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Year 2020, Volume: 16 , 18 - 28, 21.06.2020

Abstract

References

  • Adams, R. (2003). Calculus: A Complete Course. Pearson Education Canada Inc., Toronto, Ontario. Akkus, R., Hand, B., & Seymour, J. (2008).Understanding students’ understanding of functions.Mathematics Teaching Incorporating Micromath, 207, 10-13. Al-Ammary, J. (2013). Educational Technology: A Way To Enhance Student Achievement At The University Of Bahrain. The Online Journal of New Horizons in Education. 3(3), 54-65. Antwi, V., Hanson R., Savelsbergh E.R. &Eijkelhof H.M.C. (2011). Students’ understanding of some concepts in introductory mechanics course: A study in the first year university students, UEW. International Journal of Educational Planning and Administration., 1(1), 55-80. Arnon, I., Cottrill, J. Dubinsky, E., Oktac, A., Roa, S., Trigueros, M., & Weller, K. (2014), APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education, Springer, NY, Heidelberg, Dondrecht, London. https://doi.org/10.1007/978-1 -4614-7966-6 Bennett, J., & Briggs, W. (2007).Using and understanding mathematics: A quantitative reasoning approach(4th ed.). Boston: Addison Wesley. Bittinger, M. L., Ellenbogen, D. J., & Johnson, B. L. (2010). Elementary and intermediatealgebra: graphs and models (4th ed.). Boston: Addison Wesley. 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. Carlson, M. (1997). Obstacles for college algebra students in understanding functions: what do high-performing students really know? The AMATYC Review. 19. 48-59. Charles-Ogan, G. I., (2015).Utilization of MATLAB as a Technological Tool for Teaching and Learning of Mathematics in Schools.International Journal of Mathematics and Statistics Studies, 3(5), 10-24. 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. Drlik, D. I. (2015). Student understanding of function and success in calculus. A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mathematics Education, Boise State University (Unpublished). 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. Dubinsky, E. & MacDonald, M. (2001). APOS: a constructivist theory of learning in undergraduate mathematics in education research. The Teaching and Learning of Mathematics at University Level: An ICMI Study (pp. 273-280). Dordrecht: Kluwer Academic Publishers. Duval, R. (2006).A cognitive analysis of problems of comprehension in a learning of mathematics.Educational Studies in Mathematics, 61(1), 103-131. 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 MathematicalSociety. Gaisman, M. T. & Martinez-Planell, R. (2010).Geometrical representations in the learning of two-variable functions. Educational studies in mathematics, 1-32. DOI: 10.1007/s10649-009-9201-5. Goold, E. (2012). The Role of Mathematics in Engineering Practice and in the Formation of Engineers, 1(2). Huang, C.-H.(2010). Conceptual and Procedural Abilities of Engineering Students in Integration.Joint International IGIP-SEFI Annual Conference, Trnava, Slovakia. Idris, N. (2009).The Impact of Using Geometers’ Sketchpad on Malaysian Students’ Achievement and Van Hiele Geometric Thinking.Journal of Mathematics Education. 2(2), 94-107 Kashefi, H, Ismail, Z &Yusof, Y.M. (2010).Obstacles in the Learning of Two-variable Functions through Mathematical Thinking Approach. Procedia Social and Behavioral Sciences 8, 173–180. KassahunMelesse (2014). The Influence of E-Learning on the Academic Performance of Mathematics Students in Fundamental Concepts of Algebra Course: The Case in Jimma University. Ethiopian Journal of Education and Science, 9(2), 41-59. 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. Maharaj, A. (2010). An APOS Analysis of Students’ Understanding of the Concept of a Limit of a Function. Pythagoras, 1, 41-52. Maharaj, A. (2013).An APOS analysis of natural science students’ understanding of derivatives. South African Journal of Education; 33(1), 1-19. Maharaj, A. (2014). An APOS Analysis of Natural Science Students’ Understanding of Integration. Journal of Research in Mathematics Education, 3 ( 1 ), 53- 72. doi: 10.4471/ redimat. 2014.40 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. Martin-Blas, T., Seidel L. and Serrano-Fernandez A. (2010).Enhancing force concept inventory diagnostics to identify dominant misconceptions in first-year engineering physics.European Journal of Engineering Education, 35(6), 597-606. Martinez-Planell, R. &Gaisman, M. T. (2009). Students’ ideas on functions of two variables: domain, range, and representations. In Swars, S. L., Stinson, D. W., & Lemons-Smith, S. (Eds.). Proceedings of the 31st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Atlanta, GA: Georgia State University, 5, 73-80. Martinez-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. Martinez-Planell, R., Gaisman, M. T. & McGee D.(2015). On students’ understanding of the differential calculus of functions of two variables.Journal of Mathematical Behavior 38, 57–86. Metcalf, R. C. (2007). The nature of students’ understanding of quadratic functions.(PhD Dissertation, State University of New York at Buffalo, Buffalo, NY). MulugetaAtnafu, ZelalemTeshome&Kassa Michael (2015).Perception of Civil Engineering Extension Students of Addis Ababa University Institute of Technology in the Teaching of Applied Mathematics.Ethiopian Journal of Education & Science. 10 (2).51-78. Piaget, J. (1970). Genetic Epistemology.Notton Library, New York. Rittle-Johnson, B. & Schneider, M. (2012).Developing Conceptual and Procedural Knowledge of Mathematics. The Oxford Handbook of Numerical Cognition (Unpublished Paper) Rockswold, G. K. (2010). College algebra with modeling and visualization (4thed.). New York: Addison-Wesley. Sajika, M. (2003). A secondary student’s understanding of the concept of function – a case study. Educational Studies in Mathematics, 53, 229-254. Schwarzenberger, R. L. E. (1980). Why calculus cannot be made easy. Mathematical Gazette,64(429), 158–166. SolomonAreaya and AshebbirSidelil (2012).Students’ Difficulties and Misconceptions in Learning Concepts ofLimit, Continuity and Derivative.The Ethiopian Journal of Education, 32(2).1-37. Star, J. R. (2005).Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36, 404-411. doi: doi: 10.1037/a0024997 Stewart, J. (2008). Calculus: Early Transcendental, (6thed). Thompson Brooks/Cole Tall, D. (1992).Visualizing differentials in two and three dimensions.Teaching Mathematics and Its Applications, 11 (1).1-7. 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). Trigueros, M. &Martínez-Planell, R. (2007). Visualization and abstraction: Geometric representation of functions of two variables. In Proceedings of the29th Annual Conference of the North American Chapter of theInternational Group for the Psychology of Mathematics Education, T. Lamberg and L.R. Wiest, eds., University of Nevada, Reno, NV, 100-107. Trigueros, M. &Martínez-Planell, R. (2011). How are graphs of two variable functions taught? In Proceedings of the 33rd Annual Meeting of the North America Chapter of the International Group for the Psychology of Mathematics Education, University of Nevada at Reno, Reno, Nevada, available at http:// www.allacademic.com/meta/p512583_index.html. 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. Wiggins, G. (2014). Conceptual Understanding in Mathematics. (from: https://grantwiggins.wordpress.com/2014/04/23/conceptual-understanding-in-mathematics/ retrieved on 06/05/2017) Wong, W. (2001).The effects of collaborative learning on students’ attitude and academic achievement in learning computer programming.(Thesis), University of Hong Kong, Pokfulam, Hong Kong SAR.Retrieved from http://dx.doi.org/10.5353/th_b3196265.

A MATLAB Supported learning and Students' Conceptual Understanding of Domain and Range of a Function of Two Variables: Wolkite University, Ethiopia

Year 2020, Volume: 16 , 18 - 28, 21.06.2020

Abstract

A case study design was conducted at Wolkite University to investigate MATLAB supported learning and students' conceptual understanding in learning Applied Mathematics II using four different comparative instructional approaches: MATLAB supported traditional lecture method, MATLAB supported collaborative method, only collaborative method and only traditional lecture method. Four intact classes Mechanical Engineering groups 1 and 2, Garment Engineering and Textile Engineering students were selected by simple random sampling out of eight departments. The first three departments were considered as treatment groups and the fourth one “Textile Engineering” was assigned as a comparison group, randomly. Qualitative data were collected through reasoning part of the multiple choice items of pre-test and interview items of the post-test were analyzed using APOS analysis based on proposed genetic decompositions. The results of the data show that the majority of the students' conceptual understanding lies in action conception. Students' conceptual understanding on domain and range is a straight forward as that of a function of a single variable which reveals that students haven’t developed new schemata for a function of two variables, as different from a function of a single variable. Majority of the respondents were poor on extending a previous concepts to the new concept and had difficulty to represent domain and range using graph. The results also show that there is no difference between students learning through MATLAB supported in combination with collaborative approach and other instructional approaches like MATLAB supported learning in combination with traditional lecture method, traditional lecture method and collaborative method on conceptual understanding. This might be due to lack of students' experience on technology supported learning in such advanced courses. Thus, this study recommends further study on software supported learning in combination with collaborative method for betterment of conceptual understanding.

