From Cool to Helpful, #1: The Plinko Applet

So I have been reading some of  Dan Meyer‘s  series of “What can you do with this”   posts.  Cool Stuff, to be sure.

My efforts will be less ambitious, but still helpful, I hope.  If you don’t live under a rock, you know that there are a boatload of Java Applets and interactive tools out there on the web.  I don’t even want to list a small fraction of them, because I’m sure we each have our own folder of go-to applets.

So many of these are “cool.”   But the “cool”  eventually has to become a useful too to help my students learn.  And that’s where I come in.  I know that many folks have learning worksheets around these tools, and some are really great.  Many, however,  barely scratch the surface of what will actually work in a classroom.  I think that the design & sequencing of questions / tasks / set-ups  is some of the harder work I try to do.  Sometimes I have success, sometimes I don’t.

So I want to propose an invitation to “think and play:”
1.  I post an applet that I think is “cool”  for some math reason.
2. We all play with it, and THEN
3.  We put our teacher hat on and start doing some real thinking…  Specifically:

a. What questions  would you design for  your KIDS that motivate the need to use this tool?
b. When playing with this tool, what would you want kids to see , discover, or struggle with?
c. What mathematical / practice goals  would you want your kids to leave with after playing with the activity?

So Here’s the first “cool tool” I like:   It’s a Plinko Probability Applet.   It comes from the PhET project at the Uniersity of Colorado at Boulder.   This one is particularly cool for a number of reasons.  When you change probability of a ball  falling to the right,  the little pegs actually “tilt”  to the right.

Brainstorm of the quick math topics: binomial probabilities,  empirical probability converging to theoretical probability,  impact of  n and p on the  shape, center, and variability of the distribution of pegs,  yada yada yada.  That’s the easy part.

What would we design for kids?   What questions start to emerge when YOU start playing with it?  How can this get leveraged into cool stuff for kids?    What’s the important math in this?

My intentions is to “wring out”  all of the potential in using this tool.   Maybe an effective lesson or few can emerge from this.   Let’s find out.

Dear Santa: I want great online data software.

As the final days of the summer wind down for me,   I am starting the “prep time”  that all teachers go through before classes start. I get very ambitious and idealistic, and try to stay that way for as long as circumstances and my stamina allow.  This year, I have a couple of ambitious goals.   Here’s the biggest one.

I really want to  see a revolution in online statistics software tools for students and teachers.  Here’s what I want.

1.  I want a “data viewer,”  that could handle tab delimited text data, and create visual displays, summary statistics, and appropriate tests.  It should look as appealing as  www.gapminder.org

2.  I want it to have,  at a minimum,   the flexibility and  functionality of  Fathom:  Easy-to-create  dot plots, histograms, box plots, segmented bar charts, percentile plots, normal probability plots,  etc… I also want it to run appropriate statistical tests.  Gapminder is great but it does only scatter plots, and no tests / summary statistics.

3.  I want teachers and students to be able to create surveys,  invite subjects to respond with a simple URL + password,  and post  the data up there for others to use.  Data could be uploaded as private or public.

4.  I want teachers and students to be able to join / create public surveys,  and generate  databases .   I want public databases to be available on the web for all to use/ see.

5.  I want  ”dots”  to be easily replaced with easy to find icons:  guys, girls, men, women,  numbers, colors,  maybe … perish the thought…. Photos/icons  that students could upload of themselves? Each “dot”  in some displays could be a head?

6.  I want security options to range from public to completely private .

7.  I want it to be cost effective and something that people would pay for / use despte the cost.  Heaven forbid…. maybe free?

8.  I want “social network functionality.”

9.  I want pretty, simple, attractive,  and appropriate visuals.

10.  I want  educators in statistics/ data analysis in on the design of this.

11.  I want one-stop shopping.   Facebook, baby.  Google, baby.

I can think of a dozen different places that have little bits and pieces of this.   It doesn’t seem  too “pie-in-the-sky”  to  make this happen.  I am going to ask the computer science students at my school to consider working on something like this.   Bill Finzer at Fathom –  are you listening?    This could be a revolution, I think.   This seems grant-worthy.

