Posted by: lboudreau | March 1, 2011

Alternative tests

The algebra class goes better– not best friends, and the lively conversations are usually NOT about math, but at least there’s energy to redirect.  We’re trying another Big Old Fat Experiment (BOFE).  Tests in this class either seem too easy or too hard– they certainly don’t capture what students can really do.  Tomorrow in class, instead of doing the same old review problems as prep for the same old kind of test, students will create two good problems, one easy and one challenging.  I’ll assemble all their questions into their test, adding a couple of my own and citing the source for each question.  The next day they’ll take the test collaboratively, and since they’ll know who authored each question, they can turn to the “expert” for that question, and everyone will have a turn being in charge.

I like this plan for so many reasons.  No one can sit out.  I can gauge how well each student understands by the quality of his/ her question as well as class conversation and a score on a test.  These students are excited– someone is bringing brownies– and I think I have a vehicle for testing the last period of the last day before spring break.

I also like it because it encourages students to ASK GOOD QUESTIONS.  More and more, that’s the heart of my teaching.  I want students to learn, and how better to show good learning than to ask something well, especially ask peers well, since the follow-up would be that peers would have to answer, and someone will have to teach.  And mathematicians ask questions all the time– it’s the heart of the process; we know what we know because people asked “What if” at some point.  If math education is going to include training students to act like mathematicians (and I hold that it should), then they need to learn how to ask good questions.

My Honors Pre-Calculus students have done this for the last two tests.  In each case, they had the option of taking my test or designing one of their own.  It’s been transformative.  They have guidelines about quantity and quality, and we talk about specific problems as we go, but in the end, each test is a student creation, and each test shows a remarkable depth of understanding.  I see evidence that they’ve truly bought into their own education.  I hear back from students that they learned more than they expected, and they gain a deeper appreciation for what teachers must generate.

The tests are difficult to grade, so I’m tweaking the plan– it does no good to assign something that takes three weeks to return– but it’s another BOFE that seems to be paying off.

Posted by: lboudreau | September 3, 2010

Necessity and Invention

My Algebra II class is silent as the grave.  Passive affect and not the slightest peep, even when asked a question.  I totally hate it.  I talk with these students after school, in tutorial, and they’re engaged and lively, but the whole-class thing just isn’t working.  I have grown desperate.  I need them to talk with each other to learn.

Some students share that maybe since they don’t know each other yet, they’re less likely to talk.  Last year they were in different classes, with friends.  Not so much this year.

I talked with colleagues in the humanities, who, after all, have to build class room communities regularly .  Someone suggested passing around a ball using only feet.  Someone else suggested a discussion to create class rules of engagement.  I decided some sort of ice breaker was in order– no talking, since we couldn’t even muster answers to questions about the weekend.  It needed to be math-related.  And about the same time, I had to develop a lesson plan about how different functions model different real-world situations.  So, a party game about functions was born.

We put down painter’s tape on the floor for axes– in a lovely lime green– only the first quadrant.  I drafted 15 scenarios, one for each student, and they pulled them at random from the Big Box Of Functions.  They had kite line, laundry line, checkers, and recycled DVD’s to mark  features.  A few minutes to strategize about how to build a graph, and they were off.Boy as Parabola


Curve or constant?  Dots or line?

It turned out to be a successful event.  I don’t know that they’re best friends yet, but we did talk a lot of math that day.  I’ll know better how well they understood modeling as we finish the chapter.  In the meantime, the function party game stays in the library.

Posted by: lboudreau | August 19, 2010

School's In

We’re back.  Whatever the opposite is of school being out, we’re there.  (And it’s been a long, pleasant summer of not caring a fig for correct grammar.)

True to form, we’ve jumped with both feet into the deep end.  I’m pretty sure I won’t break a leg.  Here’s what’s up:

My classes have wikis this year– so much better than a class web page.  With the help of the ever-wonderful Laura Deisley, we have pages for students to post and comment on journal entries, as well as post their project work (when we get there).  The advantage here is that students get to build the site—yes, there are course documents from me, but students are really the authors.  This is student-centered learning.  I get to check on their learning and redirect skills and understanding as needed—a formative assessment of a sort.  They get to work with each other, and build on the corporate knowledge. We all get to experience deeper learning.

