Categories
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.

Edmodo

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!

Categories
Algebra

Breaking Apart Sums and Differences of Perfect Cubes

The first few days of math class…an awkward time for both students and teacher.  The kids haven’t picked up on my mannerisms yet, aren’t sure why I fly around the room like a maniac, and worse, they aren’t laughing at the jokes.  I tend to use the first few days of any class seeing how far I can put my foot on the gas…what do my students understand?  Where are there gaps?  Who will I need to sit on during year?  Without exception, I dedicate at least part of the 1st day with students at boards, shouting out review problems.  The problems are strategically chosen to allow for initial success, dust off some cobwebs, provide for discussion when we hit some road blocks, and most importantly let students know that it will be perfectly acceptable to struggle in my class….as long as you keep trying.

I’m trying a differenmt apporach with an Algebra 2 course I am teaching this semester, and hoping to build some discovery and communication moments right in the first few days.  As their first day assignment, students fill out a Google form with information about themselves: hobbies, goals, clubs, etc.  As part of the form, I am adding this task: “Tell me everything you know about this graph:”

cubic

For day 2, I’m hoping the responses will provide a review of vocabulary (intercepts, roots, solutions, even rotational symmetry perhaps?), and some table-setting for what’s to come.  In our district, I can expect that Algebra 2 students will have a solid background in linear functions and basic polynomial operations, mostly limited to quadratics.  Cubics for the most past have not been explored yet.  And while polynomial multiplication and factoring are not new, rarely do students see polynomial division before algebra 2, so I will bring this into the discussion as a new idea.  NOTE: our district uses the Everyday Math program in the early grades, which stresses partial quotients.  Wondering how this will play when I attempt polynomial division…update may be coming!

DEVELOPING FORMULAS FOR SUMS AND DIFFERENCES OF PERFECT CUBES

Starting algebra 2, students should be able to “read and recognize” the following polynomial patterns: difference of squares and perfect-square trinomials.  But beyond this, I want students to be able to relate factored form to graphs, which often seems to be marginalized in the drive to practice process.  So, one of my first lesson openers will be a short and sweet challenge.  Does the following polynomial factor?

In their teams (my students always sit in groups), I will provide some time for students to consider this problem, and observe their trials.  I expect that will have a few groups attempt (x-2)^3, which will end badly, but hopefully lead to more trials.

CubicSo, how do we cross the bridge to the formulas for differences, and sums, of perfect cubes.  Time to start looking at some graphs, in particular the functional form of the given expression:

What do we notice with this graph?  And what characteristics will be helpful with the factoring problem at hand?  Here is where I hope students drive the discussion:

  • This graph has an x-intercept of 2.
  • This means that x-2 is a factor.
  • There are no other obvious intercepts, but we can employ long division here.

So, x^3-8 DOES factor.  Do other cubics factor?  How?

With their teams, students will now be given a few more cubics to factor:

 

What patterns do we notice?  Can we develop a general rule for factoring difference of cubes, and even sums of cubes?

Guiding the discussion towards a generalization, without students feeling forced-fed, is part of the art of teaching.  Hoping these first day discussions tie together lots of previous knowledge with a discovery moment.  I am not sure how it will go, but I hope to set the table that nothing is given for free.  Show me what you know!

Categories
Technology

Twitter Resources

Resources from today’s Twitter PD session at Hatboro-Horsham HS.

Hatboro-Horsham “Coaches’ Corner” from April 2013.

Cybrary Man’s Twitter Resource site:  this is the encyclopedia of all things Twitter.  From articles to read, classroom resources, hashtags to follow, and chats to join…..it’s all here!

60 Inspiring Examples of Twitter in the Classroom: from the 21st Century Fluency Project

50 Ways to Use Twitter in the Classroom: from TeachHub

22 Effective Ways: moving up Bloom’s Taxonomy using Twitter

“The Power of Twitter Chats” video – teachers and administrators share their experiences with Twitter chats.