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Archive for the ‘Classroom Strategies’ Category

Recently, I tweeted out a link to Nat Banting’s post on whiteboards. It reminded me that I was going to write a post here about my experiences with them this year. I’ve been trying them out. I’ve done some things well. I’ve learned some things.

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The three things I like most about having students use whiteboards in class, probably in order, are:

  • How their work “pops” off the boards so that I can see it easily. As I circulate, it’s so easy to provide feedback.
  • How comfortable students are working on a dry-erase surface. They are not afraid to try things. They are not afraid to make mistakes.
  • How easy it is to group and pair students to give and receive feedback from peers when their work is on whiteboards.

The things I learned, I learned by making mistakes, and by asking you questions. Here’s one I threw out in the middle of a class in which I was making mistakes. I was having students do questions on the whiteboards, and then copy them into their notebooks. Of course, they hated it. They were doing everything twice. The high school math teacher in me is having a hard time letting go of the mentality that I must write it on the board and they must copy it down, or they haven’t learned it. I still want them to leave my class with something useful and correct written down in their notebooks for future reference. Please don’t judge me for that.

In the middle of that class, I put the call out on Twitter.

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The responses were immediate and helpful. Talk about real-time formative feedback! My pocket was buzzing in the middle of the lesson. You can see all the responses here.

Christopher Danielson (@Trianglemancsd) saw right to the heart of my question and threw back at me, “Also, how much needs to?” That’s really what I was wrestling with.

Consensus was that between none and very little of what is written on whiteboards gets transferred directly elsewhere. This whiteboard work is the learning phase. It’s messy. It’s getting transferred to their brains, honest. One suggestion what to have students take a photograph of their work if they think they will need to look back at it. Frank Noschese (@fnoschese) suggested Lens Mob as a way to create an album they could all send their work to. Jacqueline (@_Cuddlefish_) uses them a lot, and I respect her experience. I wish she blogged (too busy geocaching, I suspect). She tried to convince me to let go of the need to have stuff written down.

So the question, then, becomes what do they do AFTER they have finished the messy learning on the whiteboards? Some teachers go straight into practice. Nat Banting (@NatBanting) and Bowman Dickson (@bowmanimal) talk about having students reflect on their whiteboarding at the end.

One teacher I work with this year helps her students summarize a few key things in a “Student Study Guide” that she provides. Heather Kohn (@heather_kohn) does something similar by giving her students a guided notes page for things that she feels need to be formalized. Of course, there’s always the textbook for future reference.

I’m in the middle of figuring out what I am going to do next year. If I land back in a classroom, I will make sure I end up with a set of mini whiteboards. I may still make kids write some stuff down on paper. Don’t hate me for that.

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I take no credit for this idea at all. I was in a classroom this morning, and the teacher had the students play a game of Radical SNAP. The students were totally engaged, and were enthusiastically converting between mixed and entire radicals. It’s pretty simple to set up.

Materials: You need one deck of cards with the 10, J, Q and K removed for each pair of students, and one giant square root symbol per pair of students. This one should do the trick: Giant Root

Pair off the students in your class. Each pair gets a deck of cards, and should remove the 10, J, Q and K. Shuffle the remaining cards, and deal them so that each person has half the deck, face down.

Mixed to Entire

The students flip over their top cards. The student on the left puts his in front of the radical, and the student on the right puts hers under the radical. The first student to correctly convert the mixed radical to an entire radical wins the round.

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Entire to Mixed

The students flip over their top cards, and put them both under the radical. The first student to correctly simplify the radical or to identify that it can’t be simplified wins the round.

Photo 2-12-2014, 11 11 48 AM

 

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When I was in high school, I had a teacher who used something other than boring old “Name: __________” at the top of his tests.  He’d put things like, “Hello, my name is: _______” or “_____________ is going to ace this test.”

