Connecting Math and CS with probability game simulations

One of my goals for this school year was to build out a few interesting and relevant projects into the 7th grade curriculum, which seemed a bit dry and skill-focused. One area that seemed to beg for an application project was the first unit on Data and Probability. Since one of my other goals was to incorporate more computer science into my classes, it was a no brainer. Developing a cross-over computer science project for this grade level proved to be a bit tricky because students are all over in terms of their experience with programming - we have students who have been coding for years as well as new students who have never coded anything before. I tried to develop a project that would differentiate appropriately and allow students to either explore the CS or the Math parts in greater depth, depending on their interest in and experience with programming.

Here is the project description. You'll notice that I created three distinct strands with different goals and let students select the one that was most appropriate and interesting for them. I was also lucky that the computer science teacher was able to come to my classes for some of the time that students worked on this project. Having many intermediate checkpoints for students to submit pieces of the project was very helpful here in ensuring that I could identify those who were behind or struggling and work with them during class.

Things that I would still like to build out:

• A more robust peer editing process -- I'd like students to be able to present their optimal winning strategy to peers and get critical feedback on how convincing their reasoning is that they would be able to incorporate into their final draft
• A revised rubric to make it more concise
• Move some pieces of this project out to computer science class - this definitely took up quite a bit of time, especially because I felt that most or all of the coding work should happen during class where students would have support
• A clearer division between group and individual aspects - this is always a challenge for me when designing group projects in terms of maximizing student learning and individual accountability. Students seemed to work well together during class, but this isn't an explicit part of the project currently. 
• Some sort of final presentation - for projects like this, I think that having the final product on display or presented to others creates a much more authentic need for clarity and functionality. I haven't figured out a good way to do that for this project. Should students do a gallery walk of projects within the class? Can this be presented or shared with students in other classes somehow? What about with parents?
• Other connections - is this something that can connect to students' work from previous years so that it feels less like a stand-alone project and more like a continuation of ongoing work and thinking? Are there other aspects of this project that can connect to other disciplines, like writing? Can we build on this in future years of either computer science or math curriculum?

Starting Lesson Study and Update on Classes

This isn't going to be a very coherent post, but I need to get our current work into writing to better organize my thoughts. Here are the projects that are in progress right now:

• Lesson Study

• We've broken up our Upper School Math teachers into several groups of 3-4 teachers who teach across different grade levels. We considered doing a more traditional lesson study in which teachers plan a lesson centered around specific content, but decided to focus our efforts on developing our practice around a particular instructional routine that would be relevant across many grades and that would help us fine tune a specific pedagogical approach and learn from colleagues with whom we rarely get to work.
• Everyone read this article from KQED to orient themselves to the lesson study process in advance of our first meeting.
• Each group selected an instructional routine to plan out, teach, and refine this cycle. The routines selected were:
• Differentiation for students who learn at different paces
• Guided investigation
• Students giving feedback to each other

• In the next meeting, groups will plan a specific lesson around their instructional routine based on the first teacher who will be modeling it and decide on an observation time and what to look for when observing
• I'm super excited for this initiative to be gaining traction! We got some time to work on this while students were taking the PSAT or doing other activities, but I'm worried that if we don't get specific time off to work on this, people will become significantly less enthusiastic. 

• Parent Math Night
• Our team is working on developing an informational night to help parents better understand our program, available resources, and philosophy. It's just in the planning stages, but I think will be really helpful in getting on the same page with families. Right now, whatever information they receive when applying is the extent of it. 
• This needs to be thoughtful and informative for parents while also clearly conveying our position and getting buy-in and understanding of the program. If you have any resources or ideas to share, would love to have them.

• Math 1 is finishing our unit on Counting, Probability, and Sets, designing a game that has students analyzing probability and expected value to determine best strategy and fair outcomes. Next week, students will be playing each other's game and reflecting on what they've learned. This is a good opportunity to differentiate and identify gaps in understanding linear functions and algebraic manipulation skills as we prepare to move into a functions unit next.
• We're starting each unit with a "preview" assignment to look at prior knowledge and pre-requisite skills and concepts so that those students who have gaps can be identified and given extra support. Here is the preview assignment for linear functions.
• We're also starting the unit with another open investigation, this one more directly related to functions ("Cutting the Pie" task from IMP Year 1). I'm curious to see if students pursue a recursive or closed rule for this function. When we worked with Pascal's triangle patterns, students had a hard time moving from "each row is twice the previous row" to the rule f(x) = 2^(x-1).

• Math 2 is still in the depths of statistics, working through the Central Limit Theorem and connecting probability and the normal and binomial distributions. I'm realizing how much better I understand the material in my third year of teaching it and how much less formulaic and prescriptive my teaching is now that I have deeper content knowledge in this mathematical space. I have known that strong content knowledge is necessary, but it's amazing how much more depth is needed if you want students to explore and create and test their own theories, both in terms of creating those scenarios and in guiding the discussions that ensue. Maybe it's true then that teachers have to first progress through traditional pedagogy as they build up their depth of content knowledge before they can start to incorporate more problem-based or project-based learning. Would love some pushback on this though :)