Math PD for Substitute Teachers


I was asked to lead a math session today for district-wide subs to help them better understand the math they’d find in CCSS classrooms.  Thinking about how to craft a PD on mathematics for K-12 substitute teachers who work in any classroom from kindergarten to high school PE and everything in between was a challenge.  Like many of you, when faced with a teaching topic on which I am stumped, I head to my friends in the blogosphere

Recently, a UC Berkeley undergrad in my math pedagogy course asked if it would be considered plagiarism to use a lesson his girlfriend had taught in his current teaching placement.  My reply was that if it was a great lesson that was appropriate for his students, it wouldn’t be plagiarism at all, and was actually what all great teachers do.

So thank you, Robert Kaplinsky, as  I very much stole your work today, though I gave you credit all along the way.  I am indebted to you for inspiring my session today which somehow left a room full of subs, with VERY diverse experiences, quite excited to teach math this  year.

Between  being a teacher in my district for a long while and now having been a parent here for a long while, I was surprised to realize how many of the subs in the room I knew.  Several of them had subbed for me and many more had subbed for my colleagues and even my son.  That made this a lot more fun for us all.

They started by predicting how 8th graders would respond to the question of:

There are 125 Sheep and 5 Dogs in a Flock.  How Old is the Shepherd?

They then watched this video which is further discussed in this blog post.

Man did I have a captive audience.  My favorite comment was from a woman who admitted that she hates math and would never sub in a math class. She said that had she been asked this question, she would do what many of the kids in the video do, write down the numbers and DO something with them.  She would assume that though the question made no sense, that it was she who didn’t understand and she doesn’t trust her math abilities.  She went on to say, however, that had this question been posed in an English class, she would have been the first to question the teacher saying that it made absolutely no sense.  She challenged the group to pose this question to both a group of middle school math students and again in a middle school English class.  She was confident that outside of a math classroom, more students would speak up about how the task makes no sense.  I found that hypothesis to be brilliant (while also worrisome that she’s right).

Following this conversation we did Robert’s lesson on questioning strategies which is explained in his blog post.  In short, teachers were in groups of 3 where one role played a teacher, one a student and one was an observer who wrote down all the questions asked by the teacher.  The teacher was given slip of paper with a math problem and knew the solution that the student had gotten.  The student was given a slip of paper with the math problem and a specific misconception.  The goal of the teacher was to ask questions to determine the misconception of the student.

For example:

Student: You are working on ordering decimals from least to greatest. The problem you are currently working on is ordering the decimals 0.52, 0.714, and 0.3. You correctly place them in the order 0.3, 0.52, 0.714.  However, the reason you put them in this order is because you look at the number after the decimal like a whole number (3, 52, 714) and do not understand the significance of place value. You are confident you are correct and don’t realize that you only accidentally got the correct answer.

Teacher: Your student is working on ordering decimals 0.52, 0.714, and 0.3 from least to greatest. Determine what understanding the student has by asking questions, especially questions that encourage elaborate responses.

I LOVED this activity and the rich conversations it generated. We easily spent 45 min. role playing 3 scenarios and debriefing each one and these teachers had so much to say.  We talked a lot about how developing questioning strategies could help a student unearth misconceptions even when the math the student was working on was too complicated for the sub.

However I realized that for this group of teachers, there were so many who feared math, that they couldn’t focus on the misconceptions and instead, for some, could only focus on explaining to each other HOW TO DO the problem.  In hindsight, I think I should have modeled the conversation one could have.  I could have role played the student and had the whole room of subs role play the teacher asking questions to me.  Only I would know the misconception and the group would ask questions to determine where I was confused.  I think had we done that for one scenario, these teachers would have been able to let go of their own fears of making math mistakes a bit easier.

What a neat afternoon for me and for them!



Next Summer…

Next summer, you say.  But why?  I haven’t even begin this new school year yet. I just cleaned the lens of my document camera and tested out last year’s white board markers to see which were still keepers.  And I did such fabulous PD this past summer that I’m itching to incorporate into this year’s curriculum and pedagogy.

And gee whiz, my husband and I bought a condo in Kauai this summer so why the heck would I do ANYTHING but go here next summer?

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Darryl Yong just published a blog post on how he and Bowen Kerins create the morning math sessions at the Park City Math Institute.  Read it now, before you read any more of my post.  If you haven’t attended PCMI, you should, and Darryl’s blog post leads you to more information about it and how to apply.

Today was my first day of work at my new job, Instructional Technology Coordinator for the Berkeley Unified School District.  I’m a teacher. I’ll always be a teacher.  So explaining or even stating what my new job is seems to only happen with some contortions as I try to explain that I’m a math teacher, but I guess I’m not a math teacher anymore, but I really am a math teacher.  This summer as I have met new people while on various travels, I’ve been asked what I do.  I can’t seem to say the title of my new job without a paragraph intro about how I was a middle school math teacher, then had a second child, then wanted more flexibility and became a TSA and then and then…and now I am…blah blah blah.