When I started teaching, I did the same thing.  The kids really liked it, and any time it left room for creativity, they did some neat stuff.  Over the years, I acquired a pretty long list of them.  Whenever I created a new test or handout, I would open up the document with all of them in it, and pick one.  Sometimes I asked students to write their own. There is nothing pedagogically brilliant about this.  It just amused me.

Here’s the document.

 

 

 

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October’s issue of the NCTM Mathematics Teacher magazine included an excerpt from an interesting article in their Media Clips section.  They used a Forbes article that dealt with tween earnings, and the portion they included is:

Hollywood’s 10 top-earning tweens collectively pulled down $107 million between June 1, 2007 and June 1, 2008.   According to Alloy Media and Marketing, it’s a rabid and often indulgent fan base: America’s 20 million kids aged 8 to 12 spend $51 billion of their own money annually and influence $150 billion more in spending by their doting parents. Tied for the top spot: Hannah Montana star Miley Cyrus and Harry Potter lead Daniel Radcliffe. The young talents each banked a cool $25 million in the last year.

I love this article for the questions it could elicit.  The problem with the Mathematics Teacher Magazine treatment of this is that it follows the article with 8 questions we are supposed to ask kids.  Teachers might see this, and defer to the questions provided, thereby missing a great opportunity.  I’d much rather show students the article, and have the kids decide what would be interesting to explore further.  There are lots of potential rate and ratio questions that could come from student exploration here.

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I saw this episode of Seinfeld a couple of days ago.  Now that my WCYDWT radar is finely tuned, I realized that it would be a good clip to show in a Math 10-3 class in the unit on rate and ratios.  I know it’s a little dated (who would use a Wizard now?), but it’s still one of my favorite shows.  Click on Morty to play the clip.

The one question kids need to ask will be apparent to them, but the math will be tricky for Math 10-3 students.  In the end, it’s still not a particularly compelling problem, but maybe this is a better way of presenting it to students.

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This morning, as I was making my toast and about to put peanut butter on it, I was reminded of something I did early in my career in a Math 31 (Calculus) class.  It was at least 15 years ago, and way before we had digital cameras or Dan Meyer, but I think it definitely qualified as a WCYDWT.

One morning in the early 1990s, I was having peanut butter and toast, and had gotten near the bottom of the jar.  While scooping peanut butter out, I got it all over the handle of the knife, my hand, and then of course, my pants.

It occurred to me that the jar really was taller and narrower than it should be, and in a rare moment where everything came together for me, I realized that the shape of the jar was probably significant and we just happened to be working on Maximization and Minimization problems in Math 31.  Since digital cameras hadn’t been invented yet, the only multi-media artifact I could take into my classroom was the jar itself.

So I took my jar of peanut butter into class, slammed it down on the table in front of the class, ranted for about 5 minutes about how mad I was at Mr. Kraft for getting peanut butter on my hand and pants, and then told the class that we wouldn’t be doing Calculus that day, because I had to write a complaint letter to Mr. Kraft.  I sat down at my desk, and pretended to write, and hoped.  It took a couple minutes, but then it happened.  One student said something like, “Mr. Scammell, there must be a reason it is made in that shape.”  Another jumped in with, “It’s probably the shape that uses the least material but still has 1 kg of peanut butter in it.”  Then they argued for a bit, and decided on their own to figure it all out.  They measured, calculated, argued some more, and then told me to write my letter, because you could hold 1 kg of peanut butter in a container that was wider and shorter so my hand wouldn’t get peanut butter on it.

Again, I pretended to write while I waited and hoped.  And then they extended.  One kid stopped the whole thing, and said that there must be a reason it was the shape it was.  He observed that the lid was thicker than the other plastic, and therefore must cost more.  They re-ran their calculations based on an estimate that the lid cost twice as much as the other plastic, and then concluded that the shape was logical if we assumed the lid cost more.  It’s too bad that this was all done years before the internet hit our schools, or perhaps we could have quickly researched further to find out costs and contact numbers for Kraft.

