I am starting the school year in precalculus having students develop both their collaboration skills and their ability to model real world scenarios with mathematics. It is the beginning of the school year and many learners are still a little uncomfortable with each other and with their confidence in math class. I wanted to have a productive class discussion, and to make students feel safe to engage in dialogue around the content. I decided to create a discussion that appeared natural as a gateway to get some of the less confident learners engaged in the content.

At the start of class I presented a scenario to optimize by modeling with mathematics. Learners worked in randomly assigned small groups to develop an optimal solution and then, in the last 20 minutes of class, each group was to present their solution and reasoning. I wanted the learners in the audience to ask challenging questions to learn more about the groups thinking after each presentation.

Here is what I did:

While listening to learners work on a task in small groups, I circulated, listened, and wrote questions for each group on separate index cards. I was also thinking about how to sequence their presentations based on their approaches as described in the book, 5 Practices for Orchestrating Productive Math Discussions.

When each group was setting up to present, I would discretely hand the questions written on index cards to a less confident learners. After the group presented their thinking, I would ask, “Does anyone have any questions for this group?”

The learners would look around nervously in an awkward silence while I glared uncomfortably at a learner with an index card. Eventually, uncomfortable with the silence, the learner would ask the question on their card. Then, the presenting group would respond, which led to genuine student questions, thinking and further discussion.

By the last groups presentation, many of the learners seemed comfortable to ask questions and engage in thoughtful whole class discussion!

Soapbox debate: provide class with a debatable prompt, and a minute to think. Then student must stand and state their claim and warrant to the prompt. It’s more fun if you randomly call on students.

Always, Sometimes, Never statements: students summarize previous idea, then state their argument.

Point-Counterpoint: use would you rather questions. Students must alternate arguments, so they have to disagree with previous person.

Table debate: assign student to teams to develop arguments, and then have the teams debate.

How to encourage debate:

add debatable terms to questions – best, worst, most efficient, should, biggest, smallest, most, weirdest, coolest, always, sometimes, never

Change boring math into a debate – Given an equation, ask,

What is the best way to graph this?

Which number would you change to change the graph the most?

This graph will never go below the x axis

Full Scale Debate:

Divide the class into 4 teams. Provide students with a carefully constructed scenario and 4 different stance’s to argue (example provided with musician recording contract).

Students read a variety of texts or resources on a topic, then consider questions in a large group discussion.

examples of questions to consider:

What are some strengths and weaknesses of each presentation?

When would each text be appropriate to use?

What difficulties may students have?

This sounds like a really interesting thing to do in math class. I need to learn more and see it in action so that I can implement this effectively.

Critical thoughts to creating a successful debate culture:

the accumulation of many intentional, small teacher moves over time sets the culture of student talk

When you want students to talk to each other, the teacher must SIT DOWN. make yourself small, and not the center of attention. Encourage students to talk to each other. If it is a whole class debate, have the student talking STAND UP. Slowly back out of the center, have students call on their peers.

Start early

Keep it simple. Use basic soapbox debate for the first month or two.

explicitly talk about what active listening looks like – be very specific (not writing, looking at the speaker, knees pointing toward the person speaking…)

ideally, dedicate about 5 minutes per class 1-2 times per week

provide structure (argument = claim + warrant ) and verbal cues

Occasionally, have students do a quick write providing an image and a word bank. This will help students to practice communicating mathematically.

Keynote: Jose Luis Vilson

We need to talk about race with our students and give them a safe space to grapple with their thoughts. In math instruction, the goal is to teach students to grapple with tough problems for which the solution is not already know and work towards a logical and reasonable resolution. This same principal can be applied to social justice issues.

Some questions/statements for students:

I just want to hear what you have to say

Why do you feel this way?

Where is your compassion/empathy?

We need to become comfortable getting uncomfortable and evangelizing for our truths. Avoiding confrontation and being polite can be destructive in the end.

She shared a very complete and organized collection of quality, basic stuff. Progressions, lessons, strategies. I can’t wait to use and adapt it for my first year of teaching pre-calc in a while.

Experience Connecting Representations – David Weiss

post more equations than corresponding visuals (task is to match the visual to the equation/expression)

provide individual think time – What do you notice?

Time to discuss with a partner (teacher circulates, listens & asks a pair if they would be willing to present their thoughts to the class)

display verbal cues:

Presenter

We saw ___ so we connected ____.

_____ matches ______ because ______.

Audience

They noticed ____ so they _____.

Their connection works because ______.

5. Get presenter’s to the front. One can only speak and the other can only point. They explain their thinking for one pair. Keep this light, safe & fun. If a student does not explain clearly enough or missing key elements, just let it go, they will most likely come out in later explanations.

6. Ask a student in the class to re-explain the presenter’s thinking

7. Teacher record thinking while a new students explains.

Repeat from step 5 with a new pair of students.

Once all problems have been paired and described by the class, have the pairs try to create a visual mode for the remaining equation that was not paired to a model

Close by having students complete a written reflection.

Explore Math – Sam Shah

Sam talked about a low stakes high reward assignment that he gives his students. They have to complete 4 or 5 mini explorations on any math topics of interest to them (with incremental due dates) and complete a brief written description or some evidence of what they did.

He turned the advanced math classes into a ‘club’ called varsity math and created t-shirts, stickers, party’s and a summer camp to go with it. He also made recruiting posters and placed them at the middle schools in order to motivate students and create a buzz around taking more advanced math classes.

This is a great idea! I recently convinced 10 students at my school to take a more advanced math class and I think I will have to figure out how to adapt this concept to fit my tiny group in an effort to get this group to grow in future years.

She opened my eyes to recognizing the different skill sets that elementary and secondary teachers have and the importance of valuing these skill sets and why we should try to break down our comfort barriers to get over ourselves and learn from each other.

I think I need to write a whole additional blog post on how individuals’ comfort seeking needs really limit our happiness, growth, empathy and success. (an ongoing theme this conference)

In this session we progressed through these steps to develop a model for ranking roller coasters, but the big idea here is more about how to facilitate this process. It would apply well to geometry tasks including 3 act’s such as best square or Mathalicious’ Face Value (my post on this task).

We need to be thoughtful and intentional, not just resource collectors.

This resonated with me as I am an avid idea collector, but I struggle with how to make a curriculum coherent. I want to work on criteria for coherence and re-evaluate the content of my current classes.

I didn’t use Plickers much last school year because I don’t ask a lot of multiple choice type questions in my classes. Most are more open ended to expose depths of student understanding. This school year, I found a way to use Plickers to facilitate group discussions and I am so excited to use them more this year!

While I am effective at supporting small groups working in my classes, I am not always the best at facilitating whole class discussions. I knew I wanted to hear students thoughts and dispel myths on how to learn math early in the school year. I have started this discussion in past years using Bowman Dickson’s survey found here.

I discovered that when setting up Plickers, you do not have to select a “correct” answer. Instead I decided it would be insightful to make the multiple choice options into a Likert scale.

This way after each question I could project the response graph. It was perfect to be able to just show students their peers ideas and allow discussions to happen with little facilitation from me!

For example, when I projected this question, and then the response graph, a student said,

“How can you agree with this? We can always learn more and improve.”

Then students who agreed chimed in citing how their parents can’t do math, so they can’t do math.

To which the students who disagreed argued that you can change what you understand through learning and effort…

I let it continue occasionally asking probing questions. It was interesting to see how dispersed student responses were, and great to have this data to look at later.

I plan to complete this survey again later in the year to see if students move more towards a growth mindset with respect to learning math through the school year.

Another thought I had through this process was how Plickers could be used to facilitate Talking Point discussions too.