Grade 10 Namibian Learners' Strategies for Solving Algebraic Word Problems
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Abstract
Solving mathematical word problems is a big challenge for many learners. One reason for the challenge could be the use of inappropriate strategies in solving mathematical word problems. In Namibia, many examiners’ reports show that learners do not attempt algebraic word problems fairly in examinations. This study investigated Grade 10 learners’ strategies for solving algebraic word problems in the Ohangwena Region, Namibia. The study followed a qualitative approach. A sample of 351 Grade 10 learners from ten secondary schools participated in the study. Krulik and Rudnick’s problem-solving strategies model was adopted as the framework that guided the study. Data was collected using the Algebraic Word Problem Solving Achievement Test and analysed using content analysis. The result shows that most of the learners could not use appropriate strategies to solve the given problems. Few learners employed one or two appropriate strategies in solving the problems. The strategies used by the learners to solve the algebraic word problems in the test include Computing or Simplifying (CS); Making a Table, Chart, or List (TCL); Making a model or a diagram (MD), and Guessing, Checking, and Revising (GCR). It is recommended that teachers model different strategies for solving mathematical problems for learners while teaching mathematics.
Keywords – problem-solving, problem-solving strategies, algebraic word problem.
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How to Cite
Iilonga, H., & Ogbonnaya, U. (2023). Grade 10 Namibian Learners’ Strategies for Solving Algebraic Word Problems. Unnes Journal of Mathematics Education, 12(2), 103-113. https://doi.org/10.15294/ujme.v12i2.69364
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Ratnasari, R., & Safarini, D. (2020). Problem-solving strategies used by eight grade learners. Contemporary Mathematics and Science Education, 1(2), 20008. https://doi.org/10.30935/conmaths/8497
Schoenfeld, A. H. (2016). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics (Reprint). Journal of Education, 196(2), 1-38. https://doi.org/10.1177/002205741619600202
Sikukumwa, E. (2017). Types of strategies used to solve algebraic word problems by grade 12 ordinary level Mathematics learners of Kavango East region of Namibia (Doctoral dissertation, University of Namibia).
Szabo, Z. K., Körtesi, P., Guncaga, J., Szabo, D., & Neag, R. (2020). Examples of problem-solving strategies in mathematics education supporting the sustainability of 21st-century skills. Sustainability, 12(23), 10113. https://doi.org/10.3390/su122310113
Takahashi, A. (2017). Lesson study: The fundamental driver for mathematics teacher development in Japan. In Professional Development of Mathematics Teachers, pp. 47–61. Springer.
Tan, D. A. (2018). Mathematical problem solving heuristics and solution strategies of senior high school learners. International Journal of English and Education, 7(3), 1-17. https://doi.org/10.7160/eriesj.2018.110302
Tostado-Véliz, M., Kamel, S., & Jurado, F. (2019). A robust power flow algorithm based on Bulirsch–Stoer method. IEEE Transactions on Power Systems, 34(4), 3081-3089. https://doi.org/10.1109/TPWRS.2019.2900513
Ünlü, M. (2018). Examination of Mathematics Teacher Candidates' Strategies Used in Solving Non-Routine Problems. Acta Didactica Napocensia, 11, 97-114. https://doi.org/10.24193/adn.11.3-4.8
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Swets and Zietlinger Publishers.
Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: A survey. ZDM, 52(1), 1-16. https://doi.org/10.1007/s11858-020-01130-4
Walick, C. M. (2015). A proposed algebra problem-analysis model (Doctoral dissertation, University of Minnesota).
Yew, W. T., & Zamri, S. N. A. S. (2018). Problem solving strategies of selected pre-service secondary school mathematics teachers in Malaysia. MOJES: Malaysian Online Journal of Educational Sciences, 4(2), 17-31.
Yusoff, M. S. B. (2019). ABC of content validation and content validity index calculation. Resource, 11(2), 49-54. https://doi.org/10.21315/eimj2019.11.2.6
Bambi, C., Freese, K., Vagnozzi, S., & Visinelli, L. (2019). Testing the rotational nature of the supermassive object M87* from the circularity and size of its first image. Physical Review D, 100(4), 044057. https://doi.org/10.1103/PhysRevD.100.044057
Cardellino, P., & Woolner, P. (2020). Designing for transformation–a case study of open learning spaces and educational change. Pedagogy, Culture & Society, 28(3), 383-402. https://doi.org/10.1080/14681366.2019.1649297
Celebioglu, B., Yazgan, Y., & Ezentaş, R. (2010). Usage of non-routine problem solving strategies at first grade level. Procedia-Social and Behavioral Sciences, 2(2), 2968-2974. https://doi.org/10.1016/j.sbspro.2010.03.449
Chirove, M. (2014). Relationship between learners' mathematics-related belief systems and their approaches to non-routine mathematical problem solving: a case study of three high schools in Tshwane North district (D3), South Africa (Doctoral dissertation, University of South Africa). http://hdl.handle.net/10500/18413
Directorate of National Examinations and Assessment. (2014). Examiners’ reports. DNEA Printers.
Directorate of National Examinations and Assessment. (2015). Examiners’ reports. DNEA Printers.
Directorate of National Examinations and Assessment. (2016). Examiners’ reports. DNEA Printers.
Directorate of National Examinations and Assessment. (2017). Examiners’ reports. DNEA Printers.