PCH-1 Wiki Work 8-19-10

(As an aside here, I’m going to confess that the first meeting period for each class was about twice as long as it should have been.  I mean, I had a full hour, but I took it.  Time to wax rhapsodic over educational philosophies and pedagogical goals.  Maybe helpful to students.  Certainly made me feel better.  In any event, the phrase “deeper learning” was oft repeated.)

We’re also trying the Texas Instrument CAS calculators.  Wow, is about all I can say.  THEN, because there’s not enough of a steep learning curve already, we’re using the TI Navigator system to link all those calculators in class.  Wow, again.  Already I’m seeing a difference, and we’ve only met twice.  Today, a class of Honors Pre-Calculus students took on rational exponents with gusto.  They were really enthusiastic about the technology, not so much the math, but I don’t care.  Enthusiasm is enthusiasm, as far as I’m concerned.  And they remembered so much from a year or two ago, and they helped each other, and they tackled a couple of knotty expressions, and they asked good questions, and they even corrected my mathematical reasoning.  I am totally sold.

PCH-1 CAS 1 8-19-10PCH-1 CAS 2 8-19-10PCH-1 CAS 3 8-19-10

I haven’t yet figured out how to get CAS screen shots to the wiki.  I may have to embed them in a Word document or take some other indirect route.  But that’s a small issue.  I also have to figure out how CAS plays into assessments, but that will be a pleasure to think about.

This is the start of what promises to be a rich learning year.

Posted by: lboudreau | June 9, 2010

Final exam

We gave final exams three weeks ago.  I report on mine.  At last.

In the spring, all of my students complete two parts of a final.  The first is an exam packet with 10-12 involved problems, the sort that take a while to figure out.  They can do these packets with each other, using their notes and books, and they have about a month to do the work.  It’s collaborative and requires decent time management and critical thinking skills.  I always see good work as I grade them– this year was better than some.

My students also complete a project of some kind as half their final.  These projects are highly scaffolded: quite a few requirements (flexible, but rigorous), rubrics, process check-ups, and self-evaluations.  Far from letting teachers off the hook, well-done projects ramp up our planning and support tasks, and I might go a little overboard in an effort to demonstrate that these projects are not lightweight assignments.  Algebra II students create games or pop-up books.  Honors Pre-Calculus students create models (algebraic or 3-D scale) or research deeper topics.  These are the highlight of my teaching year.

Algebra II students gather during an alternative exam time slot to play each others’ games.  Some of the games are based off of established board games– Candyland is a popular format– but some come straight out of a student’s imagination.  They’re a lot of fun, and I can observe them in use– one of the grading criteria is playability, and it helps to see them in action.  And students get a kick out of seeing what their classmates created.  They practice skills and assess the work, and we say good-bye to the year.  Since I’ve graded exam packets by then, I know what their math chops look like– this is an opportunity to see what they can do with those chops.

Alg II Game 5-10

Some students like a small format

Some students like it big

Some students like it big

But everybody likes to play

But everybody likes to play!

Honors Pre-Calculus students gather in one big room during the exam time slot, and get creative in other ways.  This year, most students wanted to research topics that we either merely touched on during the year, or didn’t even cover.  Two taught me about hyperbolic cosines and how those functions describe the curve of a suspension cable in a bridge.  One provided a very well-done introduction to fractals, and then designed a family of his own with his software.  Another created an incredible animated presentation on vectors in sailing (using Keynote software– it’s the first time in years I missed having a Mac).

All three classes gather

All three classes gather

And share their work

And share their work

Several students analyzed real-world data to find models of best fit.  Among the best of these was on the path a dolphin takes above and below the water–sine wave, parabola, piecewise?  This student plans to study marine biology, and used the math project as an exploration of something she’s likely to pursue.  Another student, always interested in humanities, explored the math behind a classic Roman structure.

Dolphin Movement

Dolphin Movement

Vectors for Humanities Students

Vectors for Humanities Students

The best projects do come through individual passions and interests.  Another student, who’s a key sax player in the Ellington Jazz Ensemble, was inspired by the ways recording engineers have to avoid acoustic dead zones.  He built a scale model of effective and ineffective sound studios, and explained the principles involved.  Another student was intrigued by topology, a subject we only mentioned in passing, and brought a hands-on exploration of Moebius strips.  A third, who’d invited his date to prom using his own music video, wrote a song to summarize highlights from the year, and brought us to tears of laughter.

