There were so many great nuggets of information, challenges to how I think about teaching and learning, and possibilities for how I could improve my practice. I was thinking about what would be ONE thing I could really focus on and do right now, and because I want to document for myself now (and return to process later) I am sharing that with you :)
He talked a lot about practices and beliefs of high performing countries that differ from those that are common here. Many of those that seemed to really resonate with me came from Japan - here are the ones that I am focusing on right now:
- All students start a lesson "all over the place" - in America we think students who do not grasp grade-level material immediately have a mathematical illness called "gaps" while in Japan, they focus on the future mathematical health of students by connecting lower grade level methods of approaching the problem to the grade level methods and exploring how/why it works.
- Student work (approaches) is presented in a progression from easiest to understand to highest level mathematical approach. Solving a problem does not mean getting an answer, it means explaining in depth how they arrived at their conclusion(s) to prove that their answer makes sense in a way that is understandable to the students in the class (audience is not the teacher).
- The teacher solicits information about the connections between different methods from students, asking students who used one method to relate to/explain/show connection with another.
- Teacher summarizes progression of approaches, focusing on leading students to grade level (or beyond) approach.
- THIS is the point where teacher might do "direct instruction" (because all students have necessary prior knowledge to connect to grade level approach to problem).
Apparently, much of how math is taught in Japan has been shaped by writer's workshop. I thought that was interesting too.
Anyhow, there was WAY more stuff packed into that talk, but gotta process!
So here's my plan for the next two days:
Monday: Focus is on gathering evidence of student understanding (this is technically review, but I am doing it because I know it is an area of need still and also pretty much the point of 8th grade).
- Give student Dominoes Pizza prompt (I went to the online ordering tool and put a two topping medium pizza and a 4 topping medium pizza, then took a screen shot). This idea is totally based on a Mathalicious lesson, by the way. You can find that here.
- Do Notice/Wonder
- Pick some good "wonderings" to answer (I imagine we will predict the price of some other medium pizzas with different amounts of toppings, and I will push them to work towards an equation - it would be CRAZY cool if a kid asks that as a wondering... we'll see).
- SILENT independent work for 1:30 (2 minutes is still too hard! LOL)
- Continue working but discussion is permitted (I will float around room, ask questions, see different processes being used, start to pick who will present and in what order)
- Full explanation of process and why it makes sense is required. All parts of any equations must be identified and explained. (I will check in with students who I want to share to let them know so they are prepared and there won't be drama when I call them up)
- Selected students will present solutions. Audience will be looking for the best thing that student did to help them understand, and the one aspect that was the most confusing/unclear. Random select for feedback.
- As each new student presents, I will ask audience about connections from one solution strategy to the next.
- At end, I will summarize, focusing on how the different strategies are related to the equation, then ask students to add reflection on the summary to their own explanations
Tuesday: Focus is really on the explanations, giving and getting feedback, revision.
- Give students Me N Eds prompt (A sentence stating that Me N Eds charges $9.50 for a 1-topping medium pizza and $0.75 for each additional topping. The equation m = 0.75t + 9.50 is given, but variables are not defined). Students are asked to prove that the equation represents the situation. They must identify what every piece of the equation means/represents and give examples to back up their reasoning.
- Time limit for completing draft explanation (I'm starting w/ 10 min, but willing to extend some - will have to see how things go)
- Break students into pairs - one student presents to the other. The watcher chooses best thing that helped understanding to praise and suggestion for one area that was vague or confusing. Then they switch roles.
- Students have opportunity to update drafts using feedback from partners
- Selected presentations
- I will summarize and do a quick mini-lesson on extracting y=mx + b from situations, using student examples as evidence.
I am nervous about many aspects, but also hopeful that I may have finally found a way to address concept development AND reasoning/communication at the same time.
Oh... and by the way... we are having walk throughs during this too. Wish me luck! ;-)
