Category Archives: Uncategorized

You Have an Awesome Math Lesson – Share It!

Do you have an awesome math lesson? Do you like handsome cash prizes? The Rosenthal Prize for Innovation and Inspiration in Math Teaching offers a top prize of $25,000…and the 2019 winners have just been announced by the National Museum of Mathematics! Congratulations to Nat Banting, this years winner and a fun and inspiring twitter follow. I’m really looking forward to hearing more about dice outcomes auction somewhere down the road. On the link above you can read about past winners and learn about how to apply for 2020.

I applied for the Rosenthal Prize back in the spring. At that time I looked back at old blog posts for lessons which seemed to be of interest and use to teachers, and chose one which has generated many positive comments: the 35 Game. The original post describes the game and how to leverage the results to build need for compound inequalities: https://mathcoachblog.com/2016/01/07/the-35-game-for-compound-inequalities/

I was thrilled to find out later in the year that my lesson was chosen as a Finalist for the award, but then the hard work begins. There is quite a lot to submit for this prize including:

  • A complete lesson plan
  • A video of the lesson in action
  • 3 recommendation letters

Every year the “35 Game” seems to get many blog hits and comments from teachers who use it. I am hoping that sharing my lesson plan write-up with the math community will provide guidance and usefulness to those teachers who enjoy this lesson. Any feedback you have is appreciated!

Thanks to my friends and colleagues Dennis Williams, DJ Fromal and David Weber for their willingness to provide recommendation letters. I work with inspiring and wonderful educators!

Techstravaganza Resources

Desmos and Statistics! Resources from the AP Statistics Reading “Techstravaganza” – June 2019 in Kansas City, Bob Lochel and Leigh Nataro

PCTM 2019

I am proud to be the program chair for the 2019 PCTM Conference in August, with my good friend Sue Negro.

The preliminary lineup of speakers appears in the file below. With Keynotes by Dan Meyer and Robert Berry, a Desmos pre-conference the day before, and our first ever trivia night, it’s going to be a great 2 days in Harrisburg!

Register today and get all the details:
https://www.eventbrite.com/e/pctm-annual-conference-registration-52503521446

TMC Desmos Day – Stats Session

Today I am in Cleveland for 2018 Twitter Math Camp! It’s the Desmos Pre-Conference Day, and I am facilitating a session on using Desmos in Statistics classes. Below are many of the links and resources I plan to use – even if you are not in Cleveland with us, feel free to borrow from these resources.

Baseball Data Set

Comparing Data Sets and Summary Statistics

Regression Facts (Mean/mean point and slope)

Teaching the meaning of r-squared

“Release the Hounds” – my first attempt at random sampling

Participate as a student, Steal and Share

“Backpack Weights” – thinking about scatterplots (AP Stats)

Participate as a student, Steal and Share

Assembling the Model Solution

I use College Board released AP items often in my Statistics course. The problems are aligned to clearly-stated goals, and the solutions provide insight not only into the grading of AP questions but also allow students to study well-articulated explanations. You can visit the College Board Statistics website and explore. Jason Molesky’s website provides helpful guidance on using FRAPPY’s (Free-Response AP Practice…Yay!) as a formative assessment tool in AP Stats.

Each free-response solution begins with the “model solution” – the ideal explanation a student would provide for full question credit. It is not unusual for Statistics students to struggle with clear communication, and having students read and dissect the model solution can be helpful in strengthening statistical arguments. A few times this year, I have used the model solution as a formative assessment tool with an activity I call “Assembling the Model Solution”.

Here’s how it works – start with an AP Free-Response question with a narrative aspect. Today, I chose a problem which requires students to interpret a P-value, from 2009:

2009problem

The model solution contains a number of non-negotiable elements: a conditional probability, a reference to smple results, and the “extremeness” of results.

2009sol

Next, I took the model solution as broke it into small, strategic “bites”. At the same time, I added some parallel distractors and a junk phrase or two.

slips

Then, use a paper cutter and slice the Word document into phrase slices, and paper clip together. All students then received the problem and the slips of paper, with the challenge to assemble the model solution for part a of the problem.

 

The conversation were rich, and the teams mostly debated the salient aspects of the problem apprpriately. The biggest points of debate and incorrect solutions came from:

  • The difference between “sample” and “population” proportions.
  • The assumption of sameness in the treatments as the conditional aspect of P-value.

I have used this strategy a few times now, and continue to tweak how I provide the slips of paper. I’m also looking at digital options, but I like the social aspect of moving the slips of paper. The method is not ideal for everything in AP Stats, but there are a few areas in our curriculum where this fits in nicely:

  • Sampling and experimental design
  • Conclusions for inference procedures
  • Describing distribuitions.

