The Effect of Different Presentation Methods of Simple Arithmetic Word Problems on First Grade Elementary School Students' Processing Efficiency

Document Type : Research Paper

Abstract

Introduction: Working memory is responsible for processing and temporarily storing information, functioning as a complex cognitive system for storing and processing information simultaneously. This system consists of various components including the central executive component, the phonological loop, and the visuospatial sketchpad. An individual's processing efficiency within this system depends on the functioning of these different components. Processing efficiency is defined by the effort made or the resources used to complete a task, and is typically measured based on the mental effort exerted or the time spent. In arithmetic, addition and subtraction are the first operations taught. Addition and subtraction problems are typically divided into two main types based on how they are expressed: symbolic problems and word problems. Word problems use word statements (text-based) to represent situations involving addition or subtraction operation. This study focuses on simple pictorial arithmetic word problems of the change type (involving increase and decrease) with dynamic variations. According to Sweller's cognitive load theory, presenting information in different modalities (such as visual, auditory, or combination) can help reduce cognitive load. As a result, according to Cognitive Load Theory, by presenting visual and auditory systems together (due to the simultaneous use of word and visual memory capacities) greater cognitive load can be processed (leading to a reduction in cognitive load).
Method: The current study has sought to investigate the effect of different presentation methods of simple arithmetic word problems on students' processing efficiency and to compare varied effects of these methods on processing efficiency of academically weak and strong students. The research is applied in terms of purpose, and experimental (factorial design with 1 group factor and 1 presentation method) in terms of design, in which the effect of group factor (academically weak and strong students) and presentation methods of simple arithmetic word problems (pictorial, auditory and combination) on the dependent variable (processing efficiency of the studied students) is examined. The statistical population of the study comprises all the first-grade elementary school students of Yasouj in 1402-1403 (4049 students).  Through volunteer sampling, 58 students were selected as the participants of the research (29 students in each group). To select participants, students of six elementary schools (3 girls' schools and 3 boys' schools) in Yasouj were chosen as available participants. 523 students volunteered to participate in the study, out of which 58 students were selected after a screening test for identifying strong and weak students in simple arithmetic problems. Notably, students who answered 75% or more of the questions of arithmetic speed test were considered strong (20 girls and 9 boys), while those who answered 25% or fewer questions were classified as weak (14 girls and 15 boys) and participated in the study. The instrument used in the study was adapted from math problems of the first-grade math book. 24 problems were given to each participant: 8 problems in each presentation method (visual, auditory and combination) with half focusing on subtraction and the other half on addition. In order to assess processing efficiency which is defined as the time spent on answering a problem in working memory, simple arithmetic problems were used considering the time spent on answering each test individually. The time each student spent on each test was measured separately using a stopwatch. The score obtained by each student divided by the time spent on each test individually represents the student's efficiency score.
    Repeated Measures Analysis of Variance as well as Multivariate Analysis of Variance (MANOVA) were utilized to analyze the data.
Results: The results revealed that the processing efficiency of both weak and strong students in increasing problems is higher than in decreasing problems in every presentation method. In addition, the processing efficiency of both weak and strong students in combination presentation is higher than in pictorial presentation, and in pictorial presentation is higher than in auditory presentation. It is interesting to note that the same is true for the weak students. The results also indicated that there is a significant difference between the weak and strong students in terms of increasing and decreasing auditory problems, increasing and decreasing pictorial problems, and increasing and decreasing combination problems. Furthermore, the strong students showed higher processing efficiency compared to the weaker students in various problems with different presentations, and this progress is more noticeable in the strong students.
Discussion and Conclusion: According to the results of this study, mathematics teachers and instructors can facilitate students' learning process by using different methods of presenting simple arithmetic problems in their teaching. Moreover, these evaluations could have significant implications for the mathematical development of children (especially for those who struggle with math) in the future. Additionally, addressing foundational issues in subtraction problems can prevent the escalation of these difficulties and evolving into more complex challenges.
    