The games and projects have to be creative ventures using sound mathematical reasoning– they were quite good this year.  I am astonished by the breadth of student interests (although maybe I shouldn’t be at this point), and humbled by their creativity and how much I learn from them.  As students reflect on their work (self-evals are never that far away), they show how much they’ve accomplished in the year.   It is a fitting end to our work together.

Posted by: lboudreau | May 12, 2010

And what have you learned, Dorothy?

This is possibly the best line in any movie.  Ever.  It just lends itself to all sorts of scenarios.  I often use it in a slightly sarcastic tone in the class room, or with daughters at home.  (Or maybe not so slightly.)

Today, it rings earnestly for 21st century education.

I wish I’d taken a better pulse at the start of the school year, the start of Dobbs.  It’s hard to remember quite what I knew then, so much has filled the year, and so much learning seems to have been more articulating the sense of what I already knew– often the hallmark of  authentic learning.  But I know there’s a change.

I understand concepts more clearly: PLC’s, inquiry learning, project-based learning, 21st century teaching– now named and related to each other.  For example, inquiry and project learning are NOT mutually exclusive, but rather at different points on a spectrum; projects can be used to promote inquiry, and inquiry can be at the heart of projects.  It’s all in how you use the techniques.  (Read Linda Darling-Hammond, Powerful Learning, chapter 1– an outline of how inquiry learning, project learning, problem learning, and collaboration intersect.  Also read her at Edutopia for an outline of her argument for inquiry learning.)  At Lovett, we develop the core competencies– collaboration, communication, critical thinking, creativity, and global awareness (it helps that most of them start with “c”).  I plan to reach these strategic goals through a balance of 20th and 21st century methods–something old, something new, something borrowed, something blue– a mix of techniques, because I’ve also learned that a balance of approaches keeps it fresh

But how to do it?  After a year, I know better where to go for answers, whether it’s a book or a web site or a person.  For example, what IS inquiry learning to begin with?  Check out Concept2Class.  What are alternatives to assessment?  Look at Edutopia.  A PLC?  Ask DuFour.  And for just about anything, research Classroon2.0.

I’ve also forgotten the techno-anxiety; although not an expert by any measure, I am much more comfortable with using web-based tools.  My goals for next year include incorporating a wiki (eventually to become an on-line portfolio for the class, similar to Small Stones).  We’ll fold in Google earth assignments, and journal assignments.  I even grew ambitious enough and confident enough to apply for a substantial grant to provide Texas Instrument NSpire CAS units for the class room.  And because communication and collaboration fill center stage, the grant includes TI Navigator, a wireless system to link the hand held units to each other and me.  Both platforms mean a steep learning curve, but beyond that I plan to use the entire set-up with 21st century learning in mind, and present the connections at a T3 conference the next year.  (Honestly, who IS this woman?)

I’ve woven a larger web– more contacts, more connection to a wider world.  It started with 11 colleagues in the cohort, snowballed with Twitter suggestions, and reached flood stage at Educon.  It includes teachers from around the nation, teachers in Atlanta, and our intrepid TI rep, Ned Colley.

And after months of wrangling and compromise, I have a much better sense of how 21st century learning, and my vision, fit with my school and my colleagues, no small education.  For example, the History department has developed a wide repertoire of digital, collaborative venues for students to show their work :

“In short, the History Department has created a curriculum and a series of student projects that enables students to increasingly research topics independently. Through the use of technology (“blogs” and “wikis”), students are now able to share their research and opinions with each other. This student-centered dialogue encourages students to view material from a variety of global perspectives, allowing for an appreciation of the competing opinions that are constantly being presented in an ever-changing world.”
Rick Chase, Upper School History Department Head (page 7, LovettLines May 2010

The English department has also dipped its toe in the digital headwaters:

“When I observed some of the student presentations one day in this class, I immediately noticed that students were deeply invested in their work. The fact that the project begins with student choice in selecting which program they want to use gives them some in the ownership of the assignment, and in turn fuels their commitment to a successful group project. The practice of listening carefully to the podcasts and, consequently, presenting their findings to their peers gave students much practice at important oral communication skills. While synthesizing their selected stories with meaningful themes of human nature, students made both universal and personal connections to the topics.”  Debi Ohayon, Upper School English Department Head (page 6, Lovett Lines April 2010).

It’s time for the math department to take a swim.  I am working with colleagues to develop a project-based approach to regular and honors Pre-calculus.  While not full immersion, it is a start.  In conjunction with this, I’ll be part of the US “study group” to research inquiry learning.  Again, not a full-on PLC, but it fits within the culture of the US.  Even DuFour would acknowledge the necessity of fitting the model to the reality.

