Continuing to Make the Case
Joyce Evans and Diane Spresser
Saturday, 2:303:30 p.m.
The following are the overheads used in this presentation:
Overhead 1
What mathematics/science are the students learning?
What science/mathematics do teachers have to know to teach them?
What professional development do you have to provide teachers so they learn the mathematics/science>
What evidence would you provide to show they have learned?
Overhead 2
If you must demonstrate that teachers in your project have gained in their content knowledge of mathematics or science, how would you do that?
Overhead 3
What are the important mathematical concepts teachers should take away from this professional development session (and perhaps other sessions "adjacent" to it in the professional development program)?
Overhead 4
Participant Responses
Patterning
Visualization
Make generalizations (predict)
Modeling
Multiple representations
*Inductive step
Algorithmic thinking
Functions
Recursion
Overhead 5
 How might one demonstrate or "make the case" that teachers have gained in their content knowledge of these concepts?
 What strategies "for making the case" are more applicable to group assessments?
 To individual assessments?
Overhead 6
Participant Responses
 Self Reflection
 Ask teachers what evidence the might have that they know more (e.g., GRE scores)
 Group problem solving and single report
 Concepts  lessons  observations. (control experiment)
 KWL Charts classroom teaching. (What teachers say they learned)
 Capstone experiences used with teachers/
 Have teachers construct similar problems  across levels of sophistication.
 Have teachers design an assessment for students on those concepts
Overhead 7
 Use specific, selected items from Horizon classroom observations instrument. Those with the greatest "pay dirt" potential likely relate to increased sophistication of teacher's questioning strategies in the classroom and to teachers' greater depth/skill in effecting mathematical/scientific closure to class discussions.
 Adapt appropriate items or performance tasks from existing TIMSS, NAEP, New Standards test banks and administer to teachers (perhaps administer item/task to one sample of the teachers before professional development and same item/task to a second sample following professional development).
Example follows
Overhead 8
K6. Here is the beginning of a pattern of tiles.



Figure 1

Figure 2

Figure 3

If the pattern continues, how many tiles will be in Figure 6?
A. 12
B. 15
C. 18
D. 21
Overhead 9
Reproduced from TIMSS Population 1 Item Pool. Copyright 1994 by IEA, The Hague.


International Average Percent of Students Responding Correctly 

Content Category 
Performance Expectation 
Upper Grade 
Lower grade 
International Difficulty /index 
Patterns, Relations, and Functions 
Solving Problems 
63% 
52% 
530 
Overhead 10
How many tiles will be in Figure n?
Prove the generalization you stated above for all positive integers n.
Overhead 11
 Analyze "teacher talk" for indicators that show greater infusion/recognition of patterns; formulation of equations from data; generalization and abstraction; justification, verification, and/or proof.
 Analyze student achievement/performance data related to the targeted content domains, perhaps comparing with similar student data from prior years (or pre and posttests).
 Use Teacher Questionnaire to see if teachers report increased confidence in targeted content domains.
Overhead 12
Summary Points
 Those leading professional development sessions need to clearly identify the important mathematical or scientific concepts on which they will focus, structure the sessions to support this focus, and provide appropriate closure to enhance teachers' understanding of the concepts.
 There are a number of different strategies for assessing growth in teachers' mathematical/scientific knowledge: some assess this growth for the group, while others assess individual growth.
 Assessments should reflect an appropriate mix of both quantitative and qualitative strategies.
