Reform efforts in mathematics education challenge teachers to assess traditional forms of assessment and to explore and implement alternative forms of assessment. Empowering all students with mathematical literacy demands methods of assessment that reflect and enhance the present state of knowledge about learning, about teaching, about mathematics, and about assessment. This discussion highlights insightful perspectives on assessment strategies and techniques currently being addressed and implemented. A cohort of middle school mathematics teachers reveal their experiences and reflections in addressing current assessment practices and ventures in innovative and alternative approaches to assessment.
Assessment is the central aspect of classroom practice that links curriculum, teaching, and learning. (NCTM, 1995). In the Principles and Standards for School Mathematics (NCTM, 2000) assessment is designated as one of the six underlying principles of mathematics education. The Assessment Principle states: "Assessment should support the learning of important mathematics and furnish useful information to both teachers and students" (NCTM, 2000, p. 22). The emerging theme in assessment reform is to do more assessment than evaluation; to become assessors rather than evaluators. The aim is better assessment, not more. Standards were created to provide guidelines to improve mathematics education and to value the importance of alternative, as well as authentic assessment procedures and protocols. Traditional forms of assessment have been utilized in mathematics classrooms for many years. However, reform efforts in mathematics education challenge teachers to reconsider traditional forms of assessment and to explore and implement alternative approaches. Assessment of school mathematics is addressed in some manner in all of the NCTM documents (1989, 1991, 1995, 2000). It is essential that mathematics teachers be informed and proactive in addressing issues of assessment in mathematics classrooms. In response to the call for changes, a cohort of middle school mathematics teachers in a large metropolitan area reflected on their current assessment practices and ventures in alternative forms of assessment in the classroom. These teachers were participants in a grant focusing on the strengthening of mathematical content knowledge, the improvement of instructional strategies, and the implementation of new curricula fulfilling national standards and state-mandated guidelines. In the light of education reform along with the looming accountability of state-mandated guidelines, these teachers began to realize the vision of achieving mathematical power for all students. This discussion highlights middle school mathematics teacher's new perspectives as they implemented alternative assessment strategies and techniques.
What Assessment Tasks were Explored and Implemented by the Middle School Teachers?
Teachers used a variety of traditional and nontraditional approaches to student assessment. The teacher-developed assessment strategies explored and currently in practice in the classrooms of these middle school
teachers. The third column indicates the teacher’s reflections on the uses of these assessment strategies. Teachers found that short answer tests, journal writing, manipulatives, projects, concept mapping, and performance assessments revealed a broad range of capability, understanding, and communication of mathematical concepts. Many different tasks were used to create a complete picture of the students' mathematical knowledge. Strategies for evaluating performance on assessment activities also varied. Teachers used rubrics quite extensively, as they became comfortable with this system through the workshops. In addition, concept maps, journal entries, textbook assignments, and worksheets were very informative. Teachers identified sources of feedback such as group grades, participation grades, praise, peer
evaluation, and self-evaluation.
What Mathematics was Assessed? How Did State and National Guidelines and Accountability Affect Assessment Strategies?
The mathematical skills and concepts assessed by the middle school teachers in the workshop were typical for grades 6-8. As with many other state-mandated curricula objectives, as do many districts. For each grade level and each subject area, there are specific learning objectives and goals for Pre-K through 12th grade. The final an exit test that must be passed as a prerequisite for high school graduation. Within this framework of curricula are thirteen objectives that are assessed in mathematics. These have been determined by the state, but are also related to the national standards identified by the NCTM (cf. 2000). These objectives were created to help ensure quality and consistency. Learning accountability, in some school districts, is even more defined by specific objectives and goals for the grade levels.
Direct test preparation is widespread. Many teachers used the item analysis from the previous year's test to determine the areas of strengths and weaknesses to improve on the objectives that were deficient. Practice tests, six-week tests, quizzes, and a section of the student's daily homework are formatted so students can practice on how the questions are structured as well as practicing and applying the objectives. Teachers and students review and practice test-taking strategies to develop more confidence. Many of the workshop teachers felt that too much focus was placed on the standardized test, thus limiting the time available for alternative assessments. Even so, teachers valued the need for change and explored the potential of other forms of assessment. Tutoring, motivation techniques, and parental involvement were common efforts.
How Can Information from Alternative Assessment be Integrated into Grading and Reporting Progress?
The teachers shared strategies to integrate information from alternative assessment into grading policy. Alternative assessments were sometimes counted as a test grade and sometimes as a daily grade, depending on how much time was required. For example, some teachers used notebooks as test grades. It was common for teachers to offer extra credit opportunities when implementing new forms of assessment. Extra points were given for creativity and originality, hoping to build student confidence. Most of these teachers used homework to determine the depth of student understanding and which concepts needed re-teaching. Projects and journals offered students opportunities to express their ideas, understanding, and concerns. Some students worked better with manipulatives; others with pen and paper. The teachers reported a creative variety of alternative forms of assessment implemented into traditional protocol. Each type of assessment determined a certain percentage of the grade.
Discussion of the variety of assessment practices and grade recording encouraged all teachers to try more alternative forms of assessment as well as developed increase confidence in this endeavor. The teachers communicated the types and importance of assessment strategies and approaches to students and parents through many venues. Some of the ways used by the teachers include weekly reports to parents, scheduled progress reports, promoting ways parents can help students at home, tutorials after school, and Saturday school. As a result, parents and teachers participated in workshops, conferences, and conversations to encourage and support student learning. Positive reinforcements included special privileges at school and at home, award certificates, and other classroom and school acknowledgements.
Teachers reported that sometimes students do not see any correlation between what they are learning in class and what is tested. Teachers tried to address these issues by using real-world problems and scenarios.
Typical problems encountered involved students that do not study or complete homework, or that do not ask questions. These were addressed in parent conferences and student-teacher conferences. Through these many approaches, students were able to ask questions about concepts they had not mastered.
What Results Did the Teachers See as they Used Assessment to Improve Curriculum And Instructional Practices?
The teachers studied and shared strategies to improve mathematics curriculum and instructional practices. They found that different assessment instruments helped to take the focus off the "computation and accuracy" aspect of mathematics, and helped to encourage mathematical thinking. New sorts of tasks in classrooms created a more complete picture of the students' mathematical knowledge. The workshop teachers reported that assessment informed re-teaching, addressed students with math anxiety, and identified students' need for more instruction and/or reinforcement. Students were able to see the objectives mastered and not mastered, as well as their own strengths and weaknesses. Alternative assessment took the emphasis away from right/wrong answers and concentrated students and teachers on thought processes.
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