Teaching In Physics and Mathematics
Author(s)
Download Full PDF Pages: 236-246 | Views: 584 | Downloads: 115 | DOI: 10.5281/zenodo.4764450
Abstract
Most teachers today are aware that the implementation of interdisciplinary integrated teaching will bring many benefits in the formation and development of action and problem solving capacities for students. Especially Physics, Mathematics, Biology are applied sciences, experimental, is the science of life, knowledge of these subjects is always associated with natural and social factors. Students can use knowledge in many related subjects to solve a number of problems such as: Integrating knowledge of Mathematics to form computational skills, processing data in physics; Physics subject to deal with the physical properties and properties of substances, rays, energy and metabolism; or to easily explain the mechanism of the action of substances on life
Keywords
Physics and mathematics
References
i Akkoç, H., Bingolbali, E., & Ozmantar, F. (2008). Investigating the technological pedagogical content knowledge: A case of derivative at a point. In Proceedings of the Joint Meeting of the 32nd Conference of the International Group for the Psychology of Mathematics Education, and the XXX North American Chapter(Vol. 2, pp. 17-24).
ii Anderson, L. W., Krathwohl, D. R., Airasian, P. W., Cruikshank, K. A., Mayer, R. E., Pintrich, P. R., ... & Wittrock, M. C. (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives, abridged edition. White Plains, NY: Longman.
iii Artigue, M. (2000). Didactic engineering and the complexity of learning processes in classroom situations. In C. Bergsten, G. Dahland, & B. Grevholm (Eds.), Proceedings of the MADIF 2 Conference (pp. 5–20). Gothenburg: Swedish Society for Research in Mathematics Education
iv Artigue, M. (2014). Didactic engineering in mathematics education. Encyclopedia of mathematics education, 159-162.
v Bajracharya, R. R. (2014). Student application of the fundamental theorem of calculus with graphical representations in mathematics and physics.
vi Bajracharya, R., & Thompson, J. R. (2014). Student understanding of the fundamental theorem of calculus at the mathematics-physics interface. Proceedings of the 17th special interest group of the Mathematical Association of America on research in undergraduate mathematics education. Denver (CO).
vii Beichner, R. J. (1994). Testing student interpretation of kinematics graphs. American journal of Physics, 62(8), 750-762.
viii Berlin, D. F., & White, A. L. (1992). Report from the NSF/SSMA Wingspread conference: A network for integrated science and mathematics teaching and learning. School science and mathematics, 92(6), 340-342.
ix Berlin, D. F., & White, A. L. (1994). The Berlin‐White integrated science and mathematics model. School Science and Mathematics, 94(1), 2-4.
x Berlin, D. F. (2007). Using a Cultural Context to Integrate Mathematics and Science Education. Proceedings of the Ninth International Conference Mathematics Education in a Global Community, 84-88.
xi Bezuidenhout, J. (1998). First‐year university students’ understanding of rate of change. International Journal of Mathematical Education in Science and Technology, 29(3), 389-399.
xii Bezuidenhout, J., & Olivier, A. (2000, July). Students' conceptions of the integral.In PME CONFERENCE (Vol. 2, pp. 2-73).
xiii Bingolbali, E., Monaghan, J., & Roper, T. (2007). Engineering students’ conceptions of the derivative and some implications for their mathematical education. International Journal of Mathematical Education in Science and Technology, 38(6), 763-777.
xiv Boyer, C. B. (1959). The history of the calculus and its conceptual development:(The concepts of the calculus). Courier Corporation.
xv Bosch, M., & Chevallard, Y. (1999). La sensibilité de l'activité mathématique aux ostensifs: objet d'étude et problématique. Recherches en didactique des mathématiques (Revue), 19(1), 77-123.
xvi Bressoud, D. M. (2011). Historical reflections on teaching the fundamental theorem of integral calculus. The American Mathematical Monthly, 118(2), 99-115.
xvii Brousseau, G. (2006). Theory of didactical situations in mathematics: Didactique des mathématiques, 1970–1990 (Vol. 19). Springer Science & Business Media.
xviii Brousseau, G. (2008). Research in mathematics education. In M. Niss (Ed.), Proceedings of the 10th international congress on mathematical education (pp. 244–254). IMFUFA: Denmark.
xix Chevallard, Y. (1985). La transposition didactique. Grenoble. La pensée sauvage.
xx Chevallard, Y. (1989, August). On didactic transposition theory: Some introductory notes. In Proceedings of The International Symposium on Selected Domains of Research and Development in Mathematics Education. Bratislava.
