CMP conference day 1

June 20, 2016 CMP Summer Workshop Digging Deeper

Dot Walk

Our class began today with dot posters! After being given a sheet of sticky dots, we placed dots on chart paper diagrams and graphs to indicate our place. For example, a Venn diagram indicated what grades we taught, a coordinate plane poster showed years taught on the y axis and years teaching CMP on the x axis.  We made a dot plot according to our educational role (teacher, coach, administrator) and we plotted where we were from on a almost recognizable "map" of the United States. 

After all the dots were placed, our instructors led us in a Notice and Wonder where we explored patterns and addressed the yellow dot outside our Venn diagram (administrator) and the blue dot living in the ocean (he was from China.)

I see this as a great activity to use returning from summer break. I will need to think more on the categories I will use (maybe a coordinate plane looking at books read and movies watched?)

Survey of Beliefs and Fishing

We then examined our math education beliefs using a survey developed by NCTM in Principles to Action. While we all knew what our answers should be, we had a lively discussion on specific words in questions 7 (master) and question 2 (exactly.)  Knowing the right answers (principles) is at least a step towards implementing (action) mathematics in classroom that will lead to effective learning.   It's tough to see kids struggle, but if we always catch the fish (math) for them, without us they will starve (or at be unable or willing to even start a unique problem.)

How do we teach them to "fish" in math? By not answering their questions....directly. Answer  their question with another question to see just how much help they need baiting their hook! Maybe even wait until the class summarizes the problem if it is appropriate. CMP has a definite lesson flow. Launch the problem, let the students explore, and summarize as a class at the end. Both explore and summarize are excellent places to ask students questions to move them along and check for correct mathematical reasoning. Make sure their questions get answered, but help them get their on their own or you will be fishing all year for them.

Proportional Reasoning, it all Connects

With class sets of 6th, 7th, and 8th grade books we began to look at the critical concept of proportional reasoning.  This is an important step in mathematical development, moving from an additive relationship (more means you are adding) to multiplicative (comparing ratios for more per item). After a quick write on our understanding of proportional reasoning, we were given a problem to work from Comparing and Scaling in 7th grade where students are mixing juice.

Which one is the the strongest? We were given chart paper to explain our reasoning. Our facilitators  walked around, writing down some of our comments and answering questions with questions to move our thinking along. 

Several of us had done the problem already, and took a bit of a back seat. One important comment came up about students having no idea what concentrate was (especially liquid, because they were used to powder.)  

After all posters were up, we started a class discussion. First we looked at the most common solution (creating a part to whole ratio and then looking at percentages.) Then we examined and questioned several others (them most controversial looking at a digram representing 1 cup of water (unit ratio). We also examined students who just divided the first number by the second to get a decimal (2/3= .6 repeating) and then turned it into a percent and why it is not the same at the percent of part to total (40%). We discussed scaling up and down (unit ratio) as well as comparing to benchmark fractions.

We then brainstormed at all the information students could use to access this problem. Then we examined the CMP3 books to see where we could find those concepts.  Below is a summary.

Summary of concepts and where they are found

Orchestrating Productive Discussions

Our last activity of the day involved one of my favorite, and most challenging books, 5 Practices for Orchestrating Productive Mathematical Discussions.  The basic premise of this book involves pre -planning discussions including planning all the ways students will answer the problem, how the teacher will respond to any misconceptions with questions or counter examples, as well as how to sequence the discussion to make a mathematical story that connects smoothly. Quite a task when you have student variables! It is easy to see how amazing and overwhelming this concept is. In several of my lessons I have attempted to chart anticipated student responses. I will continue my work on this next year, as I find charting it makes my discusssions more relevant, efficient, and, when it goes well, beautiful!  The following is my example from the pizza problem in Comparing and Scaling investigation 2.

Chart of student responses and sequencing

Our day ended with a Ted Talk by Diane Laufenburg on How to Learn from Mistakes.