Assessing Higher Order Thinking in Mathematics

By Gerald Kulm | Go to book overview

3
Power Items and the Alignment
of Curriculum and Assessment

TEJ PANDEY

The declining test scores on NAEP, SAT, Iowa, and several state testing programs from the mid-1960s to mid-1970s have resulted in many studies and commission reports, such as A Nation At Risk, The Paideia Proposal, A Place Called School, A Study of High Schools, Educating Americans for the 21st Century, and The American High School. These reports generated concern for better education, resulting in the "excellence movement." Many states and school districts across the nation have set high expectations and goals for all learners and have devised programs for helping students and schools in ways that allow them to reach those high expectations. The ideas from effective school research have become the hallmark to promote excellence. Among many effective school practices, the one that is important to the discussion in this chapter is the organizing of clear and visible goals around which instruction can be continually targeted and implementing assessment and indicator programs to monitor the progress of students as well as of school systems. What is curriculum alignment and what are some of the issues related to curriculum, instruction, and assessment (CIA) alignment in the setting of the current reform movement?

This chapter will discuss issues and strategies in planning assessment instruments in mathematics that would support the reform. In particular, the discussion focuses on the nature of the test instruments most suitable for large-scale accountability assessment programs. It is recommended that "power items" be used for such purposes. Suggestions are offered for defining content domains and item specifications and for constructing power questions in the context of CIA alignment.


Curriculum Alignment

The NCTM Standards for School Mathematics ( 1989) states that "In assessing students' learning, assessment methods and tasks should be aligned with the content and instructional goals of the curriculum." In a broader sense, the curriculum is composed of goals and objectives, or intended curriculum, instruction, and assessment. When all three match -- that is, instruction and assessment focus on stated objectives -- then the effects of schooling are usually both understandable and impressive. In other words, instruction and assessment should both be derived from the objectives, and instruction and assessment must be designed to support each other. The greater the mismatch between the tests and instruction with the intended curriculum, the more uncertain we are about the instructional needs of the students and the effectiveness of the instructional program. To derive meaningful inferences, instruction, as well as assessment content and procedures, should be derived from the

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