KTMT Research Action Cluster Knowledge for Teaching Mathematics Tasks Update for the CSU-MTEP Convening October 10-11, 2014

KTMT RAC Partnerships and Universities Greater Louisville Mathematics Teacher Education Partnership University of Louisville University of Kentucky Cincinnati Regional Mathematics Teacher Preparation Partnership University of Cincinnati East Central Texas Mathematics Teacher Education Partnership Texas A&M University Sam Houston State University Treasure Valley MTE-P Boise State University Kent State University Partnership Kent State University

The Problem Preservice teachers experience learning in their mathematics classes very differently than they are expected to teach mathematics. The mathematics knowledge preservice teachers develop in their mathematics coursework does not fully align with the Mathematics Knowledge for Teaching needed for their profession

Cause Mathematics instructors are not commonly provided instruction or guidance for teaching. Mathematics instructors typically focus on the mathematics content not on student learning Materials for mathematics instructors do not typically provide adequate support for instruction or assessment Mathematics instructors are not commonly familiar with student challenges and misconceptions with mathematics topics Some mathematics students may not be prepared to succeed in current mathematics class formats

Purpose to develop meta-tasks guide the instruction and assessment of the mathematics knowledge for teaching of preservice and inservice teachers to develop meta-tasks to inform mathematics instructors of misconceptions and challenges for learning mathematics topics provide strategies to address them

RAC Driver Diagram

KTMT Links to Mathematical Preparation

AIM Statement By December 15, 2014 the KTMT RAC will develop and validate a prototype task that focuses on documented calculus misconceptions and supports student ways of knowing mathematics as described in the PCAST and METII. By March 15, 2015 the task will be implemented by at least 8 calculus sections across four institutions.

Measures Used Survey of calculus instructors on student misconceptions and difficulties (ready to distribute) KTMT Task pre-test (limit) KTMT Calculus post-test (limit) Calculus task on limit Instructor feedback survey

General Approach I Clarify the problem – Students and instructors seem frustrated and not as successful as desired Identify components of the problem – Student learning issues (preparation, misconceptions, etc.) – Instructor issues (preparation, tools available, focus of instruction) Target the leverage points of the problem – Address students who show up – Help instructors currently teaching – Focus on classes most students take

General Approach II Create a structure to address the problem – Provide learning experiences for students that align with MET II and Mathematical Practices of CCSSM – Share materials to inform mathematics instructors of misconceptions and challenges students face with specific mathematics topics with strategies to avoid or address those issues – Include pre- and –post tests to measure students mathematics knowledge – Embed formative assessment to inform about student learning and guide instruction – Create an teaching model for mathematics instructors that aligns with MET II and the Practices of CCSSM

Approach to Tasks Focus on mathematics instructors AND students (meta- tasks). Target change in instruction and learning Include assessment tools to measure instruction and learning Study guidelines and existing test and assessment materials Review literature for misconceptions in content area Create template and guidelines for tasks (blueprint) Form teams to develop tasks in content area Develop individual tasks with rubrics Validate tasks with external reviewers Field Test tasks and revise as needed Distribute to partners for final testing.

Current Activities NSF proposal was denied IES proposal was not encouraged Developing a prototype task to be competitive for funding.

Small group face to face meeting in Boise – to create first task and finalize model – Prepare resubmission of proposal to NSF Release calculus instructor survey Field test first task Next Steps

Participate in calculus instructor survey – Distribution – Responding to survey (if appropriate) – Providing feedback Edit drafts of tasks Field-test Tasks – Distribution – Trying in class (if appropriate) – Providing feedback Opportunities for Involvement

KTMT Questions? Comments?

Rationale for Calculus as a Focus Calculus is among the first college mathematics courses taken by all preservice secondary mathematics teachers and thus is a natural place to initiate the development of positive mathematics experiences for preservice secondary mathematics teachers. Calculus is foundational mathematics content--a gateway to higher mathematics. Calculus provides an entry point for students to make connections between college and secondary mathematics. Although most students in calculus classrooms may not be preservice secondary mathematics teachers, creating engaging experiences is important to all STEM majors as noted in the PCAST report (Olson et al., 2012).

Rationale for Calculus as a Focus Formative assessment tasks that encourage engaging learning experiences have been shown to be successful (Olson et al., 2012). Positive calculus experiences may help students to contemplate teaching as a career choice early in their college studies. Most research in mathematics education at the preservice teacher level is focused on methods and/or capstone content classes for the coursework preparation of teachers – addressing content courses is long overdue.

Calculus Instructor Survey Web-based survey Calculus instructors Students’ conceptual challenges Six sections Qosu702l79QLZQ/viewform Functions Limit Rate of Change Differentiation Integration Fundamental Theorem of Calculus

Instructors are the primary target of the tasks Creating a learning activity around the tasks Focus on embedding assessment in instruction. What is the problem What is the general approach Here is the approach ---teaching the math not the students; etc. Reconfiguring what we are doing As a teacher what is the task – meta-task How does it fit with Active learning and BCC Can there be other tasks around intro to proof. Or Abstract Algebra--- Now working in the domain of Active learning