a TMC16 Reflection

I’m overwhelmed by all the amazing that happens at TMC each year. I just left Minneapolis and am settling in at home, taking a moment to reflect on some of the things that really resonated with me. I have lots to follow up on (more blog posts!), but here’s a highlight of some of my big take-aways:

  • Varsity Math! Jonathan‘s (@rawrdimus)”My Favorite” on how he created math spirit in his Calc classes through varsity math swag reminded me that I want my dept to develop a “spirit committee” to make math more of a fun presence on our campus. Perhaps a math Olympics day? Maybe we should develop some swag.
  • PowerPoint Alternatives: Sessions on Peardeck and Desmos Activity Builder made me think more about getting out of my daily routine of PowerPoint led classrooms and having (some) days where students are following a Peardeck or working independently through a Desmos activity.
  • Desmos! OMG I have to get better at activity builder, especially for Calculus. There’s so much awesome that can deepen student understanding of these complicated topics.
  • Explore Math! I have used Sam‘s Explore Math activity with students for the past few years and I’ve loved it. Sam just reminded me how important it is, and I liked that he allowed students to use Edmund’s coloring book and watching “mathy” popular movies as some of the activities. I want to expand my Explore Math options.
  • #ExpandMTBoS! I need be active in helping spread the community. I did one step by bringing three of my awesome co-workers to their first TMC this summer! Shout outs to Erika, Caitlin and Kelsie! Now I want to think about ways to connect more LA teachers and possibly reach out to MfA NYC and LA…
  • Elementary Teachers! Tracy convinced me (and many others) in her keynote that secondary, middle and elementary school teachers should work together more. We have so much to learn from each other. It made me want to work with younger and younger students.
  • Building Groupwork! The amazing new-to-TMC Jessica (also my newbie mentee!) gave a great session on activities on how she creates great groupwork culture. I need to look more into this and plan my first week with more of these activities.
  • Teaching and Race! There were several places where people were trying to start a conversation about race, about both teachers and students. My own school has tried to start this conversation and is always looking for ways to really dig in. Becca gave a great session called “Every Student, Every Day” that reminded me of some of the things I do and believe in.
  • Reflection! Sara had many wonderful things to say, what an amazing teacher. One of the big take-aways from her flex session for me was the importance of giving myself time (1-5mins) for reflection each day. She takes a walk around the campus at the end of classes each day. I want to do something similar.

Speaking of Sara, she was in my morning session and had so many thoughtful things to say. The last day she gave everyone permission to try just one time, to fail, to jump into creating culture at an easy pace for you. We don’t have to change and make a perfect classroom tomorrow. Baby steps.

She also reminded us that teaching is an art form. There is no one right way to implement something, to set up something.

I will follow up with some more thoughts and details on some of these in later posts. For now, I’m profoundly overjoyed at all that was shared at TMC16 and am looking forward to TMC17 in Atlanta.


Unrelated, two cool sites:




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My SBG Hybrid (or How I Grade)

I have had several discussions with folks lately about my grading system, what I call a hybrid-version of Standards Based Grading (SBG), and I thought it was time to put it all down in words. I love SBG and working with teachers to develop it (in math and other subjects!). I find that the mere discussion around SBG really forces teachers to hone in on their goals and values. So let me try to share some of my stuff here.

A few starting notes:

  • I love the idea of SBG–grading categories reflect the learning goals of the class and students’ grades will consequently show/measure mastery of the topics in the class.
  • Many versions of “pure” SBG involve a large amount of standards.
  • People seem afraid that SBG won’t fit with a traditional gradebook.
  • I want a system that does not over-complicate my grading and records.
  • For me, SBG and retakes go hand-in-hand.

Both schools I have worked in required me to have some form of a traditional numeric gradebook. So, I had to make sure my version of SBG fit in those structures. I eventually created the system I will talk about below, but let me just mention that it is something I constantly work on improving. My grading systems keep changing from year to year, as I make tweaks based on reflection.

Here’s how mine works:

