Thursday, July 16, 2015

Turning 3 Challenges Into 3 Charges

My next three weeks are slammed with opportunities, via conferences and teacher trainings, to work with fellow teachers, learn from them, and share resources and thoughts about what I'm most passionate about in math education. The great thing about this two-way learning environment is that it will make me even stronger and better equipped for the upcoming school year as I support my fellows in their classroom.

If we're at the same conference or teacher training, you will be hearing me drive home the importance of the following three challenges we face as teachers of students and students of teachers:
  • Problem solving
  • Student thinking
  • Number sense
  • Why are these three challenges so important?
  • Why am I so passionate about lesson design and tech tools that meaningfully support these three challenges?
  • What resources are available to teachers to support students?
  • How do we implement said resources to support problem solving, student thinking, and number sense?
At the end of our time together during a workshop or conference, I hope you become better equipped with strategies, tools, resources, ideas, and inspiration to make them your charges for the upcoming school year.

Thanks in advance for letting me be part of your valuable PD time and for allowing me to absorb your insight and knowledge at the same time.  


Sunday, July 5, 2015

Open House: Week 1, Day 2

Last week was the first week of a four-week summer academy. I teach a 110-minute class, four days a week, and it's designed as an enrichment course: no homework, no tests, no grades. The class is titled Get Ready for Algebra and here's the working schedule for the four weeks.

It's a great opportunity for me to practice some of my skills; skills I once possessed and skills I learned this past year, but didn't practice enough. Initially I thought I'd be keeping some of my skills sharp, but I soon found out how rusty I am at various moves, ranging from facilitation, to instructional, to questioning. How do I know, I recorded three of the four days last week.

Before I break down an 8-minute video clip from the second day, I want to be clear:

1) It's Open House everyday in my classroom. Anyone is welcome at anytime. I observed so many teachers this year and am extremely grateful for the opportunity. I learned a lot by being an observer. Being an observer allows me to reflect on my own practices, not necessarily the person being observed.

2) Recording my Open House classes allows me to identify certain skills and improve them.
These are NOT self-fulfilling, self-righteous, self-absorbed, self-promoting attempts at my own teaching. If I am to encourage other teachers at video-recording their teaching in the name of professional development, I need to do it too.

3) What professions record themselves (or other professionals) as a means to strengthen their craft? I recently tweeted some professions that benefit from recording their craft, ranging from athletes to musicians to dancers to doctors to comedians to teachers. You can only get better, right?
4) I need to be vulnerable, humble, and open to improve. I intend to keep my video clips to segments shorter than 10 minutes. I picked a specific part of the class I wanted to focus on improving. Even if no one else sees your video, I hope you'll prop up a camera in your room and record 10-15 minutes of your class. Play it back and reflect. Go in the next day and make those changes (improvements) you want to make.

5) One more time: These are NOT self-fulfilling, self-righteous, self-absorbed, self-promoting attempts at my teaching. Nor do I pretend to be perfect at this stuff. I just know I can be better and video recording helps immensely. If you have the stomach to continue, you'll see my notes as I reflect on my facilitation of this Estimation 180 challenge: my wife's height.


I ask the class to share a "too low" for Mrs. Stadel's height.
I try to get the class' attention about writing down 4'10" and how it's confusing... because I know students typically write feet and inches using decimal notation (4.10).

Here's what I wish I did (or could have done):
If I had done a better job of checking student work while they're working, I would have known how the student wrote 4 feet 10 inches on her paper.
I wish I asked the student how to write 4 feet 10 inches on the whiteboard.
I could have had the student write it up on the board while all the students were working.
I should have asked her why 4'10" was a reasonable "too low".
Having her share her reasoning would strengthen her voice and mine at the same time.

I received 7'10" from another student for the "too low" and asked "Is that taller than me?"
Like the previous student, I should have asked her to share her reasoning.

"Did anyone put 6'4" as their 'too high'?"
I need to capitalize on why 6'4" would be an extremely reasonable "too high".
Five students raised their hand on camera and I remember about two others students (off camera) raised their hand as well.
I should have followed up with at least one of these seven students as to why 6'4" makes sense here.
*I usually do this... argh.

"Don't share with me, share with your neighbor. Share with your group."
Why did I not say, "I would also like you to explain your reasoning behind your answer."
This would have also bought me an extra minute to check in with at least one more student. When checking in with students, I typically have them rehearse on me so I can encourage them to share whole group in a few minutes.

