Assessment Elementary Mathematics NCTM Academy Assessment Elementary Mathematics

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

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

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

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

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.

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!

. . . the books

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

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

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

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.

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.

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

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

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

Making numbers . . .

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

Trio Number 2. . . . the pieces Task Evidence Inference

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

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

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

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.

“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?

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

Disturbed: Do Not Test!