xxi Chevallard, Y. (1992). Fundamental concepts in didactics: perspectives provided by an anthropological approach. Research in didactique of mathematics: Selected papers, 131-168.
xxii D’Hainaut, L. (1986, May). Interdisciplinarity in general education. In International Symposium on Interdisciplinarity in General Education, UNESCO.
xxiii Doorman, M., & Van Maanen, J. (2008). A historical perspective on teaching and learning calculus. Australian Senior Mathematics Journal, 22(2), 4.
xxiv Douglas, R. G. (1986). Toward a lean and lively calculus: conference/workshop to develop alternative curriculum and teaching methods for calculus at the college level, Tulane University, January 2-6, 1986 (Vol. 6). Mathematical Assn of Amer Drake, S. M., & Burns, R. C. (2004). Meeting standards through integrated curriculum. ASCD.
xxv Drake, S. M. (2007). Creating Standards-Based Integrated Curriculum: Aligning Curriculum, Content, Assessment, and Instruction. Corwin Press, A SAGE Publications Company. 2455 Teller Road, Thousand Oaks, CA 91320.
xxvi Dray, T., Edwards, B., & Manogue, C. A. (2008, July). Bridging the gap between mathematics and physics. In Proceedings of the 11th International Congress on Mathematics Education.
xxvii Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational studies in mathematics, 61(1-2), 103-131.
xxviii Đỗ Hương Trà. (2015). Nghiên cứu dạy học tích hợp liên môn: những yêu cầu đặt ra trong việc xây dựng, lựa chọn nội dung và tổ chức dạy học. VNU Journal of Science: Education Research, 31(1).
xxix Education Development Center. (1970). Final report of Cambridge Conference on School Mathematics, January 1962 – August 1970. Cambridge, MA: Author.
xxx Edwards, C. J. (2012). The historical development of the calculus. Springer Science & Business Media.
xxxi Eves, H. W. (1976). An introduction to the history of mathematics.
xxxii Fauconnier, G. T., & Turner, M. (2002). M.(2002) The way we think: conceptual blending and the mind’s hidden complexities.
xxxiii Ferrini-Mundy, J., & Graham, K. (1994). Research in calculus learning: Understanding of limits, derivatives, and integrals. MAA notes, 31-46.
xxxiv Fikhtengol'ts, G. M. (1965). The fundamentals of mathematical analysis. Elsevier. Pergamon Press.
xxxv Firouzian, S. S. (2013). Students’ way of thinking about derivative and its correlation to their ways of solving applied problems. In Proceedings of the 16th Annual conference on research in undergraduate mathematics Education (pp. 492-497).
xxxvi Firouzian, S., & Speer, N. (2015). Integrated mathematics and science knowledge for teaching framework. In Proceedings of the Proceedings of the 18th conference on Research in Undergraduate Mathematics Education.
xxxvii Frykholm, J., & Glasson, G. (2005). Connecting science and mathematics instruction: Pedagogical context knowledge for teachers. School Science and Mathematics, 105(3), 127-141.
xxxviii González-Martín, A. S., Bloch, I., Durand-Guerrier, V., & Maschietto, M. (2014). Didactic Situations and Didactical Engineering in university mathematics: cases from the study of Calculus and proof. Research in Mathematics Education, 16(2), 117-134.
xxxix Grabiner, J. V. (1983). The changing concept of change: The derivative from Fermat to Weierstrass. Mathematics Magazine, 56(4), 195-206.
xl Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational studies in mathematics, 39(1-3), 111-129.
xli Habineza, F. (2013). A case study of analyzing student teachers’ concept images of the definite integral. Rwandan Journal of Education, 1(2), 38-54.
xlii Hammer, D. (2000). Student resources for learning introductory physics. American Journal of Physics, 68(S1), S52-S59.
xliii Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. Conceptual and procedural knowledge: The case of mathematics, 2, 1-27.
xliv Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics, 65-97.
xlv Huntley, M. A. (1998). Theoretical and Empirical Investigations of Integrated Mathematics and Science Education in the Middle Grades.
xlvi Hurley, M. M. (2001). Reviewing integrated science and mathematics: The search for evidence and definitions from new perspectives. School science and mathematics, 101(5), 259-268.
xlvii Jacobs, H. H. (1989). Interdisciplinary curriculum: Design and implementation. Association for Supervision and Curriculum Development, 1250 N. Pitt Street, Alexandria, VA 22314.
xlviii Jones, S. R. (2010). Applying Mathematics to Physics and Engineering: Symbolic Forms of the Integral (Doctoral dissertation).
