Students' Perception Of Vector Representation In The Context Of Electric Force And The Role Of Simulation In Developing An Understanding
Physics Education Research (PER) results have shown that students do not achieve the expected level of competency in understanding the concepts of different domains of Physics learning when taught by the traditional teaching methods, the concepts of Electricity and Magnetism (E&M) being one amon...
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Electric Force Interactive Representation Simulation. S. Shubha B. N. Meera Students' Perception Of Vector Representation In The Context Of Electric Force And The Role Of Simulation In Developing An Understanding |
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Electric Force Interactive Representation Simulation. |
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Physics Education Research (PER) results have shown that students do not achieve the expected level of competency in understanding the concepts of different domains of Physics learning when taught by the traditional teaching methods, the concepts of Electricity and Magnetism (E&M) being one among them. Simulation being one of the valuable instructional tools renders an opportunity to visualize varied experiences with such concepts. Considering the electric force concept which requires extensive use of vector representations, we report here the outcome of the research results pertaining to the student understanding of this concept and the role of simulation in using vector representation. The simulation platform provides a positive impact on the use of vector representation. The first stage of this study involves eliciting and analyzing student responses to questions that probe their understanding of the concept of electrostatic force and this is followed by four stages of student interviews as they use the interactive simulations of electric force in one dimension. Student responses to the questions are recorded in real time using electronic pad. A validation test interview is conducted to evaluate students' understanding of the electric force concept after using interactive simulation. Results indicate lack of procedural knowledge of the vector representation. The study emphasizes the need for the choice of appropriate simulation and mode of induction for learning. : {"references": ["Stephanie V. Chasteen, Steven J. Pollock, Rachel E. Pepper, and\nKatherine K. Perkins, \"Transforming the junior level: Outcomes from\ninstruction and research in E&M,\" Phys. Rev. ST Phys. Educ. Res., vol.\n8, no. 020107, pp. 1-18, Aug 2012.", "Stephanie V. Chasteen, Rachel E. Pepper, Marcos D. Caballero, Steven\nJ. Pollock, and Katherine K. Perkins, \"Colorado Upper-Division\nElectrostatics diagnostic: A conceptual assessment for the junior level,\"\nPhys. Rev. ST Phys. Educ. Res., vol. 8, no. 020108, pp. 1-15, Sep 2012.", "S. J. Pollock, \"Longitudinal study of student conceptual understanding\nin electricity and magnetism,\" Phys. Rev. ST Phys. Educ. Res., vol. 5,\nno. 020110, pp.1-8, Dec 2009.", "Matthew A. Kohlmyer, Marcos D. Caballero, Richard Catrambone, Ruth\nW. Chabay, Lin Ding, Mark P. Haugan, M. Jackson Marr, Bruce A.\nSherwood, and Michael F. Schatz, \" Tale of two curricula: The\nperformance of 2000 students in introductory electromagnetism,\" Phys.\nRev. ST Phys. Educ. Res., vol. 5, no. 020105, pp. 1-10, Oct 2009.", "Ruth Chabay, and Bruce Sherwood, \"Restructuring the introductory\nelectricity and magnetism course,\" Am. J. Phys., vol.74, no. 4, pp. 329-\n336, Apr 2006.", "J. Clement, \"Students' preconceptions in introductory mechanics,\" Am.\nJ. Phys., vol. 50, no. 1, pp. 66-69, Jan 1982.", "I. Halloun, and D. Hestenes, \"Common sense concepts about motion,\"\nAm. J. Phys., vol.53, no.11, pp.1-18, Nov 1985.", "I. Halloun, and D. Hestenes, \"The initial knowledge state of college\nstudents,\" Am. J. Phys., vol. 53, no.11, pp. 1043-1048, Nov 1985.", "D. Hestenes, M. Wells, and G. Swackhamer, \"Force Concept\nInventory,\" Phys. Teach., vol. 30, PP. 141-158, Mar 1992. [10] R. R. Hake, \"Interactive-engagement versus traditional methods: A six\nthousand-student survey of mechanics test data for introductory physics\ncourses,\" Am. J. Phys., vol. 66, no.1, pp. 64-74, Jan 1998.\n[11] L. Viennot, and S. Rainson, \"Students reasoning about the superposition\nof electric fields,\" Int. J. Sci. Educ., vol. 14, no. 4, pp. 475-487, 1992.\n[12] C. Raduta, General students' misconceptions related to electricity and\nmagnetism, arXiv:physics / 0503132.\n[13] D. P. Maloney, T. L. O'Kuma, C. J. Hieggelke, and A.V. Heuvelen,\n\"Surveying students' conceptual knowledge of electricity and\nmagnetism,\" Am. J. Phys., vol. 69, no.7, pp. S12- S23, Jul 2001.\n[14] I. Galili, \"Mechanics background influences students' conceptions in\nelectromagnetism,\" Int. J. Sci. Educ., vol.17, no. 3, pp. 371-387, 1995.\n[15] Salomon F Itza-Ortiz, Sanjay Rebello, and Dean Zollman, \"Students'\nmodels of Newton's second law in mechanics and electromagnetism,\"\nEur. J. Phys., vol. 25, pp. 81-89, 2004.\n[16] S. Tornkvist, K. A. Pettersson, and G. Transtromer, \"Confusion by\nrepresentation on students' comprehension of the electric field concept,\"\nAm. J. Phys., vol. 61, no. 4, pp. 335-338, Apr 1993.\n[17] Thomas M. Scaife, and Andrew F. Heckler, \"Interference between\nelectric and magnetic concepts in introductory physics,\" Phys. Rev. ST\nPhys. Educ. Res., vol. 7, no. 010104, pp.1-11, Mar 2011.\n[18] Eleanor C. Sayre, and Andrew F. Heckler, \"Peaks and decays of student\nknowledge in an introductory E&M course,\" Phys. Rev. ST Phys. Educ.\nRes., vol. 5, no. 013101, pp. 1-5, Feb 2009.\n[19] Lin Ding, Ruth Chabay, Bruce Sherwood, and Robert Beichner,\n\"Evaluating an electricity and magnetism assessment tool: Brief\nelectricity and magnetism assessment,\" Phys. Rev. ST Phys. Educ. Res.,\nvol. 2, no. 010105, pp. 1-7, Mar 2006.\n[20] Rachel E. Pepper, Stephanie V. Chasteen, Steven J. Pollock, and\nKatherine K. Perkins, \"Observations on student difficulties with\nmathematics in upper-division electricity and magnetism,\" Phys. Rev.\nST Phys. Educ. Res., vol. 8, no. 010111, pp. 1-15, Mar 2012.\n[21] Colin S. Wallace, and Stephanie V. Chasteen, \"Upper-division students'\ndifficulties with Ampere's law,\" Phys. Rev. ST Phys. Educ. Res., vol. 6,\nno. 020115, pp.1-8, Sep 2010.\n[22] C. A. Manogue, K. Browne, T. Dray, and B. Edwards, \"Why is\nAmp\u00e8re's law so hard? A look at middle-division physics,\" Am. J.\nPhys., vol. 74, no. 4, pp. 344-350, Feb 2006.\n[23] Dong-Hai Nguyen, and N. Sanjay Rebello, \"Students' difficulties with\nintegration in electricity,\" Phys. Rev. ST Phys. Educ. Res., vol. 7, no.\n010113, pp.1-11, Jun 2011.\n[24] Elwin R. Savelsbergh, Ton de Jong, Monica, and G. M. Ferguson-\nHessler, \"Choosing the right solution approach: The crucial role of\nsituational knowledge in electricity and magnetism,\" Phys. Rev. ST\nPhys. Educ. Res., vol. 7, no. 010103, pp. 1-12, Mar 2011.\n[25] Noah S. Podolefsky, Katherine K. Perkins, and Wendy K. Adams,\n\"Factors Promoting Engaged Exploration with Computer Simulations,\"\nPhys. Rev. ST Phys. Educ. Res., vol. 6, no.020117, pp.1-11, Oct 2010.\n[26] Jacquelyn J. Chini, Adrian Madsen, Elizabeth Gire, N. Sanjay Rebello,\nand Sadhana Puntambekar, \"Exploration of factors that affect the\ncomparative effectiveness of physical and virtual manipulatives in an\nundergraduate laboratory,\" Phys. Rev. ST Phys. Educ. Res., vol. 8,\nno.010113, pp. 1-12, Apr 2012.\n[27] Homeyra R. Sadaghiani, \"Using multimedia learning modules in a\nhybrid-online course in electricity and magnetism,\" Phys. Rev. ST Phys.\nEduc. Res., vol. 7, no. 010102, pp.1-7, Mar 2011.\n[28] N. D. Finkelstein, W. K. Adams, C. J. Keller, P. B. Kohl, K. K. Perkins,\nN. S. Podolefsky, and S. Reid, \"When learning about the real world is\nbetter done virtually: A study of substituting computer simulations for\nlaboratory equipment,\" Phys. Rev. ST Phys. Educ. Res., vol. 1, no.\n010103, pp. 1-8, Oct 2005.\n[29] S. B. McKagan, W. Handley, K. K. Perkins, and C. E. Wieman, \"A\nResearch-Based Curriculum for Teaching the Photoelectric Effect,\" Am.\nJ. Phys., vol. 77, no.1, pp. 87-94, 2009.\n[30] S. B. McKagan, K. K. Perkins, M. Dubson, C. Malley, S. Reid, R.\nLeMaster, and C. E. Wieman, \"Developing and Researching PhET\nsimulations for Teaching Quantum Mechanics,\" Am. J. Phys., vol. 76,\nno.1, pp. 406-417, Jan 2008.\n[31] Tomi Jaakkola, Sami Nurmi, and Koen Veermans, \"A comparison of\nstudents' conceptual understanding of electric circuits in simulation only\nand simulation-laboratory contexts,\" J. Res. Sci. Teach., vol. 48, no. 1,\npp. 71-93, 2011.\n[32] Z.C. Zacharia, \"Comparing and combining real and virtual\nexperimentation: an effort to enhance students' conceptual understanding\nof electric circuits,\" J. Comput. Assist. Learn., vol. 23, no.2, pp.120-132,\nApr 2007.\n[33] Ariel Paul, Noah Podolefsky and Katherine Perkins, \"Guiding Without\nFeeling Guided: Implicit Scaffolding through Interactive Simulation\nDesign,\" AIP Conf. Proc., vol. 1513, no. 1, pp. 302-305, Jan 2013.\n[34] Guadalupe Martinez, Francisco L. Naranjo, Angel L. Perez, and Maria\nIsabel Suero, \"Comparative study of the effectiveness of three learning\nenvironments: Hyper-realistic virtual simulations, traditional schematic\nsimulations and traditional laboratory,\" Phys. Rev. ST Phys. Educ. Res.,\nvol. 7, no. 020111, pp. 1-12, Oct 2011.\n[35] W. K. Adams, A. Paulson, and C. E. Wieman, \"What levels of guidance\nelicit engaged exploration with interactive simulations?,\" AIP Conf.\nProc., vol. 1064, pp. 59-62, Jul 2008.\n[36] Knight, \"The vector knowledge of beginning physics students,\" Phys.\nTeach., vol. 33, pp. 74-77, Feb1995.\n[37] Sergio Flores, Stephen E. Kanim, and Christian H. Kautz, \"Student use\nof vectors in introductory mechanics,\" Am. J. Phys., vol. 72, no. 4, pp.\n460-468, Apr 2004.\n[38] Beichner .R., \"Testing student interpretation of kinematics graphs,\"\nAm. J. Phys., vol. 62, no. 8, pp. 750-762, 1994.\n[39] Andrew Duffy, Boston University, http://physics.bu.edu/~duffy/Ejs/.\n[40] Easy Java simulations, http://www.um.es/fem/Ejs.\n[41] Balasubrahmanya Hegde and B. N. Meera, \"How do they solve it? An\ninsight into the learner's approach to the mechanism of physics problem\nsolving,\" Phys. Rev. ST Phys. Educ. Res., vol.8, no. 010109, pp. 1-9,\nMar 2012."]} |
format |
Text |
author |
S. Shubha B. N. Meera |
author_facet |
S. Shubha B. N. Meera |
author_sort |
S. Shubha |
title |
Students' Perception Of Vector Representation In The Context Of Electric Force And The Role Of Simulation In Developing An Understanding |
title_short |
Students' Perception Of Vector Representation In The Context Of Electric Force And The Role Of Simulation In Developing An Understanding |
title_full |
Students' Perception Of Vector Representation In The Context Of Electric Force And The Role Of Simulation In Developing An Understanding |
