I am so fortunate to be participating in a two year certificate program called Math Specialists in International Schools (MSIS) at Shanghai American School. It is led by Erma Anderson (an international consultant who is a wealth of knowledge and resources about CCSS and NGSS) and Steve Leinwand (@steve_leinwand). Although I have been very appreciative of PD led by Erma several times previously, this was the first time meeting Steve. He was incredibly inspiring!
MSIS Institute #1 focused on conceptual understanding of the Number and Operations strand from K-8. (In fact, this fantastic 6 min video about the progression of multiplication by @gfletchy is a taste of some of the main ideas we explored and discussed!) It was helpful that I have taught common core as a 6th grade teacher, and that I have been seeing my own children get excited about – and sometimes struggle with – math taught from a common core perspective. I am currently teaching geometry in a HS that will be starting a slow CCSS implementation next year. Here are the key takeaways from the 1st Institute that I think every math teacher should know:
- find and/or modify existing rich tasks (check out Steve Leinwand’s Publications page and click on Great Online Math Resources – AMAZING!)
- the job of a math teacher is to teach STRATEGIES, not just rules to be memorized (school’s ‘math culture’ should be to solve using more than one strategy to show good understanding)
- being able to show conceptual understanding is difficult at first (especially for teachers who were taught procedures to memorize) but it is incredibly valuable and leads to much deeper understanding
- teachers should reflect on whether their teaching focuses on ‘arithmetic’ instead of teaching mathematics
- math is incredibly developmental; if it’s not appropriate, kids won’t be able to “get it”
- a balanced math program is inquiry-based – NOT teacher driven – and focuses on thought-provoking problems to solve
- most important CCSS mathematical practice is construct viable arguments & critique the reasoning of others
- there are not power standards but there are ‘power clusters’ that you spend more time on
- engage students through a ‘gradual reveal’ and intentional questioning
- notes copied from some ‘big ideas’ courtesy of Steve:
Steve was also able to spend one day doing a walk-through with our math department. I was lucky to have him come in to co-teach the first lesson of a unit on points of concurrency. I had created an introductory lesson based on Steve’s method of getting students engaged by asking “What do you see? What do you notice?” I was excited about using his idea of the ‘gradual reveal’ and it was so simple but so effective that I cannot believe I would not have though of it on my own. Here is how I started the unit:
The Center (PDF of PPT)
- What can you find the center of?
- How do you find the center of a triangle?
- Where would you build a hospital? (with diagram)
- What do you notice? What do you see?
As always, I ensure all students are participating through individual whiteboards and discussions with ‘elbow partners’. The last question led to students comparing and contrasting different points of concurrency (PoCs). This was followed by an ‘investigation’ using Geometer Sketchpad, which continued the next class. Next, I gave students 3 ‘real world’ problems that required them to make sense of the problem and brainstorm which PoC would be most appropriate. I loved the conversations, questions, and even arguments, that these questions inspired. It was a great way to start the unit; students were more prepared for the part of the summative assessment that involved finding the appropriate PoC for a ‘real life’ situation. Although this unit did not involve a great rich task, it was an improvement from last year! A step in the right direction 🙂
Looking forward to being inspired at the second MSIS Institute #2 in about a month.
