The EQUALS staff and the Assessment Committee of the California Mathematics
Council (1989) note the importance of assessment in promoting learning:
"Purpose of Assessment
The purpose of assessment should be to improve learning. With this in
mind, we [must] focus ... on expanding how students can demonstrate their
mathematical achievements and how teachers can gain better information about
their students. This way of looking at learning means that there will be less
need for complex scoring or grading of student work. Comparing students will
become less important than helping students understand mathematics.
What Kind of Assessment Do We Need in Mathematics?
We need mathematics assessment that:
- Matches the ideal curriculum described in such documents as
the California Mathematics Framework and the NCTM
Standards
in both what is taught and how it is experienced, with thoughtful questions that allow for
thoughtful responses.
- Communicates to students, teachers, and parents that most real problems
cannot be solved quickly and that many have more than one answer.
- Allows students to learn at their own pace.
- Focuses on what students do know and can do rather than what they don't
know.
- Won't label half of students as failures because of unrealistic
expectations that all scores should be above the 50th percentile.
- Doesn't use time as a factor, since speed is almost never relevant in
mathematical effectiveness.
- Is integral to instruction and doesn't detract from students' opportunities
to continue to learn.
What Do We Want to Assess?
We want to assess such things as:
- Students' use of mathematics to make sense of complex situations.
- Students' work on extended investigations.
- The ability of students to:
- Formulate and refine hypotheses.
- Collect and organize information.
- Explain a concept orally or in writing.
- Work with poorly defined problems or problems with more than one answer,
similar to those in real life.
- Students' use of mathematical processes, such as computation, in the
context of many kinds of problems rather than in isolation.
- The extent of students' understanding or misunderstanding about
mathematical concepts.
- Students' ability to define and formulate problems.
- Whether students question possible solutions, looking at all possibilities.
- How a students' productive work changes over time.
What Kind of Activity Should We See?
We should see students:
- Using mathematics with facility to communicate their own thinking about
complex situations through pictures, diagrams, graphs, words, symbols, or
numerical examples.
- Solving problems using a variety of mathematical tools and models, such as
manipulatives, calculators, and computers.
- Planning, inventing, designing, and evaluating their own mathematical ideas
and products.
- Being thoughtful, persistent, flexible, self-directed, and confident.
- Doing projects and activities.
- Working well together developing group problem-solving skills.
- Taking pleasure in doing mathematics.
It is essential that internal assessment for instructional decisions and
external assessment for other purposes be in agreement and that assessment
always promote student learning." (p. 4-5)
