Schedule Overview
8:30–9:00  Arrive, Signin, Snacks and Coffee  9:00–9:15  Welcome  9:15–10:15  Keynote Address: Terry Grant  10:30–11:30  Parallel Session 1  11:30–12:30  Lunch  12:30–1:30  Parallel Session 2  1:45–4:00  Keynote Workshop: Steve Blair (refreshments will be served during a break) 
Abstracts
Keynote Address
Laying the Foundation for Productive Struggle
Theresa Grant (Western Michigan University)
For many of us, the choice of a firstday activity is carefully considered. We endeavor to find a task that will both engage students in doing mathematics and set the tone for the entire semester. For over a decade I have worked on developing a Number and Operations course for preservice elementary teachers (PSTs) designed so that PSTs (re)learn mathematics through problem solving. In this keynote talk I will use the changes to the firstday activities over the years as a context for my growing understanding of the barriers to achieving productive struggle, and my views on how to best support PSTs as they make the journey from rulefollower to meaningmaker.
Session A.1 ~~Theme of Productive Struggle~~
Problems designed to discover mathematical connections
Hy Bass (University of Michigan, Ann Arbor)
Making connections is an idea widely promoted in mathematics standards, curricula, and instruction, yet learners often experience mathematics as fragmentary and disconnected. In a mathematics course (for mostly secondary mathematics teachers) I have been experimenting with problembased ways to cultivate what I term “connected mathematical thinking.” In this session I will illustrate this idea by enacting one such collective problem solving activity.
Session A.2 ~~Theme of Proof and Justification~~
Geometric Area Arguments in Courses for PreService Teachers
Nina White (University of Michigan, Ann Arbor)
In this session we’ll compare and analyze several different justifications to parallelogram area formula. The presenter will highlight one particularly elegant but challenging perspective (a “complementary area” approach) and share manipulatives for supporting PSTs with this perspective. Finally, the participants explore other applications of this particular area justification perspective.
Session B.1 ~~Theme of Productive Struggle~~
Leveraging Confusions to Develop Mathematical Reasoning
Nesrin CengizPhillips, Margaret Rathouz, & Rheta Rubenstein (University of Michigan, Dearborn)
What teaching practices develop and support high student engagement, reasoning, and justification? Using video and student work sources, participants will identify some of these strategies and understand their rationale.
Session B.2 ~~Theme of Proof and Justification~~
Why does it work? A study of the progression of student thought on how to justify an algorithm
Daniel Visscher (University of Michigan, Ann Arbor)
This session centers around videos from an oral assessment in which preservice teachers justify a multiplication algorithm. We will focus on two questions: (1) what do students think it means to justify an algorithm?, and (2) what helps or does not help students progress in their understanding of what makes a mathematical justification? Case studies will be presented in the form of video clips, and session participants will analyze student thinking and consider how to support student understanding of appropriate justification.
Keynote Workshop
Going Off the Pegs: Using an Exploration to Generate Contentbased Questions Leading to Reasoning and Proof
Stephen Blair (Eastern Michigan University)
In this handson workshop we will investigate the simple yet rich context of forming squares on a Geoboard as an example of a mathematical exploration appropriate for preservice elementary and middle school teachers. The focus of our work will be to consider how relevant mathematical content can be unearthed and used by students as they construct objects, organize results, and justify conclusions within this context. Furthermore, we will consider the usefulness of using such explorations to motivate the need for reasoning and proof as students take ownership of their work.
