American Journal of Educational Research
ISSN (Print): 2327-6126 ISSN (Online): 2327-6150 Website: http://www.sciepub.com/journal/education Editor-in-chief: Ratko Pavlović
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American Journal of Educational Research. 2018, 6(8), 1127-1136
DOI: 10.12691/education-6-8-10
Open AccessArticle

Investigating Students’ Physico-mathematical Difficulties in Classical Mechanics and Designing an Instructional Model

Danny Mutambo1, , Gurudas T. Baliga1 and Leonard Nkhata2

1Department of Physics, The Copperbelt University, Kitwe, Zambia

2Department of Mathematics and Science Education, The Copperbelt University, Kitwe, Zambia

Pub. Date: August 13, 2018

Cite this paper:
Danny Mutambo, Gurudas T. Baliga and Leonard Nkhata. Investigating Students’ Physico-mathematical Difficulties in Classical Mechanics and Designing an Instructional Model. American Journal of Educational Research. 2018; 6(8):1127-1136. doi: 10.12691/education-6-8-10

Abstract

The study investigated students’ physico-mathematical difficulties in classical mechanics and designed an instructional model. The three objectives that guided the study were namely: to identify physico-mathematical difficulties students have in classical mechanics, to explore the existing instructional models and design a suitable instructional model to address physico-mathematical difficulties in classical mechanics and to verify and evaluate the effectiveness of the designed instructional model. The study was undertaken with a purposive sample of 140 students and 10 instructors learning and teaching classical mechanics respectively from the Copperbelt University and Mukuba University on the Copperbelt Province of Zambia. A descriptive mixed method survey design approach was used. A pilot study was conducted, instruments adjusted and survey implemented, instructional model designed and evaluated for its effectiveness. Four achievement tests comprising physico-mathematical concepts, the questionnaire, interviews and focus group discussions were used to collect data. The Microsoft Excel package was used to generate tables and percentages. Qualitative data from interview and focus group discussions were analysed qualitatively by the MAXQDA (Max Qualitative Data Analysis) software. The results of the study revealed that students had physico-mathematical difficulties in classical mechanics bordering on the students’ inabilities to use vectors, graphs, functions and mathematization in classical mechanics. Furthermore, it was found that the strategy of teaching mathematical concepts before introducing concepts in classical mechanics was used at the two institutions. However, these physico-mathematical difficulties still persisted. Therefore, the study recommended that instructors in classical mechanics should have necessary background information about students before teaching them. Information includes the prior knowledge of students. The study also recommended that instructors use suitable learning methods or materials that would engage students or make abstract physico-mathematical concepts more observable.

Keywords:
physico-mathematical instructional model instructors 6L learning model

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References:

[1]  Mwangala, K. P. & Shumba, O. (2016). Physico-mathematical Conceptual Difficulties among First Year Students Learning, American Journal of Educational Research, 4(17), 1238-1244.
 
[2]  Martin, M.O et al (2009). TIMSS Advanced 2008 International Report. Boston: TIMSS & PIRLS International Study Center.
 
[3]  Uhden, O. & Pospiech, G. (2011). Mathematics in physics: Analysis of students' difficulties. Retrieved from: www.esera.org/media/ebook/strand3/ebook-esera2011_UHDEN-03.pdf. (12/12/2017).
 
[4]  Vinitsky-Pinsky, L. & Galili, I. (2014). The need to clarify the relationship between physics and mathematics in science curriculum: cultural knowledge as possible framework. Procedia-Social and Behavioral Sciences, 116, 611-616.
 
[5]  Nilsen, T. (2013). Mathematical competencies and the role of mathematics in physics education: A trend analysis of TIMSS Advanced 1995 and 2008. Acta Didactica Norge, 7(1), Art.6.
 
[6]  McDermott, L. (1990). What We Teach and What Is Learned closing the Gap, American Journal of Physics, 59, 301-315.
 
[7]  Ho, P. V. P. (2015). Instructional model in teaching translation and interpretation: a case study, Journal of Science Ho Chi Minh City Open University, 15(3), 1234-1245.
 
[8]  Saat, M. M. and Rodzalana, S. A. (2015). The Perception of Critical Thinking and Problem Solving Skill among Malaysian Undergraduate Students, Procedia - Social and Behavioral Sciences, 17(2), 725-732.
 
