Keeping Score (1999) / Chapter Skim
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Chapter 4: Assessment and Opportunity to Learn
Chapter 4: Assessment and Opportunity to Learn
Pages 55-70
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From page 55... ...
Providing such opportunity means creating access for students to the procedural, conceptual, and strategic knowledge to support a deep and robust understanding of mathematics and the know how necessary to demonstrate this multifaceted knowledge. A number of key research reports have focused attention on the importance of collecting opportunity-to-learn data to inform the interpretation of assessment data (NCTM & NRC, 1997; NRC, 1989, 1997, 1998; Porter, Kirst, Osthoff, Smithson, & Schneider, 1993; Schmidt, McKnight, Valverde, Houang, & Wiley, 1997; Stigler & Hiebert, 19971.
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From page 56... ...
This chapter draws upon this extensive body of classroomgenerated experience to present a series of recommendations and conclusions based on observations of assessment tasks in the social context of the classroom. Many of the sections of this chapter highlight barriers to opportunity to learn, such as tight sequencing of teaching and testing, inappropriate emphasis on skills acquisition activities, inappropriate task modification, the need to cover the curriculum, preconceptions of teachers, and gaps in the curriculum.
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From page 57... ...
Therefore, it is also rare that their students are required to attempt challenging non-routine tasks. This what we just studied phenomenon is not reserved for those students who are under-prepared in mathematics or for those who find learning mathematics difficult, but can be observed even in honors classes where student participation is usually marked by a high level of success.
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From page 58... ...
Instead of thinking about the task at hand and making decisions about the mathematics that might be needed to solve it, these students simply forced aspects of one template problem after another onto Shopping Carts. When students of this caliber work on non-routine assessment tasks, it is evident that they know a lot of mathematics-far more than is actually needed to solve the task.
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From page 59... ...
Such an approach will do little to inculcate a mathematical disposition or to encourage students to invest in further study of mathematics. Finally, the costs of this kind of testing can become hidden- large amounts of teacher time, and classroom resources are diverted away from teaching and learning and are used instead to prepare students for narrow tests that are at best loosely connected to a balanced curriculum.
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From page 60... ...
One serious problem with this common approach in teaching mathematics to students who are under-prepared is that there is very little evidence that it works to do anything more than teach simple calculation procedures, terms, and definitions (Hiebert, 1999~. Hiebert draws on the most recent National Assessment of Educational Progress (NAEP)
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From page 61... ...
Many teachers are particularly adept at deploying gap-closing strategies. They will often provide directive hints, construct pertinent demonstrations, introduce task scaffolding, and when all else fails they will sometimes try to walk their students through the task.
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From page 62... ...
It is difficult, however, to persuade other teachers that almost all of their students can learn to do challenging mathematics tasks and that students can learn mathematical skills at the same time that they are working on challenging tasks. This is in contrast to what seems to be a deep-seated belief that students' ability (or inability)
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From page 63... ...
They expect that their assignments will make clear not only what they are supposed to do but also the steps that they should take to do it. Many students simply do not perceive doing challenging mathematics as appropriate work for mathematics classrooms.
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From page 64... ...
One hypothesis is that the issue has less to do with specific task characteristics and more to do with students' experience with solids in their classroom. Many teachers readily confide that they often have only a few days left at the end of the tenth grade to devote to volume.
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From page 65... ...
The marginalization of solids within the curriculum has unfortunate consequences that extend beyond student preparation for the study of calculus. A study of solids and their volume provides an abundance of useful material for those seeking to enhance the learning of mathematics through an emphasis on connections, both within mathematics and with worthwhile and relevant contexts outside of mathematics.
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From page 66... ...
For many other teachers, however, conceptually oriented tasks that have the power to realize student misconceptions are to be avoided, lest these confuse students who already find learning mathematics difficult. In recent development work, New Standards staff prepared a formative assessment package to be used in a conceptual approach to the teaching and learning of slope (NCEE, 19981.
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From page 67... ...
Teachers report that some variation on this theme was impor tant in focusing student attention on the task, reducing student frustration, and increasing student tenacity. Assessment practice makes perfect developing · ~ communication Communication is one aspect of student performance that is frequently difficult to develop.
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From page 68... ...
by what teachers and students do in classrooms. Black and Wiliam draw upon a great number of research studies to argue persuasively that to enhance learning, specific attention must be paid to formative assessment.
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From page 69... ...
Provide professional development for teachers that will help them provide their students with useful and constructive feedback that can improve learning rather than compare or rank students. Structure professional development to enable teachers to recognize and appreciate student growth.
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From page 70... ...
This would provide continuity for students and enable teachers to develop a longitudinal view of the larger curriculum.
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