Assessment and Grading in High School Mathematics Classrooms

Abstract

The assessment and grading practices in 19 mathematics classes in 5 high schools in 3 states were studied. In each class the most frequently used assessment tools were tests and quizzes, with these determining about 77% of students' grades. In 12 classes other forms of assessment, such as written projects or interviews with students, were also used, with performance on such instruments counting for about 7% of students' grades averaged across all 19 classes. Test items generally were low level, were stated without reference to a realistic context, involved very little reasoning, and were almost never open-ended. Most test items were either neutral or inactive with respect to technology. Written projects usually involved more complex analyses or applications than tests did. The teachers' knowledge and beliefs, as well as the content and textbook of the course, influenced the characteristics of test items and other assessment instruments. Only in geometry classes did standardized tests appear to influence assessment.

Mathematics Teachers’ Interpretation of Higher-Order Thinking in Bloom’s Taxonomy

“…The findings in this study are consistent with research that indicates teachers tend to overestimate the level of thinking required on test items. For example, Senk, et al (1997) found that the percentage of LOT items on mathematics teachers' tests averaged 68%. Harpster (1999) found that when mathematics teachers were specifically asked to write a single task representative of HOT, 60% developed a task that assessed LOT.…”

“…However, national and international assessments in mathematics indicate that U.S. students are not doing well on items requiring the use of HOT (Mullis, et al, 2004). U.S. students performing poorly on national and international exams is reflected in the research which indicates that most U.S. teachers do not teach and assess for HOT (Kulm, 1990;Senk, et al, 1997). U.S. teachers not assessing for HOT is well-documented and is not limited to mathematics.…”

“…Similarly, Fleming and Chambers (1983) used BT to analyze over 8000 test items from K-12 teacherdeveloped tests and found that consistently across all grade levels over 90% of test items measured LOT. In a study of high school grading practices in mathematics, Senk, et al (1997) found that the percentage of LOT items on mathematics teachers' tests ranged from 53% to 90% with a mean of 68%. These studies analyzed existing tests created by teachers; in contrast, Harpster (1999) found that when mathematics teachers were specifically asked to write a single task representative of HOT, sixty-percent of teachers created a task that assessed LOT.…”

“…Similarly, Stein and Lane (1996) describe HOT as "the use of complex, nonalgorithmic thinking to solve a task in which there is not a predictable, well-rehearsed approach or pathway explicitly suggested by the task, task instruction, or a worked out example." (p. 58) Senk, et al (1997) characterized HOT as solving tasks where no algorithm has been taught, where justification or explanation are required, and where more than one solution may be possible. In general, HOT involves solving tasks where an algorithm has not been taught or using known algorithms while working in unfamiliar contexts or situations.…”

When Good Ideas Become Bad Policy: Implications of the National Voluntary Mathematics Test

“…Specifically, funding for the NVMT may be more wisely spent on a professional development program designed to improve the quality of classroom assessment used by teachers. According to mathematics educators, one of the primary factors inhibiting the success of current reform efforts is the mismatch between teacher assessment practices and the reform goals (Senk, Beckmann, & Thompson, 1997). The formal and informal assessment practices that teachers use in their classrooms significantly affect student performance in mathematics.…”