Designing an assessment tool to describe students' mathematical knowledge
Abstract
Educational reforms in most parts of the world advocate a curriculum where students can achieve higher-order understanding in mathematics similar to the National Council of Teachers of Mathematics (NCTM) Standards-based Curricula. When these reforms are implemented in the classroom, teachers often begin identifying students that had previously not been identified as successful in mathematics and who are able to perform well in higher-order learning tasks. In addition, teachers find inconsistencies between the results these students obtain in standardized tests and what they see their students doing in the classroom. This dissertation addresses this assessment inconsistency and proposes a classroom-based assessment design that can help teachers better achieve the assessment purposes advocated by the NCTM: (a) determine what a student understands about specific mathematical ideas; (b) make informed decisions about instruction; (c) make informed decisions about students; and (d) communicate to students, parents, and other educators about students' mathematical understandings. Though the purpose of this dissertation was to develop a tool that would help teachers and other educators better depict students' mathematical knowledge, the implications of using this tool for assessment purposes can be extended to students, other educators, and everyone that needs to make decisions about students, instruction, or mathematics education. From a Mathematics Education perspective, this dissertation makes important contributions for teachers and other educators to focus on assessment purposes advocated by the NCTM and Standards-based Educational reform. The Mathematics Knowledge Wheel is a tool to help teachers achieve these assessment purposes. This tool has been tested to adequately approach some of the problems identified in the use of performance-based assessments, such as: validity (consistency between learning theories and classroom practice), reliability (inter-rater agreement), and feasibility (that can be used in practice). The use of the Mathematics Knowledge Wheel in mathematics education is intended for teachers and educators to see the benefits of giving a non-judgmental value to students' work, before making any judgments or making any decisions about students and instruction. This innovative approach to assessment practices helps to better achieve the purposes of the NCTM Standards-based Educational Reform.
Degree
Ph.D.
Advisors
Lesh, Purdue University.
Subject Area
Mathematics education|Educational evaluation
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