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Archive for the ‘Student Engagement’ Category

When Dan Meyer launched his 101qs.com website in March, he invited people to upload first acts. I interpret Dan’s definition of first acts as compelling videos or photos that lead to perplexing mathematical questions. The idea of 101qs.com is for people to upload their first acts, and the other users will post questions if they are perplexed. If they are not perplexed, they skip it and move on. Each first act ends up with a perplexity score.

I spent a lot of time on the site in the past week, and have now seen every single first act that has been posted. I entered my question for those that perplexed me. I skipped those that didn’t. After all that work, I have some observations and questions.

Observations

  1. What perplexes me doesn’t necessarily perplex you. This is my lowest scoring one. It’s busy. It’s text heavy. It’s cumbersome. And I’m totally hooked. I really want to check this guy’s math. Dud.
  2. On 101qs.com, there are numerous similar examples of things that people found perplexing enough to upload, only to discover that the community of reviewers doesn’t agree. I wonder if perplexity relies at all on the presentation. I’m sure Dan would prefer that these things stand on their own; that the photo or video need no explanation or prompting. I am confident, though, that I could sell my dud in #1 to a group of students and get them perplexed. I am confident that Statler Hilton could sell this one to a group of kids with the right presentation.
  3. Videos need to hook me fast. I have a short attention span that way. Apparently other people feel the same. This one is brilliant. Why it doesn’t have a higher perplexity score is befuddling me.
  4. If I can’t tell what I’m looking at in the photo, I’m not perplexed. I’m confused. I wonder what the uploader wanted me to notice. That’s not perplexity. That’s teacher pleasing.
  5. Simple is good. This one fascinates me.

Questions

  1. Where does this go from here? Do we sort by course or topic related to the mathematics we anticipate students doing in Act II? Do we link them to Act II and Act III resources? What’s next, Mr. Meyer?
  2. How do students react to these? Do they find the same ones perplexing that their teachers do? Some of the ones I have used with great success with students are not receiving the highest perplexity scores on 101qs. This one and this one have gone over very well in the classrooms in which I have tried them. Only one of them lives in the current top 10 on the site.

Pre-Emptive Reply to Your Comments

I know. If we have to sell it, it’s probably not perplexing enough.

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@dandersod posted the following video on his blog last week.

He asked, of course, What Can You Do With This?

I decided that there was a lot I could do with it, so I worked on some editing of the video, and then I rolled it out with a group of teachers this morning to see where it would go.

Before I describe the lesson, I should point out that my first edit of the video involved crossing out some of the measurements the original video contained, as well as beeping out the commentary that mentioned the measurements.  I was limited by my video editing skill, and the software I was using. It ended up being awkward and kind of annoying, so I re-did it simply by deleting the parts I had originally wanted obscured.  The new video was much cleaner, and it had the extra benefit of not being so obvious about what I wanted students to explore.  With the beeps and blocked out numbers visible in the first edit, it was painfully evident what I wanted people to find.  The second edit allows for many more directions to be taken in the exploration, and it’s not even obvious that I have deleted anything.

Here was my lesson plan.

  1. Provide each group a ruler and a 60 g bag of gummy bears.
  2. Play the question video.
  3. Ask the students what they wonder about after seeing the video.  In this edit, they will wonder about a whole bunch of things.  I’m hoping they get to, “How many small gummy bears are equivalent to the giant bear, and what are the  dimensions of the giant gummy bear?”
  4. Elicit guesses, lower bounds, and upper bounds of reasonable answers.
  5. Ask them if they need any clarification or information that might help
  6. Turn them loose.
  7. Work the room.  Help those who are struggling.  Provide extensions for those who hammered through it.
  8. Have students share their answers.  They will be all over the place here.  Those that work with the calorie count will be closest to the “right answer”.  Those that worked with the mass will be a bit farther out.
  9. Play the answer video.
  10. Discuss discrepancies.  Is it measurement error?  Problems with the calculations?  False advertising?
  11. Eat the gummy bears.

The lesson is fun, engaging, and has great curricular fit to Alberta’s Math 20-2 course in the measurement and proportional reasoning units.

At step #3 above, some members of the group I was working with really wanted to go a different direction.  Their suggestions became cool extensions for those that got done quickly.

  1. How tall is the man in the video, who is the same height as the gummy bear from 30 feet away?
  2. How many times would you have to walk around the school to burn off the giant gummy bear?

Enjoy

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Thanks to this post on Dan Meyer’s blog, and an ensuing conversation between Dan and Curmudgeon, I was pointed to an article that I think would make a pretty compelling problem in Math 10C or Math 10-3 measurement.

The article describes a 17 year old driver who was given a $190 ticket for going 62 miles an hour in a 45 mile an hour zone. His parents, however, had installed a GPS system in his car to track his speed and driving habits, and they claim the GPS proves their son was only going 45 miles an hour at the time the ticket was issued. It appears to have taken two years of legal wrangling, before the ticket was finally upheld, and he had to pay the fine.  I wouldn’t tell the students that yet, though.