References

  • Adams, R. (2003). Calculus: A Complete Course. Pearson Education Canada Inc., Toronto, Ontario. Akkus, R., Hand, B., & Seymour, J. (2008).Understanding students’ understanding of functions.Mathematics Teaching Incorporating Micromath, 207, 10-13. Al-Ammary, J. (2013). Educational Technology: A Way To Enhance Student Achievement At The University Of Bahrain. The Online Journal of New Horizons in Education. 3(3), 54-65. Antwi, V., Hanson R., Savelsbergh E.R. &Eijkelhof H.M.C. (2011). Students’ understanding of some concepts in introductory mechanics course: A study in the first year university students, UEW. International Journal of Educational Planning and Administration., 1(1), 55-80. Arnon, I., Cottrill, J. Dubinsky, E., Oktac, A., Roa, S., Trigueros, M., & Weller, K. (2014), APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education, Springer, NY, Heidelberg, Dondrecht, London. https://doi.org/10.1007/978-1 -4614-7966-6 Bennett, J., & Briggs, W. (2007).Using and understanding mathematics: A quantitative reasoning approach(4th ed.). Boston: Addison Wesley. Bittinger, M. L., Ellenbogen, D. J., & Johnson, B. L. (2010). Elementary and intermediatealgebra: graphs and models (4th ed.). Boston: Addison Wesley. 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. Carlson, M. (1997). Obstacles for college algebra students in understanding functions: what do high-performing students really know? The AMATYC Review. 19. 48-59. Charles-Ogan, G. I., (2015).Utilization of MATLAB as a Technological Tool for Teaching and Learning of Mathematics in Schools.International Journal of Mathematics and Statistics Studies, 3(5), 10-24. 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. Drlik, D. I. (2015). Student understanding of function and success in calculus. A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mathematics Education, Boise State University (Unpublished). 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. Dubinsky, E. & MacDonald, M. (2001). APOS: a constructivist theory of learning in undergraduate mathematics in education research. The Teaching and Learning of Mathematics at University Level: An ICMI Study (pp. 273-280). Dordrecht: Kluwer Academic Publishers. Duval, R. (2006).A cognitive analysis of problems of comprehension in a learning of mathematics.Educational Studies in Mathematics, 61(1), 103-131. 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 MathematicalSociety. Gaisman, M. T. & Martinez-Planell, R. (2010).Geometrical representations in the learning of two-variable functions. Educational studies in mathematics, 1-32. DOI: 10.1007/s10649-009-9201-5. Goold, E. (2012). The Role of Mathematics in Engineering Practice and in the Formation of Engineers, 1(2). Huang, C.-H.(2010). Conceptual and Procedural Abilities of Engineering Students in Integration.Joint International IGIP-SEFI Annual Conference, Trnava, Slovakia. Idris, N. (2009).The Impact of Using Geometers’ Sketchpad on Malaysian Students’ Achievement and Van Hiele Geometric Thinking.Journal of Mathematics Education. 2(2), 94-107 Kashefi, H, Ismail, Z &Yusof, Y.M. (2010).Obstacles in the Learning of Two-variable Functions through Mathematical Thinking Approach. Procedia Social and Behavioral Sciences 8, 173–180. KassahunMelesse (2014). The Influence of E-Learning on the Academic Performance of Mathematics Students in Fundamental Concepts of Algebra Course: The Case in Jimma University. Ethiopian Journal of Education and Science, 9(2), 41-59. 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. Maharaj, A. (2010). An APOS Analysis of Students’ Understanding of the Concept of a Limit of a Function. Pythagoras, 1, 41-52. Maharaj, A. (2013).An APOS analysis of natural science students’ understanding of derivatives. South African Journal of Education; 33(1), 1-19. Maharaj, A. (2014). An APOS Analysis of Natural Science Students’ Understanding of Integration. Journal of Research in Mathematics Education, 3 ( 1 ), 53- 72. doi: 10.4471/ redimat. 