However, while a lot of experiences have shaped who I am as a teacher and now as an administrator, over the past 17 years, nothing has had as lasting impact as the summer of 2011 when my husband and I packed my then 13 year-old-step daughter, 2 year-old son, Bernese Mountain dog, two mountain bikes and who knows what else into our Subaru Outback, stopped at every McDonalds Playland between Lovelock and Winnemucca, and landed in Park City Utah.  Following my participation in PCMI’s 3 week course, I started a blog (yep, you’re reading it now), got connected to a bunch of regular math bloggers from whom I have bounced countless ideas off of, and found myself immersed in the online support world of math teachers.  Darryl’s post suggests that PCMI’s curriculum limits the amount of technology which is used.  While this is true, without a doubt, I wouldn’t have the job I have today (Instructional Technology Coordinator operating in the body of a middle school math teacher) were it not for Darryl and Bowen introducing me to Geometer’s Sketchpad and how dynamic mathematics software can allow students the opportunity to play around with visual representations of big mathematical ideas and  explore open-ended problems which elicit incredibly rich discussions.  My use of Sketchpad morphed into GeoGebra which more recently has morphed into Desmos, however the purpose of these tools remain the same.

So Thank You, Darryl, for your post and for reminding me of how I got here.  And speaking of gratitudes, Thank You Math For America, Berkeley, for urging me to go and paying my way.


Pokemon for Breakfast on the First Day of School

I’m tempted to post this without comment.  But comment I shall.

Since I’m not in the classroom, I can’t show this on the first day of school.  But if I were still teaching 8th grade math, I think I would.  Then I’d have them turn and talk, introducing themselves to a partner and discussing whatever the video made them think about.  No idea what this  video refers to?  Your partner will.  Or you’ll both lean over and ask the pair alongside you.

Somewhere along the way on that first week we’d do an activity with Desmos.  And when Friday rolled around, I’d have them do a quick write and pair-share to compare and contrast playing Pokemon Go to sharing a laptop with a partner when doing math as part of a Desmos Activity.  But sadly, I don’t have my own classroom filled with eager 13-year olds to build relationships with or affective filters to lower.

Since I now lead professional development more or less full time, I will instead show this video as part of my opening talk to the 100+ Berkeley K-12 teachers attending my department’s 3-day Instructional technology Institute.  Spoiler alert if you are a Berkeley teacher reading this…

And I do hope the Desmos folks forgive me for mentioning Pokemon Go and Desmos in the same sentence.

OH NO…video was taken down today 8/5 for copyright reasons.  So sad.

Do Something

Our country’s values are making me sad.  More sad each week as news arrives of yet another black victim in the hands of a police officer.

I have spent much of the day reading social media as I never have before: reading articles, watching videos, and reflecting on the reflections of my friends, colleagues and acquaintances on Facebook.  Posting, reposting, reading and writing are all expressions of emotion, but I urge us, especially those of us who are white to make a promise to DO SOMETHING.  We have the privilege of choosing whether or not to speak up.  DO SOMETHING.

I have compiled the articles I have come across today which have been posted by those whose opinions I greatly admire and respect. While I haven’t yet read all of these articles, I found each through someone who always pushes me to think more deeply.  I plan to add to this list in the coming week and will repost this list again.  Please share additional links here in the comments, on my Facebook, or Twitter accounts and  I will add them to this list and read them myself.  This is barely a something in the act of “DO SOMETHING” but having these in 1 place will hopefully give me and others a source of reflection and information to share with others.  Click here for a beginning of a list on articles being circulated on social media.

If you are white, like me, promise yourself you will do something.

My promises today are:

  • Have ongoing conversation with my sons about their role as white boys in being allies for people of color and speaking up for and documenting injustice when they see it.
  • Continually donating money to organizations which are supporting social justice and individuals who have suffered from racist acts of violence.
  • Get involved in local campaigns to ensure that police oversight and community policing is a priority for our elected officials.
  • Get involved in national organizations that are pushing for bringing justice to police officers who have committed racial acts of violence.
  • Talk about these issues.  In person.  Not simply over social media.
  • Not remain silent when I hear white people I know making racist assumptions or unknowingly denying their white privilege.
  • Think deeply about how to ensure that my work in the public schools is focused on issues of social justice and helping empower students to know how to advocate for themselves and speak up for and document injustices when they occur.

Many today have shared their feelings far more eloquently than I can.  Writing my emotions is not something I do well.  Speaking and listening is far easier for me.  But I need to move on from reading social media and actually take action.


Why 2:1 Laptops are Gold

Recently, my parents were visiting to celebrate my son’s 7th birthday.  They asked what projects I was involved with at work and instead of explaining, I grabbed a laptop and asked them to try out a 5th grade Desmos Activity I had recently written.