I tried the Peanut Butter Rant several more times over the years, with varying degrees of success.  Some classes got right to the one important question, while others took some prompting.

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I can’t believe I’m about to wade into the homework debate, but here goes.

When I became a consultant, they spent a great deal of time teaching me how to coach and facilitate.  One thing they taught me was to be up front about my assumptions and biases.  So here’s three pretty important ones.

  1. As a kid, I hated doing homework.
  2. As a teacher, I hated chasing kids to get their homework done.
  3. As a parent, I am learning to hate fighting with my kid to do her homework.

A few years ago, while tutoring a student, I came to the realization that most of the math homework we assign is a waste of time.  Her teacher had assigned her questions 1-15, parts a, c, and e.  She did 1a and knew how to do it.  I suggested that we move on to #2, but she was the kind of kid who did every question assigned, so she did 1c and 1e even though they were exactly like part a, but with different numbers.  It occurred to me at that point that I needed to look at how much and what kind of homework I was assigning.

I started paying more attention to which students were completing what homework assignments.  Some kids did it all, and some kids did none.  The problem is that the students who needed the practice, didn’t do the work, and the students who didn’t need the practice, diligently did every single question I assigned.

At about that time, some teachers in my department were complaining about how kids didn’t do homework.  I threw out the idea of just not assigning it at all to alleviate everyone’s (teacher, student and parent) stress.  That suggestion didn’t go over well.  In my classes, I consciously started giving less homework.  My thought was that if we assigned 4 useful questions and the kids did 3, we were way better off than if we assigned 20 rote practice questions and the kids did 6.

I also started differentiating my assignments.  Kids who needed practice got a manageable amount of practice.  Kids who needed deeper thinking got richer questions.  As a kid, I hated it when I got done an assignment, only to have the teacher give me more of the same.  I learned not to get done.  We do that to our strongest kids.  Instead of giving them better assignments, we just make them do more work, and because they’re good kids, they tend to do it.

Another change I made was to move away from giving my class practice time at the end of the lesson.  I tend to talk less than most high school math teachers.  In an 80 minute block, I try hard to keep lessons to no more than 40 minutes, so that kids have at least 40 minutes to work.  I used to give that work time at the end.  Kids were tired after a 40 minute lesson, and it was difficult to focus them on the practice questions.  I started breaking my lessons into smaller sections, so that I’d teach for 10 minutes, and then assign 2 question, then teach for 10 minutes and assign 2 questions, and so on.  By doing this, the kids really felt they had to do the questions, because it seemed like part of the lesson.  As such, I assigned far fewer questions at the end of the lesson.  Most kids had nothing to take home at all, which I felt good about, and I’m sure they felt good about.  More importantly to the people who will suggest kids need lots of practice to be successful, my student’s grades didn’t suffer by doing less homework.

If I get brave later on, I’ll add a post about how I feel about assessing homework.

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After attending a session on our revised curriculum by Dr. Peter Liljedahl, several teachers have told me that they have been inspired to spend the first week of Math 10 Combined on  establishing collaborative and problem solving practices in their classrooms.  Since we will be teaching math in a different manner than teachers and students are used to, it is important to create a safe environment in which students can explore and construct meaning through rich problems.

The idea that we will spend the first week on processes and exploration, rather than on checking off the first few curricular outcomes is frightening to some teachers.  Several have asked me what types of problems they should give students during that first week.  Below are three of my favorites.  They have loose curricular fit, but all allow for rich discussion, debate, exploration and invite multiple methods of solution.  The idea is to throw these out to students before any teaching has happened, and allow them to use any method they can to solve them.  Feel free to give me feedback, and share your own favorite problems.

Problem 1 Fred’s aunt is twice as old as Fred was when she was as old as Fred is now.  How old is Fred and how old is his aunt?

