Evaluation of Engineering &amp; Mathematics Majors' Riemann Integral Definition Knowledge by Using APOS Theory

Tokgoz, Emre

doi:10.18260/p.26777

Cited by 5 publications

(9 citation statements)

References 6 publications

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“…Understanding STEM students' conceptual calculus knowledge with their interest in the use of technology for solving calculus questions have been studied in the literature by Tokgoz et. al [1,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and the goal of this research is to investigate furthermore on the STEM major's ability to respond calculus-based questions with their ability to apply algebra and a variety of calculus concepts.…”

Section: Research Data Collection Methodologymentioning

confidence: 99%

“…In this section literature on APOS theory that relates to the evaluation of the research questions are explained. APOS theory is applied to observe students' ability to calculate Riemann integral definition recently by Tokgoz in [1]. This observation helps to understand participants' misconceptions during the application of Eqn.…”

Section: Action-process-object-schema (Apos) Theorymentioning

confidence: 99%

“…Qualitative data is displayed by using sample interview responses of the participants. Quantitative and qualitative results are used for Action-Process-Object-Schema (APOS) theory classification of the participants similar to Tokgoz [1]. Participants are asked to explain their written questionnaire responses during the interviews.…”

Section: Introductionmentioning

confidence: 99%

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An Analysis of Conceptual Integral Knowledge of STEM Majors

Tokgoz

2022 ASEE Annual Conference &Amp; Exposition Proceedings

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Importance of integral in STEM applications is well-known however the corresponding pedagogical research for understanding undergraduate and graduate students' comprehension of integral concepts has not been studied comprehensively. Students' pedagogical integral knowledge can be evaluated from different perspectives. One aspect of such an evaluation is by stating the limit definition of definite integral for a specific function and asking students to determine the function as well as the integral bounds. Another way can be asking students to calculate a given integral by applying the limit definition of integral. In this study, seventeen senior undergraduate and graduate STEM students' written questionnaire and interview responses to two definite integral questions are collected and evaluated. These participants were either enrolled or completed a Numerical Methods or Analysis course at a large Midwest university during a particular semester in the United States. Qualitative data is displayed by using sample interview responses of the participants. Quantitative and qualitative responses are incorporated into the Action-Process-Object-Schema (APOS) theory classification for the specific questions. Participants are asked to explain their written questionnaire responses during the interviews. Concluding remarks with suggestions to the mathematics educators are provided for designing exercise and assignment questions in the conclusion and future work section.

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Section: Research Data Collection Methodologymentioning

confidence: 99%

Section: Action-process-object-schema (Apos) Theorymentioning

confidence: 99%

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An Analysis of Conceptual Integral Knowledge of STEM Majors

Tokgoz

2022 ASEE Annual Conference &Amp; Exposition Proceedings

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“…20,22,23 These studies focused on engineering students ability to interrelate calculus concepts from various perspectives such as sketching the graph of a function by using asymptote, derivative, and limit knowledge as well as using trigonometric function and chain rule knowledge. [22][23][24][25] The main theme of these studies is to observe the missing conceptual knowledge of Science-Technology-Engineering-Mathematics (STEM) students for solving ordinary calculus questions.…”

Section: Introductionmentioning

confidence: 99%

Engineering Majors’ Cognitive Function Differentiation Ability

Tokgoz¹

2018 ASEE Annual Conference &Amp; Exposition Proceedings

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Derivatives of functions and their applications are important in Science-Technology-Engineering-Mathematics (STEM) fields. Pedagogical observations of the engineering students' conceptual knowledge of the derivative are necessary for finding an effective way of teaching derivative concept to students. Chain rule and its' applications in engineering education are particularly important noting that functions seen in real life engineering applications are complicated in nature and require applying the chain rule to find their derivatives. In this paper, undergraduate engineering students' conceptual derivative knowledge is observed qualitatively and quantitatively. Participants of this study were undergraduate engineering students enrolled at a mid-sized Northeast U.S. university. These students were asked to determine the derivative of a composition function as a part of a questionnaire consisting of calculus questions and were expected to apply the chain rule to solve the research question. Participants' cognitive approaches to solve the research question were investigated during the video recorded interviews. The research question was used as a part of another pedagogical research conducted at a large Midwest U.S. university to study undergraduate and graduate students' conceptual derivative knowledge. Quantitative results obtained in this article are bi-product of the participating students' schema classification introduced by Piaget and Garcia in 1989. 15 The qualitative results are students' video recorded responses to the research question evaluated by using the concept image and concept definition of Vinner and Tall 18 .

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“…that require knowledge of more than one calculus concept [1][2][3][4][5][6][7][8][9][10][11] and more research results are added every year to these results for understanding students' approach to solve these problems. New question evaluation methods have been proposed in [1] and development of new teaching styles are recommended to educators to serve STEM students better by using these results.…”

mentioning

confidence: 99%

Analysis of STEM Students Accumulating Calculus Knowledge to Graph a Function

Tokgoz,

Tekalp,

Tekalp

et al.

2022 ASEE Annual Conference &Amp; Exposition Proceedings

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It is important for Science-Technology-Engineering-Mathematics (STEM) educators to find out about STEM students' success in answering calculus questions, particularly the questions that involve more than one calculus concepts that require to know other calculus concepts. Designing appropriate questions for assignments and exams that involve calculus concepts are critical in measuring student success. Effectiveness analysis of the method used for designing such questions is also important. Efforts have been made in understanding and improving engineering students' ability to respond calculus questions in (STEM) fields that require knowledge of more than one calculus concept [1-11] and more research results are added every year to these results for understanding students' approach to solve these problems. In this work, 26 undergraduate engineering students' written and oral responses to a calculus question that involves multiple calculus concepts are recorded after Institutional Review Board (IRB) approval. Triangulation method [1] and Action-Process-Object-Schema (APOS) theory [10] are used for analysis of the collected data. The students are tested on their capability to use sub-concepts as building blocks to answer the question completely and correctly. APOS classification resulted in most of the participants Intra and Inter level classification. The Triangulation method appeared as a strong method that can be applied for analysis of the participants' calculus knowledge as it was observed in [1]. IntroductionObserving engineering students' success in responding to calculus questions, particularly investigating the details on their conceptual understanding that involve multiple calculus concepts that require knowledge of other calculus concepts has been an interest of engineering educators. Pedagogical efforts have been made in understanding and improving engineering students' ability to respond to calculus questions in Science-Technology-Engineering-Mathematics (STEM) fields

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Evaluation of Engineering & Mathematics Majors' Riemann Integral Definition Knowledge by Using APOS Theory

Cited by 5 publications

References 6 publications

An Analysis of Conceptual Integral Knowledge of STEM Majors

An Analysis of Conceptual Integral Knowledge of STEM Majors

Engineering Majors’ Cognitive Function Differentiation Ability

Analysis of STEM Students Accumulating Calculus Knowledge to Graph a Function

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