Learning and Mathematics

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Reasons for Studying - S. B. Nolen (1988)

Susan Bobbitt Nolen, of the University of Washington, argues that in order to foster meaningful learning and effective study strategies, teachers should reduce the emphasis on competition for grades and teacher recognition and instead encourage learning for its own sake. Although mathematics is not specifically adressed in the article, the findings and suggestions included in this paper have important implications for math learning and instruction. This link is particularly important in that Nolen tackles the issue of finding the underlying cause of student motivation and learning, as opposed to attempting to promote involvement in a particular task or lesson.

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Article:

Nolen, S. B. (1988). Reasons for studying: Motivational orientations and study strategies. Cognition and Instruction, 5(4), 269-287.

Overview:

Nolen's study addressed the relationship between eighth grade students' achievement goals and the way they valued and used different kinds of study strategies.

Students who were task oriented, whose goal was learning for its own sake, were more likely to value and use deep-processing strategies; for example, to try to integrate new information with what they already knew.

Students who were ego oriented, whose goal was primarily to demonstrate that they performed better than others, were more likely to value and use surface-level strategies, for example, to memorize new formulas just before a test.

Students who were focused on work avoidance were not likely to value or use either deep-processing or surface-level strategies.

Although most students believe that deep-processing strategies are more effective than surface-level strategies, they are not likely to use the former unless they value learning for its own sake and are interested in doing their best regardless of the performance of others.

Because teachers exercise an influence over students' reasons for studying, it is important to understand "the potential effects of these reasons on students' studying behaviors" (p. 284). Nolen suggests that students should be encouraged to learn for the sake of learning; that is, to learn for understanding and meaningfulness, and to not place such great importance on competition for grades and recognition in the classroom.

Quotes and Comments:

"Deep processing strategies include discriminating important information from unimportant information, trying to figure out how new information fits with what one already knows, and monitoring comprehension. Surface-level strategies include simply reading a whole passage [problem] over and over, memorizing all the new words [formulas], and rehearsing information... Deep processing is held to be more likely than surface-level processing to lead to understanding and retention of meaningful material" (p. 271). [In other words, students who use deep-processing strategies are more likely than students who use surface-level strategies to achieve a good understanding of the task.]

"... if our goal as educators is to encourage the acquisition of meaning rather than rote memorization, the results of this study suggest that fostering ego involvement through competition for grades or teacher recognition might not be the best approach. It seems instead that... we might do well to explore ways to encourage students to value learning for its own sake. Perhaps only then will our efforts to teach students effective learning strategies be met with a desire to learn and use them" (p. 285).

Links to Math:

Several other authors whose work has appeared in the Learning and Mathematics Discussions present theories that can help link Nolen's work to the specific area of mathematics.

Hiebert and Wearne (1992) compare and contrast text-based and conceptual instruction in a series of lessons on place value. Conceptually based instruction, which emphasizes understanding of the underlying concepts in mathematics, seems to be most appropriate for fostering deep-processing strategies and a task-orientation, while traditional textbook learning, which emphasizes learning "math facts and formulas" would be most compatible for children who utilize surface-level strategies and have an ego-orientation.

Papert (1993), in his book " The Children's Machine," discusses the act or art of learning, which he refers to as 'mathetics' and examines implications of considering this concept in mathematics. He relates mathetics to skills and methods such as classroom discussions, taking the time to learn instead of emphasizing quick answers, connected learning, and bricolage, or 'tinkering' which involves students exploring math on their own. The link to Nolen is contained in the idea that learning is something that the student must be involved completely in the process of acquiring knowledge, instead of being taught facts and formulas. This type of schooling could only occur if students employed a task orientation (i.e. wanted to learn for learning's sake), and employed deep-processing strategies.

Resnick (1988) approaches these ideas from another angle -- namely, in terms of how the discipline of mathematics is presented to students. She claims that math has always been presented as a "well-structured discipline" and that students learn that they cannot change or challenge mathematical fomulas, rules, and answers. She claims that if mathematics was presented as an "ill-structured discipline" in which ideas and rules could be discussed and redefined, that understanding and conceptual knowledge would be fostered. Once again, this type of meaningful comprehension can exist only in a classroom where students employ deep-processing strategies and in which they are motivated by learning rather than grades, competition, or rewards (task orientation).

The implication inherent in these articles is that promoting conceptually-based instruction, mathetics, and mathematics as an ill-structured discipline might also promote deep-processing strategies and a task-involvement (especially if evaluation and assessment were not in the form of traditional tests and grades).

References:

Hiebert, J. and Wearne, D. (1992). Links Between Teaching and Learning Place Value with Understanding in First Grade. Journal for Research in Mathematics Education, 23 (2) 98-122.

Papert, S. (1993). The Children's Machine: Rethinking School in the Age of the Computer. New York: Basic Books.

Resnick, L.B. (1988). Treating Mathematics as an Ill-Structured Discipline. In R.I. Charles & E.A. Silver (Eds.), The Teaching and Assessing of Mathematical Problem Solving (pp 32-60). Hillsdale, NJ: Lawrence Erlbaum Associates.

-- Summarized by Maria Ong Wenbourne and Jane Ehrenfeld

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