NCTM's vision of mathematics assessment in the secondary school : issues and challenges

Sparkes, Joanne J. (1999) NCTM's vision of mathematics assessment in the secondary school : issues and challenges. Masters thesis, Memorial University of Newfoundland.

[English] PDF (Migrated (PDF/A Conversion) from original format: (application/pdf)) - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (10MB) [English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. (Original Version)

Abstract

Most places one treads within the mathematics education arena there is either direct or indirect reference to two National Council of Teachers of Mathematics (NCTM) documents: Curriculum and Evaluation Standards for School Mathematics and Assessment Standards for School Mathematics. These documents place strong emphasis on mathematics as communication, reasoning, problem solving, and making connections as well as the idea that students learn best in active student-centered classrooms as opposed to more traditional passive settings. Consequently, NCTM advocates a call for change in many components of traditional mathematics teaching, including the manner in which teachers instruct and assess students. -- Folio Paper One summarizes the major recent reform efforts in mathematics education as advocated by NCTM. Sources of current theory, research, and practice are cited that adhere to the philosophical underpinnings of NCTM regarding curriculum reform. The paper examines the evolution of learning theory research as it pertains to mathematics reform efforts and, more specifically, mathematics assessment reform efforts. The paper evolves into an examination of assessment reform including NCTM's Assessment Standards and the proposed shifts in assessment practices. The varied purposes of assessment are also addressed. -- Folio Paper Two describes the necessity, stemming from a constructivist framework of learning, to change both the manner in which teachers elicit evidence of students’ mathematical thinking and the way they use that evidence to monitor students' progress and guide instructional decision making. Emphasis is placed on the idea that expanding the purposes of assessment beyond accountability and assigning grades becomes an asset to all those involved in the assessment process. Various forms of alternate assessment are described and supported with examples of current research and practice. The assessment instruments described include: journal writing, open-ended problems, interviews, formal and informal observations, portfolios, self-assessment, and teacher-made and other tests. The paper concludes by focusing on some of the advantages of multiple forms of assessment. -- Folio Paper Three discusses many of the challenges facing teachers in the area of mathematics assessment: (1) the challenge of teachers removing themselves from some of the comforts they have in their traditional practices; (2) the challenge of teachers becoming comfortable with designing alternate assessment instruments'' and recording and reporting information obtained from their use; (3) the challenge of teachers juggling demands placed on their time; (4) the challenge of teachers meeting external expectations while simultaneously remaining accountable for their actions; (5) the challenge that teachers, like students, are active constructors of their practice and, hence, it will be difficult for them to implement the assessment ideas that NCTM advocates if their vision of mathematics education is distinctly different from that of NCTM; and (6) the challenge of building and sustaining a constructivist classroom environment necessary to support alternate assessment initiatives. All of these challenges are addressed within the context of current theory, research, and practice. Finally, the paper provides a potential developmental agenda for teachers in their efforts at overcoming such challenges.

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