Conceptual frameworks for mathematics assessment

Encouraged by the publication of the NCTM Standards, several groups began defining principles that could guide the development of balanced pictures of mathematical accomplishment.

In Measuring What Counts, the MSEB put forward three fundamental assessment principles that would support effective learning of mathematics (NRC, 1993b):

  • The Content Principle—assessment should reflect the mathematics that is most important for students to learn.

  • The Learning Principle—assessment should enhance mathematics learning and support good instructional practice.

  • The Equity Principle—assessment should support every student's opportunity to learn important mathematics.

At the same time, the New Standards and Balanced Assessment organizations produced a framework for balance, based on NCTM's Standards. The seven principal dimensions of the resulting framework are outlined below (Schoenfeld, Burkhardt, Daro, & Stanley, 1993):

  • Content—assessment should reflect content in a broad sense and include concepts, senses, procedures and techniques, representations, and connections.

  • Thinking processes—assessment should engage students in a wide range of thinking processes that include conjecturing, organizing, explaining, investigating, formulating, and planning.

  • Student products—assessment should require a variety of student products that include models, plans, and reports.

  • Mathematical point of view—assessment should present mathematics as an interconnected body of knowledge, by engaging students in mathematics that is connected to realistic, illustrative, and pure contexts.

  • Diversity—assessment should be sensitive to issues of access.

  • Circumstances of performance—assessment should vary according to time allocated, whether it is performed individually, in pairs, or in groups, and whether there is opportunity for feedback and revision.

  • Pedagogics and aesthetics—assessment tasks should be engaging, believable, and understandable, and should not disenfranchise the common sense of the student.

Two years later, the NCTM Assessment Standards for School Mathematics (1995) produced a set of standards for assessment

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