Statistics Technology

The More Things Change…the More They Change

This fall, I am coming back to the classroom after 2 years serving as an instructional coach for my school district.  It’s been an exciting few weeks, setting up a classroom for the first time in a long time, and it occurred to me that I am using many, many digital tools in my classroom which simply did not exist when I last taught….just 2 years ago!!!  This reinforces the need to stay on top of new technologies and look for what fits in your class, and improved student engagement …it’s easy to fall a few generations behind.  Here’s what I am featuring in my classes this year:

Edmodo – I am already loving Edmodo for my classes, after just one week.  Best described as “Facebook for education”, Edmodo allows you to have a course-specific area online, with students given a code to join your class.  Post links, files and resources, and let students participate in online quizzes and polls.


There’s really no reason for students to ask “what did I miss” when they are absent, as Edmodo moves your class beyond the regular class period.  Has an ipad app, and many students here have installed the iPhone app.  And it’s free!  My first day student inventory moved from the standard “get this signed and fill out the questions” paper form to an online survey posted on Edmodo, which brings me to my next tool…..

Google Forms – OK, Google Forms are not new, but the entire concept of Google Drive and sharing content with students and colleagues has changed greatly in 2 years.  I am using a Google Doc calendar to plan my classes, and a shared doc is being used to team-plan Algebra 2 classes across phases.  And the first-day survey has moved online, check out my survey.  The responses served as great discussion starters for the next day.

Remind101 – this is my first time using Remind 101, and many students in our school are already accustomed to its concept.  Create an account and a class, which generates a “join” code for students and/or parents.  Then, log onto their site and send reminders of assignments, tests, quizzes, or anything you want to communicate to your classes.  It’s 1-way communication; quick, easy to use, and free.

Doc CamDocument Camera – When my department head discovered I was coming back to the classroom, he asked if I had any supply requests.  I only had one: document camera, and already this has been a great tool for my classes.  I had seen a number of teachers using document cameras in their classes, in many engaging ways.  My interest was further piqued at this year’s Best Practices Night at the AP Statstics reading.  Daren Starens, author of The Practice of Statistics, spoke on “Making Homework Count”, and a method for assessing homework he calls the “visiting artist”.  Randomly select a student, place their work under the document camera, and lead a discussion of the work.  Check “critique the reasoning of others” off your Standards of Mathematical Practice list every day!  The model I am using costs about $60, from IPEVO, and can be found on Amazon.

PollEverywhere – I do not have a set of classroom clickers, but no worries here! On day 1 of my Statistics class, student teams were asked to analyze an “unusual” data set.  To generate ideas, groups shared their observations using PollEverywhere.  Another free tool, it’s easy to set up an on-the-fly assessment.  As student ideas were generated, they appear on the wall, and the discussion flies!

Poll Everywhere

Digital Textbook Editions – I taught AP Statistics for 8 years before leaving the classroom, and used The Practice of Statistics, 2nd edition, for all of those years.  This year, we have moved to the 4th edition, with a digital version for the instructors.  I have told my students to leave their texts at home this year, unless they hear otherwise.  This is not only due to the digital textbook, but also….

Livebinders and “Flipping” Videos – For the first time, my Stats colleague and I are working to place a large amount of course content online, using Livebinders.  This is a content curating tool, and you can check out many public binders teachers have shared on many subjects. We hope that students will use this as an ongoing resource, going back to review before assessments, and creating the culture of Stats as a whole-course, rather than disconncected units.  In addition, my colleague Joel Evans has taken the notesheets to the next level!  CornellFirst, he converted many of my chapter guides to a Cornell Notes format.  But, even better, we are now “flipping” many of our lectures, through section-specific notes.  We hope this will allow for more activity-based instructional time, with a high payoff in student engagement.  In Joel’s first year of trying some flipping videos, his AP pass rate was 100%.  Does correlation imply causation?  Maybe, maybe not….but no matter how successful you feel your classroom has been, it is always a good time to review methods and take them to the next level.  Check out some of the Stats flipping videos, and our many class resources, on our AP Stats Livebinder.

So many great tools to transform your class culture.  Don’t be afraid to try something new!

Middle School Statistics

Globe-Trotting With

The Common Core places increased imporance on statistics in middle school, beyond the tasks of creating simple data displays often encountered in middle-school texts.  The new standards require that students be able to describe distributions, compare samples to populations, and design simulations:

  • CCSS.Math.Content.6.SP.B.5c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered
  • CCSS.Math.Content.7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

It’s all great table-setting for AP Statistics down the road, and working with authentic, interesting data.  In this activity, students use an online resource to perform a simulation in order to find the proportion of the earth’s surface covered with land (as opposed to water).  This is not a new activity, as a number of teachers suggest using an inflatable globe and some classroom tossing to reach estimates.  But I think the method below uses some web tools in a novel way, and encourages some authentic geography discussions.


Before diving into any simulation, I like to gather ideas from my students, to see if they have any initial estimates or backround about the problem.  Using sites like Padlet or TodaysMeet are great for encouraging and archiving discussions and participation, or you can go old-school and just record initial estimates on the board.  Asking an initial questions like: “Do you know the percentage of Earth which is covered by water” to start the discussion.  The start a discussion of sample size: “Would it be better to sample 20 points on earth, or 40 points, or 100 points?  What factors would be part of your decision?”


In this simulation, students will sample a random point on the earth’s surface, record whether the point is covered by land or water, and repeat for a given sample size.  For this, we will use the site, which generates random events, mostly things like numbers and dice, and their Random Coordinate Generator, which chooses a random location on earth and displays it using Google Earth.

Google Earth

The site works quickly, and the water/land data can often be determined without issue.  It is also easy to zoom in and out to take care of those “close calls”.  Quite a more accurate measure than the thumb-check data from the inflatable globes.  Very few issues arose in my trials with this method, but the biggest snag is Antarctica, which is land, but often appears light blue on Google Earth.  Also, a few rare occasions produced a data point above the North Pole on the map, which I discarded.  For your class, have each student generate a sample of size 10, and look at the proportion of land hits.  Below, I did 10 trials for 4 different sample sizes:


The next steps depend on the sophisitcation and grade-level of your class.  But in general, we want to know which sample size provides the best estimates.  How do you know?  Have students write explanations which defend a particular sample size.

Multiple sources (Circle graph from ChartsBin,NOAA Information) verify that about 29% of the Earth’s surface is land.  Do our trials verify this?  How often were our trials within 10% of this 29% mark?

Within 10%

As more data is collected, free site like StatKey can be used to generate appropriate graphs and statistics.



I see this as an improvement of an existing AP Stats exploration, and opening activity for Confidence Intervals for proportions, and extension into the behaviors of CI’s.  For those playing along at home, here are the calculations for 2 standard deviations (Margin of Error) for my given samples:


And the corresponding intervals, showing how often my sample proportions were captured within each interval: