PURPOSES AND METHODS OF ASSESSMENT (adapted from the National Council of Teachers of Mathematics Standards, 1989
|
Purposes (examples of questions asked) |
For Whose Use |
Unit of Assessment |
Type of Assessment | Assessment Methods |
|---|---|---|---|---|
|
Diagnostic What does this student understand about the concept or procedure? What aspects of problem solving are causing difficulty? What accounts for this student's unwillingness to attempt new problems or see the application of previously learned materials? |
Individual teacher Individual teacher
Individual teacher |
Individual student Individual student
Individual student |
Tasks that focus on a specific skill, type of procedure, concept, strategy, or a type of reasoning Each student evaluated |
Observation Oral questions that ask students to explain their procedures Focused written tasks Directed test items |
|
Instructional Feedback What do students know about the material presented? Can students apply their learning to new situations? Do students understand the connections among ideas? How shall I pace instruction? Does the class need more intensive review of more challenging material? |
Individual teacher Individual teacher Individual teacher Individual teacher Individual teacher
|
Class
|
Tasks that require an integration of know- ledge Tasks that cover a range of skills, concepts, and procedures Tasks that require the application of learning to new contexts Problem solving and reasoning tasks Tasks that vary the format and context in which the material is presented Matrix sampling test situations |
Written tests, including those that require differential methods for solutions to problems Class presentations Extended problem solving projects Observation of class discussion Take-home tests Homework, journals Group work and projects |
| Instructional Feedback
What do students know about the material presented?
Can students apply their learning to new situations?
Do students understand the connections among ideas?
How shall I pace instruction?
Does the class need more intensive review or more challenging material? |
Individual student
Parents
School
Individual student
|
Individual student
Individual student
Individual student
|
Tasks that demand the integration of material that was taught
Tasks that are intrinsically interesting and challenging to the student
Tasks that require the student to structure the material and generate solutions, in the context of the real world, as well as in math- ematics |
Extended problem solving projects
Papers or written arguments that demand thoughtful inquiry about a mathematical topic
Written tests that present problems with a range of difficulty based on expectations for course
Oral presentations |
| Generalized mathematical
achievement
How does the general mathematical capability of this student compare with others or with a national norm? |
Teachers Administrators
|
Individual student |
Tasks organized in highly reliable tests designed for maximum discrimination among students |
Standardized achievement tests |
| Program Evaluation
How effective is this instructional program in achieving our goals for mathematical learning? |
Teachers Administrators Other decision makers |
Class School |
Tasks that reflect the intent of the curriculum goals
Tasks that are aligned to the instructional methods and content of the curriculum
Matrix sampling test situations |
Student interviews
Performance tests
Criterion referenced tests
Observation of class discussions
Success of students who have completed the program |
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