PRIMARY SCHOOL CHILDREN’S DIFFICULTIES IN NUMBERS AND OPERATIONS PROBLEMS
DOI:
https://doi.org/10.29121/ijetmr.v11.i12.2024.1511Keywords:
Addition and Subtraction, Number Concepts, Grade 3, Mathematics DifficultiesAbstract
This research used a mixed-methods descriptive survey approach, where we examined the responses of 47 children in Grade 3 to numbers and operations problems. In this study, we jointly addressed one objective: (1) determining children's challenges in solving addition/subtraction and number-related problems. The problems included 14 items, each comprising 1 to 7 tasks and required participants to answer in one-on-one interview form to identify their problem-solving difficulties. In this study, we qualitatively classified and provided descriptions for the problems encountered accordingly, and we quantitatively analysed the correct and incorrect responses using only descriptive statistics. One of the key findings that stood out was that almost 50% of the children faced difficulties in comprehending and applying number concepts and skills. They exhibited challenges, such as limited knowledge in recalling basic addition/subtraction facts and expressing numbers in multiple ways. While children were observed to have the potential to address problems, they encountered greater obstacles when performing additions and subtractions. Nevertheless, their struggles with numerical problems indicated an underlying incapacity to solve arithmetic operations accurately. The implication is that most children at the start of Grade 3 did not understand number concepts and strategies for solving addition and subtraction problems and required guidance to perform the tasks.
Downloads
References
Adu, J., Acquaye, E., Buckle, & Quansah, K. B. (2009). Report of the 2007 National Education Assessment (NEA), Assessment Services Unit of the Curriculum Research and Development Division, Accra: GES.
Amar, S. (2007). Misconceptions in numbers. UGRU Journal, 5, 1-7.
Australian Curriculum Assessment and Reporting Authority. (2015). Australian Curriculum. CANBERRA ACT: ACARA.
Baker, M. J. (2019). Number Sense and the Effects on Students' Mathematical Success. Northwestern College. Iowa: Northwestern College. Retrieved From NWCommons:
Baroody, A. J. (2016). Curricular Approaches to Connecting Subtraction to Addition and Fostering Fluency with Basic Differences in Grade 1. PNA, 10(3), 161-190. https://doi.org/10.30827/pna.v10i3.6087
Baroody, J. (2006). Why Children have Difficulties Mastering the Basic Number Combinations: How to Help Them. Teaching Children Mathematics, 13(1), 22-31. Retrieved from www.nctm.orghttps://doi.org/10.5951/TCM.13.1.0022
Berch, D. B. (2005). Making Sense of Number Sense: Implications for Children with Mathematical Disabilities. Journal of Learning Disabilities, 38(4), 333-339. https://doi.org/10.1177/00222194050380040901
Bryant, D., Bryant, B., Gersten, R., Scammacca, N., & Chavez, M. (2008). Mathematics intervention for first- and Second-Grade Students with Mathematics Difficulties. Remedial and Special Education, 29(1), 20-32. https://doi.org/10.1177/0741932507309712
Bussi, B. M., & Sun, X. H. (2018). Building the Foundation: Whole Numbers in the Primary Grades. Springer Nature. https://doi.org/10.1007/978-3-319-63555-2
Caldwell, J., Kobett, B., & Karp, K. (2014). Essential understanding of Addition and Subtraction in Practice, grade K-2. Reston, VA: NCTM.
Carmack, C. M. (2011). Investigating the Effects Of Addition with Regrouping Strategy Instruction Among Elementary Students with Learning Disabilities. UNLV Theses, Dissertations, Professional Papers, and Capstones. 1089. http://dx.doi.org/10.34917/2476187
Chin, L. C., & Zakaria, E. (2015). Understanding of Number Concepts and Number Operations Through Games in Early Mathematics Education. Creative Education, 6, 1306-1315. http://dx.doi.org/10.4236/ce.2015.612130
Clarke, D., Cheeseman, J., Gervasoni, A., Gronn, D., Horne, M., McDonough, A., Montgomery, P., Roche, A., Sullivan, P., Clarke, B. A., Rowley, G. (2002). Early Numeracy Research Project Final Report: Seeking Implications for Research into Classroom Practices. Melbourne: Department of Education, Employment and Training.
Clements, D. H., & Sarama, J. (2021). Learning and Teaching Early Math: The Learning Trajectories Approach (3rd ed.). Routledge. https://doi.org/10.4324/9781003083528
Creswell, J. W. (2009). Research Design: Qualitative, Quantitative, and mIxed Methods Approaches (3rd ed.). Sage Publication, Inc.
Creswell, J. W. (2014). Research dEsign: Qualitative, Quantitative, and Mixed Method Approaches (4th ed.). Sage Publication, Inc.