You can download my file for this activity here.  Enjoy!

  • Credit to Jon Osters and the AP Stats glitterati who rightfully pointed out that my original post spelled “Yay!” incorrectly.

Today, Nothing Worked Well…and That’s OK

My 9th grade class has a quiz on statistics concepts tomorrow – standard deviation, interpreting graphs, outliers and the normal distribution. It’s a real cornucopia of stats ideas! To review, today’s class goal was to collect class-wide data using a fun applet, share using the collaboration space in OneNote, use a website to assess the data, and write our statistical summaries. A fun day filled with stats fairies and pixie dust! Here was the lineup:

  • shapesCollect data using Shapesplosion – an online game (think the old Perfection Game) developed by folks from Grinnell College. The plan was to play with, and without color. Aside: it’s OK if you disappear for a while to play with this site, it’s super-fun!
  • Share data using the collaboration space on OneNote.
  • Use the artofstat.com web apps to make graphs and produce statistical summaries.

This is what I had in mind….Here’s what really happened

  • Shapesplosion didn’t work – while I rehearsed the site on my laptop, it didn’t work for the kids. It was a Flash issue, and stopping to figure this out wasn’t in the cards. After a few minutes of hemming and hawing, I settled upon a far less fun data collection idea: Tell me a temperature you deem “cold” when you go outside, and one you deem “hot”. Not nearly as sexy as the time data I wanted…but hey, I needed a data set.  But at least we have data until…..
  • ArtOfStat was glitchy and wasn’t playing nice with copy/paste from OneNote. Kids are getting restless, we haven’t done much stats review, and I am definitely starting to lose my “big” class.

manuel.gifSo, what do you do when a lesson goes south, your objective is slowly slipping away and the kids smell chum in the water?

Remember:

It’s not the kids’ fault when your plans go kaput. You may feel like some yelling is in order, but breathe, calm down, and be honest about what went wrong.

Student learning can’t be compromised because things go south. “There’s no time” is an easy out when we get rushed, but maintaining lesson fidelity is far more important than rushing to get to “stuff”.

Maintain clear expectations. Eventually all of my students were able to review some, and I had to alter my plan of attack. But stopping class, making sure we were all on the same page and understood the statistical expectations was necessary.

It won’t be the last time stuff goes wrong….roll with it…and laugh along with it.

Cocoa Puffs and Shared Work

Shared worked problems! What a magical time to be alive! What wonders does the magic algebra worksheet have for us to enjoy today?

organ

OK….so most shared work problems suck. I apologize to my students aspiring to be pipe organ re-varnishers, but we can do so much better.

This week I used Cocoa Puffs, stopwatches and Desmos to bring some engagement to my rational expressions lessons. To start, each student was provided with a plate filled with 30 grams of Cocoa Puffs (incuding the plate) . After my 3-2-1 countdown, students picked Puffs one at a time from the plate and tossed them onto an empty plate.  As they completed the task, times were recorded for each student.

After students finished, I had them partner up and consider the question: “if you worked together with your partner on this task, with one plate of Cocoa Puffs, how long would it take you?”

Students asked a number of clariying questions (yes, there is one plate. yes, you can pick them off the plate together.), partnerships developed a few ideas. We debated the validity of many of them:

  • Many groups took the average of the two times, then divided the result by 2. This seemed reasonable to a number of groups, and led to a discussion of the vavlidity of averaging rates.
  • Some groups attempted to find a rate per gram. This was a good start, but given that groups did not know the mass of the plate (I use Chinet, so it’s bulky!), this introduced some guesswork.

To steer discussion, we focused on one student who took 80 seconds to complete the task. How much of the job did they complete after 40 seconds? After 20?  Can we write a function which depends on time here?  What does it mean? Crossing the bridge from the task time (80 seconds) to the job rate (1/80 per second) is a tricky transit. Using Desmos to show the “job” function lends some clarity.

desmos graph

From here, many partnerships felt more comfortable with establishing their own estimates.  The next day, teams shared their work and estimates on OneNote, then peer-assessed the communication.  Some of the work was wonderful, well-communicated, and served as a model for the class to emulate.

student work

puffsThe next day, we listed our calculated shared work predictions on the board, and tested our estimates. Teams timed each other with cell phone stopwatches, and did not let participants see the clock until the task was complete.

 

data

Many groups were quite close to their calculated predictions! We discussed why our predictions didn’t quite meet the actual – bumping, variability in mass, general panic – and when error is acceptable. And now we have a firm background in rates and rational functions – time to conquer those pipe organs!