Friday, November 28, 2014

Video Error Analysis (Anti-Khan style)

Something I tweeted this week:
Crystal (colleague) and Lynda (fellow) wanted to know more about this. So here's the story:

The previous week, I met with one of my high school fellows who teaches Algebra to freshman. As with all my fellows, it's been an extreme pleasure to work with her because she's hungry for ideas and will take suggestions and run with them. It was so cool to walk into her class this past week and see her running with an idea, again.

She had already taught her students ways to solve linear systems; graphically, substitution, elimination, etc. On this day, she prepared six short videos of her solving linear systems and linear inequalities using Educreations on her iPad. Students were to watch the videos and do error analysis, reporting the following on their handout:
  1. Identify the mistake(s) for each question.
  2. Explain what should have been done.
  3. Fix the mistake and complete the question correctly.
Each video was between 60 and 90 seconds in length. We both discussed what we thought would be most effective for her students and short videos was a must. Have you ever noticed how the majority of Khan videos can be extremely lengthy? Sal Khan usually talks (and repeats himself) while writing things on his digital blackboard. To me, that's a waste of someone's time. It's like you watching me type this blog post while I reread every sentence two or three times, stalling so I can finish typing. Another thing I can't stomach in Khan videos is when he fumbles around searching for colors to write with. Lastly, I find it unfortunate that the videos rarely suggest the viewer to pause and consider what's happening. Here's an example. Sorry, here's a 9+ minute example:

I suggested my fellow pause the recordings often and write the equations "offscreen" when not recording. Then, press record again when she's ready to talk and/or write something important on her screen. She also took advantage of this offscreen time to select different colors in order to emphasize different equations, steps, lines, or shading (linear inequalities).
*See the video structure below with suggested notes and style points.

It took my fellow one prep period on a minimum day to create six videos, a supplemental handout, upload the videos to Educreations, and create hyperlinks on her Haiku page for students to access all the videos. That's super impressive. Talk about an activity with meaningful and HUGE return from an efficient investment in her prep time.

When debriefing with my fellow after class, she was completely ecstatic.
I asked her, "What elements made this awesome?"
She replied:
  • it was video and new
  • they liked figuring out someone else's mistake
  • the videos were short
  • students could pause, rewind, and start the video over
  • using Desmos to show a graph of the original equations at the end (comparison)
  • gave students the idea to use Desmos to check their work/answer
  • self-pacing
  • very little hand-raising or students drowning
  • the videos were easy to make
  • she passed out the handout and said "go" instead of modeling
  • the handout had a simple structure 
  • the students did most of work, not the teacher
I love this last element the most. The two of us talked about this specific element the previous week. Now she experienced it first-hand and it's an amazing feeling. As an observer, it was awesome to see the students working hard on a meaningful task and helping each other out so it allows her, the teacher, opportunities to calmly circulate and provide support where necessary.

Student engagement and interest were high. Discussions were plenty and authentic. Students were thriving using thinking skills in the "Analyzing" category of Bloom's Taxonomy or Strategic Thinking category of Webb's Depth of Knowledge. Here's a tip I suggested when I noticed some kids plowing through a video and hadn't caught the mistake: pause and make predictions. The video structure will explain pausing and predicting more.

Video Structure:
Part 1: She takes about 8 seconds to explain her plan
*All of this was written on the screen prior to her pressing record. Style points.

Part 2: Multiply the top equation by (-5) in order to eliminate the x-terms

*Here's where we need to ask students to pause and predict what the top equation will look like after being multiplied by (-5).
  • Model this for students.
  • Build "pause and predict" prompts into the video. 
  • Circulate the room and ask students to pause and predict.
SO valuable. Don't skip "pause and predict".


Part 3: Write the new equations "offscreen". Don't record yourself writing these equations.
*Notice the new equation is written in red inkStyle points!
**Pause and predict what it will look like when combining the equations
***Catch the mistake?

Part 4: Combine the two equations.
*Another great use of "offscreen" writing.

Part 5: Find the value of y.

Part 6: Substitute the value of y into one of the original equations.
*Yet, another use of "offscreen" writing here.

Part 7: Solve for x this time.
*Ask your students to check for reasonableness.
**Find an alternate way to validate (or invalidate) their conclusion.

Part 8: Insert a screenshot of the system graphed in Desmos.
*Mind grenade: the graph doesn't match the algebraic procedure.
**HUGE style points by inserting a visual representation of the correct answer.

