TEACHERS’ PERSPECTIVES ON
PERFORMANCE ASSESSMENT
Richard
S. Kitchen
University
of New Mexico
kitchen@unm.edu
Abstract: In this research
report, six mathematics teachers describe the process of writing and
implementing performance assessment tasks for use across all mathematics
classes at their middle school. Writing
the tasks helped the teachers to articulate the entire mathematics
curriculum. This process of identifying
the important mathematics that they wanted their students to learn also unified
the faculty and made supporting the learning of low-achieving students a
priority at their school. The teachers
also discuss how the project is one aspect of the mathematics reform effort
that began at their school a decade ago.
According to reform documents, student results on mathematics performance assessment tasks provide teachers with immediate feedback regarding students’ mathematical strengths and weaknesses (NCTM 1995). Little research has been done to demonstrate just how teachers take advantage of the knowledge they acquire from the use of performance assessment tasks. Less is known about how teachers benefit by collaboratively writing, revising, implementing and scoring performance assessment tasks.
In this research paper, six mathematics teachers at Borel Middle School in San Mateo/Foster City School District in the San Francisco bay area describe how they were impacted by an assessment project that they undertook. Funded by the Coalition of Essential Schools, the teachers began writing performance assessment tasks in the summer of 1997 that aligned with their mathematics curriculum. The teachers decided to create performance assessment tasks for each unit of their mathematics curriculum to define the important mathematical ideas that needed to be taught in each unit. The goal of the project was to create performance tasks that would be cognitively demanding and assess students’ understanding of important mathematical concepts.
A premise of the project was that reforms in assessment would promote higher order thinking in the teachers’ classrooms (Kulm, 1991). The teachers also wanted to create tasks that did not simply assess facts and students’ skills in isolation, but that would require students to apply their knowledge in real-life contexts. This approach is supported by researchers who advocate revising assessment practices to support changes in instruction that are based on how children learn (see O’Day & Smith, 1993). In addition, tasks were designed to be as authentic as possible, to require students to communicate their mathematical thinking, and to elicit a range of potential responses (Wiggins, 1993). I served as a facilitator for the project, giving teachers feedback about the tasks and the alignment of the tasks to their curriculum.
Research Participants and Site
April, Joanne, Judith, Maria, George and Mike were the six participants in the study. All six have extensive experience as mathematics teachers. Five of the teachers have more than 10 years of experience teaching at Borel Middle School. Borel Middle School is a school with approximately 850 students, with a student population that is 45% minority, representing about 35 nationalities. The six participating teachers had witnessed the demographics of the school change in the past decade from a predominately white, upper-middle class school to the school with the most socio-economic diversity in the district.
The Process of Writing, Revising, Implementing and Scoring the Tasks
Mike described how writing and revising the tasks impacted the mathematics teachers at Borel: “It’s made us become more focused on certain concepts that we’re trying to teach... Really has developed into a team and everyone has a significant role. Has helped with the pacing without compromising our personal style... Keep hearing mile wide, inch deep and I took it real seriously.” By meeting regularly to discuss and write assessment tasks, the teachers were able to articulate the entire 6-8 mathematics curriculum at Borel. Maria discussed how the process of articulating the curriculum had additional benefits: “We have a common goal, doesn’t matter if it’s not your grade level. We’re each interested in what’s going on at various grade-levels and how students progress in math (from 6th grade on). This project was bigger than writing tasks. It gave us a thread that keeps us very connected with each other’s students.”
Becoming more connected with each other’s students over the course of the three years since the assessment project began has translated into changes in the teachers’ conversations and practices. Maria alluded to these changes: “We’re all very invested in the lower-end kids. Our discussion has changed over the past couple of years. Assessment, teaching, lead up to giving assessments have changed.” It has become a priority at Borel for the teachers to work together to help all of their students succeed in mathematics. The project has clearly helped to further unify the faculty. According to Joanne: “We have something we’re working on together consistently. If somebody’s running something off, we run it off for everyone. So, the consistency from one class to the next has really become a practice here. We’re all going in the same direction. Because we talk, we meet a lot, we’re unified and we like each other.”
During implementation of the tasks, the teachers noticed that most students viewed the assessments positively because their teachers had written the tasks. The students also understood the five-point rubric and how their work would be scored. According to Judith: “(We) gave them the rubric up front. Everyone has the possibility of getting a five. Everyone has the possibility to shine!” Data from the third year of task administration demonstrated that students are consistently performing better on each task at each grade-level from year to year. In addition, from examining students’ work, the teachers have discovered that many students attempt to do the extra work necessary to achieve a score of five. This finding demonstrated that the tasks stimulated the students to do their best possible work, an important characteristic of quality assessment tasks (Cooney et al, 1993).
Lastly, the teachers have discovered that analyzing students’ work on the tasks has improved their teaching. Maria found that: “By doing this, we picked up students’ misconceptions. They obviously picked up the misconceptions somewhere, probably from us... I think of better questions to ask kids, help kids follow thinking of assessment. It definitely carries over (to instruction).” Maria also discussed how assessment influenced her view of the curriculum: “I go back to the units now to be sure that we’re not spending too much time on periphery material.”
This project was one of many reforms undertaken at the school during the past decade. The initial stages of reform at Borel Middle School involved detracking mathematics classes. George discussed detracking: “(We) did tracking for years, that’s how everybody did it. When went to heterogeneous grouping, we weren’t very good at it at the beginning because we had never done it before.” April continued: “We also didn’t have the curriculum for it, we had tracked curriculum.” The faculty adopted a new reform mathematics series in the early 1990’s that made it possible to move away from tracked classes at Borel.
Not surprisingly, as the mathematics teachers began to detrack their classes with the support of the administration, angry reaction from parents ensued. According to George: “We took it on the chin. Parents were lined up for conferences. We had math nights to explain (the reforms) to parents. First part of using (our reform curriculum) was brutal. Most problems now are with 6th grade parents.” After almost a decade of detracking the mathematics curriculum at Borel, the only vestige of the traditional curriculum is several Algebra sections. The teachers were adamant in their belief that all students, not just their lower achieving students, benefited from heterogeneously organized mathematics courses.
There is also reason to believe that parents are satisfied with the changes in mathematics education at Borel. In a district-wide survey, parents were asked to respond to the statement: "I am satisfied with my child's instruction in mathematics." Seventy-nine percent of Borel parents taking the survey responded strongly agree or agree. This compares to the other three middle schools with percentages of parents who responded similarly at 66%, 62% and 56%. Interestingly, students at one of these schools consistently score higher on SAT 9 tests than students at Borel and the other middle schools in the district.
The teachers began working with elementary and high school teachers in the district to articulate the mathematics curriculum in the 1990’s. April discussed how parents viewed the articulation efforts positively: “Another thing that helped a lot with parents is talking with the high schools, the math articulation team. When we can tell parents we know what they expect, that we’re preparing them for high school, that’s a big parental concern,.” All the elementary schools in the district began using a NSF funded curriculum in grades K-5 several years ago. George stated: “The whole district is using (an NSF curriculum) at the elementary school. Now they have a calendar that they are asked to follow.” Judith talked about the 6th graders at Borel: “Last year to this year it became much more obvious that the kids are getting it. We got a much more uniform group.” The implementation of a challenging mathematics curriculum in the elementary schools in the district is helping to better prepare students for a more rigorous mathematics education at Borel Middle School.
Conclusion
This project proved to be an important piece of the reform puzzle for the mathematics teachers at Borel Middle School. The teachers indicated that the project provided them the time and resources to define their mathematics curriculum. Meeting regularly, the teachers at Borel articulated the entire 6-8 mathematics curriculum at the school and understood what their colleagues were teaching. The teachers’ analyses of students’ work on the assessment tasks informed their instruction by giving them insight about which topics needed further instruction and about student misconceptions. The students also strove to achieve high scores on the tasks, demonstrating that the tasks motivated the students to do their best work. Finally, the project supported the teachers so that helping all students succeed in mathematics became a priority at Borel.
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Wiggins, G.P. (1993). Assessing
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