xlix Jones, S. R. (2015a). Areas, anti-derivatives, and adding up pieces: Definite integrals in pure mathematics and applied science contexts. The Journal of Mathematical Behavior, 38, 9-28.
l Jones, S. R. (2015b). The prevalence of area-under-a-curve and anti-derivative conceptions over Riemann sum-based conceptions in students’ explanations of definite integrals. International Journal of Mathematical Education in Science and Technology, 46(5), 721-736.
li Jones, S. R. (2017). An exploratory study on student understandings of derivatives in real-world, non-kinematics contexts. The Journal of Mathematical Behavior, 45, 95-110.
lii Jones, S. R., Lim, Y., & Chandler, K. R. (2017). Teaching integration: How certain instructional moves may undermine the potential conceptual value of the Riemann sum and the Riemann integral. International Journal of Science and Mathematics Education, 15(6), 1075-1095.
liii Kaput, J. (1994). Democratizing access to calculus: New routes to old roots. Mathematical thinking and problem solving, 77-156.
liv Katz,V. J. (2000). Using history to teach mathematics: An international perspective (Vol. 51). Cambridge University Press.
lv Kendal, M., & Stacey, K. (2003). Tracing learning of three representations with the differentiation competency framework. Mathematics Education Research Journal, 15(1), 22-41.
lvi Kleiner, I. (2001). History of the infinitely small and the infinitely large in calculus. Educational Studies in Mathematics, 48(2-3), 137-174.
lvii Kouropatov, A., & Dreyfus, T. (2013). Constructing the integral concept on the basis of the idea of accumulation: suggestion for a high school curriculum. International Journal of Mathematical Education in Science and Technology, 44(5), 641-651.
lviii Le Thi Bach Lien., & Tran Kiem Minh. (2020). Knowledge of content pedagogy of future math teachers in Vietnam when teaching derivative topics. Journal of Science, Ho Chi Minh City University of Education, 17 (8), 1410.
lix Le Thi Hoai Chau., & Tran Thi My Dung. (2004). Integral and differential calculations in history. Journal of Science, Ho Chi Minh City University of Education, (4), 14.
lx Le Thi Hoai Chau. (2004). Exploit the history of Mathematics in teaching integral concepts.Journal of Science, Ho Chi Minh City University of Education, (2), 37-45.
lxi Le Thi Hoai Chau. (2014). Modeling in teaching derivative concepts. Journal of Science, Ho Chi Minh City University of Education, (65), 5-18.
lxii Le Thi Hoai Chau. (2017). Proceedings of the 6th International Workshop on Didactic Mathematics. The necessity of epistemological analysis for the researches on teaching activities and teacher training (pp.17-38). Ho Chi Minh City: HCMC University of Education Publishing House.
lxiii Le Thi Hoai Chau. (2018). Anthropology in Didactic Mathematics. Ho Chi Minh City: Ho Chi Minh City University of Education Press
lxiv Le Thi Hoai Chau., & Ngo Minh Duc. (2019). Training mathematics teachers in accordance with teaching to integrated math and science through teaching integration concept. Vietnam Journal of Education, 6, 48-53.
lxv Loepp, F. L. (1999). Models of curriculum integration. The journal of technology studies, 25(2), 21-25.
lxvi Lonning, R. A., & DeFranco, T. C. (1997). Integration of science and mathematics: A theoretical model. School science and mathematics, 97(4), 212-215.
lxvii Mathison, S., & Freeman, M. (1998). The Logic of Interdisciplinary Studies. Report Series 2.33.
lxviii Marrongelle, K. A. (2001). Physics experiences and calculus: How students use physics to construct meaningful conceptualizations of calculus concepts in an interdisciplinary calculus/physics course.
lxix Marrongelle, K. A. (2004). How students use physics to reason about calculus tasks. School Science and Mathematics, 104(6), 258-272.
lxx Marrongelle, K. (2010, March). The role of physics in students’ conceptualization of calculus concepts: Implications of research on teaching practice. In 2nd International Conference on the Teaching of Mathematics.
lxxi Meredith, D. C., & Marrongelle, K. A. (2008). How students use mathematical resources in an electrostatics context. American Journal of Physics, 76(6), 570-578.
lxxii National Council of Teachers of Mathematics (Ed.). (2000). Principles and standards for school mathematics (Vol. 1). National Council of Teachers of.
lxxiii Ngo Minh Duc. (two thousand and thirteen). Derivative concept in teaching Mathematics and Physics in high schools (Master thesis, Ho Chi Minh City University of Education).