Davis, E. K., & Wilmot, E. M. (2010). An investigation of Primary and JHS Teachers' Attitudes Towards Mathematics in some Selected Schools in the Central Region of Ghana. Mathematics Connection, 9, 1-10. https://doi.org/10.4314/mc.v9i1.61551
De Smedt, B., Reynvoet, B., Swillen, A., Verschaffel, L., Boets, B., & Ghesquière, P. (2009). Basic Number Processing and Difficulties in Single-Digit Arithmetic: Evidence from Velo-Cardio-Facial Syndrome. Cortex, 45(2), 177-188. https://doi.org/10.1016/j.cortex.2007.06.003
Dowker, A., & Sigley, G. (2010). Targeted Interventions for Children with Arithmetical Difficulties. Understanding Number Development and Difficulties, 65-81. https://doi.org/10.1348/97818543370009X12583699332492
Eshun-Famiyeh, J. (2005). Early Number Competencies of Children at the Start of Formal Education. African Journal of Educational Studies in Mathematics and Sciences, 3, 21-33. Retrieved from
Forrester, P. A., & Chinnappan, M. (2010). The Predominance of Procedural Knowledge in Fractions. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the Future of Mathematics Education MERGA33 (pp. 185-192). MERGA Inc.
Fuchs, L. S., Fuchs, D., Powell, S. R., Seethaler, P. M., Cirino, P. T., & Fletcher, J. M. (2008). Intensive Intervention for Students with Mathematics Disabilities: Seven Principles of Effective practice. Learn Disabil Q, 31(2), 79-92. https://doi.org/10.2307/20528819
Geary, D. C. (2004). Mathematics and Learning Disabilities. Journal of Learning Disabilities, 37(1), 4-15. https://doi.org/10.1177/00222194040370010201
Griffiths, A. H., & Howson, A. G. (1974). Mathematics Society of Curricula (Vol. II). Cambridge University Press.
Jourdain, L., & Sharma, S. (2016). Language Challenges in Mathematics Education: A Literature Review. Waikato Journal of Education, 21(2), 43-56. https://doi.org/10.15663/wje.v21i2.269
Karp, K., Caldwell, J., Zbiek, R. M., & Bay-Williams, J. (2011). Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in pre-k-grade 2. National Council of Teachers of Mathematics.
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Help Children Learn Mathematics, Washington, DC: National Research Council.
Larson, M. (2018). MY NCTM.
MacDonald, B. L., Moyer-Packenham, P. S., Westenskow, A., & Child, B. (2018). Components of Place Value Understanding: Targeting Mathematical Difficulties when Providing Interventions. School Science and Mathematics, 17-29. https://doi.org/10.1111/ssm.12258
Maclellan, E. (2012). Number sense: The Underpinning Understanding for Early Quantitative Literacy. Numeracy, 5(2), 1-19. http://dx.doi.org/10.5038/1936-4660.5.2.3
Mauhibah, R., & Karso, K. (2020). Student Difficulties in Addition and Subtraction of two-digit Numbers. The 2nd International Conference on Elementary Education, 2, pp. 618-623. Universitas Pendidikan Indonesia.
Mereku, D. K. (2014). Diploma Disease in Ghanaian Distance Education Upgrading Programmes for Teachers. Open Learning. The Journal of Open, Distance, and e-Learning, 29(1). https://doi.org/10.1080/02680513.2014.914430
Ministry of Education. (2007). Reforming Science and Mathematics Education in Basic Schools in Ghana: Report of the Committee to Review Basic School Science and Mathematics Education in Ghana. Accra: Ministry of Education.
Ministry of Education. (2012). Mathematics Curriculum for Primary Schools (Basic 1-3). National Council for Curriculum and Assessment (NaCCA), Ministry of Education.
Ministry of Education. (2014). Report on National Education Assessment in English and Mathematics at Primary 3 and Primary 6. National Education Assessment Unit/Curriculum Research and Development Division, Ghana Education Service.
Ministry of Education. (2016). Report on 2015 Early Grade Mathematics Assessment (EGMA) at Primary 2. National Education Assessment Unit/Curriculum Research and Development Division, Ghana Education Service.
Ministry of Education. (2019). Mathematics Curriculum for Primary Schools (Basic 1-3). National Council for Curriculum and Assessment (NaCCA), Ministry of Education.
Mohamed, M., & Johnny, J. (2011). Difficulties in Number Sense Among Students. Retrieved September 7, 2022 from ResearchGate:
Moller, K., Martignon, L., Wessolowski, S., Engel, J., & Nuerk, H. C. (2011). Effects of Finger Counting on Numerical Development: The Opposing Views of Neuro-Cognition and Mathematics Education. Frontiers in Psychology, 2, 328. https://doi.org/10.3389/fpsyg.2011.00328
Mullis, I. V. S., Martin, O. M., Foy, P. & Arora, A. (2012). TIMSS 2011 International Results in Mathematics. TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College.