Here’s a link to the article: Speeding Teenager

Lesson Plan

1.  Present the problem.

Give the students the following excerpt from the article:

Shaun Malone was 17 when a Petaluma police officer pulled him over on Lakeville Highway the morning of July 4, 2007, and wrote him a ticket for going 62 mph in a 45-mph zone.

Malone, now 19, was ordered to pay a $190 fine, but his parents appealed the decision, saying data from a GPS system they installed in his car to monitor his driving proved he was not speeding.

What ensued was the longest court battle over a speeding ticket in county history.

In her five-page ruling, Commissioner Carla Bonilla noted the accuracy of the GPS system was not challenged by either side in the dispute, but rather they had different interpretations of the data.

All GPS systems in vehicles calculate speed and location, but the tracking device Malone’s parents installed in his 2000 Toyota Celica GTS downloaded the information to their computer. The system sent out a data signal every 30 seconds that reported the car’s speed, location and direction. If Malone ever hit 70 mph, his parents received an e-mail alert.

Malone was on his way to Infineon Raceway when Officer Steve Johnson said he clocked Malone’s car going 62 mph about 400 feet west of South McDowell Boulevard.

The teen’s GPS, however, pegged the car at 45 mph in virtually the same location.

At issue was the distance from the stoplight at Freitas Road — site of the first GPS “ping” that showed Malone stopped — to the second ping 30 seconds later, when he was going 45 mph. Bonilla said the distance between those two points was 1,980 feet.

2.  Ask the students to discuss the article.  In the end they will come to the question we want explored.  Was young Shaun guilty of speeding?

3.  Let them answer the question.  Have them prepare a defense for Shaun, or an argument for the prosecution.

4.  Show them the Commissioner’s conclusion, based on mathematics.

Bonilla said the distance between those two points was 1,980 feet, and the GPS data confirmed the prosecution’s contention that Malone had to have exceeded the speed limit.

“The mathematics confirm this,” she wrote.

Teacher Resource

A possible solution

An extension, eventually.

I have been attempting to contact the person mentioned in this local article, but so far he hasn’t responded to me.  Similar mathematics could prove he wasn’t driving as excessively fast as the red light camera claimed, but I would need to get a copy of his ticket to show that.

Red Light Camera

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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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I got this idea from a teacher I marked diploma exams with a couple of years ago.  I’d love to credit him, but I can’t remember who he is.  This is a WCYTWT submission, or as I like to call it, WWDDWT (What Would Dan Do With This).  I used it with a couple of classes last year, and they really enjoyed it, but I used it poorly.  I did it at the end of a unit on Permutations and Combinations, so the students knew exactly what to do with it.  It wasn’t truly a problem, because they knew exactly how to solve it when I gave it to them.  I should have used it on day one of Permutations and Combinations, and let them invent the fundamental counting principle on their own.

Mozart’s Dice Game


Mozart is credited with creating a dice game, whereby you roll a pair of dice 16 times to select 16 measures to insert into a minuet section, and then a single die 16 times to select 16 measures to insert into a trio section.  For example, if you roll a 6 for the first measure, you consult a chart to see what measure number to insert into the first measure of your minuet, and so on.  The idea is that no matter what you roll, you always produce a minuet that fits whatever rules go along with a minuet.  This site explains it in a little better detail.  Mozart’s Dice Game.

WCYDWT

You give the students the history, and then you throw this site up on the SMART board.   Play Mozart’s Dice Game has a chart that looks like this:

The drop down menus let the students enter numbers that they roll on dice, so give the kids some dice, and let them enter their rolls.

Notice the link below the chart that says “Make Some Music!” Once the students have all entered their rolls, you click here and the newly created minuet will play.  There’s even a “Generate Score” link below the media player that lets you generate the score for the minuet they created.  My students loved this, and printed theirs off to try to play it on the piano themselves.

After the minuet plays, you tell the kids that even though this was written more than 200 years ago, you are pretty sure that nobody has heard the particular minuet the class just created ever before.  Ask them to discuss this statement.  They’ll say things like, “Why, did they lose the score until recently?” and dance around it until one kid finally asks, “How many minuets could be made in this game?”  Then you’ve got them and you let them play around with it.  They will invent the fundamental counting principal, determine that there are an incredibly large number of possible minuets, and even create their own interesting extensions.

One student even came in the next day with an iPhone app that generates minuets using Mozart’s Dice Game.  The only  problem with the app is that it only randomly generates minuets, and doesn’t allow you to enter your own rolls.

Update: March 11, 2016

My greatest fear was realized. The site I talk about above is no longer functional. Something about Midi Files, Flash players, and the like. I couldn’t get it to work in any browser.

I found a functional site. https://www.mozart-game.cz/

It randomly selects the measures to play, as highlighted below. You can play your own measures by clicking on the un-selected ones, so you could still have your students roll dice and create their own minuet, but you’d have to click your way across the chart. If you can keep time, it’s pretty easy. The vertical columns represent one roll of a pair of dice. So if the first roll was a 2, you’d play measure 96. In the screen shot below, the first roll was 3, the second roll was 6, and so on.

 

Mozart


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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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