For Teachers

Authentic Assessment Methods for Mathematics

By The Room 241 Team January 9, 2013

The foundation of authentic assessment revolves around evaluating a student’s ability to apply what they have learned in mathematics to a “real world” context.

Rather than rote learning and passive test-taking, authentic assessment math tests focus on a student’s analytical skills and the ability to integrate what they have learned along with creativity with written and oral skills. Also evaluated are the results of collaborative efforts of group projects. It is not just learning the process of computation that is important to know, but also how to take the finished product and apply it to another situation.

This need for an improved test to accurately assess a student’s growth has been developed. It is called the authentic assessment math test. Multiple choice tests do not often accurately reflect the individual student’s understanding of the material. It reflects whether a student is successful at memorization. Instead of tests that focus on recalling specific facts, the authentic assessment math test has students demonstrate the various skills and concepts they have learned and explain when it would be appropriate to use those facts and problem-solving skills in their own lives.

Six ways to use authentic assessment math in the classroom

Performance assessment

Students can demonstrate what they have learned and how to solve problems through a collaborative effort in solving a complex problem together. Not only do they learn how to work in a team, but also how to brainstorm and utilize their separate grains of knowledge to benefit the whole.

Short investigations

Typically, a short investigation starts with a basic math problem (or can be adapted to any other school subject) in which the student can demonstrate how he or she has mastered the basic concepts and skills. As the teacher, ask the students to interpret, calculate, explain, describe or predict whatever it is they are analyzing. These are generally 60- to-90 minute tasks for an individual (or group projects) on which to work independently, writing answers to questions and then interviewed separately.

Open-response questions

A teacher can assess the student’s real-world understanding and how the analytical processes relate by, in a quiz setting, requesting open responses, like:

• a brief written or oral answer
• a mathematical solution
• a drawing
• a diagram, chart or graph

These open-ended questions can be approximately 15-minute assessments and can be converted into a larger-scale project.

Portfolios

As students learn concepts throughout the school year, they can be documented and will reveal progress and improvements as well as allow for self-assessment, edits and revisions. They can be recorded in a number of ways, including:

• journal writing
• review by peers
• artwork and diagrams
• group reports
• student notes and outlines
• rough drafts to finished work

Self-assessment

After the teacher has clearly explained and provided the expectations prior to the project and then, once the projects are complete, ask the students to evaluate their own projects and participation. Responding to the following questions will help students learn to assess themselves and their work objectively:

• What was the most difficult part of this project for you?
• What do you think you should do next?
• If you could do this task again, would you do anything differently? If yes, what?
• What did you learn from this project?

Multiple-choice questions

Usually, multiple-choice questions do not reflect an authentic assessment math context. There are multiple-choice questions being developed that reveal an understanding of the mathematical ideas required as well as integrating more than one concept. These questions are designed to take about 2 or 3 minutes each.

Traits developed through authentic assessment math tests

This situational type of learning in which students are learning lessons on how to solve real-life problems can be utilized in mathematics. These ideas are presented as follows:

• Thinking and reasoning: Causing students to interact in such activities that include gathering data, exploration, investigation, interpretation, reasoning, modeling, designing, analyzing, formation of hypotheses, use of trial and error, generalization and solution-checking.
• Settings: Allowing the students to work individually or in smaller groups.
• Mathematical tools: The students learn to use symbols, tables, graphs, drawings, calculators and computers.
• Attitudes and dispositions: Students in this type of learning environment learn persistence, self-regulating behaviors and reflection, participation and a special enthusiasm for learning various kinds of situations.

Learn educational techniques to improve student outcomes in mathematics. Our online math education MEd Curriculum & Instruction concentration helps you know about best practices for successful teaching in a mathematics class—conforming to standards established by NCTM (National Council of Teachers of Mathematics).

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