title_fullStr |
Students' Perception Of Vector Representation In The Context Of Electric Force And The Role Of Simulation In Developing An Understanding |
title_full_unstemmed |
Students' Perception Of Vector Representation In The Context Of Electric Force And The Role Of Simulation In Developing An Understanding |
title_sort |
students' perception of vector representation in the context of electric force and the role of simulation in developing an understanding |
publisher |
Zenodo |
publishDate |
2015 |
url |
https://dx.doi.org/10.5281/zenodo.1099208 https://zenodo.org/record/1099208 |
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ftdatacite:10.5281/zenodo.1099208 2023-05-15T18:14:25+02:00 Students' Perception Of Vector Representation In The Context Of Electric Force And The Role Of Simulation In Developing An Understanding S. Shubha B. N. Meera 2015 https://dx.doi.org/10.5281/zenodo.1099208 https://zenodo.org/record/1099208 en eng Zenodo https://dx.doi.org/10.5281/zenodo.1099207 Open Access Creative Commons Attribution 4.0 https://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess CC-BY Electric Force Interactive Representation Simulation. Text Journal article article-journal ScholarlyArticle 2015 ftdatacite https://doi.org/10.5281/zenodo.1099208 https://doi.org/10.5281/zenodo.1099207 2021-11-05T12:55:41Z Physics Education Research (PER) results have shown that students do not achieve the expected level of competency in understanding the concepts of different domains of Physics learning when taught by the traditional teaching methods, the concepts of Electricity and Magnetism (E&M) being one among them. Simulation being one of the valuable instructional tools renders an opportunity to visualize varied experiences with such concepts. Considering the electric force concept which requires extensive use of vector representations, we report here the outcome of the research results pertaining to the student understanding of this concept and the role of simulation in using vector representation. The simulation platform provides a positive impact on the use of vector representation. The first stage of this study involves eliciting and analyzing student responses to questions that probe their understanding of the concept of electrostatic force and this is followed by four stages of student interviews as they use the interactive simulations of electric force in one dimension. Student responses to the questions are recorded in real time using electronic pad. A validation test interview is conducted to evaluate students' understanding of the electric force concept after using interactive simulation. Results indicate lack of procedural knowledge of the vector representation. The study emphasizes the need for the choice of appropriate simulation and mode of induction for learning. : {"references": ["Stephanie V. Chasteen, Steven J. Pollock, Rachel E. Pepper, and\nKatherine K. Perkins, \"Transforming the junior level: Outcomes from\ninstruction and research in E&M,\" Phys. Rev. ST Phys. Educ. Res., vol.\n8, no. 020107, pp. 1-18, Aug 2012.", "Stephanie V. Chasteen, Rachel E. Pepper, Marcos D. Caballero, Steven\nJ. Pollock, and Katherine K. Perkins, \"Colorado Upper-Division\nElectrostatics diagnostic: A conceptual assessment for the junior level,\"\nPhys. Rev. ST Phys. Educ. Res., vol. 8, no. 020108, pp. 1-15, Sep 2012.", "S. J. Pollock, \"Longitudinal study of student conceptual understanding\nin electricity and magnetism,\" Phys. Rev. ST Phys. Educ. Res., vol. 5,\nno. 020110, pp.1-8, Dec 2009.", "Matthew A. Kohlmyer, Marcos D. Caballero, Richard Catrambone, Ruth\nW. Chabay, Lin Ding, Mark P. Haugan, M. Jackson Marr, Bruce A.