In my role as Teacher on Special Assignment for Instructional Technology I find myself immersed in many types of projects, but the one which our district math coach often calls me ‘relentless’ is my work to get all middle school math teachers using Desmos at various times throughout the year.  In pursuit of this goal, I taught a lesson using Desmos in 5th grade classrooms at ten of our eleven elementary schools this winter when they were on Engage NY’s Module 6 which is coordinate graphing.  The students used Desmos to discuss several topics, however the stickiest and richest conversations occurred when students were trying to write their initials using T-Tables.  They’d call me over in a panic explaining that they were trying to make a C but they computer thought they were making an N:

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“Huh” was my general response.  “I wonder why that happened?”

Some continued to tinker on their own while others would call me over and say that THEIR computer had done the same thing as so-and-so’s computer…thought they were trying to make a different letter than they actually were.

So we’d talk, and eventually kids realized that the computer does just as you instruct it to do, so the order of the points in your T-Table matters.

This led me to write an Activity around this big idea which if you’re interested in trying out, can be found here.  I’d love your feedback if you have a moment to try it as because of SBA testing, I haven’t yet been able to try it out with kids, though I plan to do so in the next week.

But there we were, in my kitchen, with my parents (who I am quite sure are reading this post) asking what’s new at work.  So I gave them each a laptop and had them try out this Activity.  They were lost. Very lost.  Both because they hadn’t thought about x’s and y’s since my brother was born and because the format of a self-guided online task was completely new to them.  I offered minimal help, with just a quick crash course on how to graph coordinate pairs.  However the real help I offered was to tell them to share a single laptop.


The video  below doesn’t capture how rich their conversation was once they were sharing a single device.  Work which was at their frustration level only moments earlier when they each had their own laptop suddenly was not only fascinating to them, but do-able.  Although my dad is the one typing, just moments earlier my mom had figured out a crucial issue that had stumped them.  They are going to kill me for posting this, but it’s worth it.  When is the last time you saw 2 grandparents productively struggling through a Desmos Activity?

LiveStream Weather Ballon Launch

Anything live-stream should be publicized live (times below are Pacific-Standard).  So with no further adieu, I will simply share the announcement and links incase you want to follow this.  I will be there for the launch and post a follow-up blog with  my musings.  I’m quite excited.

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Dear students, families and colleagues:
On Wednesday, May 4, we will attempt to live stream Longfellow’s high-altitude balloon launch. Longfellow’s 8th graders have not only been working hard on refining their lab report writing skills, but also on predicting conditions at extremely high altitudes based on their understanding physical science concepts.
You may wish to watch with your students if you are a teacher, or track the flight and recovery efforts after school if you are a student. (This is a ground-, not balloon-based live stream). This is our first live stream, so bear with us – our priority is balloon launch for the students and timely recovery so they can write lab reports the next day.
Here is the tentative schedule for the live stream:
  • 10:30 am: Preflight setup, Longfellow yard.
  • 12:00 noon: 7th and 8th grade lunch begins, Longfellow yard. Final flight preparations, commentary from students and teachers.
  • 12:15-12:45 pm: FAA filed launch window (Balloon will launch during this time).
  • 12:45-3:15 pm: Balloon flight and live tracking via website.
  • 2:45 pm-??: Recovery operations. Continued live tracking and periodic field updates if cellular service is available.
You can also explore high-altitude flight predictions here and track our balloon once in flight here.
After the balloon is recovered, I will make all of the data and imagery that our sensor and camera systems collect available.
This high-altitude balloon launch would not be possible without the generous support of the Berkeley Public Schools Fund and the close collaboration of Ted Tagami and Tony So of
Matt Hinckley and Jamie Robertson
Longfellow 8th grade Science Teachers

Desmos meets Mondrian

One of my very favorite parts of being a TSA for Instructional Technology is teaching in the classroom of a brilliant teacher who is intrigued by tech, but a reluctant user of it.  Why? Because I walk away with so many incredible ideas.  I laugh that after 3 years out of the classroom, I come up with far less great classroom ideas than I used to, however I really know how to spot a good idea when I see one.

Today was one of those dreamy days.  Lara Collins, 8th grade math teacher at King Middle School in Berkeley, and I were colleagues when I was teaching math just a few year back.  In fact, I remember in 2005 when I first started teaching middle school, after a long stint as an elementary school teacher, and Lara & her partner in crime Leah Alcala took me under their wing and gave me unique, creative lessons for weeks and weeks of curriculum.

Although I co-taught with Lara today under the auspices of having students use Desmos to gain insight into solving systems of equations, I also got to see the artistic creations of the 8th grade students at King who have been doing a whole lot of dabbling in the intersection of graphing and art.

After learning about how to write the equations of horizontal and vertical lines, students were introduced to Dutch painter Piet Mondrian and did a study of his work, his use of color and the variety of ways he uses horizontal and vertical lines to create various moods. Students then created their own Mondrian-influenced graphs, with each line defined by its equation. Though they didn’t use Desmos for this project, they sure may next year.

A second art project followed soon thereafter.  Students wrote linear equations to design stained glass. Some learned how to set domain and range restrictions.


Some did the artwork on paper, while others used Desmos.  Each result is gorgeous.  So glad to have these great ideas to share with others.  Thanks, Lara!
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