Assessment of Mathematical Understanding Especially as it Relates to CMP

Assessment of Mathematical Understanding Especially as it Relates to CMP

Introduction

Assessment has become a very “hot” topic in education circles lately. Or at least, it is talked about more often and with more passion. Teachers are being judged on their students’ performance, based on assessment scores. It is the assessment by which we are judged. The reauthorization of ESEA and the ‘No Child Left Behind’ act shows the public’s (or is it the politician’s?) faith in standardized tests as a school improvement instrument. But I also know that the once-a-year test can not provide continuous information about student achievement. The traditional assessments of computation exercises, short answer questions, and word problems will not suffice any more. Typically, standardized tests measure factual knowledge, not conceptual understanding. I believe that conceptual understanding is not only what students know, but what they can do with what they know. Assessments are varied from teacher to teacher, district to district, and state to state. I did an informal survey with some of my colleagues, asking them their reasons for assessing students, and the results varied greatly. I am interested in assessment and alternative assessments in order to help further my students’ understanding of mathematical concepts. I strongly believe that the purpose of assessment to inform my instruction, which in turn will further my students understanding.

Background

According to the National Council of Teachers of Mathematics Principles and Standards 2000 Assessment Principle, “assessment should support the learning of important mathematics and furnish useful information to both teachers and students.” Assessment should be designed to “maximize student learning” and “support the learning of important mathematics and furnish useful information to both teachers and students.”

The National Education Association suggests that assessment is a “continuous flow of evidence that can only be provided by classroom assessment.” (NEA, 2003) Balanced assessments can actually promote student learning and achievement. “To maximize student success, assessment must be seen as an instructional tool for use while learning is occurring, and as an accountability tool to determine if learning has occurred.” (NEA, 2003)

The 1995 NCTM Standards acknowledged that assessment should:

1. Reflect the mathematics that students show they know and what they are able to do.

2. Enhance mathematics learning.

3. Promote equity.

4. Be an open process.

5. Promote valid inference.

6. Be a coherent process.

The Assessment Model from NCTM (2000) includes four phases of the assessment process includes planning, gathering, interpreting, and using data. The table below shows how each phase influences the next.