I began to take four estimates.
"I'm totally forgetting something."
I forgot to introduce the idea of students filling out their number lines.

I like the idea of the class filling out the same number line together on the first estimation challenge.

I explain that it's a common student misconception to put their estimate right smack in the middle of the number line, even if it's wrong.
Instead of being abstract in my explanation, I could have been more concrete by showing them an example. Let's say a student thinks Mrs. Stadel is exactly 5 feet tall (5'0"), they would still put there answer right smack in the middle. I should have put 5'0" in the middle.
Ask students: What's wrong with this?
Ask students: How can we use this number line more accurately?

I was truly lucky to get a difference of three feet between 4'10" and 7'10".
I didn't explain my thinking to students: I knew it was three feet, but didn't explain that I knew that half of 3 feet is one and a half. I should have modeled my thinking for students.

"For time reasons, I'm going to help you out"... look at me, the clock watcher. Am I really helping students out? I feel more like I'm helping me out by bailing them out. For about a minute, it's me doing the math, not the students.

How silly of me, I could have simply marked 5'10" and 6'10" on my number line breaking the distance between 4'10" and 7'10" into thirds. And again, explain my thinking.

I'll start taking your guesses.
I like when I ask students to stop me when I get to their guess on the number line.
Should I take the average? or should I have students argue it out?
I think the latter.
Here's why: that initial placeholder on the number line impacts EVERY estimate afterwards. Make it count.

I just got done taking four estimates and didn't ask for one single reason behind them...
I say, "A lot of good guesses here." because I already know the answer. I can see that the four estimates I took are in the ballpark. However, I never called on one of those four students to convince me.

I tried to dig myself out of this hole by saying, "I'm going to keep you guys in suspense."
I wouldn't say this is the best move. However, it was better than completely ignoring (or forgetting) the reasoning behind their estimates.
I went with two reasons. Half the number of guesses I received just a few minutes prior. BUMMER.

Once I revealed the answer, you can hear the "ohhs." because they were actually pretty close.
I say, "If you are within one or two inches, you should be really proud of yourself."

A student says, "Dude! I was off one inch!"
Same student, "I'm so happy!"

Maybe I missed it (or forgot by now), but a couple kids had a huge sigh of relief and were even excited about this. Seriously, that's awesome. If all we did was worry about our "answer" being exact every time, then we've lost focus on the process of estimating. Doesn't it feel absolutely awesome to have an estimate within a couple inches?

For my second day, I've seen how rusty I am and what needs improving. Moving forward:
Goal #1:
I want to cheat when placing my "too low" and "too high" on my number line from now on. Once I place my "too low", I will choose a "too high" that allows me to easily partition my number line into reasonable spacings.

Goal #2:
While students are filling out their handouts, look for 8 different students and prepare them that I'd like them to share with the class (and include reasoning):
Too low: 2 students
Too high: 2 students
Actual estimate: 4 students

Goal #3:
Ask the class who agrees or disagrees with the first estimate given.
For example, "Who disagrees with the estimate of 5'9" and would like to share why?"
Continue this with the second and third estimates given.

If you made it this far, feel free to offer any suggestions to help me get better. Thanks in advance.

Open house,

Thursday, July 2, 2015

Barbie Zip Line (2015) Part 1

Last summer I tried Barbie Zip Line and reported the experience here. I also supported a handful of Math 8 teachers interested in Barbie Zip Line during the school when they explored the Pythagorean Theorem. I have to admit, with every experience, it always felt like it could be different, possibly better.  This year, I went a different route and Part 1 just documents what I've done so far. Part 2 will be the conclusion.

First, I avoided the Pythagorean Theorem (for now). On Monday, my students already knew we would be starting Barbie Zip Line on Thursday. That was about as much information as I revealed. Everything else was structured to elicit as much student insight, information, and ideas as possible.