The bottom line through all this remains student learning, and maintaining some excitement in the class room for me (because, as we’ve established through several blog posts, it IS all about me).  After a year of accelerated learning, I look forward to using what I know for students, and to learning even more.

TUpper SNcheowols
Fine ArNtsews
Upper School History Department
The Upper School History Department continues to be innovative in three crucial areas—the introduction of globaloriented
issues and courses throughout the curriculum, the development of sequential projects in each grade that
build on each other in an intentional manner so that students can learn to think critically, and the development of
writing skills that culminate in the ability to write sophisticated research and term papers.
The History Department continues to develop the ninth grade course, “Introduction to World Cultures,” that
introduces students to major geopolitical issues. This semester course is divided into three units—Latin America, the
Middle East, and China. The emphasis in each unit is skill building as each student is asked to explore and analyze
current events. For example, students have recently been exploring the roles of women in the Middle East through the
use of class “blogs.” Through the examination of a wide variety of articles, students were encouraged to differentiate
between the impact of religion compared to the influence of other factors that might shape attitudes towards females.
Such independent projects are followed up in the tenth grade because Western Civilization has been transformed.
In several projects, students are now asked to study art and literature as propaganda in a European setting. Students
examine topics such as the Reformation, the French Revolution, and 19th-century colonization. In each instance
students are then asked to compare European development to a global counterpart.
These multicultural projects are designed to enable students to examine historical issues from multiple
perspectives. Such insights allow students to write term papers that are much more sophisticated since students
are aware that they have to construct an argument that includes evidence from a political, as well as a cultural,
perspective. Thus, the junior paper in American Studies, which must include both a historical and cultural
perspective, becomes a natural progression from the student’s point of view. American Studies has always been
a leader in allowing students to study material from multiple perspectives since students have been required to
synthesize material from both English and history classes.
Finally, the History Department continues to develop senior electives that build on a multicultural and global
perspective, while encouraging students to develop the ability to work independently. Seniors can now take a wide
variety of courses such as African Studies, Art History, Asian Studies, Economics, and U. S. Government. Next year
two new courses will be offered—Latin American Studies and a course on Presidential decision-making. Students
in many of these courses are in the process of creating an interdisciplinary “wiki”, which also includes contributions
from students in the Environmental Science class. In each class students are in the process of investigating the
viability of alternative fuels, based on scientific, political, and economic factors, in comparison to their non-renewable
counterparts. Students are researching the environmental and economic impact of each fuel. In the process, they are
able to read each other’s contributions while also being able to ask questions to any member of each contributing
class. Next year the students’ work will culminate in policy recommendations that will be sent to students in the
Presidential decision-making class, taught by Mr. Peebles and Dr. Dunkel. That class will then use information from
the other classes in order to develop a presidential policy statement regarding the environment.
In short, the History Department has created a curriculum and a series of student projects that enables students
to increasingly research topics independently. Through the use of technology (“blogs” and “wikis”), students are
now able to share their research and opinions with each other. This student-centered dialogue encourages students to
view material from a variety of global perspectives, allowing for an appreciation of the competing opinions that are
constantly being presented in an ever-changing world.
Rick Chase | Upper School History Department Head
Posted by: lboudreau | May 1, 2010

Kite Day

Every spring, after we work with vectors, and the weather warms, Honors Pre-calculus students and I head outside to fly kites.  I hang these big-a—-  kites in my room, and one year students REALLY wanted to fly them.  It was the work of a moment to link kite flying with vectors, and give us an excuse to go into the sunshine.

So, we’ve done this three years now, most of the time having to run to keep kites aloft (and adding another vector to the experience).  I always lead some sort of discussion during the period– what vectors have you experienced, what additions/subtractions/dot products, what is tension– and get some level of conversation started (but, really, what do I expect from students who’ve worked hard all year, and are now in the sunny outdoors with toys?)  This year we had good breezes, and by the afternoon, wind strong enough to fly one of the kites WAY high, until the strut snapped, and it fell out of the sky like a wounded bat, and we had to haul it in over the roof of the upper school, and across the road, and into the pine trees by the stadium… It was really high.

Anyway, it’s a good day with students, especially as we wrap up the year.  We can all use something more lighthearted at this point.  And this year I had a digital camera.  Woo-hoo!

