Teaching In Physics and Mathematics

Author(s)

Thi Hue Bui ,

Download Full PDF Pages: 236-246 | Views: 528 | Downloads: 96 | DOI: 10.5281/zenodo.4764450

Volume 10 - January 2021 (01)

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: