Today I am back with the second half(ish) of my presentation at the Northwest math conference. To get a feel for the flow or to get caught up: Part 1 of my presentation can be found here.
After the discussion on the importance of classroom culture, we jumped right into trying out a few of the activities/strategies. The first was Which One Doesn’t Belong. I have used this activity has a whole class period learning opportunity, but for this presentation I wanted to highlight it was a way to jump start math talk and group students with peers who might think about things a bit differently than they do.
I put up the previous picture and asked the attendees to move to the corner of the room representing their first impression of which picture was the odd one out. Once there, they were to discuss in their corner the reason they choose to see if they were all the same and then each corner had a chance to share out a reason (or a few) that their picture didn’t belong. Then the attendees regrouped into table groups that had at least one member from each corner represented. Teacher Note: Most of the time I’d do this activity with a more math-y example, especially one using similar math to the activity at hand. This way, the grouping by unlike thinking is even more powerful for having different views represented. I chose a non-math example for the presentation since I had no idea of the background of attendees coming in and I wanted to showcase the breadth of examples on the WODB site. This grouping strategy can be done relatively quickly (in place of a warm up, perhaps) and gets kids brains and bodies moving and in math discourse mode right away. You can find more examples of WODB on this site.
After everyone was in their new groups, we jumped into math debates. The following slide gave a jumping off place with a few examples and tips. We had a quick debate on the prompt “Which form of quadratic functions is most useful?” And then in their groups, they spent some time creating prompts or questions which could spark a debate in the classroom. I wanted to highlight a few key ideas:
1. Debates don’t have to be long, complicated or time consuming. We often have 2 minute warm up debates (like the quadratic prompt) as a way start talking and review important features.
2. Kids don’t have to be expected to stake a claim right away. Like the prompt at the bottom right of the slide below. I sometimes assign teams/sides and make them come up with reasons. As they become more comfortable, then I give them a prompt, let them pick their own side, listen to the ‘arguments’ and adjust sides if they were swayed.
3. Almost anything can be debate-able.
Some of the best math debate resources, including the TeamA/TeamB prompt above came from Chris Luzinak and Matt Baker (@pispeak and blog & @stoodle and blog respectively on twitter). I’ve heard them speak live once and have done the twitter thing to find other cool debate resources from them both. Teacher Note: Debates seem scarier to a lot of people than other forms of math talk, but we all have lots of practice arguing so its natural for a lot of students. I make sure I start with prompts that have no right side and often preface the first debates with the idea there is no right answer. Sometimes non-math prompts are good for setting up the structure you want to use (eg: What is the best superpower?). Also… talking about structure you can be rigid: “My claim is….my evidence is…” one at a time or for free flowing letting students jump in respectfully** as they wish depending on class culture and how much experience they have. I often start with more structure and relax it as the year goes on. I don’t cold call as I have seen problem with the stress/trauma of that approach, but I haven’t had a problem with students unwilling to add their voice either directly or by discussing with a peer/group and having someone else share out.
Next we moved into Stand and Talks which are very well explained (and originated?) by Sara Van Der Werf. Her post can be found here. It is basically a play on the turn and talk, but instead of sharing with the person next to you, students physically stand up and move somewhere else in the room to discuss with a peer. I had everyone do this (we ended up in small groups do to space constraints since they needed somewhere to write for the prompt).
I then put up the following slide (again, after the movement). The structure is Conjectures and Counterexamples which I learned about from Dan Finkel (@mathforlove on twitter and blog) at a math teachers circle. Basically, I put up a conjecture and show my examples and the goal is to come up with counterexamples to disprove. I combined this is Sara’s stand and talks as they work really well together. Teacher Note: One of Sara’s tip is to ask for a high number (I used 10) so that students are less likely to be “done” and disengage while others are still working. This doesn’t mean they actually need 10 to continue on to the next part of the activity.
Because this S&T was leading into a bigger activity, I had them move from chatting to grouping at a table and drawing out the counterexamples.
The next part of Conjectures and Counterexamples is lots of fun. Groups were tasked with trying to change the conjecture to make it true (unbreakable!) using the counterexamples as ideas for where the original conjecture ran into problems.
Once the groups had some time to write a conjecture, they used a gallery walk to look at other groups new conjectures and tried to break them if they could. Most were re-broken, so groups had a chance to make their conjecture even better. The idea of drafts is important. Things don’t have to be perfect right away, and looking for counterexamples can help you find holes. (Some example work from my math teacher circle can be found at the bottom of the post here.)
All too quickly, time was running out, so I switched to the last slide to leave everyone with two important thoughts. 1. Our students are kids (even the big high school seniors). We have to remember that in everything we do. This means meany things: they like to have fun/play….but also importantly they still are developing their brains so we need to be okay with them making mistakes and Acting like KIDS!! Acting up doesn’t make them bad, it makes them human. I do dumb things/say things I don’t mean and I’ve had a lot more time to mature. 2. Our kids are Brave and Awesome. When we try new things, it can be scary. Asking a teacher to introduce new ideas/structures/activities is hard and we might screw up….BUT it is also hard for our kids. WE are asking THEM to take the leap of faith and try something new/scary/exciting and more often than not they step up to the challenge and do awesome things with our crazy ideas and they are usually super okay when our idea flops as long as you model how to take responsibility and come back with another go at it.
And as a very last note (if anyone is still reading), one of the best ways to build discourse and culture in a classroom is through circles. I didn’t end up modeling this at the conference because we had too many people (an awesome thing!!) and not enough time, but I kept the slide in case anyone had an questions. We use them at my school to build community, as a piece of restorative justice, and I use them as a way to talk about math sometimes. (Here is a link to some information on circles and I’m happy to chat/answer questions via comments below).