So I need your help.   Who knows who would want to develop something like this?  

Is KeyPress still working on  updating Fathom?   It’s been at least 2 years since an update.  These days, that’s  glacial pace.  

Currently,   too many people teaching Stats/  Data analysis are using too many different tools. TI’s,  Fathom, Excel, Minitab, JMP, SPSS,  R,  SAS,  not to mention the online stats tools +Geogebra.    It seems reasonable (at least at the high school level) to construct a tool that meets the needs I outlined above. Imagine a classroom where you have easy access to a ton of databases, without a lot of time teaching kids how to use the software.  Imagine kids getting lots in some really cool data bases.  Imagine them “tinkering”  for hours, and bringing up questions in class.  Imagine asking them to find their own examples and constructing written critiques.

Accessing these files can generate important questions and investigations for kids  that are essential to their growth in statistics.

This is a bit idealistic, but it’s doable.  I’m sure of it.  We just need to time, the money, and somebody to do it.

I don’t want to hear that this can’t be done.   Tell what the obstacles are,  I’m convinced there are ways around them.   

Any ideas?

BT

PCMI: what is it all about?

You may be hearing a lot about PCMI from me and other bloggers.  What is PCMI?  The Secondary School Teachers program at PCMI  is the deepest, most transformative professional development experience I’ve ever seen for math teachers. Seriously.  Imagine 3 weeks of doing math, reflecting on teaching math and becoming a resource for math teachers.  Plus, you get to attend sessions with top-level mathematicians (for real – we’re talking Fields Medalists).

The time I’ve spent at PCMI has changed me as a teacher.  I pursued a Masters degree in Math Ed because of my contacts at PCMI.  I’ve been able to become a better teacher in my classroom, in ways that are improving how students do.  I also  have been able to be a productive influence in my math department without having to fight, push, or irritate colleagues (maybe a bit).  Plus, I read education research as a tool to inform my teaching.  The work I did at PCMI has also allowed me to win a couple of awards for teaching. I feel PCMI was the single greatest influence on my success. It’s a game-changer.

So check out all the notes and stuff we did this year.   Ask me questions.  There are a TON of cool things.  Oh yeah:  There are notes ten years back.  Each year is different.

PCMI Alumni:  Do you agree?  Tell your story.

August 1: My reflections on Orlando’s NCTM Institute on Reasoning/Sense Making.

Correction:  I referred to Lisa Henry as Lisa Meyer in an earlier version of this post.  My error, and apologies to Lisa!   

This is a long post:  hopefully future ones will be briefer!

I just returned from Orlando FL, where I presented a 75-minute workshop on “Making Rich Tasks Work” in a math class.  This happened at the NCTM Reasoning/Sense Making Institute.  Handouts for my workshop and others can be found here .  I worried about coming off as a bit of an impostor, as I still struggle to find the right times/ place to integrate these into my own classroom practice. I am, by no means an expert, but I am growing.

I tried to keep that in mind when I designed the workshop.  I didn’t want to talk at them. The bulk of the workshop came from the collaborative work of the staff of the Secondary School Teachers Program at PCMI, the Park City Mathematics Institute.  We were guided by the wise  minds of Gail Burril, James King, and Carol Hattan as well.

So here were my goals for participants, after attending the workshop:

1. An awareness that using rich tasks effectively in a classroom setting requires time and preparation.
2. A framework that could guide their future preparation:

• What’s the potential mathematics in the task (both topics and habits of mind)?
• Goals: What to I want my students to leave with after doing the task?
• Evidence: How will I know they are (not) there?
• Questions/Checkpoints: What will I say/ask to check for their understanding, and move them forward?
• Feedback:   How will the kids know if they are making progress?

