The study was conducted at Adama Science and Technology University to investigate students' conceptual understanding in learning Applied Mathematics II in general and multiple integrals in particular. A case study research design was employed on a Mechanical engineering group one student. This group was randomly selected through simple random sampling techniques. The number of students involved in this study was 50. Qualitative data were collected through reasoning part of the multiple choice items of the pre-test and interview items of the post-test were analyzed using APOS analysis based on proposed genetic decompositions. These tools were intended to investigate the conceptual understanding of students and the way they justify their answers. The study shows that the majority of the students' conception of multiple integrals could be categorized under action level whereas a few students were categorized under process conception. Students' conceptual understanding on multiple integrals of a function of two variables is a straight forward as that of a function of a single variable, which reveals that students have not developed a new schema for a function of two variables, as different from a function of a single variable. The majority of the respondents was poor at extending previous concepts to the new concept and had difficulty to represent multiple integrals using graph. Thus; the researchers recommended the utilization of an appropriate instructional approach in order to scaffold students' conceptual understanding of multiple integrals.
Published in | American Journal of Applied Mathematics (Volume 9, Issue 1) |
DOI | 10.11648/j.ajam.20210901.12 |
Page(s) | 10-15 |
Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
Copyright |
Copyright © The Author(s), 2021. Published by Science Publishing Group |
APOS Theory, Conceptual Understanding, Functions of Two Variables, Multiple Integrals
[1] | Teshome Yizengaw (2004). The Status and Challenges of Ethiopian Higher Education System and its Contribution to Development. The Ethiopian Journal of Higher Education, 1 (1). |
[2] | MoE (2008). General Education Quality Improvement Package (GEQIP). |
[3] | Eyasu G., Kassa M. & Mulugeta A. (2018). MATLAB Supported Learning and Students’ Conceptual Understanding of Functions of Two Variables: Experiences from Wolkite University. Bulgarian Journal of Science and Education Policy (BJSEP), 12, (2). |
[4] | Majid, M. A. (2014). Integrated Technologies Instructional Method to Enhance Bilingual Undergraduate Engineering Students' Achievements in the First Year Mathematics: A thesis submitted for the degree of Doctor of Philosophy, Brunel University, London, United Kingdom. |
[5] | Winkelman, P. (2009). Perceptions of mathematics in engineering. European Journal of Engineering Education, 34 (4), 305-316. |
[6] | James, W. & High, K. (2008). Freshman-Level Mathematics in Engineering: A Review of the Literature in Engineering Education. American Society for Engineering Education. |
[7] | Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning (pp. 334-370). New York: MacMillan. |
[8] | Kerrigan, S. (2015). Student Understanding and Generalization of Functions from Single to Multivariable Calculus. Honors Baccalaureate of Science in Mathematics project submitted to Oregon State University. |
[9] | Martínez-Planell, R., & Gaisman, M. T. (2012). Students’ understanding of the general notion of a function of two variables. Educational Studies in Mathematics, 81 (3), 365-384. |
[10] | Tewksbury, R. (2009). Qualitative versus quantitative methods: understanding why qualitative methods are superior for criminology and criminal justice. Journal of theoretical and philosophical criminology, 1 (1). |
[11] | Adams, R. (2003). Calculus: A Complete Course. Pearson Education Canada Inc., Toronto, Ontario. |
[12] | Stewart, J. (2008). Calculus: Early Transcendental, (6^{th}ed). Thompson Brooks/Cole. |
[13] | Trigueros, M., & Martinez-Planell, R. (2010). Geometrical representations in the learning of two variable functions. Educational Studies in Mathematics, 73 (1), 3–19. doi: 10.1007/s10649-009-9201-5. |
[14] | Martínez-Planell, R. &Gaisman, M. T. (2013). Graphs of functions of two variables: Results from the design of instruction, International. Journal of Mathematical Education in Science and Technology, 44 (5), 663-672, DOI: 10.1080/0020739X.2013.780214. |
[15] | Robert, A. & Speer, N. (2001). Research in the teaching and learning of calculus /elementary analysis (pp. 283-299). In: Holton, D., Artigue, M., Kirchgräber, Hillel, J., Niss, M. & Schoenfeld, A. (Eds.). The teaching and learning of mathematics at University level. Berlin: Springer. |
[16] | Cornu, B. (1981). Advanced Mathematical Thinking. In Nesher, P. and Kilpatrick, J. (eds), Mathematics and Cognition. (pp 113-134). |
[17] | Orton, A. (1983). Students’ Understanding of Integration. Educational Studies in Mathematics, 14, 1-18. |
[18] | Dubinsky, E., & Harel, G. (1992). The nature of the process conceptions of function. In G. Harel E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy, MAA Notes 25, pp. 85–106). Washington, DC: Mathematical Association of America. |
[19] | Eisenberg, T., & Dreyfus, T. (1994). On understanding how students learn to visualize function and transformations. In E. Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), Research incollegiate mathematics I, 4 (45–68). Providence, RI: American Mathematical Society. |
[20] | Metcalf, R. C. (2007). The nature of students’ understanding of quadratic functions. (PhD Dissertation, State University of New York at Buffalo, Buffalo, NY). |
