Analysis of solving mathematical word problems using dynamic assessment for scaffolding construction

Andi Saparuddin Nur, Kartono Kartono, Zaenuri Zaenuri, Rochmad Rochmad

Abstract


Students need the ability to solve word problems can connect mathematics with the context of everyday life. However, students experience many difficulties and need assistance in the form of scaffolding can to solve story problems well. Dynamic assessment is an alternative approach to constructing the form of scaffolding that students need to solve mathematical word problems. This study aims to analyze the students' difficulties in solving word problems and the required form of scaffolding through dynamic assessment. The subjects of this study consisted of 177 students spread across ten public junior high schools in Jeneponto Regency, South Sulawesi Province. There is a four-word problem that is tested and analyzed using dynamic assessment. Student solutions are grouped based on the type and form of scaffolding needed, namely; level 5 (no solution), level 4 (without analysis/unrepresentative), level 3 (computational error), level 2 (incomplete procedure), level 1 (lack of thoroughness in the final stage). The form of scaffolding is constructed to help students solve mathematical word problems step by step at each level. The use of scaffolding accompanied by instructions helps students develop word problem-solving skills. Dynamic assessment can be considered to be integrated with the mathematics learning process that supports scaffolding construction to solve students' word problems.

Keywords


Word problems; Scaffolding; Dynamic assessment; Problem solving; Mathematics

References


A. Panaoura, “Computers in human behavior improving problem solving ability in mathematics by using a mathematical model : a computerized approach,” Comput. Human Behav., vol. 28, no. 6, pp. 2291–2297, 2012, doi: 10.1016/j.chb.2012.06.036.

I. Di Leo and K. R. Muis, “Confused , now what ? a cognitive-emotional strategy training ( cest ) intervention for elementary students during mathematics problem solving,” Contemp. Educ. Psychol., vol. 62, no. May, p. 101879, 2020, doi: 10.1016/j.cedpsych.2020.101879.

Y. P. Xin, “The effect of a conceptual model-based approach on ‘additive’ word problem solving of elementary students struggling in mathematics,” ZDM, 2018, doi: 10.1007/s11858-018-1002-9.

L. Li et al., “Assessing kindergarteners ’ mathematics problem solving : The development of a cognitive diagnostic test,” Stud. Educ. Eval., vol. 66, no. May 2019, 2020, doi: 10.1016/j.stueduc.2020.100879.

U. Özkubat, A. Karabulut, and E. Rüya, “Mathematical problem-solving processes of students with special needs : a cognitive strategy instruction model ’ solve it !’,” Int. Electron. J. Elem. Educ., vol. 12, no. 5, pp. 405–416, 2020, doi: 10.26822/iejee.2020562131.

L. Verschaffel, S. Schukajlow, J. Star, and W. Van Dooren, “Word problems in mathematics education : a survey,” ZDM, 2020, doi: 10.1007/s11858-020-01130-4.

P. Andrews and C. Xenofontos, “Analysing the relationship between the problem-solving- related beliefs, competence and teaching of three Cypriot primary teachers,” J. Math. Teach. Educ., 2014, doi: 10.1007/s10857-014-9287-2.

J. Xie and J. O. Masingila, “Examining interactions between problem posing and problem solving with prospective primary teachers : a case of using fractions,” Educ. Stud. Math., vol. In Press, 2017, doi: 10.1007/s10649-017-9760-9.

S. R. Powell, K. A. Berry, and S. A. Benz, “Analyzing the word-problem performance and strategies of students experiencing mathematics difficulty,” J. Math. Behav., vol. 58, no. January, p. 100759, 2020, doi: 10.1016/j.jmathb.2020.100759.

W. Van Dooren, S. Lem, H. De Wortelaer, and L. Verschaffel, “Improving realistic word problem solving by using humor,” J. Math. Behav., vol. In Press, 2018, doi: 10.1016/j.jmathb.2018.06.008.

C. Csíkos and J. Szitányi, “Teachers ’ pedagogical content knowledge in teaching word problem solving strategies,” ZDM, vol. 52, no. 1, pp. 165–178, 2020, doi: 10.1007/s11858-019-01115-y.

L. S. Fuchs, D. L. Compton, D. Fuchs, K. N. Hollenbeck, C. F. Craddock, and C. L. Hamlett, “Dynamic Assessment of Algebraic Learning in Predicting Third Graders ’ Development of Mathematical Problem Solving,” J. Educ. Psychol., vol. 100, no. 4, pp. 829–850, 2008, doi: 10.1037/a0012657.

I. Elia, “Word problem solving and pictorial representations : insights from an exploratory study in kindergarten,” ZDM, 2019, doi: 10.1007/s11858-019-01113-0.

B. Kaur, “The why , what and how of the ‘ model ’ method : a tool for representing and visualising relationships when solving whole number arithmetic word problems,” ZDM, vol. 0, no. 0, p. 0, 2018, doi: 10.1007/s11858-018-1000-y.

F. Bingolbali and E. Bingolbali, “One curriculum and two textbooks : opportunity to learn in terms of mathematical problem solving,” 2018.

B. Kaur, “Difficulties with problem solving in mathematics,” Math. Educ., vol. 2, no. 1, pp. 93–112, 1997.

E. Novak and J. Lynne, “Studying preservice teacher math anxiety and mathematics performance in geometry , word , and non-word problem solving,” Learn. Individ. Differ., vol. 54, pp. 20–29, 2017, doi: 10.1016/j.lindif.2017.01.005.

Z. Xin and L. Zhang, “Cognitive holding power, fluid intelligence, and mathematical achievement as predictors of children’ s realistic problem solving,” Learn. Individ. Differ., vol. 19, no. 1, pp. 124–129, 2009, doi: 10.1016/j.lindif.2008.05.006.

T. Lowrie, “The utility of diagrams in elementary problem solving,” Cogn. Dev., vol. 55, no. May 2019, p. 100921, 2020, doi: 10.1016/j.cogdev.2020.100921.

J. A. González-calero, A. Berciano, and D. Arnau, “The role of language on the reversal error . A study with bilingual Basque-Spanish students,” Math. Think. Learn., vol. 22, no. 01, pp. 1–19, 2020, doi: 10.1080/10986065.2020.1681100.

C. Haywood and C. S. Lidz, Dynamic Assessment in Practice. Cambridge: Cambridge University Press, 2007.

N. L. Popa and R. L. Păuc, “Dynamic assessment, potential giftedness and mathematics achievement in elementary school,” Acta Didact. Napocensia, vol. 8, no. 2, pp. 23–32, 2015.

D. H. Allsopp, M. M. Kyger, L. Lovin, H. Gerretson, K. L. Carson, and S. Ray, “Instruction and student outcomes mathematics dynamic assessment informal assessment that responds to the needs of struggling learners in mathematics,” Teach. Except. Child., vol. 9, no. May, pp. 6–16, 2016.

J. Elliott, “Dynamic Assessment in Educational Settings : Realising potential,” no. October 2014, pp. 37–41, 2010, doi: 10.1080/00131910303253.

E. L. Grigorenko, “Dynamic assessment and response of intervention: two sides of one coin,” J. Learn. Disabil., vol. 42, no. 2, pp. 111–132, 2009, doi: 10.1177/0022219408326207.

L. S. Fuchs, D. Fuchs, K. Prentice, C. L. Hamlett, R. Finelli, and S. J. Courey, “Enhancing mathematical problem solving among third-grade students with schema-based instruction,” J. Educ. Psychol., vol. 96, no. 4, pp. 635–647, 2004, doi: 10.1037/0022-0663.96.4.635.

E. L. Grigorenko, “Dynamic assessment and response to intervention: Two sides of one coin,” J. Learn. Disabil., vol. 42, no. 2, pp. 111–132, 2009, doi: 10.1177/0022219408326207.

M. K. Cho and M. K. Kim, “Investigating Elementary Students ’ Problem solving and teacher scaffolding in solving an III-structured problem,” Int. J. Educ. Math. Sci. Technol., vol. 8, no. 4, pp. 274–289, 2020.

K. Achmetli, S. Schukajlow, and K. Rakoczy, “Multiple solutions for real-world problems, experience of competence and students’ procedural and conceptual knowledge,” Int. J. Sci. Math. Educ., vol. 17, no. 8, pp. 1605–1625, 2019, doi: 10.1007/s10763-018-9936-5.

R. Kenney, T. An, S. H. Kim, N. A. Uhan, J. S. Yi, and A. Shamsul, “Linear programming models: identifying common errors in engineering students’ work with complex word problems,” Int. J. Sci. Math. Educ., vol. 18, no. 4, pp. 635–655, 2020, doi: 10.1007/s10763-019-09980-5.

R. Ramírez, B. M. Brizuela, and C. Ayala-Altamirano, “Word problems associated with the use of functional strategies among grade 4 students,” Math. Educ. Res. J., 2020, doi: 10.1007/s13394-020-00346-7.




DOI: http://doi.org/10.11591/ijere.v11i2.22535

Refbacks

  • There are currently no refbacks.


Copyright (c) 2021 Institute of Advanced Engineering and Science

International Journal of Evaluation and Research in Education (IJERE)
p-ISSN: 2252-8822, e-ISSN: 2620-5440

View IJERE Stats

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.