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Continuing to Make the Case

author: Joyce Evans, Diane M. Spresser
presented at: 1998 LSC PI/Evaluator Meeting
published: 01/24/1998
posted to site: 10/21/1998

Continuing to Make the Case

Joyce Evans and Diane Spresser
Saturday, 2:30-3:30 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



Make generalizations (predict)


Multiple representations

*Inductive step

Algorithmic thinking



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 post-tests).

  • 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.