[21] | Rockswold, G. K. (2010). College algebra with modeling and visualization (4^{th}ed.). New York: Addison-Wesley. |
[22] | Akkus, R., Hand, B., & Seymour, J. (2008). Understanding students’ understanding of functions. Mathematics Teaching Incorporating Micromath, 207, 10-13. |
[23] | Carlson, M., Oehrtman, M., & Engelke, N. (2010). The precalculus concept assessment: a tool for assessing students’ reasoning abilities and understandings. Cognition and Instruction, 28, 113-145. DOI: 10.1080/07370001003676587. |
[24] | Davis, J. D. (2007). Real world contexts, multiple representations, student-invented terminology, and y-intercept. Mathematical Thinking and Learning, 9, 387-418. DOI: 10.1080/10986060701533839. |
APA Style
Eyasu Gemechu, Amanuel Mogiso, Yusuf Hussein, Gedefa Adugna. (2021). Students' Conception on Multiple Integrals of a Function of Several Variables: A Case of Adama Science and Technology University. American Journal of Applied Mathematics, 9(1), 10-15. https://doi.org/10.11648/j.ajam.20210901.12
ACS Style
Eyasu Gemechu; Amanuel Mogiso; Yusuf Hussein; Gedefa Adugna. Students' Conception on Multiple Integrals of a Function of Several Variables: A Case of Adama Science and Technology University. Am. J. Appl. Math. 2021, 9(1), 10-15. doi: 10.11648/j.ajam.20210901.12
AMA Style
Eyasu Gemechu, Amanuel Mogiso, Yusuf Hussein, Gedefa Adugna. Students' Conception on Multiple Integrals of a Function of Several Variables: A Case of Adama Science and Technology University. Am J Appl Math. 2021;9(1):10-15. doi: 10.11648/j.ajam.20210901.12
@article{10.11648/j.ajam.20210901.12, author = {Eyasu Gemechu and Amanuel Mogiso and Yusuf Hussein and Gedefa Adugna}, title = {Students' Conception on Multiple Integrals of a Function of Several Variables: A Case of Adama Science and Technology University}, journal = {American Journal of Applied Mathematics}, volume = {9}, number = {1}, pages = {10-15}, doi = {10.11648/j.ajam.20210901.12}, url = {https://doi.org/10.11648/j.ajam.20210901.12}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20210901.12}, abstract = {The study was conducted at Adama Science and Technology University to investigate students' conceptual understanding in learning Applied Mathematics II in general and multiple integrals in particular. A case study research design was employed on a Mechanical engineering group one student. This group was randomly selected through simple random sampling techniques. The number of students involved in this study was 50. Qualitative data were collected through reasoning part of the multiple choice items of the pre-test and interview items of the post-test were analyzed using APOS analysis based on proposed genetic decompositions. These tools were intended to investigate the conceptual understanding of students and the way they justify their answers. The study shows that the majority of the students' conception of multiple integrals could be categorized under action level whereas a few students were categorized under process conception. Students' conceptual understanding on multiple integrals of a function of two variables is a straight forward as that of a function of a single variable, which reveals that students have not developed a new schema for a function of two variables, as different from a function of a single variable. The majority of the respondents was poor at extending previous concepts to the new concept and had difficulty to represent multiple integrals using graph. Thus; the researchers recommended the utilization of an appropriate instructional approach in order to scaffold students' conceptual understanding of multiple integrals.}, year = {2021} }
TY - JOUR T1 - Students' Conception on Multiple Integrals of a Function of Several Variables: A Case of Adama Science and Technology University AU - Eyasu Gemechu AU - Amanuel Mogiso AU - Yusuf Hussein AU - Gedefa Adugna Y1 - 2021/03/17 PY - 2021 N1 - https://doi.org/10.11648/j.ajam.20210901.12 DO - 10.11648/j.ajam.20210901.12 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 10 EP - 15 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20210901.12 AB - The study was conducted at Adama Science and Technology University to investigate students' conceptual understanding in learning Applied Mathematics II in general and multiple integrals in particular. A case study research design was employed on a Mechanical engineering group one student. This group was randomly selected through simple random sampling techniques. The number of students involved in this study was 50. Qualitative data were collected through reasoning part of the multiple choice items of the pre-test and interview items of the post-test were analyzed using APOS analysis based on proposed genetic decompositions. These tools were intended to investigate the conceptual understanding of students and the way they justify their answers. The study shows that the majority of the students' conception of multiple integrals could be categorized under action level whereas a few students were categorized under process conception. Students' conceptual understanding on multiple integrals of a function of two variables is a straight forward as that of a function of a single variable, which reveals that students have not developed a new schema for a function of two variables, as different from a function of a single variable. The majority of the respondents was poor at extending previous concepts to the new concept and had difficulty to represent multiple integrals using graph. Thus; the researchers recommended the utilization of an appropriate instructional approach in order to scaffold students' conceptual understanding of multiple integrals. VL - 9 IS - 1 ER -