[9]  Shankar, R. (1994). Principles of Quantum Mechanics, (2nd Ed.), New York: Plenum.
 
[10]  Angel et al. (2004). Physics: Frightful, But Fun Pupils’ and Teachers’ Views of Physics and Physics Teaching, Science education, 88, 683-706.
 
[11]  Woolnough, B. E. (1994). Why students choose physics, or reject it, Physics Education, 29(5), 368-374.
 
[12]  Stadler, H., et al. (2000). Do boys and girls understand physics differently? Physics Education, 35, 417-422.
 
[13]  Kuo, E. et al. (2013). How students blend conceptual and formal mathematical reasoning in solving physics problem. Science Education, 97(1), 32-57.
 
[14]  Sherin, B. (2001). How Students Understand Physics Equations. Cognition and Instruction, 19(4), 479-541.
 
[15]  Sherin, B. (2006). Common sense clarified: The role of intuitive knowledge in physics problem solving. Journal of research in science teaching, 43(6), 535-555.
 
[16]  Huffman, D. (1997). Effect of Explicit Problem Solving Instruction on High School Students’ Problem-Solving Performance and Conceptual Understanding of Physics. Journal of Research in Science Teaching, 34(6), 551-570.
 
[17]  Meltzer, D. E. (2002). The relationship between mathematics preparation and conceptual learning gain in physics: A possible “hidden variable” in diagnostic pre-test scores, American Association of Physics Teachers, 70 (12), 1259-1268.
 
[18]  Redish, E. F. (2005): Problem solving and the use of mathematics in physics courses, presented at the worldview on physics education in 2005: Focusing on change, Delhi, August 21-26, 2005.
 
[19]  Bagno, E. et al. (2008). Meeting the challenge of students’ understanding of formulae in high-school physics: a learning tool, Physics Education, 43(1), 75-82.
 
[20]  Deary, I. J., et al. (2007). Intelligence and educational achievement, Intelligence, 35(1), 13-21.
 
[21]  Debacker, T. K., & Nelson, R. M. (2000). Motivation to learn science: Differences related to gender, class type, and ability. The Journal of Educational Research, 93(4), 245-254.
 
[22]  Bransford, D., et al (1999): How people learn: Brain, mind, experience and school in National Academy Press. Washington D.C. p.50.
 
[23]  Kohl, P.B. & Finkelstein, N.D. (2006). The effects of representation on students solving physics problems: a fine-grained characterization, Physics Review Special Topic Physics Education Resources, 2(010106).
 
[24]  Sadaghiani, H. R. (2005) (unpubl.): Conceptual and mathematical barriers to students learning quantum mechanics. PhD thesis, The Ohio State University, 2005.
 
[25]  Uhden, O. & Pospiech, G. (2011). Mathematics in physics: Analysis of students' difficulties. Retrieved from: www.esera.org/media/ebook/strand3/ebook-esera2011_UHDEN-03.pdf. (12/12/2017).
 
[26]  Boone, H. N. (2012). Return to current issue analyzing Likert data, Journal of Extension, 50(2), 1167-1173.
 
[27]  Hadzidaki, P., et al. (2000). Quantum mechanics: a systematic component of the modern physics paradigm, Physics Education, 35, 386-392.
 
[28]  Steinberg, R., Wittmann, M., and Redish, E. (1996). Student Difficulties with Math in Physics: Why Can’t Students Apply What They Learn in Math Class? AAPT Announcer, 26(2), 70.
 
[29]  Steinberg, R., Wittmann, M., and Redish, E. (1997). Mathematical Tutorials in Introductory Physics, AIP Conference Proceedings 399, 1075-1092.
 
[30]  Steinberg, R., Wittmann, M., and Redish, E. (1997). Mathematical Tutorials in Introductory Physics, AIP Conference Proceedings 399, 1075-1092.
 
[31]  Rosengrant, D., A. Van Heuvelen. (2009). Do students use and understand free-body diagrams? Physical Review Special Topics - Physics Education Research 5(1): 010108.
 
[32]  Sharp, J. & L. Zachary (2004). Using the van Hiele K-12 Geometry Learning Theory to Modify Engineering Mechanics Instruction. Journal of STEM Education: Innovations and Research, 5(1-2): 35-41.
 
[33]  The Zambian Ministry of Finance, Department of planning, The Zambian vision 2030. (2006). Retrieved from www.mof.gov.zm (10/11/17).
 
