Reflections on Quiet: The Power of Introverts in a World that Can’t Stop Talking

Cooperative work abounds (and should) in school settings.  Introverts play an important role, often craving the recognition they cannot command.  This book appeals to my own moments of conflict–extroverted at times, but needing time to recover and find my own, peaceful introvert.  Classroom takeaways (to read and re-read throughout the school year), paraphrased from the book by Susan Cain:

  1. Love is essential; gregariousness is optional.  Think quality of relationships over quantity.
  2. The secret of life is to put  yourself in the right lighting: the spotlight or the lamplight.
  3. Respect needs for socializing and for solitude; they differ for everyone.
  4. Spend your free time the way you like, not the way you think you’re supposed to like.
  5. If your children are quiet, help them make peace with new situations and new people, but otherwise let them be themselves.
  6. As a teacher, enjoy the gregarious and participatory students while cultivating the shy and gentle ones.
  7. As a leader, remember that one third to one half of people are introverted, whether they appear to be or not.
  8. To foster creativity, provide quiet thinking time (with students or colleagues) before sharing ideas publicly.
  9. The trick in life is not to amass all the different kinds of available power, but  to use well the kind you’ve been granted.  Introverts are offered keys to private gardens full of riches.



Integrating Geometry and Biology–an activity

I’m excited to share the results of my work over the past few summers! Here’s hoping that my joy in creating and gathering applied math materials spreads to students and teachers.  All will benefit from connecting mathematics topics to subjects that high school students may study concurrently.  I hope this will boost student engagement and generate classroom questions worth exploring further.

Prepare for a few activities connecting mathematics, science and US History through student inquiry. I created these with Kelley Durkin at Peabody College in Nashville, TN thanks to an EE Ford grant to the University School of Nashville. Feel free to use any or all of the activities and consider them licensed under the Creative Commons.

Links to some materials below:

Using Geometry to Talk about Cells Improved Final Using Geometry to Talk about Cells Improved Teacher Version Final

More activities to come …

Teacher Nerd Saturday Evening

After teaching for 27 years, this is the first year that I am teaching Geometry.  I’m thinking in new ways as deductive reasoning and problem-solving join with representations that often don’t involve numbers.  I’m continually impressed by my ninth graders who open their brains to this creative process.

This evening, I once again practiced what I preach to students in my advanced geometry class.  A particular proof eluded me yesterday and earlier today.  I had to draw my own diagram and create my own logical process (again, without any numbers involved).  I’m not wedded to the topics of any one chapter and don’t always expect a proof to fit a given set of theorems, so I don’t always find an direct, elegant path.  Today, after I walked away from the proof (and my many diagrams), I cleared my brain and tried one more time.  Eureka!  I’m reconnecting with and addicted to the adrenaline rush of … Geometry.

I included my proof below so I could remember this happy nerd experience on a Saturday night.






Teaching with my student

On Friday, I met with my former student (now colleague and co-teacher) to plan our first week of Advanced Geometry.  I am excited to work with her and encouraged by her innate sense of the part technology will play in our course.  Communication, investigation and independence form the educational pillars for our classrooms while deduction and content mastery form the math-specific ones.  Our discussions abut homework clarified that we both select problems that spark student curiosity, involving both logical and formal algebraic thinking.  (Yes, we know that algebraic thinking is logical!)  One of our goals for students is to engage them with proof through meaningful, though-provoking questions and leaving additional, repetitive practice for them to pursue on their own.  So, we’re skipping lots of book problems that ask “Segment AB is congruent to CD.  Prove that the segment formed by AB+EF is congruent to the segment formed by CD+EF.”  Character comes from intrigue, not tedium!  I hope I was one of the teachers who helped my new colleague to use this approach…

changing courses = broader vision

I’ve taught math in independent schools for 27 years, starting with 9th graders in Algebra I and expanding to 12th graders in Calculus.  After 10+ years primarily in the Calculus arena, this year’s step over to Standard Algebra II and Advanced Precalculus broadened my view of what engages students and how they learn persistence.

This may sound like a no-brainer, but while planning each class I actively kept in mind that boosting student engagement means captivating student curiosity.  This can mean generating math applied tasks, counter-intuitive problems (and more counter-intuitive problems) or images and video.

In addition to changing my own course assignment for the school year, I went to California for the Reinventing Mathematics Edudcation conference that brought new insight, inspiration, new connections and took me away from my comfortable Southeast zone.  (The Culver City Hotel with it’s Wizard of Oz theme brought a smile with every sparkling red shoe!)  Hearing Ilana Horn suggest that focusing math instruction on applied mathematics and setting aside more theoretical discussions “underestimates a student’s imagination” ended the conference beautifully and encouraged teachers to help students “get messy with” and “play with” mathematics.

Reflecting on my 27th year of teaching leaves me satisfied, wanting to know more and … eagerly eyeing the hammock in my backyard!

Thoughts from a Math Chair

In this blog, I will reflect on discussion topics for the math department at the University School of Nashville.  The scope of some topics suit the needs of our 9-12 math faculty while others aim for a broader 5-12 audience.  Summer articles will include discussion prompts that lead to rich discussions along with a summary of thoughts and ideas.  I hope that these blog entries help other high school department chairs generate rich discussions within their faculty while also letting me reflect on the process within USN.



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