Here was the “rich task” that I started with:  It was a problem that was inspired  from Ben Sinwell’s NCTM Illuminations task: 

Wendy has “cars” of length 1 and 2. She will string these together to make “trains.”   How many different trains can Wendy make of length    5?   6?   8?   n?    A   2-1-2 train and a 2-2-1 train are different.   

I will leave it to y’all to discuss the choice of wording / phrasing I used to launch this task.

Here’s what they had to do after doing the math:

If you are going to use the trains problems in your classroom:

1. Pick one mathematical goal and one ‘habit of mind’ goal for your students.
2. Describe evidence that your students are (not) making progress towards your goals.
3. What questions/checkpoints will you prepare ahead of time to move students’ progress forward?
4. What feedback will students get? Who gives it?

This is easier said than done, I think.   I was worried I gave them too big a challenge.  But the point was not to complete the challenge:  I just wanted them to engage a bit in the framework that seems to help me.

Lisa Henry’s response to my session made me feel good.  Given that she had attended sessions by Peg Smith and Dan Meyer as well, I felt like that I had succeeded in putting together a productive session for at least a few people.  Plus, she thought I had only been teaching for 7-10 years.  Perhaps I came off a bit “inexperienced?”  I’d like to think my daily regimen of Neutrogena and vitamins helped. I’ll be starting my 17^th year of teaching high school this August.  But if I looked younger,  THANKS  Lisa!  She also mentioned how more experienced teachers (like myself) may tend to use classroom experience as a basis for informing their classroom practice.  I strongly believe that classroom experience is just as important as using current research to inform instruction. You need to learn about and know your students and school deeply.

My own assessment:

Overall, I was pleased that participants were willing to engage in the mathematical task, and do their best on a pretty tough challenge: identify specific learning goals and questions for a problem that they barely understood.  Sometimes they put up some good possible goals, evidence to look for, and questions to ask students as they monitored work.  I was especially pleased that they were willing to give some strong critiques to their colleagues work (anonymously, via post-it notes).   I worried that during the “feedback” stage, I’d only see a bunch of  “god job…. nice poster” comments that lacked specificity. That did not happen for the most part.

Evidence of Participant thinking during the session:

I’m glad I saved the poster papers and took photos.  The anonymity of using the post-its allowed participants to be very clear about what they saw (or didn’t see) in the posters: “It think this question is too leading.”   “Is this really a math goal, or just a topic?”   I was happy that people were seeing the need to get more specific with their comments.  The time crunch made this hard, but taking the time to do this well is, I think, important.

One participant remarked that in a classroom, the negative tone of some comments might cause some distress with kids, and many agreed. I see her point: you don’t want to emotionally derail a kid’s progress.  This brought out the importance of establishing norms about peer-to-peer commentary, which was nice to see emerge.

Eighty cards were passed out at the start of the session:  I think I got about 45 back. For 25-35, maybe there was little / no take-away?  Non-response bias really sucks, don’t you know?

For the others, responses fell into two main categories:

“This is great. I’m going to do what you just did in my class (gallery walk).”  As much as I liked the “niceness” of these,   I wondered if some of these comments missed the point I was hoping for them to get: I don’t want people to imitate what I’m doing and try to retro-fit it for the wrong purpose.  On the other hand, maybe some of these teachers became more aware of one technique for getting students to work together, commit to a set of ideas, write them down, and receive feedback.

“I need to do more preparation before I use a ‘cool’ problem in the classroom.” These responses reflect more of what I was hoping for: a greater awareness of the need to be more intentional and purposeful as a designer of classroom time.

My favorite comment involved an awareness and a specific thing to re-think in future teaching plans: “I may need to re-think how I use rich tasks in the classroom, and maybe use them more  to help kids practice the reasoning that’s important, and not grade their work.”  This is precisely what assessment for learning means to me: using tasks as a tool to help teachers and students learn from each other.