilizations, students in my section of math have been divided into Mesopotamians and Egyptians. Each will build a pyramid in the style of its civilization. The math will emerge as necessary as each group decides what materials it will use, the dimensions of its building, the geometry required, the physics of architectural design. These projects should be on display at the performances of 'Gilgamesh' in mid-December. Other projects will evolve as our school service and theme-based work in Global Citizenship and Circle of Life develops over the course of the academic year.
NEXT STEPS
We have settled upon the work of an innovative scholar, teacher, mentor, and gamer, Henri Picciotto of Beirut and San Francisco, to help shape the direction of our seventh and eighth grade students. Henri is the author of a highly regarded algebra textbook--after whose publication, he founded a professional organization called Escape the Textbook. For more on his approach, and more of his plentiful materials, go to http://www.mathedpage.org/. Henri is also a former colleague of mine from the Urban School of San Francisco. His vision of math education, in part:
Mathematics education is not just about preparing students for "practical" matters and helping the economy. It is an important part of human culture of sense-making, and should be introduced as such to all students from a young age. In addition to being useful, math is fun and beautiful. We should not lose sight of this as we attempt to make the curriculum more relevant through greater reliance on applications.
Finally, another word from David Bornstein.
Even deeper, for children, math looms large; there’s something about doing well in math that makes kids feel they are smart in everything. In that sense, math can be a powerful tool to promote social justice. “When you have all the kids in a class succeeding in a subject, you see that they’re competing against the problem, not one another,” says [Canadian mathematician and teacher John] Mighton. “It’s like they’re climbing a mountain together. You see a very healthy kind of competition. And it makes kids more generous to one another. Math can save us.
The Latest on Exhibitions
When in doubt, my ten students should be working on their exhibitions, all of which will take place this week.
To summarize, an exhibition is a thirty-minute show featuring two lessons of approximately equal length.
Each student will teach a lesson on his or her Farm-to-Table topic, and one on any other piece of portfolio work undertaken at SK in the fall of 2012.
Exhibitions are formal events and are attended by the homeroom teacher, at least one other SK staff member, family members, and at least two peers (though most will be attended by our full homeroom).
Here are the times and topics.
Trent (12:45-1:15, November 13)
FTT: How does a cow become a steak?
Portfolio: 'Maus', Art Spiegelman
Taylor (1:30-2:00, November 14)
FTT: What is the history of corn?
Portfolio: hoop house
Evan (2:15-2:40, November 14)
FTT: How does Iowa soil compare to Michigan soil?
Portfolio: exercise and brain (esp. archery)
Denali (3:00-3:30, November 14)
FTT: What is the most popular livestock raised in the US?
Portfolio: tapestry
Jonathan (3:30-4:00, November 15)
FTT: How is poison used in agriculture?
Portfolio: themed gardens design for Summers-Knoll
Saul (4:15-4:45, November 15)
FTT: From bean to bar, how is chocolate made?
Portfolio: trebuchet from Science Club
Jianmarco (5:00-5:30, November 15)
FTT: What is the best way to transport food?
Portfolio: origins and consequences of farming in Mesopotamia
Mike (1:30-2:00, November 16)
FTT: How do old farming methods compare to new ones?
Portfolio: fiction writing
Isobel (2:15-2:45, November 16)
FTT: How are piglets raised in family and factory farms?
Portfolio: American Math Race
Daniel (3:45-4:15, November 16)
FTT: How has wheat changed in recent years?
Portfolio: 'Hero', Christopher Moore
To summarize, an exhibition is a thirty-minute show featuring two lessons of approximately equal length.
Each student will teach a lesson on his or her Farm-to-Table topic, and one on any other piece of portfolio work undertaken at SK in the fall of 2012.
Exhibitions are formal events and are attended by the homeroom teacher, at least one other SK staff member, family members, and at least two peers (though most will be attended by our full homeroom).
Here are the times and topics.
Trent (12:45-1:15, November 13)
FTT: How does a cow become a steak?
Portfolio: 'Maus', Art Spiegelman
Taylor (1:30-2:00, November 14)
FTT: What is the history of corn?
Portfolio: hoop house
Evan (2:15-2:40, November 14)
FTT: How does Iowa soil compare to Michigan soil?
Portfolio: exercise and brain (esp. archery)
Denali (3:00-3:30, November 14)
FTT: What is the most popular livestock raised in the US?
Portfolio: tapestry
Jonathan (3:30-4:00, November 15)
FTT: How is poison used in agriculture?
Portfolio: themed gardens design for Summers-Knoll
Saul (4:15-4:45, November 15)
FTT: From bean to bar, how is chocolate made?
Portfolio: trebuchet from Science Club
Jianmarco (5:00-5:30, November 15)
FTT: What is the best way to transport food?
