Students’ semantic reasoning characteristics on solving double discount problem

Lydia Lia Prayitno(1*), Purwanto Purwanto(2), Subanji Subanji(3), Susiswo Susiswo(4), Ninik Mutianingsih(5)

(1) Mathematics Education Department, Universitas PGRI Adi Buana Surabaya
(2) Mathematics Education Department, State University of Malang
(3) Mathematics Education Departement,State University of Malang
(4) Mathematics Education Departement, State University of Malang
(5) Mathematics Education Departement, Universitas PGRI Adi Buana Surabaya
(*) Corresponding Author


Semantic is associated with the relationship between symbol, reference, and the problem’s context involved in the problem-solving process which also involves reasoning and decision-making. Hence, this study describes the characteristics of students’ semantic reasoning to solve the double discounts problem. 51 high school students in Sidoarjo participated in this qualitative study. The data were collected through 15-20 minutes problem-solving tests. The students' answers were grouped into correct and wrong answers. The correct answers were then regrouped once more based on the strategies used by the students to answer the test and to identify their semantic reasoning characteristics. The data were analyzed by reducing, classifying the think-aloud and observing. Then the similarity of characteristics of students' semantic reasoning when solving the double discount problem was identified. To test the accuracy of the data, triangulation method was used. This semantic reasoning was identified by  (1) giving the problem situation, (2) stating the keywords and their meaning, (3) stating the relationship, (4) transforming it into a mathematics statement, (5) calculating based on their strategies, (6) decision making, and (7) completing the answer interpretation. This study contributes to developing basic knowledge in interpreting each process of solving ill-structured problems until finding a solution. 


Discount question, double discount, ill-structured problems, problem-based learning, semantic reasoning

Full Text:



Abdillah, A., Nusantara, T., Subanj, S., Susanto, H., & Abadyo, A. (2016). The students decision making in solving discount problem. International Education Studies, 9(7), 57–63.

Adu-Gyamfi, K., Stiff, L. V., & Bossé, M. J. (2012). Lost in translation: Examining translation errors associated with mathematical representations. School Science and Mathematics, 112(3), 159–170.

Alcock, L., & Inglis, M. (2008). Doctoral students’ use of examples in evaluating and proving conjectures. Educational Studies in Mathematics, 69(2), 111–129.

Bakry, M. N. B. B. (2015). The process of thinking among junior high school student in solving HOTS question. International Journal of Evaluation and Research in Education, 4(3), 138–145.

Bassok, M., Chase, V. M., & Martin, S. A. (1998). Adding apples and oranges: Alignment of semantic and formal knowledge. Cognitive Psychology, 35(2), 99–134.

Bergqvist, T., Lithner, J., & Sumpter, L. (2004). Reasoning characteristics in upper secondary school students’ task solving. In C. Bergsten & B. Grevholm (Eds.), Mathematics and language (pp. 71–77). Malmö: Svensk Förening för MatematikDidaktisk Forskning.

Bossé, M. J., Adu-Gyamfi, K., & Chandler, K. (2014). Students’ differentiated translation processes. International Journal for Mathematics Teaching & Learning, 828, 1–28.

Bossé, M. J., Adu-Gyamfi, K., & Cheetham, M. (2011). Translations among mathematical representations: Teacher beliefs and practices. International Journal for Mathematics Teaching & Learning, 12(2), 1–23.

Cai, J., & Nie, B. (2007). Problem solving in Chinese mathematics education: Research and practice. ZDM Mathematics Education, 39(5–6), 459–473.

Cirino, P. T., Morris, M. K., & Morris, R. D. (2007). Semantic, executive, and visuospatial abilities in mathematical reasoning of referred college students. Assessment, 14(1), 94–104.

Clement, J. J. (2008). Does decoding increase word problem solving skills? Action Research Projects, 32.

Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (4th ed.). Boston: Pearson.

Davis, J. (2013). Student understandings of numeracy problems: Semantic alignment and analogical reasoning. The Australian Mathematics Teacher, 69(2), 19–26.

Dawkins, P. C. (2012). Extensions of the semantic/syntactic reasoning framework. For the Learning of Mathematics, 32(3), 39–45.

Gagatsis, A., & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem solving. Educational Psychology, 24(5), 645–657.

Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87(1), 18–32.

Holisin, I., Budayasa, I. K., & Suwarsono, St. (2017). Comparison of male and female primary school student reasoning profiles in solving fractional problems. International Journal of Environmental and Science Education, 12(6), 1553–1565.

Hwang, W.-Y., Chen, N.-S., Dung, J.-J., & Yang, Y.-L. (2007). Multiple representation skills and creativity effects on mathematical problem solving using a multimedia whiteboard system. Journal of Educational Technology & Society, 10(2), 191–212.

Jonassen, D. H. (1997). Instructional design models for well-structured and III-structured problem-solving learning outcomes. Educational Technology Research and Development, 45(1), 65–94.

