Written by Xin Ma and Richard Millman, University of Kentucky
(News Bulletin, November 2005)
Assessment can be carried out by using formative or summative techniques. Summative assessment activities are used to judge or sum up achievement. Formative assessment activities can be used to improve performance or practices. Formative assessment encompasses any activities undertaken by teachers or students that provide feedback that will be used to modify teaching and learning activities (Black and William 1998, p. 9). Reflection on such feedback is crucial; it enables teachers and students to identify their strengths and weaknesses and to consider whether changes are needed.
To illustrate what formative assessment looks like in action, we would like to share an assessment activity that we use with future elementary school teachers at the University of Kentucky (UK) in the yearlong content sequence. This activity incorporates both self-assessment and peer assessment, enabling students to learn while judging their own work or the work of others. It is also based on the NCTM Principles and Standards and requires students to think about mathematics individually as well as in small groups.
Individually, students are asked to read content-based journal articles and other writings about mathematics. They make an oral presentation about some part of mathematics covered in their reading. Then each student is paired with another student and asked to critique their partner’s presentation.
Although the students are focused on preparing their presentations and believe that they are evaluating other students’ presentations, our real intention for assigning this activity is to assess whether they have internalized the essential message that we want them to take away from the course—the notion that a thorough understanding of mathematical content is the centerpiece of good pedagogy.
Because we do not emphasize the importance of content knowledge when explaining the assignment, the peer assessments that evaluators write reveal their personal criteria for the presentations. The written responses also tell us whether the peer evaluators are aware of the important connection between the presenters’ knowledge of mathematical content and the quality of the presentations.
It is common for us to receive peer assessments that either don’t mention content issues or deal with them only in a cursory manner. This indicates that students are not consciously aware of how the presenter’s content knowledge influences the effectiveness of the presentation. However, during informal conversations, peer evaluators have often told us that the presenter’s enthusiasm for the mathematics content was important and had a positive influence on their evaluation.
This peer-assessment phase of the assignment naturally leads students into a reflective self-assessment phase, in which they begin to realize that the “enthusiasm” that appealed to them should not substitute for the presenter’s understanding of the mathematics content. After coming to this conclusion, students understand why they need to focus more on their own content knowledge in the future.
This assignment and the use of peer-assessment and self-assessment leave our students with a memorable personal experience that illustrates the importance of content knowledge in effective teaching.
The feedback that we have received from class participants has been resoundingly positive—the pervasive role of content knowledge in mathematics education cannot be emphasized enough to preservice teachers. Equally important to helping students come to this understanding is that we are modeling NCTM’s Assessment Principle by integrating formative assessment techniques into a content mathematics course for future teachers. It is our hope that through this multifaceted experience with assessment our students will learn to use assessment effectively in their own classrooms.
For More Information
To learn more about self-assessment, we recommend that readers consult pages 72–76 of NCTM’s Mathematics Assessment: A Practical Handbook for Grades 3–5 (2001), edited by Jean Kerr Stenmark and William S. Bush (available at www.nctm.org/catalog).
Black, Paul, and Dylan William. “Assessment and Classroom Learning.” Assessment in Education: Principles, Policy and Practice 5 (March 1998): 7–68.