lxxiv Ngo Minh Duc. (2016). Teaching derivative concepts in relation to subjects with physics. Journal of Science, Ho Chi Minh City University of Education, (7 (85)), 41.
lxxv Ngo Minh Duc. (2017). Integrated perspective in teaching integral concepts. Journal of Science, Ho Chi Minh City University of Education, 14 (4), 20-28.
lxxvi Ngo Minh Duc. (2017). Consider the pedagogical transformation of the concept of integral in connection with physics at high schools in Vietnam. Proceedings of the 6th International Conference on Didactic Mathematics (pp.103-112). Ho Chi Minh City: HCMC University of Education Publishing House.
lxxvii Nguyen, D. H., & Rebello, N. S. (2011). Students' understanding and application of the area under the curve concept in physics problems. Physical Review Special Topics- Physics Education Research, 7 (1), 010112
lxxviii Nguyen Phu Loc. (2006). Improve the efficiency of teaching calculus in high schools in the direction of approaching some problems of mathematical methodology. Education Science Doctoral Thesis. Vinh University.
lxxix Nguyen The Son. (2017). Building integrated topics in teaching math in high school. Education Science Doctoral Thesis. Vietnam Institute of Educational Science.
lxxx Nguyen Thi Ha. (2016). Integrating Mathematics in guiding students to solve Genetic problems (Biology 12). Journal of Science, Hanoi National University, 32 (1), 68- 72.
lxxxi Nguyen Thi Nga. (2018). Mathematics - Physics interdisciplinary in teaching vector topics in high schools: Researching personal relationships of teachers of Mathematics and Physics. Journal of Science, Ho Chi Minh City University of Education, 15 (1), 40-47.
lxxxii Nikitina, S., & Mansilla, V. B. (2003). Three strategies for interdisciplinary math and science teaching: A case of the Illinois Mathematics and Science Academy. Project Zero, the Harvard Graduate School of Education-Interdiciplinary Studies Project, 1-21.
lxxxiii López-Gay, R., Sáez, J. M., & Torregrosa, J. M. (2015). Obstacles to mathematization in physics: The case of the differential. Science & Education, 24 (5-6), 591-613.
lxxxiv Oliveira, A. R. E. (2014). A History of the Work Concept. Springer.
lxxxv Orton, A. (1983a Students' understanding of differentiation. Educational studies in mathematics, 14 (3), 235-250.
lxxxvi Orton, A. (1983b). Students' understanding of integration. Educational studies in mathematics, 14 (1), 1-18.
lxxxvii Pape, S. J., & Tchoshanov, M. A. (2001). The role of representation (s) in developing mathematical understanding. Theory into practice, 40 (2), 118-127.
lxxxviii Perkins, D. (2012). Calculus and its origins. MAA.
lxxxix Pham Si Nam. (two thousand and thirteen). Improve the effectiveness of teaching a number of analytical concepts for high school students specializing in Mathematics on the basis of applying constructivist theory. Education Science Doctoral Thesis. Vinh University.
xc Piaget, J., & Cook, M. (1952). The origins of intelligence in children (Vol. 8, No. 5, p.18). New York: International Universities Press.
xci Roegiers, X. (2001). Une pédagogie de l'intégration: compétences et intégration des acquis dans l'enseignement. De Boeck Supérieur.
xcii Roundy, D., Dray, T., Manogue, C. A., Wagner, J. F., & Weber, E. (2014). An extended theoretical framework for the concept of derivative. In Proceedings of the 18th Annual Conference on Research in Undergraduate Mathematics Education (pp. 838-843).
xciii Sahin, Z., Yenmez, A. A., & Erbas, A. K. (2015). Relational Understanding of the Derivative Concept through Mathematical Modeling: A Case Study. Eurasia Journal of Mathematics, Science & Technology Education, 11(1).
xciv Stillwell, J. (2002). Mathematics and its History. The Australian Mathem. Soc, 168.
xcv Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational studies in mathematics, 12(2), 151-169.
xcvi Tall, D. (Ed.). (1991). Advanced mathematical thinking (Vol. 11). Springer Science & Business Media.
xcvii Tall, D. (1993). Students’ difficulties in calculus. In proceedings of working group (Vol.3, pp. 13-28).
xcviii Thompson, P. W. (1994a). The development of the concept of speed and its relationship to concepts of rate. The development of multiplicative reasoning in the learning of mathematics, 179-234.
xcix Thompson, P. W. (1994b). Images of rate and operational understanding of the fundamental theorem of calculus. Educational studies in mathematics, 26(2-3), 229-274.
Cite this Article: