Chrissy Nesbitt July 18, 2008
“How Does Your Donut Measure Up?” a performance assessment product inspired by Paula Maida and Michael Maida’s lesson plan, (2006). How Does Your Doughnut Measure Up. Mathematics Teaching in the Middle School, 11 (5), 212.
Users and Uses: This performance assessment was designed primarily for students, to engage them in the process of measurement and guide them in deep thinking about strategies for approximating the surface area and volume of complex figures. Learning Targets: This performance assessment measures a range of skills. The learning targets below are listed in the assessment product next to the corresponding sections of the analytic scale. They represent an amalgam of various NCTM standards and the goals set forth in the Measurement unit of Sadlier-Oxford’s Progress in Mathematics 6th grade text. This list may seem long, but the concepts addressed are all intrinsic to the task of measuring a donut and donut box. • • • • • • • •
Student uses precise vocabulary to communicate mathematical ideas. (area, perimeter, circumference, diameter, face, lateral surface, volume, surface area, efficient, accurate) Student is able to perform math operations with accuracy using a calculator. Student is able to use common benchmarks to select appropriate methods for estimating surface area and volume. Student is able to analyze precision, accuracy, and approximate error in measurement situations. Student is able to select appropriate units and tools to measure length and circumference. Student is able to apply techniques and tools to accurately find length and circumference to appropriate levels of precision. Student is able to develop and use formulas to determine the area of circles, rectangles, and more-complex shapes. Student is able to develop strategies to determine the surface area and volume of selected prisms, cylinders, and morecomplex shapes.
Assessment Method: Performance assessment lends itself to measuring deep thinking, which is one of the purposes of this assessment. The task of measuring an irregular object requires students to develop and explain strategies for adapting formulas they know to the real world. Performance assessment is also a means for improving student affect towards math; the authenticity of the task (and the authenticity of the donut!) can serve as powerful motivators. Avoiding Mismeasure The scoring tool for this assessment is not intrinsically safe from bias. My desire to include multiple well-defined targets made it inefficient for me to write a full rubric for this assessment; instead, I developed an analytic scale with four gradations, ranging from novice to advanced. In order to avoid bias, I will collect student samples over time to serve as anchors for making decisions. In the meantime, I
will use different strategies to prevent bias. For example, I will score one criterion for all students at the same time, and I will revisit some of the first few projects after scoring all of them. Validity The criteria being evaluated in this assessment are derived directly from the learning targets of the preceding lesson. In the analytic scale, these criteria are listed next to the sections of the assessment in which they can be measured. By making sure the assessment corresponds with what was taught in class, I tried to ensure that the inferences made using this assessment tool are valid. On the other hand, only written evidence is accepted in this assessment; this limits its validity for determining studentsâ€™ ability to measure surface area and volume. This assessment would need to be supplemented by classroom discussions and observations to get a well-rounded picture of studentsâ€™ learning in this area. Reliability The reliability of this assessment is enhanced by the number of measurements students are required to complete. I also made an effort to improve reliability by wording questions clearly and presenting only one question at a time. Positive Consequences As mentioned above, this assessment was designed to motivate students. The worksheet also guides the students in metacognition and self-reflection, which have been shown to lead to improved learning. Lastly, the analytic scale is available to the student. The criteria are clearly delineated and intuitively grouped, enabling students to understand teacher feedback and engage in self-assessment. Practicality and Efficiency The assessment is practical; it can be completed during class with a reasonable amount of materials. The analytic scale is also an efficient method of grading when the criteria are so numerous. Performance or Scoring Criteria As mentioned above, the criteria were designed to be specific, student-friendly, and closely aligned with learning targets. There are a large number of critera so that students can receive accurate feedback on where their strengths and weaknesses lie. Anticipated Feedback Students Will Receive Students will receive feedback from teacher comments and the analytic scale. After they receive this feedback, they will be guided in self-assessment. Students will be prompted to reflect in their math journals on what they learned; what skills they have mastered; and what skills need improvement.
Possible Instructional Decisions This assessment will demonstrate studentsâ€™ ability to perform measurements and make clear to the teacher which students need support in this area as they move on. This assessment will also be an indicator of studentsâ€™ comfort with mathematical vocabulary and communication. Studentsâ€™ performance on this assessment will affect the level of scaffolding the teacher supplies when pre-teaching vocabulary, as well as the amount of time devoted to teaching communication skills. Summary Comments I used this opportunity to turn a motivational learning activity into a systematic measure of student learning. This exercise has helped me integrate quality assessment into an active learning environment. Developing this assessment product has helped me to see that, at their best, quality assessment and active learning are inseparable; they feed off one another.