Posted by: lboudreau | May 1, 2010

On a Roll

We’re wrapping up the school year.  Only those who have taught understand quite what that implies.  To say the pressure’s on is a ludicrous understatement.  But we’re pros, and we will do everything necessary, plus some.  It’s why I’m on a roll.

Also, because I have funding for CAS.  The Lovett Parents Association, bless them, funded my request for a chunk o’ change to get Texas Instruments equipment.  We’ll have 20 NSpire hand held CAS units and a Navigator wireless system to connect them all.  (The Computer Algebra System crunches variables as well as numbers, which means we can handle mechanics in fairly short order, and get to further explorations.  I hope.)  It means I have to get more training.  Training to this point has been more about investigation and general understanding; now, it must be about deeper learning and creating ways to fold it into existing curriculum.  Work to be done over the summer.  Ooh.  I’ll have to stay on a roll.

Also on a roll because we have an US PLC.  Of sorts.  That I get to be a member of, but didn’t have to plan (and there was much rejoicing).  I mentioned it in a comment on Ted’s blog, but will say here that, while it’s not quite what I expected, I am looking forward to the work we’ll do.

This PLC (actually “study group”) was introduced at an US faculty meeting last week.  The entire meeting was devoted to 21st century learning, which warmed the cockles of my heart, but I’m going to confess something here, something that reveals the black interior of my soul.  Or at least the contradictory nature of it.  I was delighted and reassured to see that so many colleagues share this goal of inquiry learning, of innovation and rethinking how students learn best.  To see that a number of us geek out in the name of education.  But a part of me resented the fact that I’m behind the power curve.  I knew about the inquiry-based physics class, but I didn’t know about the creative uses of technology already in place.  Here, I thought I was a trend-setter, and I am merely one of the herd, and a lagging one at that.  Rather ticked me off.  I was a skitch miffed that I wasn’t asked to share what I do in class, until I realized I may not have all that much to share of a whizz-bang nature.  And I didn’t particularly like having someone tell me what I had to do in order to establish a 21st century class room, since I think I already have a good idea, and don’t need someone spelling out the rules, as if there were rules (and I developed a deeper sympathy for colleagues who may also resent even the ideas I propose).

So there, I said it– I was delighted and annoyed all at once, and once again demonstrated how it’s all about me.

Didn’t we say something in August about how these blogs were to be reflection tools, and roll over into confessionals some time in the beginning of May?

Posted by: lboudreau | April 16, 2010

My favorite things

We’re taking a conics test in Honors Pre-calculus today, in fact, right in the middle of one as I write.  It is one of my favorite days in the year.  The test is collaborative.  The material is squirrelly, there’s a lot of detailed information, and students are a little tired at this point.  But this test brings out some of their best work, and they really engage with the math and with each other.  They strategize about how to collaborate (this period chose to work at tables for 40 minutes, and come together for the final 25 minutes– they’ve just taken a time check amongst themselves).  They get louder and louder as the period winds up.  They leave recharged and smiling.  I love that.  I love the fact that some of the pressure is off, and they have a chance to show their smarts in a good light.  I love that they have to figure out how to work with each other– including how to check each others’ work.  The big caution here is not to rely too much on the “smart” kids; everyone can make a mistake and if the entire class simply accepts an answer, everyone risks missing the points.  Quieter, less confident students make a big difference when they speak up.  They learned this last time, when one of the quietest students tried to get classmates to check an answer.  No check, no verification– oops.

Collaborative tests are among the most important tools in my assessment toolkit.  I wouldn’t give every test collaboratively– sometimes I really need to gauge individual understanding– but this chapter lends itself well to working together.  It’s also right before final exams, for which they’ll be working together on the exam packet; today functions as a warm-up.

Posted by: lboudreau | March 28, 2010

Students #2

A short blog this week.  I simply want to share my excitement about a student’s idea for his spring final.  We’ve introduced matrices briefly into Honors Pre-calculus, with a discussion about their use in computer animation– basically, points are presented in a 2x “number of points” sized matrix, which is multiplied by another matrix, which changes the locations of those points in some way.  They could shift, rotate, flip, expand, contract, or do any combination of those.  Of course, the computer animation we see on the screen is much more complex, but it’s cool to see the foundation at work.  Rather like studying cell biology– why does it do what it does?

