A Latin math problem?

One of my Latin classes found a math problem lying on the floor that one of my advisees dropped during first period. Because we’re working on the structure of Latin sentences, we tried translating this into Latin. It’s not a perfect translation by any means, but it shows the four types of sentenced they have learned, the use of both new vocabulary and common vocabulary from their readings, and use of both subjects and direct objects.

Tres viri obesi veniunt ad caupona. Viri sedent comedere cibum, et volunt comedere multos cibos. Comedent cibos et lactos bibent. Syngrapha est decemquintii denarii. Omnis viri solvent quintii denarii. Caupo excipit pecuniam. Spectat qui tres viros sunt amicos. Donat ad famulo retro pecuniam, id est quintii denarii. Sed famulus fraudulentus est. habet duos denarios et donat omnos viros unum denarium. Omni viri nunc solvent quattuor denarii. Famulus habet duos denarii. Sunt Decemquattuor denarios. Ubi est unus desiderarius denarius?

Here the part that really pleased me. The first Latin class took the English math problem and rewrote it in Latin. The second Latin class took the Latin translation and decoded it into English. And, beautifully, the second group was able to understand and solve the correct math riddle.

A good day’s work!

Two Design Events for Middle Schoolers

Independent Day School of Middlefield is hosting two Design events open to teams of Middle Schoolers, one is on November 3, 2012; the other is on April 6, 2013.

• November 3, 2012: Redesign the Electoral College.  Students have to develop a proposal to amend or replace the Electoral College, while still keeping in mind its original intents: to balance the states’ populations and rights against one another; to keep the balance between rural and urban centers; and to avoid having the presidential election turn into a popularity contest.  Design your proposal ahead of time, then bring it to be tested by other teams on November 3. Right before the election, too.
• We’re also hosting the New England Design Symposium on April 6, 2013. The theme this year for participating teams will be Food and Landscape.  Each team is invited to submit a problem portfolio explaining a given problem around food in their community, and its relation to (or lack of relation to) the landscape around it.  This problem is very broadly defined, in order to give maximum leeway to the designers and to the challenging teams.

I hope that some of the CAIS middle schools will think about participating in one or both of these events; we had a really good time at NEDS last year, and I hope some of the other schools will think about joining us for these events.

“I met the challenge and I succeeded”

As I was leaving the house tonight on an errand, I passed my neighbor on the porch.  He’s an older guy, late 50s or early 60s.  The years… hmm… have not been kind.  He looks hard-ridden and put away wet, as the old expression goes, and run down.  Normally he’s out on the front stoop of the building smoking a cigarette in a posture that suggests that it was a hard day, and he’s not going to have too many more like it before there’s a closed-casket ceremony at a funeral parlor with only one person attending.

Tonight he was more animated than I’ve ever seen him.  He had his cellphone out, and he had no cigarette in his hand, and he was overjoyed at whatever it was that he’d achieved, and he was shouting into the phone, almost, but joyously, “No, you don’t understand… I met the challenge, and against all odds, I succeeded.  I made it work.  Me.  I did it.”

I have no idea what he was doing or what he did to succeed — I was, as I say, on a somewhat urgent errand, and I didn’t have time to stop and talk to him.  But I think this is the essence of what we want kids to experience after a Design Thinking or a Makery experience: the indomitable joy and fierceness that comes from completing a project, even in the face of difficulty and indignity, and succeeding anyway.

My neighbor achieved that yesterday. What can I do to help my students achieve that sense of themselves tomorrow?

Revisiting the Watchtower, as design exercise

This post has been getting some notice recently, from back in 2007. I wanted to highlight it, and set it in some sort of common relevance, as a possible design exercise for a medieval history class. You could do something similar, I suppose, with almost any era in history. Here’s the constraints:

1. You’re a medieval engineer. You work for a king (or maybe a queen like Eleanor of Aquitaine). You’ve been tasked with building a castle. Not really a castle. A tower — your king/queen doesn’t have a lot of money for construction right now, and getting this tower built is a priority. There’s fast, cheap, and good… pick any two you like.
2. The tower has to be between forty and sixty feet tall. It’s going to be a watch tower, and the main part of the roof has to have a signal station on top of it, in the form of a large pile of sticks to be set on fire if something goes wrong. All those sticks, and that fire, have to be high up — and the knight and his military force with him have to have a place to live, and from which they can see the surrounding country.
3. The story of a building like a tower has got to be about 10 feet high — so this tower is four to six stories tall. It might have a low-ceilinged area, like a basement (maybe two); and it might have a high-cielinged area like a great hall. The tower isn’t going to be a grand construction. The base can’t be any larger than 30′x30 feet, and it can’t go more than 10′ deep in the ground.
4. There’s going to be a knight assigned to the hall. He’s going to have two squires, who will be young men between 15-18. He’ll have maybe four pages, who will be between 7 years of age and 15 years of age. There will be somewhere between 8 and 15 additional men (some infantry, some archers who will want more private quarters because they are more likely professional soldiers) stationed with him, of varying rank and social station. The knight has a wife, who will want some private quarters for herself and her husband; and they have a household of 6-10 servants.
5. The walls are going to have to be ten feet thick at the base to support the weight of the upper levels, and they can rarely be less than three feet thick because the building material is stone.

Now here’s the challenge:

• Using graph paper at a scale of 1 square = 2 feet, design a plan and elevation for the tower.
• Include — stairways between levels; cooking, eating and activity spaces like a great hall, sleeping, and (ahem!) elimination facilities for the residents, including private or semi-private living quarters for the knight and his wife; storage for food and essentials for the household for up to 4 months (winter + siege supplies); defensive positions to protect the tower-house against attack; support columns from basement to upper floors (to support the weight of the watchfire on the roof); show the position of doors and windows; positions of heating elements like fireplaces and chimney flues; water-storage capability for long sieges or winter, for cooking and cleaning.
• Do not include: technology too advanced for the time period, e.g., electric light or water-driven plumbing.
• Use David Macaulay’s book Castle as both inspiration and guide to certain construction techniques
• Conclude with an estimation of the labor force needed to construct your proposed tower, and a rough outline of the project calendar, (e.g, dig foundation in March, make foundations in April, build 1st floor in May, etc.) Remember the limitations of the era’s technology in designing the workforce estimates and project calendar.
• Extra Credit: Build a model that shows the outside of your tower.
• SUPERDUPER  Extra-Special credit: Build a model of your tower that includes both internal and external structural detail.

And… Just because I’m nice, and because I want to get used to the idea of publishing and then editing, and building up a library of tools and projects: DT Medieval Engineer <- Here’s that whole exercise, pre-loaded into a PDF, ready to hand out and use in class.

Class idea: current events

I want to talk about current events class. You may have a current events class in your class right now. Maybe it works something like this you tell every student to bring in an article, that deals with some current subject in the news, and then you spend — or more likely waste — an entire class, talking about the various articles. Does that sound familiar?

Try something different. Ask each kid to bring in an article, but set it up a little bit beforehand. Create a box. In the box put a number of slips of paper, each of which has a region of the world or a region of the news to report on. Make sure that none of the categories are something silly, like movies or sports. Sports news is interesting, but it doesn’t shape the world nearly as much as economics or politics — things that our kids generally avoid. And although sometimes major sports events shape public policy, it’s much better for kids to become invested in political and economic news. Unfortunately many kids are not particularly interested in this kind of news…

How to get them involved?

This is what I’ve decided to do with my own class. I have such a box. In the box are about 20 slips of paper, each of which has the name of a major region of the world written on it. The categories include subjects like: the Middle East, South America, North America, Africa, European Union, Great Britain, Asia, Australia, India, Russia, and China. There are also bits of American domestic news included in the box: things like economics, business, technology, science, culture, plus the Northeast, the South, the midwest and northwest….

Every week on Thursday I assign each group of students to a “desk”. The desk is not actually a physical desk in the classroom, but an area of concern. They get an entire week to find two or three important headlines from that region of the world or that area of American domestic news. The following Thursday, a week after getting the assignment, our class comes together. One of my American history sections plays the role of the United States department of defense. The other section gets to be the US department of state. And yes, they ask each other questions – and yes, they are allowed to lie.