Problem 2 Three businessmen check into a hotel (in the olden days, when hotels were cheaper).  The desk clerk charged them $30, so they each paid $10.  Later on, the desk clerk realized he had made a mistake, and the room charge should only have been $25.  The desk clerk sent a bellboy up to the room with $5 change.  Unsure how to divide the $5 evenly among the three men, the bellboy gave each man $1 back, and kept $2 for himself.  Now each man has paid $9, for a total of $27.  The bellboy has $2 which brings the total money up to $29.  But the men originally paid $30.  Where is the missing dollar?

Problem 3 – The Jail Cell Problem In a prison, there are 100 cells numbered 1 to 100.  On day 1, a guard turns the key in all 100, unlocking them.  On day 2, the guard turns the key in all the even-numbered cells, thereby locking them.  On day 3, the guard turns the key in all the cells numbered with multiples of 3, thereby altering their state.  For example, if the cell was unlocked, he locks it.  If it was locked, he unlocks it.  On day 4, he turns the key in all the cells that are numbered with multiples of 4, thereby changing their state.  He continues this process for 100 days, at which time all the prisoners in unlocked cells are set free.  Which prisoners are set free?

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Eric Mazur is a Harvard Physics professor.  I came across this video when somebody posted it on Dan Meyer’s blog in response to another person who was demanding data to prove that Dan’s methods would work.  Professor Mazur has data to prove the merit of his shift from being a lecture style instructor to an instructor who facilitates peer teaching.  Peer teaching is definitely a strategy we could employ in our revised curriculum in Alberta.  If a University Physics professor can facilitate learning without having to tell his students everything, then certainly a high school math teacher who wanted to teach for understanding could emulate this process.  This video is about 80 minutes long, but is worth the time if you can spare it.  For those who can’t, I’ve summarized the key points below.

The reason that Professor Mazur switched his style was because his students were not showing gains when he compared pre-test results to post-test results.  Despite going through an entire term of his lecture style physics class, students could not show a significant improvement in their understanding of basic physics.

His Key Messages:

  • Students who have recently learned something are better at explaining it to other students than a teacher who learned and mastered it years ago. It is difficult for a teacher who has mastery of a concept to be aware of the conceptual difficulties of the beginning learner.
  • Give students more responsibility for gathering information and make it our job to help them with assimilation.
  • You can’t learn Physics (or Math or anything) by watching someone else solve problems.  You wouldn’t learn to pay the  piano by watching someone else play.  You wouldn’t train for a marathon by watching other people run.  If you want to learn problem solving, you have to do the problems.
  • Better understanding leads to better problem solving.  The converse of this statement is not necessarily true.  Better problem solving does not necessarily indicate better understanding.
  • Education is no longer about information transfer.
  • He says that in his original methods he covered a lot, but the students didn’t retain much so the coverage was basically meaningless.  In his new method, he has relaxed the coverage a little bit, but increased the comprehension enormously.

The Peer Instruction Process

  • Students pre-read the lecture notes or text.
  • Class is then used for depth, rather than coverage.
  • Depth is attained through what he calls a concept test.

The Concept Test:

  1. A question is posed.
  2. The students think silently about the question for a minute or so and it must be completely silent in the class.
  3. Students answer individually and vote by show of hands or by SMART Response systems.
  4. Peer discussion.  Defend your answer.
  5. Revised group answer.
  6. Explanation

Then he will “lecture” for a couple of minutes, and repeat the process with his class.

Benefits of his process:

  • This process promotes active engagement.  “It is impossible to sleep through class, because every few minutes, your neighbor will start talking to you.”
  • He can continually assess where his students are.

Challenges:

  • Teachers have to find the right questions to ask in their classes.
  • Students will write on their evaluations that professor Mazur isn’t teaching them anything and that they have to learn everything themselves.

My take on all this:

I see this process as being one we could employ in our high school classes.  I don’t think we’d expect kids to pre-read sections of the textbook, but we could certainly present problems to them in this manner and allow them to explore and construct solutions without having to tell them so much.

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