Mullis, I. V. S., Martin, O. M., Gonzalez, E. J., & Chrostowski, S. J. (2004). TIMSS 2003 International Mathematics Report. TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College.
Mulwa, E. C. (2014). The Role of the Language of Mathematics in Students' understanding of Number Concepts in Eldoret Municipality, Kenya. International Journal of Humanities and Social Science, 4(3), 264-274.
National Council of Teachers of Mathematics. (2000). Curriculum and Evaluation Standards for School Mathematics. Reston: VA: NCTM.
Obed, K. (2019). Error and Misconceptions in Basic Mathematical Operations - Third and Fourth Graders in Vanuatu. NUE Journal of International Educational Cooperation, 13, 73-79.
Ojose, B. (2015). Students' Misconceptions in Mathematics: Analysis of Remedies and what Research says. Ohio Journal of School Mathematics, 72, 30-34.
Okpoti, C. A. (2004). Basic School Pupils' Strategies in Solving Subtraction Problems. Mathematics Connection, 4, 31-37. https://doi.org/10.4314/mc.v4i1.21498
Prathana, P., Wongwanich, S., & Sujiva, S. (2014). An Analysis of Elementary School Students' Difficulties in mAthematical Problem Solving. Procedia - Social and Behavioral Sciences, 116, 3169 - 3174. http://dx.doi.org/10.1016/j.sbspro.2014.01.728
Republic of Ghana. (2015). The Composite Budget of the Effutu Municipal Assembly for the 2015 fiscal year. Efutu Municipal - Winneba. Ghana Press.
Senftleben, M., Handler, M., Khoury, P., Lee, & Nari. (2012). Study on Misappropriation of Signs.
Siniguian, M. T. (2017). Students Difficulty in Solving Mathematical Problems. International Journal of Advanced Research in Engineering and Applied Sciences, 6(2), 1-12.
Sood, S., & Jitendra, A. (2007). A Comparative Analysis of Number Sense Instruction in Reform-Based and traditional mathematics textbooks. Journal of Special Education, 41(3), 145. 157. https://doi.org/10.1177/00224669070410030101
Torbeyns, J., & Verschaffel, L. (2015). Mental Computation or Standard Algorithm? Children's Strategy Choices On Multi-Digit Subtractions. European Journal of Psychology of Education, 31(2), 1-36. https://doi.org/10.1007/s10212-015-0255-8
USAID/Ghana Learning. (2018). Ghana Numeracy Pilot Impact Evaluation 2017 Baseline Report. Accra: FHI360 USAID/Ghana Partnership for Education
Van de Walle, J. A., Karp, K. S., & Bay-Willaims, J. M. (2016). Elementary and Middle School Mathematics: Teaching Developmentally (9th ed.). Pearson Education.
West Africa Examinations Council. (2012). Basic Education Certificate Examination, Chief Examiners Report. Ministry of Education.
Widjaja, W., Stacey, K., & Steinle, V. (2008). Miskonsepsi Tentang Bilangan Desimal Dari Calon Guru. Widyadharma, 18(2), 141-154.
Yang, D.C. (2003). Teaching and learning Number Sense - An Intervention Study of Fifth-Grade Students in Taiwan. International Journal of Science and Mathematics Education, 1, 115-134. https://doi.org/10.1023/A:1026164808929
Yang, D.C., Li, M. F., & Li, W. J. (2008). Development of a Computerised Number Sense Scale for 3rd Graders: Reliability and Validity Analysis. International Electronic Journal of Mathematics Education, 3, 110-124. https://doi.org/10.29333/iejme/222
Yilmaz, Z. (2017). Young Children's Number Sense Development: Age-related Complexity Across Cases of three Children. International Electronic Journal of Elementary Education, 9(4), 891-902.
Zanzali, N. A. A., & Ghazali, M. (2018). Assessment of school children's Number Sense. 30-38. Retrieved from 2020, February 9.
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Elizabeth Abugri, Damian Kofi Mereku
This work is licensed under a Creative Commons Attribution 4.0 International License.
License and Copyright Agreement
In submitting the manuscript to the journal, the authors certify that:
- They are authorized by their co-authors to enter into these arrangements.
- The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal.
- That it is not under consideration for publication elsewhere.
- That its release has been approved by all the author(s) and by the responsible authorities – tacitly or explicitly – of the institutes where the work has been carried out.
- They secure the right to reproduce any material that has already been published or copyrighted elsewhere.
- They agree to the following license and copyright agreement.
Copyright
Authors who publish with International Journal of Engineering Technologies and Management Research agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY-SA 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors can enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or edit it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) before and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
For More info, please visit CopyRight Section