After every story, I asked the students what their department should do about it. Sometimes they decide to ask for more information from the other class. This involves sending a memo to the relevant department — either state to defense, or defense to state. The result is that the two classes are asking questions to one another about the business of the nation.

The second thing that they got to do, is make a “recommendation to the president.” Recommendations to the president get posted on index cards on that narrow strip of bulletin board above the whiteboard in my classroom… you have one too; I’m sure it’s useless. Except its going to fill up with advice to the president…

Someone in class today asked me, “Mr. Watt, who gets to play the president? You?”

I replied, “well, Mr. Obama is the president. “And then I explain, that Mr. Obama gets to be the president. (Maybe Romney will replace him, but it doesn’t seem likely) Meeting, that the president actually has to make decisions, and those decisions are based on the real news. And the president has to make decisions based on the recommendations of the Department of Defense, and the Department of State.

Do you see where this is going? By posting our recommendations to the president, our classes get to see exactly what it is that the president does and what advice he must have gotten from the people that report to him, and advise him. So, my students also get to see how decisions are actually made in the real world, and compare their own results with a public decision-maker’s actions. They get ro be part of a decision tree, not all of ir.

Presidents receive information from subordinates, in the same way that CEOs get advice from their subordinates, as school principals get advice from their teachers and subordinate administrators. In other words, my students as they’re learning current events, have to role-play out the decisions that other people are doing this work for real in the government, amd get to see what results actually happened in the real world. Call it fantasy Department of State instead of fantasy football.

Kids live in a highly complex world. For most of their lives, kids today have been instructed or enabled to live in fantasy worlds.. Some but not all of them are video games; some of them are imaginary ideas about wealth and power that they have picked up from television and from the Internet. But such fantasy realms can only offer preprogrammed responses, not genuine decision-making. Fantasy sports league are at least rooted in the statistics of real players…

So current events classes can be gameified. Presidential decisions are actually involving thousands of people making small decisions based on the news that they have available and sending data up the chain of command. By helping them role-play out a part of that decision-making process, I hope to teach my students to be better decision-makers as adults. In other words, the play is the thing in which we catch or at least learn the conscience of our kings.

N.B.: today’s blog entry was assembled using Dragon dictation for the first time. I am planning to post this directly as I am traveling today, but I hope that the ideas here will be somewhat obvious, even before I’ve had a chance to clean up the text. Have a lovely weekend.

Learning to Think

Scott McLeod today writes at Dangerously Irrelevant: Here are two quotes from Education and Learning to Think, an interesting little research-based book published by the National Research Council way back in 1987!

Higher order thinking is nonalgorithmic. That is, the path of action is not fully specified in advance.

In other words, a curriculum isn’t going to make all your students into perfect higher-order thinkers.

Higher order thinking tends to be complex. The total path is not “visible” (mentally speaking) from any single vantage point.

In other words, you have to learn multi-step processes and think about matters from a systemic point of view, not just ‘fill in the bubble’.

Higher order thinking often yields multiple solutions, each with costs and benefits, rather than unique solutions.

Or, A, B, C, and D…. and ‘C’ is the best cost-benefit solution for our budget at the moment, unless that state grant comes in… then plan B.  How many kids do you know that find multiple solutions to the same problem? Do they do that in school?

Higher order thinking involves nuanced judgment and interpretation.

Higher order thinking involves the application of multiple criteria, which sometimes conflict with one another.

The factors that the teacher sees are not the only ones on the field of play; authentic learning requires solutions that please more than one person.

Higher order thinking often involves uncertainty. Not everything that bears on the task at hand is known.

Higher order thinking involves self-regulation of the thinking process. We do not recognize higher order thinking in an individual when someone else “calls the plays” at every step.

If I, the teacher, ‘know’ the answer, then my students are playing guessing games… not thinking.  If students don’t have a say in what they’re learning, they aren’t thinking, either.

Higher order thinking involves imposing meaning, finding structure in apparent disorder.

Higher order thinking is effortful. There is considerable mental work involved in the kinds of elaborations and judgments required. (p. 3)

Isaac Newton and Johannes Kepler sorted through thousands of pieces of apparently random data to solve the theoretical frameworks of gravity, and the motion of the planets.  It took them years.  Yet we expect kids to come to clear understandings of important processes in 40-minute classes.