  1. Standards/Goals: I started by listing all my goals/standards for the semester, what I called Learning Goals (LGs). Thinking of all the content goals or topics we cover in a semester–there are a lot! I wanted to keep things as simple as possible, so over the years I have gotten in the habit of grouping some of the goals into more umbrella goals, aiming for about 8-10 LGs for a semester. As an example, here are my LGs from the first semester of my 7th grade math class. LearningGoalsMy second LG was a combination of many goals including being able to multiply integers, divide integers, and solve multi-step integer equations using order of operations. This is an example of the way my LGs are more umbrella topics. I want to avoid getting too granular with my LGs so there are not too many and that grading can be simpler. For me, a LG is a collection of related topics that I will teach over the course of about 2 weeks (give or take some days).
  2. Categories: There is a reason that I have 9 LGs for each semester–it makes my gradebook work with easy numbers. I didn’t seek out 9. I had more than 9 at various times over the years, but I’ve learned my “sweet spot,” the number that I can easily fill a semester with and that will work for a simple record keeping process. If each LG is a category in my gradebook, and if I weight each LG as 10% of the grade, then that makes up 90% of my gradebook. The other 10%, what I now call the “Effective Effort” category makes up the final 10%. So my gradebook categories look like this: Screen Shot 2016-06-30 at 7.47.44 PMNotice, I no longer have categories labeled Quizzes, Projects, etc. Instead, all these assessment grades are part of the appropriate LG categories. In other words, quizzes, tests and projects make up 90% of my class. The Effective Effort category is where I put grades for homework (which I grade just on completion…my philosophy) and any other classwork points (if you grade on attendance/tardiness, groupwork, participation, etc). What I love about this system, is looking at a student’s grade might look like this: Screen Shots Grades.png These are from a second semester in my middle school class. Can you tell what this student mastered? What she needs help on? Let me clarify the assignments listed:
  3. Quizzes: I give a quiz at the end of each LG, about every 1-2 weeks. These are the summative assessments for each of the LGs, but they are formative assessments for the class. You can see these quizzes in the student gradebook snapshot above. Notice that I also had a graded homework assignment “DeltaMath HW 1” for LG1. My quizzes are always out of 10 points (just to make it easy and consistent) and any other small assessments for the LGs are worth 5 points.
  4. Tests: I see a test as an assessment of multiple LGs all at once. To make grading and recording simple, I write my tests as if they are separate quizzes stapled together. For instance, in the picture above of the student’s grades, you can see there was a Unit 5 Test. This test was 3 pages long, and each page was an assessment of a different LG (LG1, LG2, and LG3). That is why there are three different places the Unit 5 Test is listed in the gradebook. The test was out of 30 points total, but I gave three different 10-point quiz-like grades, instead of a single 30-point grade.
  5. Parent-Teacher Understanding: I need to pause for one second to mention how much teachers and students appreciate this system. Teachers can look at the gradebook of a student they advise and have a detailed conversation about areas of weakness. Parents and tutors can do the same. Rather than saying a student’s grade is low due to some quiz or test, teachers and parents can see that the grade is low due to struggle with a specific topic or two. The gradebook makes more sense. This allows the adults and students to make clear action plans for studying and improvement thanks to the Retakes.
  6. Retakes: An important part of SBG for me is allowing multiple opportunities for re-assessment. If a student struggled with a particular topic on a quiz or test, I allow a retake at any time during the semester. A few notes on that:
    •  A student must make an appointment with me for a retake. It is a privilege, and I reserve the right to say no at any time.
    • Often the retake is just a new quiz, but some students who struggle with test anxiety have worked out alternative methods with me (such as an oral quiz or teaching me how to solve new problems at the board).
    • If the score improves, I replace the old score with the new score.
    • If the score is lower, I do not change the grade, but I have a long conversation with the student about studying and “feeling ready” for a retake…this helps keep down the number of retakes that do not have improved scores after the first month.
    • A student can only retake ONE LG per day.
    • If a student retakes a LG after a test (say the student in the picture above wanted to retake LG2 after a low quiz grade of 75% and a test grade of 60%) and the score is an improvement, I replace all the grades in that category with the new and improved grade, as the student has improved that LG (not just the quiz).

This is my system. I’ve honed in more and more over the years on what I value, what works best for me and for my students, and what is simplistic enough to maintain clarity.



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Thinking on Exit Slips

My school recently had a full day PD with author Ron Ritchhart, author of “Making Thinking Visible.” It was a great PD, and I really wanted to incorporate some of his concrete activities into my practice. One of them having student complete this prompt:

“I used to think ________________________________

but now I think _________________________________”

I wasn’t sure at first where to incorporate it in my class. Then, I decided to use it as an exit ticket. I did this with my seventh graders, after a week of studying rates and ratios. Here are some of the responses:

  • I used to think I couldn’t do them and they were too hard. Now I think I can do them and they’re aren’t that hard!
  • I used to think there was only one way to solve ratios, but now I know there are multiple ways to solve these problems.
  • I used to think that ratios were made up of only two numbers. Now I think there has to be at least two numbers.

I loved these responses better than giving them some random ratio problem as the exit slip because I got to see more of their understanding and thinking, and what I loved even more is through this honest sharing, students were clear if they were still lost. One student wrote

  • I used to think ratios were hard. Now I think they are still hard, maybe getting a little better.

I’ve found that when I give an exit slip problem to solve, students do really well, probably because they have mastered the ability to copy some technique I displayed in class. However, seeing that they got a problem correct on an exit slip doesn’t always clearly tell me who is struggling and who is not.

To push this further, to show how much I value their thinking, I added a spot on my wall where I hung a bunch of these index card exit slips under the title “Our Current Thinking on Ratios…”

I’m thinking in the future I will only do exit slips that involve thinking routines like this. I feel like I gained so much more!