Directorate of National Examinations and Assessment. (2018). Examiners’ reports. DNEA Printers.
Duru, A., Peker, M., Bozkurt, E., Akgün, L., & Bayrakdar, Z. (2011). Pre-service primary school teachers’ preference of the problem solving strategies for word problems. Procedia-Social and Behavioral Sciences, 15, 3463-3468. https://doi.org/10.1016/j.sbspro.2011.04.319
Elia, I., van den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Ex¬ploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in math¬ematics. ZDM Mathematics Education, 41, 605-618. https://doi.org/10.1007/s11858-009-0184-6
Ferrucci, B. J., Yeap, B. H., & Carter, J. A. (2003). A Modelling approach for enhancing problem-solving in the Middle Grade. Mathematics Teaching In The Middle School, 8(9), 470-475.
Gavaz, H. O., & Yazgan, Y. (2021). Non-routine problem solving and strategy flexibility: A quasi-experimental study. Berlin Studies Transnational Journal of Science and Humanities, 5(3), 40-54. https://doi.org/10.33902/JPR.2021370581
Gilbert, G. E., & Prion, S. (2016). Making sense of methods and measurement: Lawshe's content validity index. Clinical Simulation in Nursing, 12(12), 530-531. https://doi.org/10.1016/j.ecns.2016.08.002
Grønmo, L. S., Lindquist, M., Arora, A., & Mullis, I. V. (2015). TIMSS 2015 Mathematics Framework. Timss, 11, 28.
Jarrett, D. (1999). The inclusive classroom: Mathematics and Science Instruction for Learners with Learning Disabilities. It's Just Good Teaching. Northwest Regional Educational Laboratory. https://eric.ed.gov/?id=ED433647.
Jones, A., Swaboda, N., & Ruggeri, A. (2020). Developmental changes in question-asking. The questioning child: Insights from psychology and education, 118-143. https://doi.org/10.1017/9781108553803.007
Kaur, B. (2008). Problem solving in the mathematics classroom (Secondary). National Institute of Education, Nanyang Technological University.
Krulik, S., & Rudnick, J. (1996). The new sourcebook for teaching reasoning and problem-solving in junior and senior high school. Simon & Schuster Company. https://doi.org/10.12691/education-5-3-16
Lee, K., Ng, S. F., & Bull, R. (2018). Learning and solving algebra word problems: The roles of relational skills, arithmetic, and executive functioning. Developmental psychology, 54(9), 1758. https://doi.org/10.1037/dev0000561
Mabilangan, R. A., Limjap, A. A., & Belecina, R. R. (2011). Problem solving strategies of high school students on non-routine problems. Alipato: A Journal of Basic Education, 5, 23-46.
Polya, G. (1985). How to solve it (2nd ed.). Princeton University Press.
Rahayuningsih, S., Sirajuddin, S., & Nasrun, N. (2020). Cognitive flexibility: exploring students’ problem-solving in elementary school mathematics learning. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 6(1), 59-70. https://doi.org/10.23917/jramathedu.v6i1.11630
Ratnasari, R., & Safarini, D. (2020). Problem-solving strategies used by eight grade learners. Contemporary Mathematics and Science Education, 1(2), 20008. https://doi.org/10.30935/conmaths/8497
Schoenfeld, A. H. (2016). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics (Reprint). Journal of Education, 196(2), 1-38. https://doi.org/10.1177/002205741619600202
Sikukumwa, E. (2017). Types of strategies used to solve algebraic word problems by grade 12 ordinary level Mathematics learners of Kavango East region of Namibia (Doctoral dissertation, University of Namibia).
Szabo, Z. K., Körtesi, P., Guncaga, J., Szabo, D., & Neag, R. (2020). Examples of problem-solving strategies in mathematics education supporting the sustainability of 21st-century skills. Sustainability, 12(23), 10113. https://doi.org/10.3390/su122310113
Takahashi, A. (2017). Lesson study: The fundamental driver for mathematics teacher development in Japan. In Professional Development of Mathematics Teachers, pp. 47–61. Springer.
Tan, D. A. (2018). Mathematical problem solving heuristics and solution strategies of senior high school learners. International Journal of English and Education, 7(3), 1-17. https://doi.org/10.7160/eriesj.2018.110302
Tostado-Véliz, M., Kamel, S., & Jurado, F. (2019). A robust power flow algorithm based on Bulirsch–Stoer method. IEEE Transactions on Power Systems, 34(4), 3081-3089. https://doi.org/10.1109/TPWRS.2019.2900513
Ünlü, M. (2018). Examination of Mathematics Teacher Candidates' Strategies Used in Solving Non-Routine Problems. Acta Didactica Napocensia, 11, 97-114. https://doi.org/10.24193/adn.11.3-4.8
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Swets and Zietlinger Publishers.
Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: A survey. ZDM, 52(1), 1-16. https://doi.org/10.1007/s11858-020-01130-4
Walick, C. M. (2015). A proposed algebra problem-analysis model (Doctoral dissertation, University of Minnesota).
Yew, W. T., & Zamri, S. N. A. S. (2018). Problem solving strategies of selected pre-service secondary school mathematics teachers in Malaysia. MOJES: Malaysian Online Journal of Educational Sciences, 4(2), 17-31.
Yusoff, M. S. B. (2019). ABC of content validation and content validity index calculation. Resource, 11(2), 49-54. https://doi.org/10.21315/eimj2019.11.2.6