KTMTResearch Action Cluster

Knowledge for Teaching Mathematics Tasks

Update for the CSU-MTEP ConveningOctober 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 UniversityTreasure 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

Create a “gold

standard”To develop

shared measures and benchmarks for teacher preparation

programs and their

graduates.

More and better new teachers

To graduate <target

number> secondary

mathematics teachers who achieve these benchmarks

with an emphasis on increasing diversity.

I. Shared vision of preparationCreate shared understanding and commitment among mathematicians, mathematics educators, and K-12 partners.

II. Clinical preparationImprove teacher candidates’ intern experiences by partnerships with mentor teachers and other stakeholders.

III. Mathematical preparationDevelop teacher candidates’ knowledge of mathematics needed to support student learning.

IV. Recruitment and retentionAttract, retain, and graduate an adequate supply of teachers.

A. Stakeholder involvement.B. Institutional support.C. Focus on student learning.D. Building a learning mindset.E. Tools for collaboration.

A. Mentorship.B. Partnerships.C. Evaluation.

A. MET II recommendations.B. Ways of knowing and learning.C. Coherence of courses.D. Assessment of knowledge.

A. Recruitment to program.B. Retention in program.C. Retention in profession.

KTMT

Improvement Target Primary Drivers Secondary Drivers

Relation to Overall Drivers

RAC Driver Diagram

I. MET II RecommendationsAlign content of university mathematics courses METII recommendations

II. Ways of Knowing and LearningExplicitly and visibly engage students in the ways of knowing mathematics as described in METII and the CCSSM Standards for Mathematical Practice in their university mathematics courses

III. Coherence of CoursesTeach college mathematics in ways that explicitly and visibly connect to secondary school mathematics content and practices

Develop meta-task activities that make connections between school mathematics and university mathematics for classes that are part of the preservice preservice (and inservice) secondary teacher preparation program

Develop meta-task activities that address misconceptions in university mathematics classes that are part of the preservice preservice (and inservice) secondary teacher preparation program

Develop meta-task activities that address mathematics knowledge for teaching for university mathematics classes that are part of the preservice (and inservice) secondary teacher preparation program

Develop meta-task activities that provide active learning experiences for university mathematics classes that are part of the preservice preservice (and inservice) secondary teacher preparation program

Task Development Outline

1. Task description2. Rubric3. Core mathematical

ideas and challenges4. Questions for teacher

reflection5. Discussion of

successful examples of student work

6. Discussion of student misconceptions

7. Analysis of the task data

8. Summary of student understandings and misunderstandings

9. Implications for instruction

10. Initial focus on limit

as topic

IV. Assessment of KnowledgeUse formative and summative assessments to guide instruction and inform programs

ChangesKTMT Secondary Drivers

KTMT Tertiary Drivers

Develop meta-task activities that provide experiences and formative feedback to guide instruction and improve student learning

KTMT Links to Mathematical Preparation

C. Coherence of courses.

The meta-task activities will develop the first prototype for calculus I on the topic of limit. Subsequent tasks will address other courses such as Introduction to Proof, Abstract Algebra, Geometry, etc. to provide a consistent approach across the mathematics courses that a are part of the preparation and development of secondary teachers of mathematics

KTMT

B. Ways of knowing and learning.

The meta-task activities will draw upon the research literature on student misconceptions and challenges to provide focus on the activities and assessments

D. Assessment of knowledge.

The meta-task activities will contain pre- and post-assessments to assist in measuring learning of key constructs of the task. In addition formative assessment activities will be included to help guide and modify instruction

A. MET II recommendations.

The meta-task activities will use MET II recommendations to guide their development, implementation, and assessment

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?