[34]  Bao, L. (1999). Dynamics of Student Modeling: A Theory, Algorithms and Application to Quantum Mechanics, Ph. D. Dissertation, University of Maryland.
 
[35]  Rebman, G & Viennot L, (1994). Teaching Algebraic Coding: Stakes, Difficulties, and Suggestions, American Journal of Physics, 62, 423-727.
 
[36]  Battista, M. (1999). Geometry Results from the Third International Mathematics and Science Study, Teaching Children Mathematics, 5, 367-373.
 
[37]  Steinberg, R., Wittmann, M., and Redish, E. (1996). Student Difficulties with Math in Physics: Why Can’t Students Apply What They Learn in Math Class? AAPT Announcer, 26(2), 70.
 
[38]  Prain, V. and & Waldrip, B. (2006). An exploratory study of teachers’ and students’ use of multi-modal representations of concepts in primary science, International Journal Science Education, 28, 1843.
 
[39]  Manogue, C. (2003) .Bridging the Vector Calculus Gap, AAPT Announcer, 33(4), 135.
 
[40]  Hestenes, D. (2003). Oersted Medal Lecture 2002: Reforming the Mathematical Language of Physics. American Journal of Physics, 71, (2), 104-121.
 
[41]  Gilakjani, A. P., Leong, L., & Ismail, H. N. (2013). Teachers’ use of technology and constructivism. I. J. Modern Education and Computer Science, 4, 49-63.
 
[42]  Kaya, H., & Böyük, U. (2011). Attitude towards physics lessons and physical experiments of high school students, European Journal of Physics Education, 2(1), 38-49.
 
[43]  Ronen, M., & Eliahu, M. (2000). Simulation - A bridge between theory and reality: The case of electric circuits, Journal of Computer Assisted Learning, 16, 14-26.
 
[44]  Boone, H. N. (2012). Return to current issue analyzing Likert data, Journal of Extension, 50(2), 1167-1173.
 
[45]  Breslow, L. (2004). Findings from ten formative assessments of educational initiatives at MIT. MIT Teaching and Learning Laboratory. Retrieved 10 September 2017 from http://web.mit.edu/annualreports/pres04/15.11.pdf (21/10/2018).
 
[46]  Cook, M., (2006). Visual representations in science education: The influence of prior knowledge and cognitive load theory on instructional design principles, International Journal of Science Education, 90, 1073-1091.
 
[47]  Evans, J. St. B. T. & K. E. Stanovich. (2013). Dual-process theories of higher cognition: Advancing the debate. Perspectives on Psychological Science, 8: 223-241.
 
[48]  Kahneman, D. (2011). Thinking, fast and slow. New York, NY: Farrar, Straus and Giroux.
 
[49]  Simons, H. (2009). Case study research in practice. Los Angeles, CA: Sage.
 
[50]  Lee, C. & Kim, C. (2014). An implementation study of a TPACK-based instructional design model in a technology integration course, Education Technology Research, 62, 437-460.
 
[51]  Novak, J. D. (1992). A paper presented at the meetings of the American Educational Research Association, San Francisco, California on April 24.
 
[52]  Cook, M., (2006). Visual representations in science education: The influence of prior knowledge and cognitive load theory on instructional design principles, International Journal of Science Education, 90, 1073-1091.
 
[53]  Patrice, V. &Amade-Escot C. (2014). Analysis of conditions leading to a productive disciplinary engagement during a physics lesson in a disadvantaged area school. International Journal of Educational Research, 64, 170-183.
 
[54]  Vavougios, D. & Karakasidis, T. E. (2008). Application of ICT Technology in Physics Education: Teaching and Learning Elementary Oscillations with the Aid of Simulation Software. iJET, 3 (2), 53-58.
 
[55]  Michell, L. (2001). E-Learning methods offer a personalized approach. InfoWorld, April. 2001
 
[56]  Reijo M. (2000). The concept of experiential learning and John Dewey's theory of reflective thought and action, International Journal of Lifelong Education, (19)1, 54-72.
 
[57]  Breslow, L. (2004). Findings from ten formative assessments of educational initiatives at MIT. MIT Teaching and Learning Laboratory. Retrieved from http://web.mit.edu/annualreports/pres04/15.11.pdf (21/10/2017).