Kaur, B., & Yeap, B. H. (2001). Semantic characteristics that make arithmetic word problems difficult. Numeracy and Beyond: Proceedings of the 24th Annual Conference of the Mathematics Education Research Group of Australasia Incorporated, 555–562.

Liang, C.-C., Tsai, S.-H., Chang, T.-Y., Lin, Y.-C., & Su, K.-Y. (2016). A meaning-based english math word problem solver with understanding, reasoning and explanation. Proceedings of COLING 2016, the 26th International Conference on Computational Linguistics: System Demonstrations (pp. 151–155). Osaka, Japan: The COLING 2016 Organizing Committee.

Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67(3), 255–276.

Littlefield, J., & Rieser, J. J. (1993). Semantic features of similarity and children’s strategies for identifying relevant information in mathematical story problems. Cognition and Instruction, 11(2), 133–188.

Mairing, J. P. (2017). Thinking process of naive problem solvers to solve mathematical problems. International Education Studies, 10(1), 1–11.

Mao, X., & Sen, C. (2018). Physics-based semantic reasoning for function model decomposition. Volume 1A: 38th Computers and Information in Engineering Conference, 1–12.

Meyer, K. (2014). Making meaning in mathematics problem-solving using the Reciprocal Teaching approach. Literacy Learning : The Middle Years, 22(2), 7–14.

Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: A sourcebook of new methods. Baverly Hills: SAGE Publications.

Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative data analysis (3rd ed.). California: SAGE Publications.

Murphy, C. (2015). Authority and agency in young children’s early number work: A functional linguistic perspective. Proceedings of the 38th Annual Conference of the Mathematics Education Research Group of Australasia, 453–460.

National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. United States of America: The National Council of Teachers of Mathematics Inc.

Nesher, P., & Katriel, T. (1977). A semantic analysis of addition and subtraction word problems in arithmetic. Educational Studies in Mathematics, 8(3), 251–269.

Özcan, Z. Ç., İmamoğlu, Y., & Bayraklı, V. K. (2017). Analysis of sixth grade students’ think-aloud processes while solving a non-routine mathematical problem. Educational Sciences: Theory & Practice, 17(1), 129–144.

Panasuk, R. M., & Beyranevand, M. L. (2011). Preferred representations of middle school algebra students when solving problems. The Mathematics Educator, 13(1), 32–52.

Pape, S. J. (2004). Middle school children’s problem-solving behavior: A cognitive analysis from a reading comprehension perspective. Journal for Research in Mathematics Education, 35(3), 187–219.

Paradesa, R. (2018). Pre-service mathematics teachers’ ability in solving well-structured problem. Journal of Physics: Conference Series, 948(1), 012015.

Patelli, A., Calinescu, R., & Wang, H. (2014). Semantic reasoning for autonomic IT systems. Proceedings of the 19th International Doctoral Symposium on Components and Architecture, 13–18.

Polya, G. (1973). How to solve it (2nd ed.). Princeton, N.J: Princeton University Press.

Prayitno, L. L., Purwanto, P., Subanji, S., & Susiswo, S. (2018). Identification errors of problem posed by prospective teachers about fraction-based meaning structure. International Journal of Insights for Mathematics Teaching (IJOIMT), 1(1), 76–84.

Sardi, Rizal, M., & Mansyur, J. (2018). Behaviour of mathematics and physics students in solving problem of vector-physics context. Journal of Physics: Conference Series, 1006, 012019.

Shi, S., Wang, Y., Lin, C.-Y., Liu, X., & Rui, Y. (2015). Automatically solving number word problems by semantic parsing and reasoning. Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, 1132–1142.

Shin, N., Jonassen, D. H., & McGee, S. (2003). Predictors of well-structured and ill-structured problem solving in an astronomy simulation. Journal of Research in Science Teaching, 40(1), 6–33.

Stylianou, D. A. (2013). An examination of connections in mathematical processes in students’ problem solving: Connections between representing and justifying. Journal of Education and Learning, 2(2), 23–35.

Sukoriyanto, J., Nusantara, T., Subanji, S., & Chandra, T. D. (2016). Students thinking process in solving combination problems considered from assimilation and accommodation framework. Educational Research and Reviews, 11(16), 1494–1499.

Swastika, G. T., Nusantara, T., Subanji, & Irawati, S. (2020). Alteration representation in the process of translation graphic to graphic. Humanities & Social Sciences Reviews, 8(1), 334–343.

Uhden, O., Karam, R., Pietrocola, M., & Pospiech, G. (2012). Modelling mathematical reasoning in physics education. Science & Education, 21(4), 485–506.

Xin, Y. P., Jitendra, A. K., & Deatline-Buchman, A. (2005). Effects of mathematical word problem—solving instruction on middle school students with learning problems. The Journal of Special Education, 39(3), 181–192.

Article Metrics

Abstract view(s): 108 time(s)
PDF: 98 time(s)


  • There are currently no refbacks.