Portfolio: origins and consequences of farming in Mesopotamia
Mike (1:30-2:00, November 16)
FTT: How do old farming methods compare to new ones?
Portfolio: fiction writing
Isobel (2:15-2:45, November 16)
FTT: How are piglets raised in family and factory farms?
Portfolio: American Math Race
Daniel (3:45-4:15, November 16)
FTT: How has wheat changed in recent years?
Portfolio: 'Hero', Christopher Moore
'Gilgamesh' Rehearsal Schedule
Here is our schedule of remaining 'Gilgamesh' rehearsals and key dates. Please note that the actors will be setting down their scripts for good on Monday, November 19.
|
Gilgamesh schedule
|
||||
|
12
11:30-12:30:
Jianmarco, Isobel,
(pp 2-19)
|
13
11:30-12:30:
measure for costumes (Eileen, Robbin)
3:30-4:30:
Jianmarco, Isobel, Evan, Danny, Kaeli, Melissa
(pp 21-31)
|
14
11:30-12:30: Alexandra,
HK, Cory, Mike, Trent, Jianmarco
(pp 4-6, 17-19,
31-34)
12:30-1:30: run
show (all 5-8s)
|
15
11:30-12:30: HA,
Jonathan, Noah, Jianmarco, Alexandra, Matthew
(pp 1-2, 20-21)
|
16
10:00-11:00: all
third and fourth graders, Saul, Jianmarco, Alexandra, Cory, Trent, Aristea,
Isobel, Evan, HK, Mike
(pp 4-6, 31-34)
|
|
19
11:30-12:30:
Jianmarco, Isobel, Evan, Danny, Kaeli, Melissa
(pp 21-31)—OFF BOOK
(lines must be memorized)
production
meeting 3.30
|
20
3:30-4:30: Jianmarco, Isobel,
(pp 2-19)— OFF BOOK
(lines must be memorized)
|
21
Thanksgiving
holiday
|
22
Thanksgiving
holiday
|
23
Thanksgiving
holiday
|
|
26
REHEARSE ALL FILMING
THIS WEEK
specifics await scheduling with
Brian Lillie, videographer
11:30-12:30: Huwawa battle
|
27
Entire cast and all production
support called for after-school rehearsal, 4:00-6:00
|
28
2:30-3:30 run show (entire cast,
including third & fourth graders)
OFF BOOK
(lines must be memorized)
|
29
11:30-12:30: Huwawa battle
production
meeting 3.30
|
30 2:30-3:30 run show
10:00-11:00: all
third and fourth graders, Saul, Jianmarco, Alexandra, Cory, Trent, Aristea,
Isobel, Evan, HK, Mike
(pp 4-6, 31-34)
OFF BOOK
film pantheon scene?
(lines must be memorized)
|
|
1-3 (including weekend)
prepare lighting and set
construction
11:30-12:30: Huwawa battle
Film Scorpions & Ishtar?
|
4
Entire cast and all production
support called for after-school rehearsal, 4:00-6:00
OFF BOOK
(lines must be memorized)
|
5
12:30-2:00 run show (entire cast,
including third & fourth graders)
|
6
11:30-12:30: Huwawa
battle
production
meeting 3.30
|
7
10:00-11:00: all
third and fourth graders, Saul, Jianmarco, Alexandra, Cory, Trent, Aristea,
Isobel, Evan, HK, Mike
(pp 4-6, 31-34)
|
|
10
rehearsals to be announced
|
11
rehearsals to be announced
|
12
Scenes performed for younger students
during the school day
Entire cast and all production
support called for after-school rehearsal, 4:00-6:00
|
13
PERFORMANCE
call is 5:45 pm
curtain at 7:00
|
14 & 15 (including
Saturday)
PERFORMANCES
call is 5:45 pm
curtain at 7:00
|
'Gilgamesh' in Production
We have been rehearsing 'Gilgamesh' for three weeks now. In some ways, it is a simple production; in others, the most complex I've undertaken.
Unlike any previous play I've directed, 'Gilgamesh' is woven into the fabric of my students' ongoing academic work and their daily schedule. This is one of the great assets of working at a school like Summers-Knoll, where our objective is to make the experience of learning as authentic as possible. Authentic experiences are more inspiring, more durable, and deeper than conventional seat-work study, though that aspect plays a crucial role in skill development.
To this end, we embrace project-based learning, theme-based learning, and public exhibitions.
Project-based learning requires students to organize their work around deliverable, integrated, and interest-driven plans. A solid project has greater value, develops skills, requires collaboration and support, and pays off with a demonstration or clear product. 'Gilgamesh' achieves all of these, in addition to deepening everyone's understanding of the fall's primary theme, Ancient Civilizations.
