The end of the twentieth century was marked by a change in education systems at K-12 levels across the country and abroad. Our government agencies at every level have initiated efforts to improve the education offered to all students by holding schools, teachers, and students accountable for academic learning and achievement (Rothman, 1995). In the field of mathematics education, concerns about curricula, instructional practices, and levels of student achievement led to publication of standards for curriculum and evaluation, teaching, and assessment by the National Council of Teachers of Mathematics (1989, 1991, 1995, 2000). These documents outline a vision for mathematics education that shifts away from the computation-laden curriculum of the past and toward a challenging, concept-driven curriculum that empowers students to solve problems and reason logically. The standards articulate five general goals for all students (NCTM, 1989, p. 5):
Starting with ‘Calculus Reform’ efforts in the late 80’s and the 90’s, the focus of educational attention has been broadened to include development of the standards of intellectual development, content, pedagogy, and assessment beyond K-12 level. These standards will provide college and university systems and individual instructors with a focus for their efforts to assist students in reaching their academic potential.
Whether the accountability systems tied to standards will result in better instruction and academic success for all learners remains open to question. There are indications of positive outcomes of the reform effort, but we need much more evidence before we call it a success. Nevertheless, effects of the new accountability systems include increased emphasis on the importance of student assessment and an interest in integrating the processes of teaching, learning, and assessment. Pre-reform systems focused on instruction -- and educators perceived assessment as a necessary evil -- but the push for standards and for tests aligned with those standards has placed assessment in a prominent position in the instructional process. Instructors are more often focusing on students’ learning and conceptual understanding and are asking themselves early and often, "How will I know if students know, understand, and are able to apply the content of this discipline?"
In this paper we describe the development of an initial database for online formative assessment to be used as independent or supplemental material for a precalculus course. We developed our questions in WebCT, a system for easy online course management, using Bloom’s Taxonomy for their framework. This is an ongoing process, so you will not find a wide spectrum of questions in our database at this point. We believe that what we have so far is worth sharing, and we expect publication of our work to initiate collaboration with faculty from other institutions. Our intention in the development so far has been to emphasize the use of assessment items as "reflective tools" for students and as informative tools for instruction, not as a "testing tools" -- we will explain the difference later. In the following sections we describe the course and the online assessment tools, with special focus on the types of questions used in the assessment.
As you review our progress on the database, please keep in mind the Nine Principles of Good Practice for Assessing Student Learning (American Association for Higher Education, undated):
We are currently involved in two national projects that have been established with the goal to help university instructors in the transition towards standards-based teaching and learning. One of these is Quality in Undergraduate Education (QUE), a national project of faculty at selected four-year public institutions and their partners at two-year colleges, who are working together to establish content standards and develop aligned assessments to guide undergraduate education. There are projects in many states supported by the Education Trust under the P-16 umbrella that use standards-based teaching and learning as a tool for integrating grade school and college curriculum. In Georgia, we are involved in PACTS: Performance Assessment for Colleges and Technical Schools, a project to develop free response assessment items that may be used in college admission decisions.