\nSherwood, and Michael F. Schatz, \" Tale of two curricula: The\nperformance of 2000 students in introductory electromagnetism,\" Phys.\nRev. ST Phys. Educ. Res., vol. 5, no. 020105, pp. 1-10, Oct 2009.", "Ruth Chabay, and Bruce Sherwood, \"Restructuring the introductory\nelectricity and magnetism course,\" Am. J. Phys., vol.74, no. 4, pp. 329-\n336, Apr 2006.", "J. Clement, \"Students' preconceptions in introductory mechanics,\" Am.\nJ. Phys., vol. 50, no. 1, pp. 66-69, Jan 1982.", "I. Halloun, and D. Hestenes, \"Common sense concepts about motion,\"\nAm. J. Phys., vol.53, no.11, pp.1-18, Nov 1985.", "I. Halloun, and D. Hestenes, \"The initial knowledge state of college\nstudents,\" Am. J. Phys., vol. 53, no.11, pp. 1043-1048, Nov 1985.", "D. Hestenes, M. Wells, and G. Swackhamer, \"Force Concept\nInventory,\" Phys. Teach., vol. 30, PP. 141-158, Mar 1992. [10] R. R. Hake, \"Interactive-engagement versus traditional methods: A six\nthousand-student survey of mechanics test data for introductory physics\ncourses,\" Am. J. Phys., vol. 66, no.1, pp. 64-74, Jan 1998.\n[11] L. Viennot, and S. Rainson, \"Students reasoning about the superposition\nof electric fields,\" Int. J. Sci. Educ., vol. 14, no. 4, pp. 475-487, 1992.\n[12] C. Raduta, General students' misconceptions related to electricity and\nmagnetism, arXiv:physics / 0503132.\n[13] D. P. Maloney, T. L. O'Kuma, C. J. Hieggelke, and A.V. Heuvelen,\n\"Surveying students' conceptual knowledge of electricity and\nmagnetism,\" Am. J. Phys., vol. 69, no.7, pp. S12- S23, Jul 2001.\n[14] I. Galili, \"Mechanics background influences students' conceptions in\nelectromagnetism,\" Int. J. Sci. Educ., vol.17, no. 3, pp. 371-387, 1995.\n[15] Salomon F Itza-Ortiz, Sanjay Rebello, and Dean Zollman, \"Students'\nmodels of Newton's second law in mechanics and electromagnetism,\"\nEur. J. Phys., vol. 25, pp. 81-89, 2004.\n[16] S. Tornkvist, K. A. Pettersson, and G. Transtromer, \"Confusion by\nrepresentation on students' comprehension of the electric field concept,\"\nAm. J. Phys., vol. 61, no. 4, pp. 335-338, Apr 1993.\n[17] Thomas M. Scaife, and Andrew F. Heckler, \"Interference between\nelectric and magnetic concepts in introductory physics,\" Phys. Rev. ST\nPhys. Educ. Res., vol. 7, no. 010104, pp.1-11, Mar 2011.\n[18] Eleanor C. Sayre, and Andrew F. Heckler, \"Peaks and decays of student\nknowledge in an introductory E&M course,\" Phys. Rev. ST Phys. Educ.\nRes., vol. 5, no. 013101, pp. 1-5, Feb 2009.\n[19] Lin Ding, Ruth Chabay, Bruce Sherwood, and Robert Beichner,\n\"Evaluating an electricity and magnetism assessment tool: Brief\nelectricity and magnetism assessment,\" Phys. Rev. ST Phys. Educ. Res.,\nvol. 2, no. 010105, pp. 1-7, Mar 2006.\n[20] Rachel E. Pepper, Stephanie V. Chasteen, Steven J. Pollock, and\nKatherine K. Perkins, \"Observations on student difficulties with\nmathematics in upper-division electricity and magnetism,\" Phys. Rev.\nST Phys. Educ. Res., vol. 8, no. 010111, pp. 1-15, Mar 2012.\n[21] Colin S. Wallace, and Stephanie V. Chasteen, \"Upper-division students'\ndifficulties with Ampere's law,\" Phys. Rev. ST Phys. Educ. Res., vol. 6,\nno. 020115, pp.1-8, Sep 2010.\n[22] C. A. Manogue, K. Browne, T. Dray, and B. Edwards, \"Why is\nAmp\u00e8re's law so hard? A look at middle-division physics,\" Am. J.\nPhys., vol. 74, no. 4, pp. 344-350, Feb 2006.\n[23] Dong-Hai Nguyen, and N. Sanjay Rebello, \"Students' difficulties with\nintegration in electricity,\" Phys. Rev. ST Phys. Educ. Res., vol. 7, no.\n010113, pp.1-11, Jun 2011.