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Attitudes and preferences of calculus students in using multiple representations to solve accumulation function problems.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Attitudes and preferences of calculus students in using multiple representations to solve accumulation function problems./
Author:	Heller, Shanley.
Description:	1 online resource (238 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 77-09(E), Section: A.
Contained By:	Dissertation Abstracts International77-09A(E).
Subject:	Mathematics education. -
Online resource:	click for full text (PQDT)
ISBN:	9781339650098

Attitudes and preferences of calculus students in using multiple representations to solve accumulation function problems.
Heller, Shanley.

Attitudes and preferences of calculus students in using multiple representations to solve accumulation function problems. - 1 online resource (238 pages)

Source: Dissertation Abstracts International, Volume: 77-09(E), Section: A.

Thesis (Ed.D.)--University of Massachusetts Lowell, 2016.

Includes bibliographical references

It has been well-documented that few high school Calculus students understand the relationship between the derivative and integral and, consequently, their relationship to the accumulation function. Also, students have difficulty utilizing this relationship when solving non-routine problems. Some research studies have shown that understanding the nature of the accumulation function may help students develop comprehension of the relationship between the derivative and integral. The derivative and integral, the mathematical models of certain real world phenomena and processes, can be presented to learners via multiple representations including word descriptions, graphs, diagrams, and tables. The available research shows that students exhibit certain attitudes and preferences towards the different representations of structurally the same concept. This study was designed to gain insight into the nature of students' conceptual understanding of the accumulation function. Advanced Placement (AP) Calculus students were surveyed in order to capture their attitudes and preferences when using multiple representations in solving problems involving the accumulation function. In particular, this study investigated proficient learners' strategies while solving problems, and inquired into proficient learners' ability to translate between multiple representations of structurally the same concept, as well as their structural or operational understanding of the accumulation function. Data were collected from three schools in the Northeastern United States. Ninety-two Advance Placement Calculus students completed a survey developed exclusively for the study. Ten surveyed students were interviewed. Analysis of data from the surveys and interviews focused on trends in students' attitudes and preferences when solving accumulation function problems in multiple representations, recognizing structurally the same concept in multiple modes, and utilizing strategies when solving accumulation function problems.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781339650098Subjects--Topical Terms:

1148686
Mathematics education.
Index Terms--Genre/Form:

554714
Electronic books.

Attitudes and preferences of calculus students in using multiple representations to solve accumulation function problems.
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245 1 0 $a Attitudes and preferences of calculus students in using multiple representations to solve accumulation function problems.
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300 $a 1 online resource (238 pages)
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500 $a Source: Dissertation Abstracts International, Volume: 77-09(E), Section: A.
500 $a Adviser: Regina Panasuk.
502 $a Thesis (Ed.D.)--University of Massachusetts Lowell, 2016.
504 $a Includes bibliographical references
520 $a It has been well-documented that few high school Calculus students understand the relationship between the derivative and integral and, consequently, their relationship to the accumulation function. Also, students have difficulty utilizing this relationship when solving non-routine problems. Some research studies have shown that understanding the nature of the accumulation function may help students develop comprehension of the relationship between the derivative and integral. The derivative and integral, the mathematical models of certain real world phenomena and processes, can be presented to learners via multiple representations including word descriptions, graphs, diagrams, and tables. The available research shows that students exhibit certain attitudes and preferences towards the different representations of structurally the same concept. This study was designed to gain insight into the nature of students' conceptual understanding of the accumulation function. Advanced Placement (AP) Calculus students were surveyed in order to capture their attitudes and preferences when using multiple representations in solving problems involving the accumulation function. In particular, this study investigated proficient learners' strategies while solving problems, and inquired into proficient learners' ability to translate between multiple representations of structurally the same concept, as well as their structural or operational understanding of the accumulation function. Data were collected from three schools in the Northeastern United States. Ninety-two Advance Placement Calculus students completed a survey developed exclusively for the study. Ten surveyed students were interviewed. Analysis of data from the surveys and interviews focused on trends in students' attitudes and preferences when solving accumulation function problems in multiple representations, recognizing structurally the same concept in multiple modes, and utilizing strategies when solving accumulation function problems.
520 $a It has been found that proficient learners preferred accumulation function problems to be presented in multiple modes at the same time. In this study, proficient learners showed a slight preference for problems presented in words, as compared to problems presented in symbols or tables. Also, graphical representations, which required a certain depth of knowledge and ability to recognize the different relationship between multiple concepts, were not favored by the participants. Interestingly enough, among problem-solving strategies, such as finding the area under the curve, Riemann sums, "velocity vs. time," the "product of the units," and a rule, the participating students preferred the rule "the integral of the rate equals the amount." It is important to note, the language offered in quotations is colloquial, however, unfortunately widely-used in classrooms. Participants identified as proficient learners, who could fluidly translate between representations, showed flexibility in using different strategies in solving accumulation problems, thus demonstrated an understanding of the mathematical relationships. It is concluded that to facilitate students' development of conceptual understanding and procedural skills with the accumulation function, the problems should be presented in multiple ways. In addition, the use of imprecise mathematical language may inhibit students' conceptual understanding of the accumulation function.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics education. $3 1148686
650 4 $a Education. $3 555912
650 4 $a Secondary education. $3 1179560
655 7 $a Electronic books. $2 local $3 554714
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