Keywords

Main Subjects

References

Alamolhodaei, H. (2009). A working memory model applied to mathematical word problem solving. Asia Pacific Education Review, 10(2), 183-192. DOI: 10.1007/s12564-009-9023-2.
Allen, K., Higgins, S., & Adams, J. (2019). The relationship between visuospatial working memory and mathematical performance in school-aged children: A systematic review. Educational Psychology Review, 1-23. DOI: 10.1007/s10648-019-09470-8.
Alloway, T. P., & Alloway, R. G. (2010). Investigating the predictive roles of working memory and IQ in academic attainment. Journal of Experimental Child Psychology, 106(1), 20-29. DOI: 10.1016/j.jecp.2009.11.003
Azizi Mahmmodabad, M., Liaghatdar, M. J., & Oreyzi, H. (2019). The effectiveness of teaching image-based arithmetic problems on students' active memory performance and their processing efficiency. Journal of Educational Psychology Studies, 16(35), 165-190. Doi: 10.22111/jeps.2019.5056 [In Persian]
Baddeley, A. D. (2006). Working memory: An overview. Working Memory and Education, 1-31.‏ https://doi.org/10.1016/B978-012554465-8/50003-X
Baddeley, A. D., Hitch, G. J., & Allen, R. J. (2009). Working memory and binding in sentence recall. Journal of Memory and Language, 61(3), 438-456. https://doi.org/10.1016/j.jml.2009.05.004
Bedyńska, S., Krejtz, I., & Sedek, G. (2019). Chronic stereotype threat and mathematical achievement in age cohorts of secondary school girls: Mediational role of working memory, and intellectual helplessness. Social Psychology of Education, 22(2), 321-335. DOI: 10.1007/s11218-019-09478-6
Berends, I. E., & Van Lieshout, E. C. (2009). The effect of illustrations in arithmetic problem-solving: Effects of increased cognitive load. Learning and Instruction, 19(4), 345-353.‏ https://doi.org/10.1016/j.learninstruc.2008.06.012
Campbell, J. I., Fuchs-Lacelle, S., & Phenix, T. L. (2006). Identical elements model of arithmetic memory: Extension to addition and subtraction. Memory & Cognition, 34(3), 633-647. DOI: 10.3758/BF03193585
Campbell, J. I. D., & Xue, Q. (2001). Cognitive arithmetic across cultures. Journal of Experimental Psychology: General, 130, 299–315. DOI: 10.1037/0096-3445.130.2.299
Carpenter, T. P., & Moser, J. M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15(3), 179-202. https://doi.org/10.2307/748348
Davoudi, K., Rostgar, A., & Alamian, V. (2011). First-grade math teacher's book. General Department of Textbook Printing and Distribution. [In Persian]
De Corte, E., & Verschaffel, L. (1981). Children's solution processes in elementary arithmetic problems: Analysis and improvement. Journal of Educational Psychology, 73, 765–779. https://doi.org/10.1037/0022-0663.73.6.765
Demetriou, A., Makris, N., Tachmatzidis, D., Kazi, S., & Spanoudis, G. (2019). Decomposing the influence of mental processes on academic performance. Intelligence, 77, 101404. https://doi.org/10.1016/j.intell.2019.101404
Dewolf, T., Van Dooren, W., & Verschaffel, L. (2017). Can visual aids in representational illustrations help pupils to solve mathematical word problems more realistically? European Journal of Psychology of Education, 32, 335-351. DOI: 10.1007/s10212-016-0308-7
Educational Research and Planning Organization. (2023). First-grade math. Offset Company. [Persian]
Eysenck, M., Payne, S., & Derakshan, N. (2005). Trait anxiety, visuospatial processing, and working memory. Cognition & Emotion, 19(8), 1214-1228. https://doi.org/10.1080/02699930500260245 10.‏ DOI: 10.1007/s11858-019-01070-8
Friso-Van den Bos, I., Van der Ven, S. H., Kroesbergen, E. H., & Van Luit, J. E. (2013). Working memory and mathematics in primary school children: A meta-analysis. Educational Research Review, 10, 29-44. DOI: 10.1016/j.edurev.2013.05.003
Fuchs, L. S., Fuchs, D., Compton, D. L., Hamlett, C. L., & Wang, A. Y. (2015). Is word-problem solving a form of text comprehension? Scientific Studies of Reading, 19(3), 204-223. DOI: 10.1080/10888438.2015.1005745
Fuchs, L., Fuchs, D., Seethaler, P. M., & Barnes, M. A. (2020). Addressing the role of working memory in mathematical word-problem solving when designing intervention for struggling learners. ZDM Mathematics Education, 52, 87-96. https://doi.org/10.1007/s11858-019-01070-8
Gall, M., Borg, W., & Gal, J. (2004/1381). Qualitative and quantitative research methods in educational sciences and psychology. Translated by Ahmad Reza Nasr et al. Tehran: Samt Publications. [Persian]
Heejung, L., & Hyunjoo, Y. (2023). A study on the representation utilization ability of academic achievement levels in mathematics problem solving: Focusing on the 4th and 6th grades of elementary school.
Hossaini Khah, K., Nikdel, F., & Noushadi, N. (2019). The effectiveness of training self-regulation strategies on processing efficiency and working memory function of high school girl students. Research in Cognitive and Behavioral Sciences, 8(15), 33-48. Doi: 10.22108/cbs.2020.111297.1206 [In Persian]
Izadi, M. (2012). A comparative content analysis of the first-grade math curriculum goals and content of the math textbook in Iran, Japan and America (State of California).  Unpublished Masterʼs Thesis). Islamic Azad University Fars Science and Research Branch, Shiraz, Iran. [Persian]
