We are Better Together

We are better together.  Say that out loud.  Go ahead.  I’ll wait.

We are better together. 

I just returned home from Edcamp Math and Science at Eden Prairie High School.  (Beautiful campus, by the way.  Thank you for hosting us.)  I’ve made a conscious decision over the last year or so to only attend conference sessions on topics I’m already using so that I can refine and improve.  It’s too easy for me to get swept away in the glitz of new classroom tools that draw me in with edu-buzz-agogy like “classroom engagement” and “streamlined feedback.”  Instead, I focused on two things:  Number Talks and Desmos.

I attended Christy Pettis and Terry Wyberg’s session on Number Talks at the state math teacher conference last May and learned a lot, so you didn’t have to twist my arm to get me to listen to them again.  A quick survey of the room revealed that the group ran the gamut of novice to expert when it came to experience with this transformative classroom routine.  I’ve used these in my classroom regularly and was still able to gain many useful strategies to make this process even better.  I loved how Christy was able to turn the strategies into area models so that students make that connection.  That was something I had not thought of but will definitely be implementing starting Monday.    Again, it’s worth repeating:  We are better together.   Here are my notes:


Next up:  Desmos.  The program speaks for itself but it was lovely to have someone on their payroll available to demonstrate its flexibility.  Thanks, Christopher.  Who knew projector mode was so amazing! And I never knew how to create a dragable point.  Child’s play, I know, but new to me.


Right before lunch, I joined Seth Leavitt for a conversation on race in math and science.  An overarching theme was that students of color are over-represented in remedial math classes.  Seth encouraged a continued conversation with leaders from our school districts on equity and access in mathematics and science.  I’m committed to this ongoing discussion in St. Francis and to ensuring our students of color have opportunities to take high level mathematics.

Thanks, Casey Rutherford, for organizing this again this year and allowing us to get together and get better.  Teaching is hard, but we are better together.





Conceptual Function Foundation

I’ve taught College Algebra for a number of years.  This course and College Trigonometry replace Pre-Calculus at our school.  I’ve struggled with helping kids with functions because of the variety of background knowledge they have on the topic.  I have tons of good activities, but never one that really built a conceptual foundation of the important features of functions in general.  It’s not that it’s impossible to create a conceptual foundation after procedures have been introduced.  It’s just really difficult to do.  (Remember this post from Christopher Danielson?)Enter New Visions for Public Schools.  Unit One of their Algebra 2 course allows kids to make sense of families of functions in their own way.

You can see the details yourself on the link, but in summary, kids sort graphs according to their own criteria and then build a definition of a key graph feature and re-sort accordingly.  Students then form new groups and share their key feature with their classmates.  Finally, the group as a whole creates statements that link the key features together.

Dan Meyer states that math is the process of confusing and unconfusing.  This progression does that perfectly.  Conceptual Understanding Achievement unlocked!


  • Students are asked to make sense of graphs based on their prior knowledge.
  • They develop a need for certain vocabulary such as “turning points” as they discuss key features of the graph. For example: https://twitter.com/Veganmathbeagle/status/651451109387730944
  • They need to take responsibility for their learning because they need to teach it to other students during the “jigsaw” portion.
  • They have to ask clarifying questions of each other rather than of the teacher creating student-centered discussion.

The real beauty was watching three days of making sense of graphs come together with the vocabulary.  The students are asked, with their groups, to find how the key features are related and how they are not related.   I wish I had an audio recording because it was some of the most beautiful student discussion I may have ever heard.  I captured this moment just so I could remember it:

Students discussing how function features are related and how they are not related.

Students discussing how function features are related and how they are not related.

Also, here is one of the reference graphs a student made:


Where Do We Go From Here?

Hundreds of students come in and out of my classroom every year.  And after four short years in high school, they are onto the next stage of their lives, whatever that might be.  I get a few friend requests on Facebook from former students, but very few relative to the number of students I’ve taught over the last eleven years.  Seeing them grow into adults with spouses and jobs and families always brings me joy. But so many of them I never hear from again, and there’s nothing wrong with that.  They go out into the world and grow up.  We have to assume we did the best we could to make a positive impact.

I have a folder in my file cabinet where I keep special mementos from students:  thank you notes, drawings, and other delights I’ve collected over the years.  Andrew Stadel recently requested memorable moments from our teaching careers and so I went digging through this file folder to find Algebra version of M.C. Hammer’s Can’t Touch This that I adapted for my class made up of mostly choir and band 9th graders. [No, I’m not sharing it, and No, there was no cell phone video back then].

As I dug into that folder, I also found this:


It didn’t seem to have the same pick-me-up tone as the other papers in the folder, but I know exactly why I kept it – to remind myself of my privilege.  To make sure I am always cognizant of the struggles my students endure when they aren’t in my classroom. And to make it clear to myself that I teach people first, not mathematics.

Never for one second did I believe that this kid ended up in jail as he was convinced back then.  I reached out to him using my old stand-by:  Facebook.  Not only is this student not in jail, but he is thriving as an entrepreneur in IT, has a child on the way, and is living happily with his beautiful fiance.  With his permission, I am telling his story of triumph over his adolescent years where happiness seemed out of reach and success seemed hopeless.  His story of resilience has made a positive difference for me as an educator and will continue to help the future students that step into my classroom year after year.