Its value is in the entertainment and education it provides its audience, the academic knowledge it promotes regarding early civilizations and universal themes (love and loss in particular), and the deep and challenging experiences its actors and crew must undertake. It develops a multitude of skills, but I will highlight one, articulated by Isobel Roosevelt, who plays Gilgamesh's mother, Ninsun: empathy. Isobel pointed out that acting requires you to get into the skin of another person, to understand her on a deep level. As a history teacher, I always held that history and literature teach empathy above all else--an understanding of why people make the decisions they do. Isobel emphasized the degree to which this happens in theater.
The collaboration required in a production is unrivalled. To that end, I want to thank the many faculty and families who have stepped in: Tracy Gallup and Val Tibbs-Wynne, designing art and backdrops with their students; Eileen Weiser, who, with Robbin Hitchins' help, is masterminding a massive costuming job; Brian Lillie, who is filming three sequences that will be shown during the performance; Cara Talaska and Adam Riccinto, who are combining forces to develop the music score, both live and recorded; Dennis Bowman, who has volunteered to be our master carpenter; Chris Barbeau, who is both choreographing our combat dances and overseeing the lighting of the production; George Albercook, who is developing our special effects (like a bowl of water that spontaneously begins to steam).
Joanna Hastings, Matt Berg, and Karen Bayoneto are continuing my education in the culture of Summers-Knoll, consistently raising the questions that need to be answered, often answering them before they even rise to my attention. Chris Swinko, Mark Benglian, Jason DePasquale, and Shan Cook have been flexible with their schedules and thoughtful in helping me organize a rehearsal schedule for no fewer than 36 students--about 42% of the SK student body. Joanna Hastings has been a theatrical colleague of mine for years, and we've been talking about 'Gilgamesh' since the summer.
You can see that this is a community-wide experience. There's still room for more help, of course--especially with costuming. Please let me know if you're interested in pitching in.
Let's hope the pay-off will be worthwhile. I have high hopes indeed.
Unlike any previous play I've directed, 'Gilgamesh' is woven into the fabric of my students' ongoing academic work and their daily schedule. This is one of the great assets of working at a school like Summers-Knoll, where our objective is to make the experience of learning as authentic as possible. Authentic experiences are more inspiring, more durable, and deeper than conventional seat-work study, though that aspect plays a crucial role in skill development.
To this end, we embrace project-based learning, theme-based learning, and public exhibitions.
Project-based learning requires students to organize their work around deliverable, integrated, and interest-driven plans. A solid project has greater value, develops skills, requires collaboration and support, and pays off with a demonstration or clear product. 'Gilgamesh' achieves all of these, in addition to deepening everyone's understanding of the fall's primary theme, Ancient Civilizations.
Its value is in the entertainment and education it provides its audience, the academic knowledge it promotes regarding early civilizations and universal themes (love and loss in particular), and the deep and challenging experiences its actors and crew must undertake. It develops a multitude of skills, but I will highlight one, articulated by Isobel Roosevelt, who plays Gilgamesh's mother, Ninsun: empathy. Isobel pointed out that acting requires you to get into the skin of another person, to understand her on a deep level. As a history teacher, I always held that history and literature teach empathy above all else--an understanding of why people make the decisions they do. Isobel emphasized the degree to which this happens in theater.
The collaboration required in a production is unrivalled. To that end, I want to thank the many faculty and families who have stepped in: Tracy Gallup and Val Tibbs-Wynne, designing art and backdrops with their students; Eileen Weiser, who, with Robbin Hitchins' help, is masterminding a massive costuming job; Brian Lillie, who is filming three sequences that will be shown during the performance; Cara Talaska and Adam Riccinto, who are combining forces to develop the music score, both live and recorded; Dennis Bowman, who has volunteered to be our master carpenter; Chris Barbeau, who is both choreographing our combat dances and overseeing the lighting of the production; George Albercook, who is developing our special effects (like a bowl of water that spontaneously begins to steam).
Joanna Hastings, Matt Berg, and Karen Bayoneto are continuing my education in the culture of Summers-Knoll, consistently raising the questions that need to be answered, often answering them before they even rise to my attention. Chris Swinko, Mark Benglian, Jason DePasquale, and Shan Cook have been flexible with their schedules and thoughtful in helping me organize a rehearsal schedule for no fewer than 36 students--about 42% of the SK student body. Joanna Hastings has been a theatrical colleague of mine for years, and we've been talking about 'Gilgamesh' since the summer.
You can see that this is a community-wide experience. There's still room for more help, of course--especially with costuming. Please let me know if you're interested in pitching in.
Let's hope the pay-off will be worthwhile. I have high hopes indeed.
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