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As we approach Halloween, I just wanted to say how important it is to me to decorate my classroom. It creates a cool atmosphere with my students, and the process of decorating provides a great opportunity to bond with students. I use decorating as a great opportunity to have small talk with students without any guidelines/structure. I get to know them and bond with them.

Here are some pics of what my students and I did this year!


And my costume this year…

IMG_8807 IMG_8812

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Limits as Buffering

I was trying to make limits more interesting for my students and promote better understanding, and I came across this blog post that compared limits a moment when you are watching a video (in this case a soccer game) and your computer goes black for “buffering”. Click on this link for a better explanation:


Putting these screen shots on separate slides, students used what they knew about minutes 3:58, 3:59, 4:01, and 4:02 to predict what happened at exactly minute 4:00.

This led to students making tables for functions and comparing”buffering” to ERROR (on the calculator).

After the first day, I noticed a few students who were exploring a limit as x approaches 4 by making a table with x-values 1, 2, 3, 4, 5, 6. I wanted to emphasize the importance of “zooming in” further. So on day two I made my own set of screen shots (this time using a volleyball game), and I showed screen shots of minutes 2:00, 3:00, 5:00 and 6:00. We discussed how screen shots of these moments was not enough info to predict what happened at 4:00. Too much could have happened between minute 3:00 and minute 5:00!

We were able to come back to the comparison between the soccer game and the volleyball game screen shots throughout the week.

Lastly, I want to mentioned that Bowman has a great blog post on limits with an activity that I also used one day:


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Army Men: Adding Negatives

Thanks to Julie R, I started teaching adding integers (my first topic of the year) using army men. The students LOVED it! So here’s how I did it:


  • Ordered over 100 red and 100 grey army men online.
  • Put 10 grey and 10 red army men into a ziploc baggie for each pair in my class.

The Lesson:

  • Passed out a baggie full of army men (10 red, 10 grey) to each pair
  • Gave students the following rules on a slide:
    • Each partner gets 10 army men of one color.
    • The grey men are called the Positive Army.
    • The red men are called the Negative Army.
    • Partners have to clear a “battlefield” between their army men.
    • Anytime a grey army man meets a red army man on the battlefield, it is a fight to the death.
  • Walked through three examples with them:
    • Starting with “1 + (-1)” I had each partner put one army man onto the battlefield. Since it is a fight to the death, we know there will be 0 men left on the battlefield. Hence 1 + (-1) = 0.
    • We defined this as a zero pair.
    • Then we did “5 + (-2)”, discussing what the answer is and why it must be positive.
    • Lastly, we did “7 + 1”, where there is no battle (the positive army is just adding reinforcements) because there are no negative army men on the battlefield to fight.
  • Then, I gave the students a dozen adding integers problems to work out. I insisted that they act out the “battles” with their army men.

This was such an awesome hands on lesson, and even though we didn’t come back to army men again, the students still brought it up. They knew that 63 + (-80) was going to have a negative answer because there were more negative army men. They also would discuss how 63 army men on both teams will cancel out (subtract).

Huge thanks to Julie for the great recommendation!

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Changing Schools, Part 1: #TMCHANGE

This summer, I moved from my New York City public high school to an independent, all-girls school (teaching middle and high school) in Los Angeles, CA. My new school is dramatically different, but amazing! I’m so excited. The Head of School at my new school is framing this year using Gratitude. So, in the spirit of gratitude, I want to shout out some of the amazing MTBoS people and ideas that have helped make this transition as smooth as it could have been:

  • Julie for sharing all of her amazing middle school activities. Thanks to her, I’m blowing away my co-planners! Army men, stickers, etc, etc, etc = AMAZING LESSONS!
  • Julie for sending me amazing colored pens that I used to write colorful notes to all my advisees!
  • Elizabeth, forever my teaching soul-mate, for inspiring me with Talking Points this summer and sharing all those wonderful resources.
  • Sam Shah, my DH! His amazing virtual filing cabinet and other ideas just blow me away.
  • Thank you cards (that Sam pushed me to buy!) that allowed me to express my gratitude to those co-workers who helped me in these first few days and build lasting relationships with them.
  • Mattie for sending a hilarious dubsmash video that made me giggle after an exhausting, emotional day.
  • Alex Overwijk for inspiring me to cover all my walls with dry-erase boards. It’s SO GREAT!
  • Mary Bourassa for sharing with everyone here amazing Which One Doesn’t Belong site. I think my new math dept colleagues are impressed by this resource!
  • The outstanding MTBoS friends I have made who checked in on me, made me laugh, sent good vibes, or helped me choose a spirit animal. As warm and supportive as my new school is, I needed all of you to get through the past week and a half. Without you all, I would have been crying at my desk at least five times this week.


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