1. 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

2. 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

3. 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.

4. 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

5. 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.

6. 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

7. 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

8. 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?

9. 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

10. 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

11. 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)

12. 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

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

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

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

16. 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

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

18. 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?

19. 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.

20. 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?

21. 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