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

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

• 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

• 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

• 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

Improvement
Target
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.
Relation to Overall Drivers
Primary Drivers
I. Shared vision of preparation
Create shared understanding and commitment among mathematicians, mathematics educators, and K-12 partners.
Secondary Drivers
A. Stakeholder involvement.
B. Institutional support.
C. Focus on student learning.
D. Building a learning mindset.
E. Tools for collaboration.
II. Clinical preparation
Improve teacher candidates’ intern experiences by partnerships with mentor teachers and other stakeholders.
III. Mathematical preparation
Develop teacher candidates’ knowledge of mathematics needed to support student learning.
IV. Recruitment and retention
Attract, retain, and graduate an adequate supply of teachers.
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

KTMT
Secondary Drivers
KTMT Tertiary
Drivers
I. MET II Recommendations
Align content of university mathematics courses
METII r ecommendations
II. Ways of Knowing and Learning
Explicitly 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 Courses
Teach college mathematics in ways that explicitly and visibly connect to secondary school mathematics content and practices
IV. Assessment of Knowledge
Use formative and summative assessments to guide instruction and inform programs
Changes
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 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 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
Develop meta-task activities that provide experiences and formative feedback to guide instruction and improve student learning
Task Development Outline
1. Task description
2. Rubric
3. Core mathematical ideas and challenges
4. Questions for teacher reflection
5. 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

KTMT Links to Mathematical Preparation
A. MET II recommendations.
The meta-task activities will use MET II recommendations to guide their development, implementation, and assessment
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
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
D. Assessment of knowledge.
The meta-task activities will contain pre- and postassessments 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
KTMT

• 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.

•
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

• 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

• 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

• Focus on mathematics instructors AND students (metatasks).
• 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.

• 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

• 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