One of my students is studying computer animation at Lovett.  If I understand correctly, he’s using programs and designing animation that have matrices built in.  He’s not necessarily creating the matrix.  But he wants to open the “guts” of his programming,and  tie the two strands into a coherent demonstration for his peers.  I can’t wait to see what he does, and learn on the way.  I am no expert on programming or animation.

A shout-out here to Bernadette’s blog, too, about her writer’s work shop.  While we don’t have mathematician’s work shops (maybe we should), I think there are ways to incorporate the flow of work in math: feedback in smaller groups, to class discussion and filling in the gaps, then back to smaller groups to refine final products.

Posted by: lboudreau | March 21, 2010

Students #1

As promised, a blog on actual, real-life students, the persons on the planet who are, after all, the focus of my work.

While I’m not exactly sure what action research is, I think it includes measuring outcomes as you go.  In the case of teaching, it means studying students and understanding as teaching progresses, especially if there is teaching change afoot.  One of the things we’ll include in any sort of plan for Pre-calculus classes next year is gauging how well students do against some sort of current benchmark.  Don’t know yet what that benchmark is, or how we’ll measure anything, but it’s on the list.  However, I don’t necessarily have to wait for next year– I can share observations now.

The first concerns the spring final.  I give an alternative final at the end of the spring term, one of my favorite things, and here’s why: students get really engaged.  Last spring, and even now, students started asking about their work in the first part of March, and the buzz grows about not having to take a two-hours exam.  Friday in classes we talked briefly about it (it pays to start talking early on, so students have a longer lead time to think and brainstorm) and eyes lit up, and we shared interesting project ideas.  They really like that they get to determine the type of final product– research, model, construction, or product-yet-to-be-determined.  The fact that it’s open appeals to them, or at least to the 20 or so students who have talked with me.  I assure them that the standards are high, but also very clear, and we will have class time to work on this.

The day of the final, students convene to share their work, and that is a very fine two hours.  Everyone presents something, whether talking or simply sharing a table project.  We don’t have time for everyone to present orally, and, again, students like that choice.  I tell them that, if they’re not going to talk, then their presentation has to be especially clear.  We spend a good part of that two hours simply going from table to table to ask questions and explain work.  The decibels rise as students become more animated, and a great deal of teaching goes on as, say, the student who now knows about base 8 number systems shares with the student who studied the parabolic equations of the jumps she and her horse make in competition.  Or the student who built a scale model of a coliseum, complete with conic equations, talks probability with the student who researched game theory.  Two hours go quickly.

The breadth of topics is astonishing.  Some of these subjects are further explorations of concepts in the course.  Some are toe-dips into waters completely outside the curriculum.  The variety provides a fitting end to a year’s study of wide-ranging concepts, which is merely preparation for even wider ranges in college.

I ask students to complete a self-evaluation, which includes questions about what they’ve learned.  I always get answers that include specific math skills or concepts, and students are invariably enthusiastic about what they’ve done, or simply about the chance to show their stuff in new ways.  I need to find ways to ask about the meta-understanding of core competencies: communication, collaboration, critical thinking.  But for now, I see a great deal of evidence from students that they learned and they enjoyed the learning.  (For the record, I never got this same sort of excitement over a two-hour final…)

My second observation concerns course pacing.  I have to admit, I’m not the best at touching base with colleagues about where they are in a course.  We share the same curriculum, based in large part on what we think students will need in future courses, so I pace us to finish those topics.  If we need to slow down, we do, of course, and there is time built into the year to do that.  But we’ve been able to stay on track most of the year.  I think I’m pretty rigorous in grading, and grades look fine (even compared to other teacher’s classes), and students give ample evidence they understand, so overall I keep the pace.

I learned in the last couple of weeks my classes are about a chapter ahead of others.  My first thought: I’m pushing too hard.  My second thought: no.  Perhaps learning through discussion and engagement is, after all, a more efficient way to do it.  If I elicit what students already know, and we talk about it, perhaps we get a better recall of what’s come before, and can use it more quickly.  And maybe there’s a lot to be said for lively student involvement in a class, even if I have to quiet them down with every breath I take.  At least their minds are on.  At any rate, I see evidence that what we do in class promotes learning.

I don’t have statistical measurements for any of this– those will be in place better next year.  For now, I am encouraged by what students say and demonstrate.  It would be good to share the experience, maybe  ask others to come see what happens on final day.  Maybe post some on the web site as a test for next year’s wiki.

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