\n[24] Elwin R. Savelsbergh, Ton de Jong, Monica, and G. M. Ferguson-\nHessler, \"Choosing the right solution approach: The crucial role of\nsituational knowledge in electricity and magnetism,\" Phys. Rev. ST\nPhys. Educ. Res., vol. 7, no. 010103, pp. 1-12, Mar 2011.\n[25] Noah S. Podolefsky, Katherine K. Perkins, and Wendy K. Adams,\n\"Factors Promoting Engaged Exploration with Computer Simulations,\"\nPhys. Rev. ST Phys. Educ. Res., vol. 6, no.020117, pp.1-11, Oct 2010.\n[26] Jacquelyn J. Chini, Adrian Madsen, Elizabeth Gire, N. Sanjay Rebello,\nand Sadhana Puntambekar, \"Exploration of factors that affect the\ncomparative effectiveness of physical and virtual manipulatives in an\nundergraduate laboratory,\" Phys. Rev. ST Phys. Educ. Res., vol. 8,\nno.010113, pp. 1-12, Apr 2012.\n[27] Homeyra R. Sadaghiani, \"Using multimedia learning modules in a\nhybrid-online course in electricity and magnetism,\" Phys. Rev. ST Phys.\nEduc. Res., vol. 7, no. 010102, pp.1-7, Mar 2011.\n[28] N. D. Finkelstein, W. K. Adams, C. J. Keller, P. B. Kohl, K. K. Perkins,\nN. S. Podolefsky, and S. Reid, \"When learning about the real world is\nbetter done virtually: A study of substituting computer simulations for\nlaboratory equipment,\" Phys. Rev. ST Phys. Educ. Res., vol. 1, no.\n010103, pp. 1-8, Oct 2005.\n[29] S. B. McKagan, W. Handley, K. K. Perkins, and C. E. Wieman, \"A\nResearch-Based Curriculum for Teaching the Photoelectric Effect,\" Am.\nJ. Phys., vol. 77, no.1, pp. 87-94, 2009.\n[30] S. B. McKagan, K. K. Perkins, M. Dubson, C. Malley, S. Reid, R.\nLeMaster, and C. E. Wieman, \"Developing and Researching PhET\nsimulations for Teaching Quantum Mechanics,\" Am. J. Phys., vol. 76,\nno.1, pp. 406-417, Jan 2008.\n[31] Tomi Jaakkola, Sami Nurmi, and Koen Veermans, \"A comparison of\nstudents' conceptual understanding of electric circuits in simulation only\nand simulation-laboratory contexts,\" J. Res. Sci. Teach., vol. 48, no. 1,\npp. 71-93, 2011.\n[32] Z.C. Zacharia, \"Comparing and combining real and virtual\nexperimentation: an effort to enhance students' conceptual understanding\nof electric circuits,\" J. Comput. Assist. Learn., vol. 23, no.2, pp.120-132,\nApr 2007.\n[33] Ariel Paul, Noah Podolefsky and Katherine Perkins, \"Guiding Without\nFeeling Guided: Implicit Scaffolding through Interactive Simulation\nDesign,\" AIP Conf. Proc., vol. 1513, no. 1, pp. 302-305, Jan 2013.\n[34] Guadalupe Martinez, Francisco L. Naranjo, Angel L. Perez, and Maria\nIsabel Suero, \"Comparative study of the effectiveness of three learning\nenvironments: Hyper-realistic virtual simulations, traditional schematic\nsimulations and traditional laboratory,\" Phys. Rev. ST Phys. Educ. Res.,\nvol. 7, no. 020111, pp. 1-12, Oct 2011.\n[35] W. K. Adams, A. Paulson, and C. E. Wieman, \"What levels of guidance\nelicit engaged exploration with interactive simulations?,\" AIP Conf.\nProc., vol. 1064, pp. 59-62, Jul 2008.\n[36] Knight, \"The vector knowledge of beginning physics students,\" Phys.\nTeach., vol. 33, pp. 74-77, Feb1995.\n[37] Sergio Flores, Stephen E. Kanim, and Christian H. Kautz, \"Student use\nof vectors in introductory mechanics,\" Am. J. Phys., vol. 72, no. 4, pp.\n460-468, Apr 2004.\n[38] Beichner .R., \"Testing student interpretation of kinematics graphs,\"\nAm. J. Phys., vol. 62, no. 8, pp. 750-762, 1994.\n[39] Andrew Duffy, Boston University, http://physics.bu.edu/~duffy/Ejs/.\n[40] Easy Java simulations, http://www.um.es/fem/Ejs.\n[41] Balasubrahmanya Hegde and B. N. Meera, \"How do they solve it? An\ninsight into the learner's approach to the mechanism of physics problem\nsolving,\" Phys. Rev. ST Phys. Educ. 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