Assessment

Assessment should be ongoing and based on student performance. Students should be assessed throughout the TEAMS Mathematics module so that their individual performance, as well as their performance as a group member, can be considered. Performance assessment produces valuable information on what concepts need to be reviewed or retaught and what concepts the class as a whole understands. Assessment can be directed at the concepts being taught or at behaviors during group work. Try recording observations of and interviews with students. Attempt to stay away from "Friday is testing day" syndromes. Do a little bit of assessment when the timing is right. As lessons are facilitated, ask students questions to determine their level of understanding of the concept. At the end of each module, ideas, activities, or suggestions are included to help teachers assess. Check national and state standards for guidelines.

Purpose of Assessment

The purpose of assessment should be to promote student learning. In order to do this, teachers should emphasize:

• assessing what students know and how they think about mathematics
• making assessment an integral part of teaching
• focusing on a broad range of mathematical tasks and taking a holistic view of mathematics
• developing problem situations involving a number of mathematical ideas
• using multiple assessment techniques, including written, oral, and demonstration formats
• using calculators, computers, and manipulatives in assessment.
  

These characteristics are outlined in The Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989, pg 191) and are emphasized in the fourteen evaluation standards.

Suggestions

Here are a few suggestions to get you started on performance assessment.

• Select one important idea or concept.
• Determine what concept knowledge is required for the understanding of that idea.
• Determine what thinking would lead to understanding.
• Be open as you are assessing. Be sure to look for paths to understanding and processes students are using as they clarify their thinking.
• Use a variety of techniques such as:

- interviewing students

- journal writing- ask students to write to a directed question

- oral reports or projects

- written reports/posters or drawings

- portfolios

Student Involvement

Involve students in the assessment process. Let them help to make the decisions on what is or is not acceptable.

• Students can assist in the development of a rubric for assessing a problem/project.
• Let students assess their own and other students' work. Assessing their own work gives students an "inside" look at what is expected.
• Students should be given the opportunity to revise their work until they are satisfied with the product. Provide anonymous examples of unacceptable, good, and outstanding work.

Rubrics

Rubrics can have from two (2) to six (6) levels (points). Rubrics with two levels are for scoring work as acceptable or not acceptable (revise and resubmit). Rubrics using from three to six levels are usually more complex and specific as to what is being taught. Below is a four level rubric sample. Teachers can work with students to decide specific concept understandings necessary for each level.

GENERAL FOUR LEVEL RUBRIC

(adapted from Mathematics Assessment: Myths, Models, Good Questions, and Practical Suggestions)

Level 4 - Outstanding/Insightful

• Complete response with clear, coherent, unambiguous, and elegant explanation
• Includes clear and simple diagram
• Communicates effectively to an identified audience
• Shows understanding of the question's mathematical ideas and processes
• Identifies all the important elements of the question
• Includes examples and counter examples
• Gives strong supporting arguments
• Goes beyond requirements of the problem

Level 3 - Essentially Complete

• Good solid response with some of the characteristics above, but probably not all
• May be less elegant, less complete
• Does not go beyond requirements of the problem

Level 2 - Rework/Revise

• Reasonably complete response, but the explanation may be muddled or incomplete
• Diagrams may be inappropriate or unclear
• Seems to understand mathematical ideas, but may not be able to express clearly

Level 1 - Reteach/Restart

• Omits significant parts or all of the question and response
• Makes major errors
• Uses inappropriate strategies

The National Council of Teachers of Mathematics has published Asssessment Standards for School Mathematics. Look for guidelines and suggestions in it.