Intellectual Development Beyond Elementary School VII: Teaching for Proportional Reasoning

Kurtz, Barry L.; Karplus, Robert

doi:10.1111/j.1949-8594.1979.tb13867.x

Cited by 29 publications

(13 citation statements)

References 7 publications

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“…In view of the prevalence of the additive procedure, it seems to be particularly important that students have experiences which allow them to compare situations embodying a constant difference relationship (e.g., the ages of two children) and those obeying a constant ratio. A highly effective teaching program for proportional reasoning has recently been described (Kurtz, 1976;Kurtz and Karplus, 1979;Wollman and Lawson, 1978); it would seem to have promise to improve student competence in this area. Another approach might be better coordination between the teaching of ratio in mathematics classes and the application in science classes.…”

Section: Discussionmentioning

confidence: 99%

Intellectual Development Beyond Elementary School VIII: Proportional, Probabilistic, and Correlational Reasoning

Karplus

Adi

Lawson

1980

School Sci & Mathematics

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Concern with the development of formal reasoning has been stimulated by the increasing recognition that formal reasoning is related to student success in secondary and college science and mathematics courses (Arons, 1976;Bauman, 1976;Griffiths, 1976;Herron, 1975;Karplus, 1978;Kolodyi, 1975;Lawson and Renner, 1975;Sayre and Ball, 1975;Shayer, 1972Shayer, , 1973Shayer, , 1974Suarez, 1977). In this article we shall report on our study of six group-administered tasks that have not been previously used in the United States with student groups of widely differing ages. We seek to answer these questions:1. What categories are required for classifying the subjects' responses on tasks requiring proportional, probabilistic, or correlational reasoning?2. How effective are these tasks for assessing these aspects of formal reasoning? 3. What implications for teaching are suggested by the observed distributions of student responses among the categories required? SUBJECTS The subjects were 505 students from sixth grade to college sophomores, ranging in age from 11.5 to 20.0 years. Somewhat over 400 of the subjects were enrolled in elementary and secondary schools located in a middle-to upper-middle-class suburban community in the San Francisco Bay area. The eighth graders were tested in English classes, the tenth graders in biology, and the twelfth graders in social studies to obtain representative samples not biased with respect to mathematics and science background. The college students were freshmen and sophomores enrolled in two physical science courses for non-majors at the University of California, Berkeley. The numbers and grade levels of the students are summarized in Table 1.

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Section: Discussionmentioning

confidence: 99%

Intellectual Development Beyond Elementary School VIII: Proportional, Probabilistic, and Correlational Reasoning

Karplus

Adi

Lawson

1980

School Sci & Mathematics

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“…In a study of older students, in the 9th grade, Kurtz and Karplus (1979) were successful in producing a significant gain in about 50% of the students. A control group getting traditional instruction also showed an improvement.…”

Section: Group Interventionsmentioning

confidence: 99%

Proportional reasoning: A review of the literature

1985

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This paper presents a review of the research on proportional reasoning. Methodologies used in proportional reasoning studies are presented first. The discussion is then organized around the following topics: strategies used to solve proportion problems, including erroneous strategies; factors that influence performance on proportion problems, both task-related and subject-related; training studies. The discussion is accompanied by suggestions for educational and research applications.For a mathematician, a proportion is a statement of equality of two ratios, i.e., a/b = c/d. Although most people are probably unaware of the mathematical definition of proportions, they do use them in familiar situations. Proportions are also widely used in more scientific contexts. Despite its importance in everyday situations, in the sciences, and in the educational system, the concept of proportions is difficult. It is acquired late (see, for example, Newton et al. 1981, or Pallrand, 1979. Moreover, many adults do not exhibit mastery of the concept (e.g., Capon and Kuhn, 1979).Because it is both useful and difficult to master, proportional reasoning has been the object of many research studies in the last 25 years. During this period, the research has become increasingly sophisticated, changing from a view of proportional reasoning as a global ability, or a manifestation of a general cognitive structure, to a more differentiated view focusing on describing the procedures used in proportional reasoning and how they are influenced by task and person parameters. However, as the studies became more differentiated in style some parameters were studied in detail without attention being paid to other tasks parameters. As a result, the body of research suffers from many gaps, it lacks cohesiveness and it is difficult to apply to mathematics education.It is the purpose of this paper to: (1) organize the research findings around the relevant task and subject parameters, (2) suggest research to fill the gaps in the literature, and (3)suggest ways to apply these findings in education. It begins with a discussion of the methodologies used in studying proportional reasoning. M E T H O D O L O G YStudies of proportional reasoning have employed different methodologies and tasks. A list of the tasks used in various experimental studies can be found in

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“…(l'iaget's mechanism for equilibration of the structure is dialectical and he would not argue with Riegel in principle, but would disagree with Riegel's emphasis.) Other researchers have also suggested that a fifth stage might exist (e.g., Arlin, 1975;Sinott, 1975;Labouvie-Vief, 1982). These formulations of the fifth stage all reflect dissatisfaction with the definition of the structure of the formal stage as described by Inhelder and Piaget (1 958).…”

Section: Historical Perspective On Piagetian Theorymentioning

confidence: 99%

“…Many unsuccessful studies attest to this assertion (e.g., Levine & Linn, 1977;Linn, 1980b). In contrast, subjects have been taught to control variables on a wider variety of problems (Linn, 1980a) or to apply proportional reasoning more consistently (Kurtz & Karplus, 1979). Thus, it is possible to differentiate between teaching previously unfamiliar strategies and teaching new applications of available strategies.…”

Section: Effect Of Educational Interventions To Change Reasoningmentioning

confidence: 99%

Theoretical and practical significance of formal reasoning

Linn¹

1982

J Res Sci Teach

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Piaget's theory has profoundly influenced science education research. Following Piaget, researchers have focused on content‐free strategies, developmentally based mechanisms, and structural models of each stage of reasoning. In practice, factors besides those considered in Piaget's theory influence whether or not a theoretically available strategy is used. Piaget's focus has minimized the research attention placed on what could be called “practical” factors in reasoning. Practical factors are factors that influence application of a theoretically available strategy, for example, previous experience with the task content, familiarity with task instructions, or personality style of the student. Piagetian theory has minimized the importance of practical factors and discouraged investigation of (1) the role of factual knowledge in reasoning, (2) the diagnosis of specific, task‐based errors in reasoning, (3) the influence of individual aptitudes on reasoning (e.g., field dependence‐independence), and (4) the effect of educational interventions designed to change reasoning. This article calls for new emphasis on practical factors in reasoning and suggests why research on practical factors in reasoning will enhance our understanding of how scientific reasoning is acquired and of how science education programs can foster it.

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Intellectual Development Beyond Elementary School VII: Teaching for Proportional Reasoning

Cited by 29 publications

References 7 publications

Intellectual Development Beyond Elementary School VIII: Proportional, Probabilistic, and Correlational Reasoning

Intellectual Development Beyond Elementary School VIII: Proportional, Probabilistic, and Correlational Reasoning

Proportional reasoning: A review of the literature

Theoretical and practical significance of formal reasoning

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