Reasoning and Argumentation Getting it started and sustained

Mathematical Reasoning “From children’s earliest experiences with mathematics, it is important to help them understand that assertions should always have reasons.” d “Why do you think that?” “Does anyone have a different answer?” “Oh, really?” National Council of Teachers of Mathematics (NCTM) (2000).Principles and Standards for School Mathematics. Reston, VA: NCTM.

What do you get when you add two odd numbers? An even…. …. an odd The sum of two odd numbers: Really?

Mathematical Reasoning “Classrooms in which students are encouraged to present their thinking and in which everyone contributes by evaluating one another’s thinking provide rich environments for learning mathematical reasoning.” y x ½ x y y x National Council of Teachers of Mathematics (NCTM) (2000).Principles and Standards for School Mathematics. Reston, VA: NCTM. What can we say about the second rectangle and the triangle? A = ½ x * y A = ½ base x height If this is such a good thing, how do we get it going in our classrooms?

Ideas in Action: Get a Second Sentence Are you sure? Is there a way you could figure that out? How does that help you? Why …. ? This ^ is a place holder for the video.

Argumentation & Reasoning How did this teacher orchestrate her curriculum and her instruction so as to enable or scaffold student involvement in reasoning? This ^ is a place holder for the video.

Argumentation & Reasoning How did this teacher orchestrate her curriculum and her instruction so as to enable or scaffold student involvement in reasoning? She decided to create extra time for test prep … ; consulted with a colleague about discourse; required students first to engage in a problem that mattered to them and that was in their ZPD; picked questions that had multiple solution paths; scaffolded their discussion: – taught a lesson on how to disagree; – provided them with productive starter questions, etc.; had them grade one another with a rubric; had management issues well in hand.

Activities for Discussion Sections Divide into interest groups. Tasks 1.Discuss how you see teaching argumentation is a holistic process. 2.Discuss the difficulties in teaching argumentation and reasoning, the tools or strategies that you think are helpful to your students. Provide some of the tools or strategies you would like to share with others. 3.Pick a problem provided in the handouts or create your own problem. Discuss the math practices, SBAC claims and CCSS math contents used and your teaching strategies of helping students solve the problems and truly understand the math concepts behind.