2014.40 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. Martin-Blas, T., Seidel L. and Serrano-Fernandez A. (2010).Enhancing force concept inventory diagnostics to identify dominant misconceptions in first-year engineering physics.European Journal of Engineering Education, 35(6), 597-606. Martinez-Planell, R. &Gaisman, M. T. (2009). Students’ ideas on functions of two variables: domain, range, and representations. In Swars, S. L., Stinson, D. W., & Lemons-Smith, S. (Eds.). Proceedings of the 31st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Atlanta, GA: Georgia State University, 5, 73-80. Martinez-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. Martinez-Planell, R., Gaisman, M. T. & McGee D.(2015). On students’ understanding of the differential calculus of functions of two variables.Journal of Mathematical Behavior 38, 57–86. Metcalf, R. C. (2007). The nature of students’ understanding of quadratic functions.(PhD Dissertation, State University of New York at Buffalo, Buffalo, NY). MulugetaAtnafu, ZelalemTeshome&Kassa Michael (2015).Perception of Civil Engineering Extension Students of Addis Ababa University Institute of Technology in the Teaching of Applied Mathematics.Ethiopian Journal of Education & Science. 10 (2).51-78. Piaget, J. (1970). Genetic Epistemology.Notton Library, New York. Rittle-Johnson, B. & Schneider, M. (2012).Developing Conceptual and Procedural Knowledge of Mathematics. The Oxford Handbook of Numerical Cognition (Unpublished Paper) Rockswold, G. K. (2010). College algebra with modeling and visualization (4thed.). New York: Addison-Wesley. Sajika, M. (2003). A secondary student’s understanding of the concept of function – a case study. Educational Studies in Mathematics, 53, 229-254. Schwarzenberger, R. L. E. (1980). Why calculus cannot be made easy. Mathematical Gazette,64(429), 158–166. SolomonAreaya and AshebbirSidelil (2012).Students’ Difficulties and Misconceptions in Learning Concepts ofLimit, Continuity and Derivative.The Ethiopian Journal of Education, 32(2).1-37. Star, J. R. (2005).Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36, 404-411. doi: doi: 10.1037/a0024997 Stewart, J. (2008). Calculus: Early Transcendental, (6thed). Thompson Brooks/Cole Tall, D. (1992).Visualizing differentials in two and three dimensions.Teaching Mathematics and Its Applications, 11 (1).1-7. 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). Trigueros, M. &Martínez-Planell, R. (2007). Visualization and abstraction: Geometric representation of functions of two variables. In Proceedings of the29th Annual Conference of the North American Chapter of theInternational Group for the Psychology of Mathematics Education, T. Lamberg and L.R. Wiest, eds., University of Nevada, Reno, NV, 100-107. Trigueros, M. &Martínez-Planell, R. (2011). How are graphs of two variable functions taught? In Proceedings of the 33rd Annual Meeting of the North America Chapter of the International Group for the Psychology of Mathematics Education, University of Nevada at Reno, Reno, Nevada, available at http:// www.allacademic.com/meta/p512583_index.html. 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. Wiggins, G. (2014). Conceptual Understanding in Mathematics. (from: https://grantwiggins.wordpress.com/2014/04/23/conceptual-understanding-in-mathematics/ retrieved on 06/05/2017) Wong, W. (2001).The effects of collaborative learning on students’ attitude and academic achievement in learning computer programming.(Thesis), University of Hong Kong, Pokfulam, Hong Kong SAR.Retrieved from http://dx.doi.org/10.5353/th_b3196265.
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Details

Primary Language English
Journal Section Articles
Authors

Eyasu Gemechu This is me

Kassa Mıchael This is me

Mulugeta Atnafu This is me

Publication Date June 21, 2020
Published in Issue Year 2020 Volume: 16

Cite

APA Gemechu, E., Mıchael, K., & Atnafu, M. (2020). A MATLAB Supported learning and Students’ Conceptual Understanding of Domain and Range of a Function of Two Variables: Wolkite University, Ethiopia. The Eurasia Proceedings of Educational and Social Sciences, 16, 18-28.