2. Assessment Elementary Mathematics
NCTM Academy
Assessment
Elementary Mathematics

3. University of Tennessee
Presented by:
Dr. Vena M. Long
University of Tennessee

4. Life is good for only two things, discovering math and teaching mathematics
Simon Poisson

5. 2nd grade teacher extraordinaire!
. . . and
Peggy Rae Summers
(my baby sister. . .)
2nd grade teacher extraordinaire!

6. No student in my class is going to misbehave more than me!PR

7. NCTM Assessment Academy Elementary
Participants will begin to think about assessment in different ways by exploring how assessment can promote equity and lead to valid inference about mathematics learning, reflect the mathematics that all students should know and be able to do, and enhance mathematics learning.

8. September 29, 2004
Session I: Who are we and what are we going to be doing?
Session II: External Assessment: “Show me the money!”
September 30, 2004
Session III: Standards based Instruction and Assessment
Session IV: Break-out
October 1, 2004
Session V: Centers: The mathematics and the assessment
Session VI: Portfolios: What, When and How
Session VII: How to get it all together and where to put it!

9. . . . the books

13. Legally defensible . . . Purpose/Type Content Questions-specifications
Field Testing the items
The Test
Field Testing the test
Validity
Reliability

14. Issues for you Scaled scores Item response theory
Keeping the proper perspective
Knowing and using . . .

15. How do I know whether I should change my assessment strategies?
Currently limited to tests, quizzes, and short answer questions
Your goals include conceptual understanding
and problem solving as well as procedural competency
You want to know how students think
You want to monitor growth
Students, parents, and others want information
beyond grades and scores
K-2 p.15

17. Assumptions
ASSUMPTION 1: Every student is capable of achieving mathematics power.
ASSUMPTION 2: Evidence about student mathematical performance is needed for a variety of purposes.
ASSUMPTION 3: Information needs to be collected from multiple sources:
observations
student responses to questions
student products, etc.

18. Assumptions
ASSUMPTION 4: Since to gather evidence of student performance is to sample, and to infer from samples is error-prone, multiple sources of information should be gathered, organized and related to minimize inferencing errors.
ASSUMPTION 5: Teachers should be the primary assessors of student performance.
ASSUMPTION 6: Students should grow in confidence and in their ability to evaluate their own progress and performance.

19. Goals of Mathematics Education
Value Mathematics
Confidence in Ability
Problem Solving
Communicate Mathematically
Reason Mathematically

20. The “Standards” Assessment should reflect important mathematics.
Assessment should enhance mathematical learning.
Assessment should promote equity.
Assessment should be an open process.
Assessment should promote valid inferences.
Assessment should be a coherent process.
p.2 K-2

22. Major Shifts AWAY FROM:
Assessing only knowledge of specific facts/isolated skills
Comparing students to other students
Designing “teacher-proof” assessment systems
Assessment process secret, exclusive, fixed
Restrict students to a single way to demonstrate mathematical knowledge
TOWARD:
Assessing full mathematical power
Comparing to established criteria
Giving support/credence to teachers’ informed judgment
Assessment process public, participatory, dynamic
Giving multiple opportunities to demonstrate full mathematical power
p. 5, 3-5

23. Making numbers . . .

24. Trio Number 1. . . . the pattern
Observing
Documenting
Testing

25. Trio Number the pieces
Task
Evidence
Inference

26. Trio Number 3. . . . the mathematics
Conceptual understanding
Procedural proficiency
Processes (problem solving, reasoning, etc.)
Disposition

27. Informal
Use to guide instruction
. . .or formalize with documentation

28. give information about a
Work Habits
Approach to
task
Choice of Materials
An observation can
give information about a
student’s . . .
Use of Materials
Interaction
Interactions
Use of language ?
Perseverance

29. Making numbers . . . 5 3 2
The next roll is a 4. In which of the 2 remaining places would you
put the number? Explain why.

30. “MY” Generic Scoring Guide
4 – Wonderful – complete, clear, accurate, elegant, to-die-for
3 – Satisfactory –correct, but nothing to get excited about
2 – Fixable – needs more work but maybe not more instruction
1 – HELP!! – additional instruction needed
0 – Knock, Knock- anybody there?

31. Analytic Rubric 4, 3, 2, 1, 0 for each: Correct answer
Clear and accurate explanation
Neatness and organization (?)

38. Disturbed:
Do Not Test!