Keeping Score (1999) / Chapter Skim
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Chapter 2: A Model for Assessment Development: Achieving Balance
Chapter 2: A Model for Assessment Development: Achieving Balance
Pages 10-30
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From page 10... ...
, indicated a clear need for new mathematics assessments that would embrace mathematical goals that had not been considered in traditional norm-referenced tests. Because it is tempting, in any process of change, to concentrate solely on aspects that were previously ignored, the main theme of this chapter is achieving balance in assessing various aspects of mathematical knowledge, including skills that were adequately assessed by traditional tests as well as newer goals such as problem solving and mathematical communication.
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From page 11... ...
Thinhing processes assessment should engage students in a wide range of thinking processes that include conjecturing, organizing, explaining, investigating, formulating, and planning. Student products assessment should require a variety of student products that include models, plans, and reports.
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From page 12... ...
The challenge for task designers, therefore, becomes that of translating what is being advanced by these conceptual frameworks into worthwhile assessment opportunities for all students. Types of assessment An assessment that carries out these visions for balance must take a broad view of assessment, encompassing various types of student products and circumstances of performance.
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From page 13... ...
Embedded assessment also can be used as a component of portfolio assessment. In Vermont, for example, embedded assessments are used to compile student portfolios, and these contribute to the statewide assessments in mathematics.
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From page 14... ...
In the New Stan"dards Reference Examinations, tasks are designed with the following categories in mind: Mathematical Skills Conceptual Understanding Mathematical Problem Solving These three categories are comparable to the mathematical abilities categories used by the National Assessment of Educational Progress [NAEP] in their assessment of mathematics: procedural knowledge, conceptual understanding, and problem solving (National Assessment Governing Board, 1995~.
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From page 15... ...
This approach allows assessment of students' factual and procedural capabilities without confounding them with other capabilities. Conceptual understanding as an assessment target When tasks focus on conceptual understanding, they require students to use an idea, reformulate it and express it in their own terms.
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From page 16... ...
Conceptual understanding tasks make little or no procedural or strategic demands on students. This approach allows assessment of students' conceptual understandings without confounding them with other capabilities.
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From page 17... ...
For more information contact National Center on Education arid the Economy, 202-783-3668 or www.ncee.org formulate an approach to a problem; select the mathematical procedures, concepts, and strategies necessary, and then deploy these when implementing a solution; and · draw a conclusion. If students are to formulate an approach, the task should not provide too much structure or directive instruction (either explicitly or implicitly)
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From page 18... ...
Choosing problem-solving tasks that require students to make high-level use of skills and concepts that they have learned one or even two years previously does not mean that standards are necessarily going to be lowered. On the contrary, grade-level appropriate assessment of skills and concepts can be assessed by tasks that are specifically designed to do just that, and so the standards of technical skill and conceptual understanding can be protected.
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From page 19... ...
For more information contact National Center on Education and the Economy, 202-783-3668 or www.ncee.org Problem-solving tasks should make medium-level procedural and conceptual demands on students. Worthwhile problem-solving tasks can assess the way in which students use skills and concepts that they have fully absorbed.
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From page 20... ...
One content area, three different tasks The tasks Find the Volume, Gutter, and Shark Soda are presented here to illustrate assessment tasks that measure mathematical skill, conceptual understanding, and mathematical problem solving, respectively. They also illustrate how differently structured tasks that all focus on the same content area can be used to measure procedural, conceptual, and strategic aspects of mathematical learning.
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From page 21... ...
Maintaining skills while achieving depth and balance Many traditional mathematical skills remain essential and need to be maintained, rather than ignored, in any effort to promote conceptual understanding and problem solving. Using different tasks for each of these assessment objectives makes it possible to report separate scores for mathematical skills, conceptual understanding, and mathematical problem solving.
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From page 22... ...
To do so would be to neglect at least two other dimensions: mathematical connections and mathematical communication, both of which are of critical importance because they are both strong indicators of mathematical power. Assessing mathematical connections A balanced assessment must provide evidence about whether students are able to use mathematical skills and concepts as they are connected within mathematics or to some real-world context.
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From page 23... ...
Achieving success on such problem-solving tasks will help students to absorb prior knowledge more fully, strengthen their understandings, and help them to accommodate new ideas. Examples of types of tasks that capture the spirit of the conceptconcept connections are provided in the Core Assignments developed recently by the National Center on Education and the Economy (NCEE)
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From page 24... ...
Instead of using mathematical connections in working from the physical structure to its mathematical representation, students are asked in this exercise to use the mathematical representation to make inferences about the physical structure. Both teachers and students have reported that this approach has helped them to better understand how the slope of the graph is related to the area of the base of the container.
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From page 25... ...
. Assessing mathematical communication In contrast to mathematical connections, all assessment tasks require at least some communication.
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From page 26... ...
On-demand examinations and tests simply cannot assess problem solving, mathematical connections, or mathematical communication adequately (Arcavi, Kessel, Meira, & Smith, 1998~. Also, on-demand examinations cannot assess students' capabilities in problem-posing, careful revision of argument, extended work, presentation, or organization of material from outside sources.
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From page 27... ...
One model is to construct charts as templates that might be used by an assessment specialist when evaluating the balance of a school, district, or state assessment system. Although in some schemes, such charts might focus on aspects of learning such as thinking processes, the charts that follow build from the ideas presented earlier in the chapter on circumstances of performance, on-demand assessment, and mathematical connections.
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From page 28... ...
For example, Chart 1 provides the opportunity to map content expectations onto the assessment system, allowing some of those expectations to be developed through extended work with feedback and revision, oral presentations, and the construction of responses that are not necessarily written. Chart 2 is to be used for focusing on the on-demand components of an assessment system.
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From page 29... ...
Examination scores could, as an alternative, be made up of two scores~ne that is derived from the on-demand component, and one that is derived from coursework; that is, work that is generated as a course requirement, and could include a range of responses that are written, oral, video, or built. Chart 3 can be used to trace the path of mathematical connections throughout the entire assessment system.
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From page 30... ...
O Problem solving Snark Soda and communication (measurement) Embedded assessment Long-term projects and Investigations Concept Representation Connections 30 Shannon
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