Kamii, C., Lewis, B. A., & Kirkland, L. D. (2001). Fluency in subtraction compared with addition. The Journal of Mathematical Behavior, 20, 33–42. DOI: 10.1016/S0732-3123(01)00060-8
Lathifaturrahmah, L., Nusantara, T., Subanji, S., & Muksar, M. (2024, February). Analysis of mathematics students’ problem-solving skills in making prediction mathematical representations. In AIP Conference Proceedings (Vol. 3049, No. 1). AIP Publishing.‏
Moradi, A., Afsardeir, B., Parhoon, H., & Sanaei, H. (2016). Cognitive performance of patients with Multiple Sclerosis (MS) in autobiographical, working and prospective memory in comparison with normal people. International Journal of Behavioral Sciences, 10(1), 49-54.
Moradi, A., Cheraghi, F., & Farahani, M. (2008). The effect of anxiety and tasks presentation manner on processing efficiency and performance of components of working memory.  Journal of Modern Psychological Researches, 3(11), 77-98. [In Persian]
Moreno, R., & Mayer, R. E. (1999). Cognitive principles of multimedia learning: The role of modality and contiguity. Journal of Educational Psychology, 91(2), 358. DOI: 10.1037/0022-0663.91.2.358‏
Panaoura, A. (2007). The interplay of processing efficiency and working memory with the development of metacognitive performance in mathematics. The Mathematics Enthusiast, 4(1), 31-52. DOI: 10.54870/1551-3440.1057
Passolunghi, M. C., & Costa, H. M. (2019). Working memory and mathematical learning. In A. Fritz, V. G. Haase, & P. R Räsänen, P. (Eds.), International Handbook of Mathematical Learning Difficulties (pp. 407-421). Springer, Cham. https://doi:10.1007/978-3-319-97148-3_25
Passolunghi, M. C., Vercelloni, B., & Schadee, H. (2007). The precursors of mathematics learning: Working memory, phonological ability and numerical competence. Cognitive Development, 22, 165–184. DOI: 10.1016/j.cogdev.2006.09.001
Peters, G., De Smedt, B., Torbeyns, J., Ghesquière, P., & Verschaffel, L. (2012). Children’s use of subtraction by addition on large single-digit subtractions. Educational Studies in Mathematics, 79, 335-349. DOI: 10.1007/s10649-011-9308-3
Purcar, A. M., Bocoș, M., Pop, A. L., Roman, A., Rad, D., Mara, D., … & Triff, D. G. (2024). The effect of visual reasoning on arithmetic word problem solving. Education Sciences, 14(3), 278.‏ DOI: 10.3390/educsci14030278
Rasmussen, C., & Bisanz, J. (2005). Representation and working memory in early arithmetic. Journal of Experimental Child Psychology, 91(2), 137-157. https://doi.org/10.1016/j.jecp.2005.01.004
Rosyada, M. I., & Wibowo, S. E. (2023). Analysis of mathematics problem-solving ability based on ideal problem-solving steps given student learning styles. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 12(1), 1332-1343.‏ DOI: 10.2991/assehr.k.211122.014
Santosa, A. D., & Khotimah, R. P. (2023, June). Mathematical problem solving ability from student’s learning style in material Barisan class XI science 2 senior high school 1 CEPER. In AIP Conference Proceedings (Vol. 2727, No. 1). AIP Publishing.‏ DOI: 10.1063/5.0141447
Stellingwerf, B. P., & Van Lieshout, E. C. (1999). Manipulatives and number sentences in computer aided arithmetic word problem solving. Instructional Science, 27, 459-476.
Sweller, J. (1994). Cognitive load theory, learning difficulty, and instructional design. Learning and Instruction, 4(4), 295-312. https://doi.org/10.1016/0959-4752(94)90003-5
Sweller, J., Van Merrienboer, J. G., & Paas, F. (1998). Cognitive architecture and instructional design. Educational Psychological Review, 10, 251-296. DOI: 10.1023/a: 1022193728205
Syah, A., Harizahayu, H., Al Haddar, G., Annisah, A., & Pratiwi, E. Y. R. (2023). Improving students' mathematical problem-solving ability through the use of external representations. Journal on Education, 5(2), 5313-5323.‏ DOI: 10.31004/joe.v5i2.1274
Upu, H., Ihsan, H., & Armayanti, A. K. (2024). Solving mathematics problems based on visual information processing. Asian Journal of Education and Social Studies, 50(3), 219-225.
Van Lieshout, E. C., & Xenidou-Dervou, I. (2018). Pictorial representations of simple arithmetic problems are not always helpful: a cognitive load perspective. Educational Studies in Mathematics, 98(1), 39-55. DOI: 10.1007/s10649-017-9802-3
Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems. Learning and Instruction, 4(4), 273-294. https://doi.org/10.1016/0959-4752(94)90002-7
Wong, W. K., Wu, S. W., Lee, C. W., & Hsu, W. H. (2007). LIMG: Learning-initiating instruction model based on cognitive knowledge for geometry word problem comprehension. Computers & Education. 48, 582-601. DOI: 10.1016/j.compedu.2005.03.009
Xenidou-Dervou, I., Molenaar, D., Ansari, D., van der Schoot, M., & van Lieshout, E. C. D. M. (2017). Nonsymbolic and symbolic magnitude comparison skills as longitudinal predictors of mathematical achievement. Learning and Instruction, 50, 1–13. https://doi.org/10.1016/j.learninstruc.2016.11.001
Studies in Learning & Instruction
Volume 16, Issue 2
September 2024
Pages 28-1

Files

History

  • Receive Date: 03 April 2024
  • Revise Date: 29 July 2024
  • Accept Date: 20 August 2024

Share

How to cite

Statistics