Video Error Analysis (Anti-Khan style)

Something I tweeted this week:

@TUSDconnect HS Alg. class doing error analysis w/ teacher-made videos: making predictions, discussion, corrections. pic.twitter.com/9Tlpd6rLmP
— Andrew Stadel (@mr_stadel) November 24, 2014

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 ink. Style 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

Number Sense Conversations

I've put the elevator speeches to rest. Today's two minute speech went well... I think. As one event concludes, I'm excited to resume my ongoing thoughts about number sense and students.

Working with teachers and students, I can't help but be inundated with thoughts about things I miss, look forward to, and will be challenged with this year in and out of the classroom. However, there's one thing I crave more than anything else, and that's working with students, which usually entails having number sense conversations with students.

Today, I had rich number sense conversations with students in Math 7, Math 8, and high school Algebra classes. As I sit here and put the finishing touches on the slides for my upcoming conference workshop, Get Students to Argue in Class With Number Sense Activities, I can't put to words how valuable it is to allow students to talk about math in math class. That's an oversimplification, but we seriously need to provide our students with opportunities to talk to each other, even argue with each other. Mathematical Practice 3:

Construct viable arguments and critique the reasoning of others.

Steve Leinwand sums it up best:

These nine words may be the most important words in the entire Common Core effort. 

Last December at CMC North, I was honored to give an Ignite talk about something I'm passionate about: number sense and student conversations. It's titled: Number Sense: I Don't Like This Game Anymore.

Students are hungry for number sense conversations in math class. I really do believe. If you don't believe me, just put up this picture in your class and ask your students, "How long would it take to use all of that?" Then ask them to convince you of their conclusion.

As October quickly approaches, I look forward to seeing you at an upcoming conference this school year. In the meantime, I hope to post more about number sense.

Number Sense,
1005

DLC

The first day of school is this coming Wednesday. I've never been two days away from the start of school and done so little preparation. It's weird. It's really weird. Here's why:

I won't be:

• greeting students at my door
• having students estimate my height
• having students estimate the total class' height
• passing out papers with school/class procedures
• setting up grade books
• making seating charts
• hanging up stuff in my room
• preparing for back to school night
• preparing homework, notes, photocopies, etc.
• sharing with my students the math I saw during the summer

My favorite vacation #estimation180 moment from this week. pic.twitter.com/KIBI8uUjYk
— Andrew Stadel (@mr_stadel) August 16, 2014

Admittedly, I won't terribly miss items four through nine. However, the first three and the last always hold a special place in my math heart.

I'll be one of about fifteen Digital Learning Coaches (DLC) in my district this year. I'll be supporting 8-10 middle school math teachers who volunteered to be a DLC Fellow. Together, we'll be finding ways to integrate technology in their classrooms to meet the needs of their students while providing powerful learning experiences. Every time I look at technology or think about implementing some program, application, or digital tool, I look to ask myself (and the teacher), "will this [digital tool] be a more effective and efficient way for student and teacher to learn mathematics, gather data, assess understanding, or communicate?"

I will be:

• frequently in the classroom with students and teachers (thank goodness!)
• listening to teacher needs, desires, and goals
• building relationships with students and teachers
• building number sense with students and teachers
• having (mathematical or non-mathematical) conversations with students and teachers
• developing/designing lessons
• teaching (co-teaching or modeling), if necessary
• sharing many of the wonderful resources from you (the MTBOS)

I know I will miss the classroom and having my own students. However, I look forward to designing lessons and testing them out on different students throughout the district.  I look forward to learning so many things from both the teachers and students. It'll be an extreme pleasure, honor, and learning experience for me to be working alongside so many different teachers and students.

DLC,
249