For those of you who don't have 1:1 devices in your schools, no sweat. I still recommend you make a video of some sort. Borrow an iPad from someone. Create an Educreations video for error analysis. Use the tips and techniques mentioned here. Your videos should be less than 90 seconds. Play it to your class. Pause the video to have students make predictions and/or discuss possible errors. I guarantee you, good things will happen.

Style points,
1209


Tuesday, November 11, 2014

#PuzzleMath ideas

Tonight, my son wanted me to work with him on his new puzzle.

I don't know your strategy for doing puzzles, but I find all the corners first and then start putting the border together before I start working on the inside. Look at that box again. Would you be able to determine the dimensions (in puzzle pieces) of this puzzle by knowing the total number of pieces?

That was my first question:
A) If you know the total number of puzzle pieces, could you think of the all the possible dimensions (in puzzle pieces) of the puzzle?

Answer:
This puzzle will either be a 1x35 or 5x7.

Then came the next question:
B) Estimate the actual dimensions (in puzzle pieces) given the picture on the box?

Answer:
I'm going to go with 5x7 because five and seven are the only factors of 35 that would reasonably make the rectangular picture on the front of the box. The puzzle should be 5 pieces high and 7 pieces across from left to right.

With a box of 35 pieces, these questions aren't too ridiculously challenging. However, I know there are crazier puzzles out there in the world; puzzle with 500, 750, 1000 pieces, etc. That's where I called on Twitter to help out. Like a champ, the #MTBoS came through and hopefully will continue to come through with #puzzlemath.

Below are some of the tweets I received followed by additional math questions I'm curious about.






Additional Questions:
C) If you think you know the dimensions, could you determine:
  • The number of corner pieces
  • The number of border (non-corner) pieces
  • The number of inside pieces
If so, could you write a rule for any of these?

D) Knowing these quantities, say you randomly choose a puzzle piece, what are the chances it's:
  • A corner piece
  • A border (non-corner piece)
  • An inside piece
  • The exact center (if possible) piece
Please add to the collection of puzzles and questions by tweeting with the hashtag #puzzlemath.

Puzzlemath,
1050

Roofs Are Expensive!

Today is Veteran's Day. If you personally know a veteran, say "thank you" to them somehow: call, email, text, or in person. If you don't know a veteran, then ask a friend if they know a veteran and if they do, ask them to say "thank you" on your behalf.

Because today is Veteran's day, my district isn't in service today. Therefore, I was able to sleep in a few minutes longer today. I woke up to the sound of this pitter-pattering on the roof of our house. Not five minutes later, my 4.5 year-old son walks into the room and says he hears something that woke him up. I wonder what? Ha.

He climbs in bed with me and I ask him if he knows what the sound is. I proceed to tell him the sounds he hears are birds walking around on the roof hitting the roof with their beaks. When we moved into our house, there was a fake owl tied to our roof. Supposedly it keeps birds away. Not too sure it's all that effective, but we keep it up to have an occasional laugh.

My son thinks that the birds might start to ruin the roof and that we'll have to replace it.
Son: That will probably cost more than $100 to fix.
Me: How much more?
Son: Probably like one-hundred, one thousand dollars.
If you read my Pumpkin Seeds post, you know that his vocabulary includes a thousand now which is the biggest number he currently "knows". I use "knows" very loosely.
Me: Oh, I see. Well, which number is bigger? One hundred or one thousand?
Son: One thousand!
Me: Right. So we say the bigger number first, like this, "One thousand, one hundred."
Son (whispering to himself): One thousand. One hundred.
Me: That's a lot of money.
Son: Maybe one hundred twenty?
Me: Oh, so that's smaller than one thousand, one hundred.
Son: I KNOW! TEN THOUSAND!
Me: How do you know?
Son: Well, we have a big roof. We would need a lot of wood. We'd have to go to Home Depot and get all the things. 
Me: So we can buy all the things from Home Depot?
Son: Yes.
Me: And then would we put the roof on by ourselves or have some worker-men do it for us.
Son: You and I can do it Dad.
It dawns on me. Geez, I hope it's not $10,000. That's a lot of money. At the same time, I'm glad my son doesn't know the concept/magnitude of "A million" yet. Regardless, I have no idea what a new roof might cost, let alone how to put a new roof on. But maybe I'll save a lot of money on the labor because I have a 4.5 year-old son extremely willing to climb on top of our house and help install a new roof.

Roofing,
1023

P.S. I'm enjoying these conversations and posting about them.
Today felt like Mathematical Practice 4 with my son.