#talklessAM (or the nitty gritty on starting debate)

I just got back from TMC16, where I was lucky to get to co-facilitate a three-part morning session called “Talk Less, Smile More: Getting Students to Discuss and Debate Math” for a big group of awesome teachers! My co-facilitator Mattie was awesome! The group was awesome! What a great time!

Gloating aside, one question that always comes up when I talk about introducing debate is How to Start? In the session, we talk about sentence starters, writing good questions, and give participants time to experience the activities, but there’s still that question on how to explicitly begin. On top of this, I just had a phone conversation with a great public school teacher in LA that had been to a workshop of mine a month earlier. He is going into his third year, but his commitment to try debate this coming year and his deep questioning of the how to get started was inspiring. Through all these conversations, I’ve tried to nail down all the important details of how I begin, and I thought I’d share the nitty gritty on how I get these routines started in my classroom.

(Disclaimer: this is just a detailed account of how I do it. There is no one way, but hearing this may help you figure out your way.)

Day 1: First day of school is usually a little chaotic: students need to find the room, find a seat, fill out and decorate a nameplate, get a syllabus or supply list, etc. Sometimes the classes are also short. So I usually don’t debate on Day 1. However, I do get the community of discussion going by forming a circle and having students  introduce themselves, usually with their name, where they are from, and then something goofy like “my one superpower would be” or “if I could be any cartoon character.” I follow that up by doing some math. It is my philosophy that in a math class, we should do some math every day. There are a lot of great open ended, all level problems to start with like the Locker Problem, The Camel Problem or the card challenge “Skip Flip.” I will have to share these in another post.

Day 2: I want to introduce debating as soon as possible. So Day 2 is usually the day. When students enter, they see directions on the board to create an argument for three different topics. As they file into their assigned seats, they silently take out their notebooks and attempt to write an argument for each prompt. The slide looks like this:

Screen Shot 2016-07-25 at 1.57.43 PM

After some writing time, I have all the students stop and tell them that before we begin, I need to teach them HOW to make an argument/how to debate. (This used to make total sense at my old school when I was the debate coach, but students at my new school don’t seem to mind.) I show the following slides:

Screen Shot 2016-07-25 at 1.58.54 PM.png

Screen Shot 2016-07-25 at 1.59.00 PM.png

I briefly give the definition of an argument, but I try to minimize that. The key is the way we breakdown an argument into Claim and Warrant. So I define those two words for the students and then say that the mathematical formula for an argument is


I stress that the only thing they have to takeaway from this slide is the sentence starter:

 “My claim is…   and my warrant is…”

I also have this hung on all four walls of my classroom. It is important to have it on multiple walls so that students can see it no matter what direction they are facing during a discussion.

Screen Shot 2016-07-25 at 2.00.36 PM.png

The next slide takes us back to the original three questions that I want students to make arguments about. This is when I give them the directions for how to do a “Soapbox Debate.” (This phrase is a bit outdated to our students, but I love explaining it to them.) Directions are:

  1. When you are called on, you must stand.
  2. You must use the words “my clam is…   my warrant is…”
  3. If you are not speaking, your shoulders and knees must turn toward the speaker.
  4. Our eyes should be on the speaker (who should be standing)
  5. Only the person standing is speaking. The rest of us are listening.

When I give the directions, it is done orally and they are not numbered. I simply explain them. I just listed them out for ease of reading.

Then (and this is where it takes a moment of bravery on the teacher) I jump in with the first speaker! Some notes on this:

  • I usually ask for volunteers in the first days of school because I don’t want to make a shier student too uncomfortable (and I will work out ideas with them later)
  • That said, sometimes students can all be quiet. So I may have to cold-call on students. It can be startling, but I try to do it with as much positivity and as non-pushy as possible.
  • I make the speaker stand. Even if they don’t want to. I just smile/laugh, say it’s ok, and tell them to stand up.
  • I correct the speaker on the spot if they don’t use the words Claim and Warrant.
  • I sit down before I call on the first speaker. I want the speaker to be the only one in the room standing.
  • I am hyper-vigilant that every student is turned toward the speaker and looking at the speaker. Though I have passed over the discussion control to a student, I am working even harder to make sure everyone is following along (while trying to keep all messaging positive).
  • After the first student, I (still sitting) call on another.
  • Depending on the question and responses, I may only have 3, 4 or 5 speakers for each question. That means 3 students share their favorite movie, then I move onto the second topic and have a few students share out. Sometimes it’s only 1 or 2 for whatever reason. I try to read the room.

And that’s it. Overall, it may take 5-10mins only. I am very actively watching students, correcting body language and sentence starters.

The rest of class may not involve explicit debating again. Early in the year, I tend to just spend roughly 5 minutes per day doing debate activities as the warm up. Then, even though I do not explicitly do a formalized soapbox debate, the culture of student discussion often spills over into rest of class.

Final Thoughts:

  • Standing is important. Students may be a little uncomfortable but it is important in establishing the culture and getting students a little out of their comfort zone/passive learning.
  • Using the sentence structure “my claim is…my warrant is…” is something I stick to in every response. In later weeks, I may not bother to correct students who don’t use this exact structure, but stressing it in the beginning sets the pattern that answers always have two parts in my class. Students just get in the habit of always explaining their work.
  • When I introduce all the structures, I always start with some kind of “fun” topic, like the best movie or best musician. After that we only debate math. It helps to lower the stress of learning a new structure if the content is something students find interesting and are easily opinionated about.

And that’s really it. Everything else I do throughout the year is just variations on soap box debating, a mix of oral (standing) debates and written work that includes warrants (explaining).


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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…

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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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