I started by projecting this slide:
Students discussed in their groups and a few shared whole group. I jotted down a few quick notes:
I love this informal language. Would this be an opportunity to work in slope? Maybe. I wouldn't force it as I'm confident we'll have plenty of other opportunities.
Me: Has anyone her gone zip lining before. 
A few hands go up.
Me: How would you describe it to someone in the class who has never been?
Katherine: Awesome!
Me: How would you describe what zip lining is to someone unfamiliar to it?
Katherine: You wear this harness. You ride down a line...
Mateo: You have two cables attached to you in case one of them breaks, there's a backup. Someone pushes you at the beginning and you ride along a cable...
Me: Great. Thanks. Would it help if we saw pictures or video of someone zip lining to give everyone a better perspective?
Everyone: YES!
Me: Here's what Google Images has for "zip line pictures". 
Me: A good business model will provide their customers with a safe and thrilling experience. Therefore, I'd like you all to fill out this Google Form with the following prompts and questions:
  • Briefly describe the characteristics of a DEATH zip line.
  • Briefly describe the characteristics of a BORING zip line.
  • Briefly describe the characteristics of a JUST RIGHT zip line. 
  • What information would be useful to know when building a zip line?
  • If we had a small scale zip line in class, what data can we collect from the small scale? 
I'm fascinated by the results. I learned I need to truly value, trust, and use my students' intuition way more often and when launching a lesson/activity. Check out their results here. These results will help guide Desmos Part 2. However, first we need to do Desmos Part 1.

The actual zip line quad.
Desmos Part 1
Students go to this Desmos graph and quickly create three zip lines.

Once they are done, they head over to this Padlet page and post their Desmos graph for their classmates (and me) to see.

Desmos Part 2
*I will post what students do in Barbie Zip Line (2015) Part 2.
Before going outside, students begin doing a small scale version of the zip line inside the classroom. Here are the materials:
  • 3 paper clips
  • 2 measuring tapes
  • 1 string (100 inches)
  • iPad (for Desmos part 2)
  • iPad or phone timer
Record their data inside of this pre-made Desmos template.
*If you go the route of the Pythagorean Theorem, adjust your table accordingly.

Here's a handout for each student. After collecting their data, students will be expected to draw a pretty descriptive scale picture of their zip line on this handout. They'll also need to predict how long it will take their doll to complete her zip line ride.

As you can see from the handout and expectations, I'm placing a big emphasis on the following:
  • Scale
  • Proportional reasoning
  • Rate of change (or slope)
  • Rate
No mention of Pythagorean Theorem. Find out if it stays that way in my Barbie Zip Line (2015) Part 2 post, next week.

Zip 1,

P.S. Most importantly, my son was really excited to visit my class today and partake in the Barbie Zip Line adventure. I was really excited too. DUH!

Wednesday, July 1, 2015

Tacos For (almost) Everyone

Do you remember when I blogged about the Ultimate Task for Vertical Planning: Stacking Cups? If not, feel free to check it out at your convenience. I've got another task for you that can be used at multiple grade levels: Dan Meyer's Taco Cart.

When asking:
Who will reach the taco cart first?
there are so many mathematical opportunities awaiting us. Here are a few:

Math 6 (maybe Math 7)
Pass out this handout during Act 2 and tell students you will only give them one dimension. Choose wisely.
Read more about this great technique on Fawn's blog post about Mr. Meyer's Taco Cart.
It simply is brilliant. Students are measuring the dimensions (distances) on the paper and using proportional reasoning to figure out the real life distances. I recommend students use centimeters when measuring the dimensions of the triangle on the handout. I really enjoy this technique.

Math 8
If you're a math teacher and you see the picture Dan provided for Act 2, your intuition will most likely steer you in the direction of the Pythagorean Theorem. Go for it!
Geometry (HS)
Let's say you have already used Taco Cart during the year to apply the Pythagorean Theorem or Distance Formula (Desmos). How about we extend the mathematics and look for more right triangle relationships in Taco Cart. I noticed that the hypotenuse is about twice the length of the shorter leg. Let me connect that to the context of the story: Ben's distance is about twice the distance Dan travels in sand. That's right, Dan gave us a 30-60-90 right triangle. Pro skills there, Dan.
*I'm not saying the 30-60-90 relationship is the most intuitive, but we'd be helping students make connections with previous learning. 

Algebra and Beyond
As you move into the sequels provided on the website, there's a lot of higher level math. Depending on the question, the problem-solving is fun. I worked with a high school group of math teachers who found it extremely challenging to solve the question:
What path to the taco cart would take the least amount of time?
Overall, this is such a fun and meaningful task. Dan has given us a treat! Today, my students did such a great job arguing, sharing theories, identifying variables, and using their intuition even before I unveiled any information from Act 2. It was awesome! I'm avoiding the use of the Pythagorean Theorem this round. I went Fawn-style by giving students only one dimension on their Act 2 handout. So good!

Tacos por favor,