Computer Experiences in Learning Composition of Functions

Ayers, Thomas; Davis, George E.; Dubinsky, Ed; Lewin, Philip

doi:10.2307/749068

Cited by 28 publications

(8 citation statements)

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“…Our work in this area began with Ayres et al (1988) and is closely related to Dubinsky and Lewin (1986) and Dubinsky et al (1989). The students in the present study were mainly sophomore and junior math majors preparing to be high school, middle school or elementary school math teachers.…”

Section: Process Conception Of Function 249mentioning

confidence: 91%

Development of the process conception of function

Breidenbach¹,

Dubinsky

Hawks³

et al. 1992

Educ Stud Math

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272

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Our goal in this paper is to make two points. First, college students, even those who have taken a fair number of mathematics courses, do not have much of an understanding of the function concept; and second, an epistemological theory we have been developing points to an instructional treatment, using computers, that results in substantial improvements for many students. They seem to develop a process conception of function and are able to use it to do mathematics. After an introductory section we outline, in Section 2, our theoretical epistemology in general and indicate how it applies to the function concept in particular. In Sections 3; 4, and 5 we provide specific details on this study and describe the development of the function concept that appeared to take place in the students that we are considering. In Section 6 we interpret the results and draw some conclusions.

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Section: Process Conception Of Function 249mentioning

confidence: 91%

Development of the process conception of function

Breidenbach¹,

Dubinsky

Hawks³

et al. 1992

Educ Stud Math

Self Cite

272

View full text Add to dashboard Cite

show abstract

“…As a part of the larger study, the researcher developed 35 exercises from amongst the 22 types presented in Table 1. These exercises were informed by and adapted from previous research (Ayers, Davids, Dubin‐sky, & Lewin, 1988; Dubinsky, 1992; Eisenberg and Dreyfus, 1994; Moschovich and Arcavi, 1993). The exercises covered two content areas: operations on functions and periodicity, and three representations: graphs, tables, and equations.…”

Section: Instrumentsmentioning

confidence: 99%

David's Understanding of Functions and Periodicity

Gerson

2008

School Sci & Mathematics

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This is a study of David, a senior enrolled in a high school precalculus course. David's understandings of functions and periodicity was explored, through clinical interviews and contextualized through classroom observations. Although David's precalculus class was traditional, his understanding of periodic functions was unconventional. David engaged in sense making behaviors even though these behaviors were not encouraged or explicitly taught. A careful analysis of his work revealed that David's understandings of functions, function notation, and periodicity were compartmentalized. However, David was able to skirt compartmentalization through flexibility in problem solving, translation between representations, and transfer of mathematical information from one representation to another.

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“…Studies at the "swell" level of change usually involved a closer look at the role of the technology in learning or cognition-how it can be used to support problem solving (Blume & Schoen, 1988;Heid, 1988;Kraus, 1982;Szetela, 1982;Szetela & Super, 1987;Wheatley, 1980) or how it affected students' learning of particular ideas (Ayers, Davis, Dubinsky, & Lewin, 1988;Behr & Wheeler, 1981;Clements & Battista, 1989;Clements & Battista, 1990;Edwards, 1991;Hatfield & Kieren, 1972;Noss, 1987;Olive, 1991;Szetela, 1979;Thompson, 1992;Thompson & Dreyfus, 1988). In these studies the educational activity was more deeply affected by the technology, the researchers were more oriented toward students' mathematical conceptualizations, and they placed less emphasis on controlled comparisons.…”

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confidence: 99%

Technology in Mathematics Education Research: The First 25 Years in the JRME

Kaput¹,

Thompson²

1994

Journal for Research in Mathematics Education

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The first 25 years of the JRME overlap with the first decades of electronic technologies in education. Hence the growth of technology and research in mathematics education have tended to occur in parallel. But the interactions among mathematics education research, developments in technology, and the evolving nature of school mathematics and learning are complex. To some extent, the technology was superimposed on both school practice and research in mathematics education. On the other hand, it has become increasingly evident that the technology altered the nature of the activity using it. We will use the metaphor of deep-water ocean waves to illustrate the complex interactions between technology and research in mathematics education. At the surface level are the waves themselves-short term events very much affected by local conditions such as winds and eddies. Then there are swells, of longer duration, of more distant origin, and affected by larger-scale local conditions such as temperature and currents. To distinguish waves from swells requires us to analyze wave behavior over longer periods of time and to situate that behavior within a larger context of interacting forces. Finally, there are tides whose origins are to be found outside the frames of reference for swells and waves and whose behavior is measured in time units an order of magnitude greater than the others. One can focus on any level of wave activity in isolation from the others, describing its behavior and its effects on craft or beaches. But the different levels of activity interact in subtle yet significant ways. We characterize surface, wave-level studies as those that used calculators or computers as adjuncts to existing curricula and instruction. In such studies the computer or calculator either was used primarily as an aid to computation (

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Computer Experiences in Learning Composition of Functions

Cited by 28 publications

References 0 publications

Development of the process conception of function

Development of the process conception of function

David's Understanding of Functions and Periodicity

Technology in Mathematics Education Research: The First 25 Years in the JRME

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