Modeling the Mole Understanding with Mathematical Reasoning
The amount of substance, expressed in the units of moles is an essential concept in chemistry and physics. Students entering physics courses usually possess a chemistry background. However, this study showed that their understanding of units of matter on the microscopic level is fragile, and needs improvement. Research shows that the complexity of interpretations of quantities expressed as ratios; molar mass or atomic mass makes formulating a dimensional analysis or proportion of these ratios unclear to students. Based on these findings, this study proposes applying equations of fundamental constants and proportional reasoning, instead of ratios, as the main building blocks to formulate conversion algorithms. In the line of that, a deductively designed lecture was delivered to a group (N=25) freshman college physics students. While on the pretest, only (N=4, 16%) correctly converted a mass of a substance expressed in kilograms to a number of moles, on the posttest the percentage of correct answers increased (N=20, 80%) suggesting that proportional reasoning coupled with fundamental constants brings clarity to the process and improves its understanding.
Bunce, D., Gabel, D., Herron, J. D., & Jones, L. (1994). Report of the Task Force on Chemical Education Research of the American Chemical Society Division of Chemical Education. J. Chem. Educ., 71(10), 850.
Clark, F., & Kamii, C. (1996). Identification of multiplicative thinking in children in grades 1–5. Journal for Research in Mathematics Education, 27(1), 41–51
Coffield, F. (Ed.). (2000). The necessity of informal learning. Bristol, UK: The Policy Press
Confrey, J. (2008, July). A synthesis of the research on rational number reasoning: a learning progressions approach to synthesis. Paper presented at the 11th International Congress of Mathematics Instruction, Monterrey Mexico.
Dominic, S. (1996). What's a Mole for? Journal of chemical education, 73(4), 309.
Dahsah, C., & Coll, R. K. (2008). Thais grade 10 and 11 students’ understanding of stoichiometry and related concepts. International Journal of Science and Mathematics Education, 6(3), 573-600.
Erceg, N., Aviani, I., Mešić, V., Glunčić, M., & Žauhar, G. (2016). Development of the kinetic molecular theory of gases concept inventory: Preliminary results on university students’ misconceptions. Physical Review Physics Education Research, 12(2), 020139.
Fach, M., De Boer, T. & Parchman, I. (2006). Results of an interview study as basis for the development of stepped supporting tools for stoichiometrics problems, University of Oldenburg of Pure and Applied Chemistry. The Royal Society of Chemistry, Germany
Fang, S. C., Hart, C., & Clarke, D. (2014). Unpacking the meaning of the mole concept for secondary school teachers and students. Journal of Chem. Educ. 91(3), 351-356.
Herron, J. D. (1975). Piaget for chemists. Explaining what "good" students cannot understand. Journal of Chem. Educ., 52(3), 146.
Indriyanti, N. Y., & Barke, H. D. (2017, August). Teaching the mole concept with sub-micro level: Do the students perform better? In AIP Conference Proceedings (1868(1), p. 030002). AIP Publishing.
Johnstone, A. H. (1971). Topic Difficulties in Chemistry. Education in Chemistry, 8(6), 212-213.
Kolb, D. (1978). The mole. J. Chem. Educ., 55(11), 728.
Dahsah, C., & Coll, R. K. (2007). Thai grade 10 and 11 students' conceptual understanding and problem-solving ability in stoichiometry. Research in Science and Technology Education, 25, 227-241.
Milton, M. J. (2013). The mole, amount of substance and primary methods. Metrologia, 50(2), 158.
Miyakawa, T., & Winsløw, C. (2009). Didactical designs for students’ proportional reasoning: an “open approach” lesson and a “fundamental situation”. Educational Studies in Mathematics, 72(2), 199-218.
Musa, U. (2009). Teaching the mole concept using a conceptual change method at the college level. Education, 129(4), 683 – 691.
Niaz, M. (1989). The role of cognitive style and its influence on proportional reasoning. Journal of Research in Science Teaching, 26(3), 221-235.
Niaz, M. (1987). Estilo cognoscitivo y su importancia para la enseñanza de la ciencia. Enseñanza de las Ciencias, 5(2) 97-104.
Shadish WR, Cook TD, Campbell DT (2002) Experimental and quasi-experimental designs for generalised causal inference. Houghton Mifflin, Boston
Siswaningsih, W., Firman, H., & Khoirunnisa, A. (2017, February). Development of Two-Tier Diagnostic Test Pictorial-Based for Identifying High School Students Misconceptions on the Mole Concept. In Journal of Physics: Conference Series (Vol. 812, No. 1, p. 012117). IOP Publishing.
Schmidt, H. J. (1990). Secondary School students’ strategies in stoichiometry. International Journal of Science Education, 12, 457-471.
Scott, F. J. (2012). Is mathematics to blame? An investigation into high school students' difficulty in performing calculations in chemistry. Chemistry Education Research and Practice, 13(3), 330-336.
Sokolowski, A. (2018). Scientific Inquiry in Mathematics-Theory and Practice: A STEM Perspective. Springer.
Soon, W., Lioe, L. T., & McInnes, B. (2011). Understanding the difficulties faced by engineering undergraduates in learning mathematical modeling. International Journal of Mathematical Education in Science and Technology, 42(8), 1023-1039.
Staver, J. R., & Lumpe, A. T. (1995). Two investigations of students' understanding of the mole concept and its use in problem-solving. Journal of Research in Science Teaching, 32(2), 177-193.
Tullberg, A., Strömdahl, H., & Lybeck, L. (1994). Students’ conceptions of 1 mol and educators’ conceptions of how they teach ‘the mole.’ International Journal of Science Education, 16(2), 145-156.
Uce, M. (2009). Teaching the mole concept using a conceptual change method at the college level. Education, 129(4), 683-692.
Whelan, P. M. (1977). Introduction to the mole in the teaching of ideal and real gases. Physics Education, 12(5), 279.