Keeping Score (1999) / Chapter Skim
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Chapter 3: Assessment and Opportunity to Perform
Chapter 3: Assessment and Opportunity to Perform
Pages 31-54
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From page 31... ...
One of the most striking aspects of task development is just how hard students find many tasks that are designed to assess conceptual understanding or problem solving. Time and again when tasks were piloted in classrooms tasks that appeared to provide students the opportunity to show what they know the tasks were for some reason inaccessible for most students.
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From page 32... ...
This chapter briefly describes the task-development process and then illustrates several key concepts that emerged while attempting to construct tasks that provide students with opportunities to perform. In particular, some tasks create cognitive overload by attempting to assess skills, conceptual understanding, 32 Shannon
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From page 33... ...
Task kernels are tried out in a small number of classrooms under the observation of a task designer who makes rudimentary judgments about the tasks' measurement targets. The preliminary tasks are sent to an expert review panel, together with the initial judgments about their measurement targets.
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From page 34... ...
When cognitive overload stymies opportunity to perform The task Hang Glider (Figure 7) simultaneously requires mathematical skill, conceptual understanding, and mathematical problem solving.
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From page 35... ...
Reprinted with permission from the Balanced Assessment project, University of Califorrtu~, Berkeley. Finding a second equation relating ~ and w is much more difficult.
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From page 36... ...
The data suggest that only the most talented of students will have enough experience to access these concepts and to use them in the sophisticated way that Hang Glider demands. In other words, Hang Glider is a task that asks students to make strategic use of concepts that are, for the majority of tenth grade students, not fully integrated into the students' existing conceptual frameworks (Hiebert & Carpenter, 1992~.
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From page 37... ...
Tasks entailing a high strategic hurdle often provide a false negative assessment of what students understand about underlying concepts. Creating access while preserving task integrity One of the design challenges associated with developing almost any non-routine task is that of creating access without radically altering the intended measurement target.
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From page 38... ...
Perhaps the reluctance results from the long tradition of creating assessments composed entirely of bite-sized tasks and parceling out bite-sized assignments for students to do in their mathematics classes. Classrooms need to become places where students are given the opportunity to learn and then practice how to formulate and implement their own approaches to challenging, non-routine tasks.
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From page 39... ...
, students were presented with two versions of a task involving shopping carts. The relatively unscaffolded version was called Supermarket Carts (Figure 9~.
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From page 40... ...
Students worked on the task individually under the impression that only one task was being administered. In response to the scaffolded Shopping Carts, almost all students managed to develop an appropriate linear function to model the nested carts, but in response to the unscaffolded Supermarket Carts, 40 Shapiro?
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From page 41... ...
In recognition of its substantial strategic hurdle, Supermarket Carts would be primarily a problem-solving task. The carefully constructed questions that direct an approach in Shopping Carts, on the other hand, reduce the strategic hurdle considerably, so that it would be categorized as an assessment of conceptual understanding.
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From page 42... ...
how the context can inhibit opportunity to perform. Scaffolded and unscaffolded versions of the task Storage Containers were produced by replacing the carts in each of Shopping Carts and Supermarket Carts with stackable storage containers.
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From page 43... ...
In addition, the choice of scale factor, 1/24 in the drawings of the carts and 1/10 in the drawings of the containers, emerged as a strong influencing characteristic (Shannon & Zawojewski, 19951. The scale factor of 1/24 provided a greater hurdle in the unscaffolded Supermarket Carts than in the scaffolded Shopping Carts.
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From page 44... ...
In contrast to both Shopping Carts and Storage Cor~tair~ers, however, many students working on Paper Cups will immediately decompose the cup into the following two parts, which they sometimes label as the body and the brim, as illustrated in the student solution in Figure 10. This decomposition enables many students to create the required formula directly in terms of the height of body of one cup plus the height of x brims, as illustrated in the remainder of this student's response (Figure 111.
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From page 45... ...
Paper Cups emerges, therefore, as a task that has a relatively high strategic hurdle, is appropriately challenging, and yet can be presented without relying on any directive questioning. It is a type of task that can be quite beneficial to use with students who are not accustomed to solving context-based problems.
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From page 46... ...
. In view of this recommendation, the research into the relative effects of replacing carts with containers and then containers with cups leads to questions about the relative effects of the specifics of linear function tasks that rely on contexts such as car rental charges, phone call charges, and electricity charges.
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From page 47... ...
The variables that need to be represented in physical structures comprised of cups or books are more concrete and more visible for students than are the quantities such as cost and time in tasks involving rental cars and telephones or quantities such as cost and kilowatt-hours in tasks involving utility bills. If students are taught about linear functions using contexts they can visualize in a concrete tangible way, it is hoped that they will be able to apply the ideas they have learned to less obvious situations.
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From page 48... ...
Indeed, their place is in assessment tasks designed specifically to assess mathematical skills and concepts, and these assessment tasks might well be those that use scaffolding intentionally to target specified aspects of mathematics. Turning task miscues into opportunity to perform The effort that is put into developing assessment tasks and identifying their assessment targets will be wasted if similar effort is not paid to the interpretation of student work.
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From page 49... ...
. An initial version of the assessment task asked students to explain how they would create such a tape.
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From page 50... ...
When the graphic was adjusted so that it no longer had the appearance of a right triangle, no further applications of the Pythagorean Theorem to this linear function task emerged. More important, once students were freed from the unintended task miscue, they were able to show what they did know or could figure out about modeling the length of the lace needed as a function of the number of lace holes.
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From page 51... ...
Turning elephant traps into learning opportunities With regard to assessment, the term elephant trap refers to an unintended task hurdle or a task hurdle that provides no information other than the observation that large numbers of students consistently arrive at a common incorrect response. The task Broken Plate (Figure 12)
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From page 52... ...
Reprinted with permission from New Standards_. For more information contact National Center on Education and the Economy, 202-788-3668 or www.ncee.org typified student performance on the initial version.
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From page 53... ...
The student is given the opportunity to ref lect on an incorrect response, resolve the conflict, and produce the correct response. The technique of giving students a wrong answer and asking them to supply a correct one is recommended in a recent publication commissioned by the NAEP Validity Studies (Jakwerth, Stancavage, & Reed, 19991.
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From page 54... ...
In addition to developing its own tasks, New Standards sought kernel tasks from many sources, including The Balanced Assessment Project, mathematics teachers from across the U.S., curriculum developers, and task developers in Australia and England. Perhaps the most sound practical advice is that all revisions to high-stakes assessments should be tried out with students to explore the effect of these revisions on opportunity to perform.
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