Teacher Content Knowledge a Mile High How do we effectively assess and enhance teacher content knowledge? Doris Kimbrough, Principal Investigator Barbara Bath, Project Director Rocky Mountain Middle School Math Science Partnership (RM-MSMSP) University of Colorado at Denver and Health Sciences Center

Overview of our NSF-MSP The Partnership 5 higher education institutions 7 local school districts Additional educationally oriented partners Collaboration with U.S. Department of Education MSP through Colorado Department of Education

Project Goals Enhanced teacher quality through implementation of content-rich professional development coursework; Increased middle school student access to challenging curriculum through implementation of research-based curriculum in mathematics and science; Improved diversity in the teacher pipeline coupled with enhanced preparation in mathematics and science.

Summer Academy 2005 Mathematics Algebraic Patterns and Functions Geometry Statistics & Probability Science Atoms and Properties of Matter (Chem) Cells, Human Systems, and Heredity (Biol) Earth Processes I (Geol) Forces and Motion (Phys) Co-development and co-teaching model was employed in all courses

Teacher Content Inventory (TCI) Proposal described development and implementation of a Teacher Content Inventory (TCI) as a way to measure teacher content knowledge as applied to teaching of mathematics and science and to determine effectiveness of professional development coursework.

Teacher Content Inventory Purpose Originally intended to drive content of professional development courses Proved difficult to implement Chicken/egg problem Pre/post model to assess effectiveness of professional development courses Added value to participating teachers Instructional goals being met Teacher self-assessment Course selection Pre-requisite determination

Measuring Teacher Content Knowledge Problems Intimidation Perceived as punitive: threat to salary, promotion, & status Psychologically and professionally demeaning Reluctance Classic content and measures not connected to practice of teaching Lack of reliable and effective measures Outcome How will information be used? Professional development support

Measuring Teacher Content Knowledge in Mathematics—Literature Deborah Ball, Bill Bush, Liping Ma “Pedagogical content knowledge” is different from what is measured by standardized tests How teachers hold knowledge may matter more than how much knowledge (Ball et al.) Procedural or conceptual? Connected to big ideas or isolated in small bits? Compressed or conceptually unpacked?

Measuring Teacher Content Knowledge in Mathematics—Literature Bill Bush et al. Math content domains Numbers/Computation Geometry/Measurement Probability/Statistics Algebraic Ideas Types of Knowledge Memorized Knowledge Conceptual Understanding Problem Solving/Reasoning Pedagogical Content Knowledge

Measuring Teacher Content Knowledge in Science—Literature Less available: science trailing behind mathematics Factual vs. procedural Force Concept Inventory Horizon Research Inc. (Physics) Bill Bush et al. (Biology) Literature on common misconceptions

How did we implement TCI? How do you tie content-based questions to instructional practice? Ball et al. Domain map: description of topics and knowledge to be measured Assessment items ideologically neutral “common” knowledge (everyone) “specialized” knowledge (teaching-focused)

Assessing “Specialized Knowledge” Ball et al. Ms. Harris was working with her class on divisibility rules. She told her class that a number is divisible by 4 if and only if the last two digits of the number are divisible by 4. One of her students asked her why the rule for 4 worked. She asked the other students if they could come up with a reason, and several possible reasons were proposed. Which of the following statements comes closest to explaining the reason for the divisibility rule for 4? (Mark ONE answer.) Four is an even number, and odd numbers are not divisible by even numbers. The number 100 is divisible by 4 (and also 1000, 10,000, etc.). Every other even number is divisible by 4, for example 24 and 28 but not 26 It only works when the sum of the last two digits is an even number

How did we implement TCI? Bush et al. Information packet gives sample questions in different mathematical content domains and knowledge types.

How did we implement TCI? Paradox: Independent measure of teacher “specialized” content knowledge vs. Assessment of effectiveness of professional development coursework

How did we implement TCI? Course TCI Algebraic Patterns & Functions Bush et al. Geometry RM-MSMSP developed (Juraschek) Statistics & Probability

How did we implement TCI? Course TCI Atoms & Properties of Matter (Chem) RM-MSMSP developed (Kimbrough & Banzragch) Cells, Human Systems, and Heredity (Biol) Bush et al. (bad match) Earth Processes I (Geol) RM-MSMSP developed (2 divergent aspects) Forces and Motion (Phys) Horizon Inc. + Force Concept Inventory

How did we implement TCI? Chemistry Instructionally based Misconception-based distracters Geometry Geology Interesting dichotomy Stressed that TCI not be tied to course grades

Developing Instructionally-focused questions Activity Problem: The product of three consecutive numbers is 32,736 What are the numbers? Some of your students solve this problem by dividing 32,736 by 3, how would you address this approach? Some of your students perform a lengthy trial and error approach. How would you deal with them? How else could you approach this problem?

Developing Instructionally-focused questions Activity Problem: In a unit on force and motion, students have been pushing small carts across their tables to the right and observing the motion. The teacher asks the students to draw a diagram showing all the horizontal forces on a cart once it leaves the student’s hand and is rolling across a level table. Draw (correct and incorrect) diagrams that her students might have produced and discuss them.

Developing Instructionally-focused questions Activity Problem: You are teaching your students about solubility of salts in liquids and you realize that they are confused about the difference between melting and dissolving. How would you address this misconception? Would you address it differently if you taught 5th grade vs. 8th grade?

Conclusions Connecting content questions to instructional practice allows assessment of “specialized knowledge” Enhances teacher buy-in and recognition of importance Need better match between TCI and professional development coursework, particularly in the sciences TCI not always an effective measure of course effectiveness (Biology) TCI results could be used to drive PD course content (as originally intended) Additional courses are presenting us with new challenges for next summer