1. Black Swamp Math Teachers’ Circle
Funding for this project through the Ohio Board of Regents Improving Teacher Quality Grant

2. WELCOME
Discourse
Devil and Daniel Webster
Mathematical Practices

3. Mathematical Discourse

4. Phil Daro
Telling vs. Tilling

5. What is Discourse?

6. Discourse
Mathematical discourse includes the purposeful exchange of ideas through classroom discussion, as well as through other forms of verbal, visual, and written communication.

7. Discourse gives students opportunities to:
Share ideas
Clarify understandings
Construct convincing arguments regarding why and how things work
Develop a language for expressing mathematical ideas
Learn to see things from other perspectives
Promotes reasoning and problem solving
Develops conceptual understanding d

8. 5 Practices for Using Student Responses
1. Anticipating student responses prior to the lesson
2. Monitoring students’ work on and engagement with the tasks
3. Selecting particular students to present their mathematical work
4. Sequencing students’ responses in a specific order for discussion
5. Connecting different students’ responses and connecting the responses to key mathematical ideas

10. Mindset
Fixed or
Growth
Carol Dweck

11. What is a MTC?
A Math Teachers’ Circle is a professional development community of mathematics teachers and professors who meet regularly to work on rich mathematical problems. The goals are to encourage teachers as mathematicians, connect mathematics professors with K-12 education, and build a community of mathematics professionals committed to fostering a love and understanding of mathematics among all students.

12. The Devil and Daniel Webster
Gabriel – Ask teachers to share some thoughts on what anyone might say are “qualities” of the Devil. --jot these down on the board or poster paper.
So with these qualities, “can we trust the devil?”
We should rigorously examine his proposition, without giving up, to see if we would take his deal.

13. The Devil and Daniel Webster
The Devil made a proposition to the attorney Daniel Webster. The devil was in need of a lawyer and so he proposed to pay Daniel for services in the following way:
The Devil said, “Daniel, on the first day I will pay you $1000 early in the morning. At the end of the first day, you must pay me a commission of $100, so your net salary that day is $900. At the start of the second day, I will double your salary to $1800, but at the end of the second day, you must double the amount that you pay me to $200. And so on and so forth. Will you work for me for one month?”
Gabriel – Revisit Task Norms and Presentation norms of our Math Teacher Circle – No stealing ice-cream
Ask teachers to share some thoughts on what anyone might say are “qualities” of the Devil. --jot these down on the board or poster paper.
So with these qualities, “can we trust the devil?”
We should rigorously examine his proposition, without giving up, to see if we would take his deal.
Work on the tasks alone at first…negotiate with your shoulder partner when to share ideas.
Gabriel will select and sequence.
ENCOURAGE Teachers to represent their answer in different ways, tables, graphs, equations
Move to next slide during share time…

14. How did You Explore the Devil’s Proposition?

15. What are some other mathematical questions that could be explored?
Can we represent this with an explicit algebraic formula?
Picking your favorite month of the year, how much would you owe the devil?
How could you modify the problem so that the Devil’s proposition seems like a good deal longer than 10 days?

16. Daniel Webster and the SMP’s
Gabriel – “The SMP’s are Daniel Websters’ Friends in his pursuit to solve and refute the Devil’s Proposition.”
Now that we have thoroughly explore the task, let’s consider the SMP’s
Divide all the teachers into 8 groups. Have each group explore a particular SMP and justify whether they used it in the solving of the Devil’s Proposition.
--Teachers must use text from the SMP paragraphs to count it as evidence of that SMP
“The SMP’s are Daniel Webster's Friends in his pursuit to solve and refute the Devil’s Proposition.”

17. Reflections What did you learn about problem solving?
What did you learn about teaching problem solving?
What would you do differently?