cheesemonkey wonders

cheesemonkey wonders
Showing posts with label complex numbers. Show all posts
Showing posts with label complex numbers. Show all posts

Friday, August 22, 2014

WEEK 1 - PROJECT 'MAD MEN' -- Classroom Rules PSA Skits

Leonard Bernstein once said, "To achieve great things, two things are needed — a plan and not quite enough time." I decided to put that principle to the test this first week at my new school by assigning a project on Day 1 that thew together strangers with an absurd but achievable goal: given a particular classroom rule or guideline, create a Public Service Announcement  (i.e., a 30-second "TV commercial" in the form of a skit) whose purpose was to motivate viewers to follow the rules/guidelines for the good of the group.

I created a set-up, instructions, and a rubric for the group project. And my students did not disappoint.

The idea was to get students to think about the consequences of their actions and choices, but their ideas for implementation exceeded even my wildest dreams. Most skits followed a "slice of life" strategy, but the ones that really blew us all away were the ones that parodied existing campaigns.

Two brilliant PSAs started from already-iconic Geico insurance commercials, but the one that left me with tears running down my cheeks was a take-off on Sarah McLachlan's ASPCA spots. The song, "In the arms of the angels..." began playing, and student "Sarah" appears onstage making the exact same kind of appeal she makes in those ads. They had the tone, cadence, and music exactly right, and they clearly understood the emotionally manipulative rhetorical strategy — the seemingly endless list of forms of ignorance designed to eventually provoke self-recognition in almost everyone. Their "mathematical justification" was as follows: the narrator enters and says, "In the past year alone, texting in class tragically cost 5 of Doctor X's students their lives. Remember, think twice before texting in class — there may be fatal consequences for your grade, and for you!

It was pure and inspired genius.

I also loved the spot-on impressions of my teacher persona. One student gave a pitch-perfect parody of my "Function Basics" talk that made me both cringe and laugh my ass off simultaneously.

The best thing about this assignment was that it really pushed the voice of authority downward, into the student community itself. Whatever they made of the experience, they owned it.

I am going to try and remember this for later in the semester, when we've become too routinized.

This is definitely going to be an ongoing part of my repertoire of Day 1 activities. I got through what I neded to,  then gave them the rest of the abbreviated period to collaborate. The time pressure was a thing of art.

It was perfectly imperfect — exactly the way first days ought to be.

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UPDATE:

Here is the link to a generified Word document that you can customize for your own class:

PROJECT MAD MEN- classroom rules PSA generic.doc

And here are the three sample 30-second PSAs I showed my classes to give them ideas:

'You Lost Your Life!' – game show hosted by the Crash Test Dummies (Since Vince & Larry, the Crash Test Dummies, were introduced to the American public in 1985, safety belt usage has increased from 14% to 79%, saving an estimated 85,000 lives, and $3.2 billion in costs to society)
'
What could you buy with the money you save?' - throwing things over a cliff (You could purchase TVs, bicycles, and computers with the money most families spend on wasted electricity)
'Five Seconds' – at highway speeds, the average text takes your eyes off the road for 5 seconds (Five seconds is the average time your eyes are off the road while texting. When traveling at 55mph, that's enough time to cover the length of a football field)

Saturday, February 8, 2014

Arithmetic of Complex Numbers Placemat Activity - Algebra 2 + Complex Instruction (CI)

Just because you have an all-groupwork and all-Complex Instruction (CI) format doesn't mean you don't need practice activities too.

Our Algebra 2 kids were getting the concepts of complex numbers and complex conjugates, but were still kinda shaky in terms of fluency in working with them.

Based on ideas I stole borrowed a long time ago from the fabulous Kate Nowak (@k8nowak, http://function-of-time.blogspot.com) and the equally fabulous Rachel Kernodle (@rdkpickle, http://sonatamathematique.wordpress.com ), I proposed a placemat activity to my ever-game Algebra 2 teaching team and they dove right in.

Set-Up
We have typical CI four-person table teams set up in each of our rooms, with each person assigned a specific role based on where they're seated at the table. Our roles are Facilitator, Resource Manager, Recorder/Reporter, and Team Captain, although of course, your mileage may vary. Each role has specific tasks they are expected to perform; for example, only the Resource Manager may call the teacher over for a group check-in or a group question (in our program, teachers only accept and answer group questions).

Each table was given:
  • two, double-sided "placemat" sheets for doing work in the center of the table
  • a set of problem cards (there are four sets, one for each round of play; to simplify clean-up and organization, I printed each round of cards single-sided on a different color of paper, one set per table group. I've got 7 tables in my room, so I made seven sets of cards. I laminated them and clipped them together, but hey, that's just me)
  • the sum to which all four answers for any given round should add up
The sum for each round was written on the whiteboard, though it could have been projected via document camera or Keynote/Powerpoint slide.

Objectives
We had mathematical objectives for the activity as well as CI or norms-based, group work objectives. My students in particular needed reinforcement in group work norms and collaboration. Our objectives were:

     Math Objectives

  • achieve greater fluency in the arithmetic of complex numbers (including the distributive property)
  • deepen understanding of and fluency with the powers of i
  • deepen understanding of and fluency with complex conjugates

     Group Work Objectives

  • work in the middle of the table
  •  same problem, same time (no one moves on until everyone moves on)
  • using table group members as resources

The next time I run this activity, I will definitely give a Participation Quiz because the group work norms are so beautifully reinforced in this activity.

How We Ran It
Recorder/Reporter writes the sum in the central oval of the first side of the placemat. Each group member gets a problem card for round 1 (problem a) and works his or her problem on his or her quadrant of the placemat.

When everybody is finished with their problem, the Facilitator facilitates the addition of all four answers. If they add up to the given sum for that round, the Resource Manager calls the teacher over for a "checkpoint" and the next set of cards for the subsequent round of work.

If their answers don't add up to the given sum, they need to work together through everybody's work on the placemat to diagnose what went wrong and where, as well as how to fix it. Then when they've fixed it, they call the teacher over for a checkpoint and the next set of cards for the subsequent round.

Group Work Benefits — Reinforcing Norms
For my classes, the greatest benefits of this activity came from the fact that it forced students to work in the middle of the table, to use each other as resources, and to talk mathematics. Getting kids to work in the middle of the table is the hardest part of CI, in my view, because it goes against the grain of most of their in-school conditioning. The placemat format makes it nearly impossible NOT to work in the middle of the table. And once they're doing that, it seemed like everything else ran pretty smoothly.

I especially liked the fact that this activity created a context in which students experienced an intellectual need for the using the rules of arithmetic for complex numbers and for the powers of i. It was situationally motivated, but extremely targeted.

Sums for Each Round 
The sums for each round are as follows (if you find an error, please speak up):
  • Round 1 (problem a):   26-73i
  • Round 2 (problem b):  0
  • Round 3 (problem c):  165
  • Round 4 (problem d):  2 – 48i
PDF Files for the activity
These are available also on the Math Teacher Wiki on the Algebra 2 page. If you haven't visited the Math Teacher Wiki, you don't know what you're missing.