The ability to solve physics problems in symbolic and numeric representations


  • Umrotul Umrotul State University of Malang
  • Aurelia Astria L. Jewaru State University of Malang
  • Sentot Kusairi Universitas Negeri Malang
  • Nugroho Adi Pramono Universitas Negeri Malang



symbolic representation, numeric representation, Physics problem solving, linear motion kinematics


The aim of this study is to analyze the ability of students to solve the problems of linear motion kinematics expressed in symbolic and numeric representation. Research was survey with cross-sectional design. Research subjects included 26 first year undergraduate students in physics at one of the State Universities in Malang which was consisted of 10 men and 16 women. The research instrument was open-ended test of linear motion kinematics problems expressed in symbolic and numeric representations with a reability of 0,807 The research data were analyzed using descriptive and non-parametric inferential statistics. The results showed that the ability of students to solve linear motion kinematics problems in both symbolic and numeric representation was medium. Students had difficulty solving physical problems in both symbolic and numeric representations. It was also found that the problems of linear motion kinematics in symbolic representations were more difficult for students to solve than numeric representations. The study suggested further research to explore the causes of student difficulties more authentically, e.g. by interviewing or thinking aloud.

Author Biography

Aurelia Astria L. Jewaru, State University of Malang

I am a student pursuing a master's degree in physics education. 


L. Bollen, P. Van Kampen, C. Baily, M. Kelly, and M. De Cock, Student difficulties regarding symbolic and graphical representations of vector fields, Phys. Rev. Phys. Educ. Res. 13 (2017) doi: 10.1103/PhysRevPhysEducRes.13.020109.

M. De Cock, Representation use and strategy choice in physics problem solving, Phys. Rev. Spec. Top.-Phys. Educ. Res. 8 (2012) 1. doi: 10.1103/PhysRevSTPER.8.020117.

S. Furwati, Sutopo, and Zubaidah, PENINGKATAN PEMAHAMAN KONSEP HUKUM NEWTON PADA SISWA SMP, Pros. TEP PDs Transform. Pendidik. Abad 21 (2017) 471.

P. Klein, A. Muller, and J. Kuhn, Assessment of representational competence in kinematics, Phys. Rev. Phys. Educ. Res. 13 (2017) 1. doi: 10.1103/PhysRevPhysEducRes.13.010132.

H. Tms and J. Sirait, “Representations Based Physics Instruction to Enhance Students’ Problem Solving,” Am. J. Educ. Res. 4 (2016) 1. doi: 10.12691/education-4-1-1.

M. Hill and M. D. Sharma, “Students’ representational fluency at university: A cross-sectional measure of how multiple representations are used by physics students Using the representational fluency survey,” Eurasia J. Math. Sci. Technol. Educ., 11 (2015) 1633. doi: 10.12973/eurasia.2015.1427a.

E. Puspitaningtyas, S. Hasanah, S. Kusairi, and E. Purwaningsih, “Physics students’ responses when asked to select and solve motion kinematics problems in various representations,” AIP Conf. Proc. 2330 (2021), doi:10.1063/5.0043437.

B. Ibrahim and N. S. Rebello, Representational task formats and problem solving strategies in kinematics and work, Phys. Rev. Spec. Top.-Phys. Educ. Res. 8 (2012) 1. doi: 10.1103/PhysRevSTPER.8.010126.

A. Purwanti, Sutopo, and H. Wisodo, Penguasaan Konsep Materi Kinematika pada Siswa SMA Kelas X dengan menggunakan Pembelajaran Multirepresentasi, J. Pendidik. Teor. Penelitian, dan Pengemb. 2 (2017) 575.

N. H. Dienyati, I. K. Werdhiana, and U. Wahyono, Analisis Pemahaman Konsep Siswa berdasarkan Multirepresentasi pada Materi Usaha dan Energi Kelas XI SMAN 1 Banawa Tengah, 8 (2020) 74.

H. Liaw, Y. R. Yu, C. C. Chou, and M. H. Chiu, “Relationships between Facial Expressions, Prior Knowledge, and

Multiple Representations: a Case of Conceptual Change for Kinematics Instruction,” J. Sci. Educ. Technol. (2020), doi:


R. J. Beichner, Testing student interpretation of kinematics graphs, Am. J. Phys., 62 (1994) 750 doi: 10.1119/1.17449.

P. L. Hale, Kinematics and Graphs: Students’ Difficulties and CBLs, Math. Teach. 93 (2000) 414.

M. Planinic, Z. Milin-Sipus, H. Katic, A. Susac, and L. Ivanjek, Comparison of student understanding of line graph slope in physics and mathematics, Int. J. Sci. Math. Educ. 10 (2012) 1393. doi: 10.1007/s10763-012-9344-1.

M. L. Rosenquist and L. C. McDermott, “A conceptual approach to teaching kinematics,” Am. J. Phys., 55 (1987) 407. doi: 10.1119/1.15122.

N. Erceg and I. Aviani, Students’ Understanding of VelocityTime Graphs and the Sources of Conceptual Difficulties, Croat. J. Educ. Hrvat. ˇcasopis za Odgoj i Obraz., 16 (2014) 43. doi:10.15516/cje.v16i1.505.

G. Zavala, S. Tejeda, P. Barniol, and R. J. Beichner, “Modifying the test of understanding graphs in kinematics,”

Phys. Rev. Phys. Educ. Res. 13 (2017) 1. doi: 10.1103/PhysRevPhysEducRes.13.020111.

E. Torigoe and G. Gladding, Same to us, different to them: Numeric computation versus symbolic representation, AIP Conf. Proc. 883 (2007) 153. doi: 10.1063/1.2508715.

E. Torigoe, How numbers help students solve physics problems, (2011) 1. [Online]. Available: htt://

E. T. Torigoe, Unpacking Symbolic Equations in Introductory Physics, (2015) 1. Available: htt://

J. L. Docktor and J. P. Mestre, “Synthesis of discipline-based education research in physics,” Phys. Rev. Spec. Top.-Phys. Educ. Res. 10 (2014) 1. doi: 10.1103/PhysRevSTPER.10.020119.

E. F. Redish and E. Kuo, Language of Physics, Language of Math: Disciplinary Culture and Dynamic Epistemology, Sci. Educ. 24 (2015) 561 doi: 10.1007/s11191-015-9749-7.

D.-H. Nguyen, “Students’ Difficulties With Multiple Representations in Introductory Mechanics.,” Online Submiss 8 (2011) 559.

E. T. Torigoe and G. E. Gladding, Connecting symbolic difficulties with failure in physics, Am. J. Phys. 79 (2011) 133. doi:10.1119/1.3487941.

C. S. Hung and H. K. Wu, Tenth graders’ problem-solving performance, self-efficacy, and perceptions of physics problems with different representational formats, Phys. Rev. Phys. Educ. Res. 14 (2018) 20114 doi: 10.1103/PhysRevPhysEducRes.14.020114.

P. Nieminen, A. Savinainen, and J. Viiri, Erratum to Force concept inventory-based multiple-choice test for investigating students’ representational consistency Phys. Rev. Spec. Top.- Phys. Educ. Res. 6 (2010) 5. doi: 10.1103/PhysRevSTPER.6.029903.