Academic journal article Academic Exchange Quarterly

A Response to the NCTM Standards: Confidence and Competence Project ([C.Sup.2])

Academic journal article Academic Exchange Quarterly

A Response to the NCTM Standards: Confidence and Competence Project ([C.Sup.2])

Article excerpt


The purpose of this paper is to share the development and the design of a mathematics reform project, Confidence and Competence ([C.sup.2]). [C.sup.2] was a series of workshops that developed the content and pedagogical knowledge of teachers that is necessary to support reform-oriented mathematics instruction and assessment. [C.sup.2] emerged in a manner that is very different from most educational reform projects. This article describes the conceptualization of [C.sup.2] and the results of the evaluation in the fall of 1998.


Project Conceptualization

A few years ago, three friends were discussing the changes that were taking place in the Jefferson County School District. Jefferson County is a suburban school district that is near Denver, CO and serves approximately 88,000 students. The district was in the process of implementing Standards Based Education. One of the friends was an experienced mathematics teacher within the district and another was the Jefferson County School District Mathematics Project Coordinator. Both women had witnessed the district's teachers struggling to reform their classrooms based on the districts (Jefferson County Public Schools, 1996), state (Colorado State Department of Education, 1995) and the NCTM Standards Documents (1989; 1991; 1995).

The third friend was a faculty member in the Mathematical and Computer Sciences Department at the Colorado School of Mines. She was well aware of the research in mathematics education that suggests that elementary, middle school and high school teachers mathematical knowledge is often incomplete and/or fragmented (e.g., Post, Harel, Beher & Lesh, 1991; Ball, 1990; Simon, 1993). Additionally, research suggests that teachers from other countries often have a deeper conceptual understanding of mathematics than do their counter parts in the United States (Yang & Cobb, 1995). Adding to this problem is the fact that a large number of middle school and high school teachers are providing instruction in a field other than the field in which they are certified (Ingersoll, 1999).

Through the course of their discussion, these women determined that a lack of sufficient content knowledge was unlikely to be the sole contributor to the difficulties that the districts' teachers were experiencing. Recent efforts to reform mathematics education (NCTM, 1989; 1991) had resulted in changes to the recommended approaches to mathematics instruction. In the past, teachers were expected to transfer their content knowledge to students and students were expected to passively absorb this information. Many researchers currently believe that learning occurs when students actively integrate new concepts into their knowledge structure (Baxter & Glaser, 1998). In this view of the learning process, the teachers' role has changed from presenting information to providing activities that stimulate students' interests and active participate in the learning process.

Also as a result of the reform effort, perceptions of classroom assessment have changed (NCTM, 1995). In the past, assessment was conceived as a method for measuring students' knowledge after instruction had taken place. Assessment is currently considered to be a method for examining students' knowledge throughout the learning process. Assessment evidence may be used to examine the effectiveness of previous instruction and to inform how future instruction should proceed (Van den Heuvel-Panhuizen, 1994). The three friends hypothesized that the districts' teachers whose pedagogical training had preceded the current reform effort were unlikely to have the necessary skills to implement the previously described visions of instruction (Kober, 1993) and assessment (Stiggins, 1990; 1991; 1999). They decided to create a professional development program for teachers that would address not only mathematical content, but also the knowledge of mathematics that is essential to effective teaching. …

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