Collins, Brown, and Newman (1990) introduced the term “scaffolding” to describe aspects of learning environments such as the kinds of help teachers offer as well as the nature of written tasks (see also Collins, Brown, and Holum, 1991). For discussion and examples of the idea of scaffolded and unscaffolded assessment tasks and differences in student responses to each, see Keeping Score (Shannon, 1999, pp. 39–48).
Teacher actions may help to scaffold a novel task or may reduce it to a familiar task. This is sometimes described as maintaining or reducing the challenge or complexity of the task, or in terms of letting students struggle or not struggle. Doyle describes novel tasks based on observations of U. S. classrooms:
Novel work consists of assignments for which students are required to assemble information and operations from several sources in ways that have not been laid out explicitly in advance by the teacher. Novel tasks in math, for example, would involve such processes as deciding which operation fits a particular problem or combining algorithms already learned into a chain of operations to solve a problem. (Doyle, 1988, p. 173)
A “novel task” might also be described as a task that is a problem for students (see the first meaning of problem in Problems and problem solving) and, in the language of calculus reform, as a task that is not a “template problem” (Douglas, 1986).
Doyle describes difficulties U. S. teachers may have in using novel tasks:
In comparison to lessons with familiar work, introductions to novel tasks are sometimes lengthy and work involvement and productivity are sometimes low . . . students sometimes respond to the ambiguity and risk involved by negotiating directly with teachers to increase the explicitness of product specifications or reduce the strictness of grading . . . In sum, novel work stretches the limits of classroom management and intensifies the complexity of the teacher’s task of orchestrating classroom events. (Doyle, 1988, p. 174)
The U.S. teachers that Doyle observed sometimes did not use novel tasks. When teachers did use novel tasks, they often avoided the tensions that Doyle describes by changing the demands of the task in various ways, providing models for students to work from, or frequently calling students’ attention to particular steps in algorithms. The results were considerable:
Tasks which appear on the surface to elicit comprehension or analytical skills (e.g., in teacher presentations to the class or in student tests) are often accomplished in circumstances that alter fundamentally the character of their demands on students. (Doyle, 1988, p. 175)
By contrast, some of the lessons from other countries—such as S1, HK4, and J3—show students doing what appears to be novel work that is not altered from the teacher’s initial intent.
The TIMSS Video Study contrasted problem statements with their implementations in public class work (see Making connections and Problems and problem solving). In the U.S. classrooms studied, 17% of the problem statements were classified as “making connections,” but only 1% of the problem implementations were classified as “making connections” (U.S. Dept. of Ed., 2003, pp. 99 and 101). The reduction of task demands Doyle describes may be responsible for the difference between the percentage of “making connections” problem statements and implementations in U. S. classrooms.
Collins, A., Brown, J. S., & Holum, A. (1991). Cognitive apprenticeship: Making thinking visible. American Educator, 6–11, 38–46.
Collins, A., Brown, J. S., & Newman, S. E. (1990). Cognitive apprenticeship: Teaching the crafts of reading, writing, and mathematics. In L. B. Resnick (Ed.), Knowing, learning, and instruction: Essays in honor of Robert Glaser (pp. 453–494). Hillsdale, NJ: Lawrence Erlbaum Associates.
Douglas, R. (Ed.). (1986). Toward a lean and lively calculus (MAA notes no. 6). Washington, DC: Mathematical Association of America.
Doyle, W. (1988). Work in mathematics classes: The context of students’ thinking during instruction. Educational Psychologist, 23(2), 167–180.
Shannon, A. (1999). Keeping score. Washington, DC: National Academy Press.
U.S. Department of Education, National Center for Education Statistics (March 2003). Teaching mathematics in seven countries: Results from the TIMSS 1999 Video Study, NCES (2003-013), by A. M.-Y. Chiu, W. Etterbeek, R. Gallimore, H. Garnier, K. Bogard Givvin, P. Gonzales, J. Hiebert, H. Hollingsworth, J. Jacobs, N. Kersting, A. Manaster, C. Manaster, M. Smith, J. Stigler, E. Tseng, and D. Wearne. Washington, DC: Author.
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