Scott McLeod goes on: The seventh item on the list, self-regulation, is one that I think is particularly lacking in many K-12 schools because the teachers “call the plays” so much of the time…

The blog entry ends with what Scott thinks is the money quote:

The goals of increasing thinking and reasoning ability are old ones for educators. . . . But these goals were part of the high literacy tradition; they did not, by and large, apply to the more recent schools for the masses. Although it is not new to include thinking, problem solving, and reasoning in someone’s school curriculum, it is new to include it in everyone’s curriculum. It is new to take seriously the aspiration of making thinking and problem solving a regular part of a school program for all of the population . . . It is a new challenge to develop educational programs that assume that all individuals, not just an elite, can become competent thinkers. (p. 7)

Nearly every literate society in the world regarded reading a very short list of classic books as the key to becoming a thoughtful and rational human being… books which they were careful to separate out from a muddled stack of sacred scriptures.   Now, students read digests and abridged versions of these classics, and we call it a day.

Assume you had a school of around a hundred students, and that you had them for 5-9th grade: what books would you want them to read cover to cover, assuming they only read one great book a year?  What are the hard books, that would make them think?

Tempered Radical: False Transparency. . .

So I immediately tried to counsel my students to safety.  “Are you sure you want to try out for football?  It’s a pretty tough sport, you know.  Why not wait for the basketball, baseball or soccer season?”

Their reply blew me away:  “We’re going to be great at football, Mr. Ferriter.  We completely dominate in Madden 2008 on our PlayStations.  No one can beat us!”

These two boys who had never played an organized sport in their life—-let alone an organized sport where physicality is essential for success and where brutal hits are commonplace—-had convinced themselves that football was the right sport for them because of their video game prowess.  In their minds, mastering skills with digital players on an electronic field in their living rooms translated somehow into an belief that they would excel on a real field wearing real pads trying to tackle 200-pound kids without breaking their necks!

Wild, huh?  […]

Are middle schoolers—-who love fantasy and imagination to begin with—confused, failing to find the line between fiction and reality when determining what they “know” and “can do?”
Interesting questions, huh?

From the Tempered Radical: The Danger of False Transparency

It is an interesting question. Today was graduation at my school, and we said farewell to our ninth graders — our top grade.  The students who have just left are not so confused about the line between video fiction and reality.  But the grades after them seem to be much more fluid.

The thought occurs to me, though… GUITAR HERO and similar games are always improving.  Is there going to come a time when the student fantasy, “I am a great guitar player” is going to collide with the technological marvel of a GUITAR HERO guitar that will mimic the ability to play guitar more closely?  

Will our fantasist simulations ever be indistinguishable from reality? What will school look like when that happens?  Is it going to occur in my professional lifetime, or in some Tomorrrowland I may never see?

Increasingly, I think it will be in my professional life — medical advances and life expectancy changes mean that I may easily work another forty years before retiring.  In now’s climate of Future Shock, 40 years is an eternity — 80 machine generations, 50 medical generations, 100 biotech generations.  The horse may even learn to talk.

Dwarven Kingdom

Dwarven Kingdom
Originally uploaded by anselm23.

So, as a gamer, I’m always interested in building new locations or settings for games. Moria, the dwarven kingdom in LORD OF THE RINGS, kind of sets the standard for dwarven ways. Yet given their interactions with the surface, compared with other earth-resident races, it always seemed to me that the dwarven kingdom belonged in a cleft in the rock.

Here, I’ve used Picknik’s tools to label the map with some of the regions or territories within the Dwarven kingdom of Westcleft, a surface-dwelling dwarven princedom on the western slopes of the Fogtooth Mountains.

The original picture is of a cleft in a sand-covered snowbank in the school parking lot. I wish there’d been some greenery, but no such luck.

The photo on Flickr has roll-over notes with additional ideas for what happens in each place or region. I don’t have a good sense of scale yet, but I’m figuring it’s a day’s march between Three Road City and Black Rock Tower. So it’s really more of a city-state than a principality or kingdom.

Lovely Game!

A friend of mine introduced me to this new game: Play Auditorium. It’s delightfully addicting. I like it.

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