Assessing students’ mastery and misconceptions in the fundamental operations on integers
Nurul Ain J. Harun, Kyrille Grace A. Cuevas, Olivia I. Asakil, Jayson V. Alviar, & Leo Jay V. Solon
Abstract
One of the common misconceptions affecting mathematics performance of high school students involves operating integers. Evidently, students who were exposed to modular learning demonstrate poor mastery of the pre-requisite skills. This study aimed to assess the mastery level and misconceptions of the Grade 7 students involving operations on integers. A descriptive research design was used with a total of sixty-two (62) conveniently chosen Grade 7 students were twenty-nine (29) were males and thirty-three (33) were females. The Mean Percentage Scores (MPS) per operation on integers were calculated to describe the mastery level and the assessment results were analyzed to identify possible misconceptions of the students in operating integers. Similarly, data were analyzed using the Welch t-Test to determine if there is a difference in the level of mastery between the male and female students. Findings show that the overall MPS result is 50.56%, indicating that the students demonstrated Average Near Mastery (AVR) of the concepts involving operations on integers. In addition, there was no significant difference between the mastery level of male and female grade 7 students. Although the students demonstrated Average Near Mastery (AVR) in the given assessment, the item analysis showed various misconceptions and errors exhibited by the students regardless of sex and section. Students’ misconceptions include subtracting integers and dealing with negative numbers. Hence, an intervention is needed to address the misconceptions in subtracting integers and a reinforcement is proposed to enhance the students’ mastery in other operations on integers.
Keywords
operations on integers, mastery level, mean percentage score, misconceptions
Author information & Contribution
Nurul Ain J. Harun. Senior High School Student at Tairan National High School – Basilan Division – BARMM-MBHTE
Kyrille Grace A. Cuevas. Senior High School Student at Tairan National High School – Basilan Division – BARMM-MBHTE
Olivia I. Asakil. Senior High School Student at Tairan National High School – Basilan Division – BARMM-MBHTE
Jayson V. Alviar. Corresponding author. Secondary School Teacher 1 at Tairan National High School – Basilan Division – BARMM-MBHTE. Corresponding email: jvalviar@up.edu.ph
Leo Jay V. Solon. Secondary School Teacher 1 at Tairan National High School – Basilan Division – BARMM-MBHTE
Disclosure statement
No potential conflict of interest was reported by the author(s).
Funding
This work was not supported by any funding.
Institutional Review Board Statement
Data and Materials Availability
The data supporting the findings of this study are available from the corresponding author upon reasonable request.
AI Declaration
Notes
Acknowledgement
References
Ali Rahman, E.S., Shahrill, M., Abbas, N., & Tan, A. (2017). Developing students’ mathematical skills involving order of operations. International Journal Of Research in Education and Science (IJRES), 3(2), 373-382. doi:10.2190/ijres.327896
Alsina, C., & Nelson, R. (2006). Math made visual: Creating images for understanding mathematics. United States of America: The Mathematical Association of America. doi:10.5948
Basilio, K. D., Asanon, F. J., Sahidena, R. A., Abdul, A. J., Espacio, L.-G. P., & Alviar, J. V. (2022). Ready or not ready: Extent of readiness in mathematics of grade 7 students. International Journal of Academic Pedagogical Research (IJAPR), 6(8), 81-85.
Booth, J. L., & Koedinger, K. R. (2008). Key misconceptions in algebraic problem solving. Human Computer Interaction Institute. Retrieved from https://www.researchgate.net/publication/281131215_Key_misconceptions_in_algebraic_problem_solving
Cetin, H. (2019). Explaining the concept and operations of integers in primary school mathematics teaching: Opposite moel sample. Universal Journal of Educational Research, 365-370. doi:10.13189
Delos Santos, K. B., Eduarte, A. R., Juaban, J. L., Abdul, R. J., Najimin, L. A., & Alviar, J. V. (2022). Effects of video tutorials on the mathematics achievement of students in modular distance learning. International Journal of Multidisciplinary Research and Publications, 5(2), 150-155.
Department of Education. (2019). PISA 2018: National report of the Phlippines. Retrieved from https://www.deped.gov.ph/wp-content/uploads/2019/12/PISA-2018-Philippine-National-Report.pdf
Department of Education. (2016). K to 12 Mathematics Curriculum Guide. Retrieved from https://depedbohol.org/v2/wp-content/uploads/2016/03/Math-CG_with-tagged-math-equipment.pdf
DepEd Memorandum no. 160 series of 2012. (n.d.). Maximizing utilization of the National Achievement Test (NAT) results to raise the achievement levels of low performing schools.
Dube, A., & Robinson, K. (2018). Children’s understanding of multiplication and division: Insights from a pooled analysis of seven studies conducted across seven years. British Journal of Developmental Psychology, 206-219. doi:10.1111/bjdp.12217
Jamaludin, N. H., & Maat, S. M. (2020). A systematic literature review on students misconceptions in mathematics. Academic Research in Business and Social Sciences, 10(6), 127-145. doi:10.6007/IJARBSS/v10-i6/7273
Fadillah, S., & Susiaty, U. (2019). Developing refutation text to resolve students’ misconceptions in additon and subtraction of integers. Beta: Jurnal Tadris Matematika, 12(1), 14-25. doi:10.20414/betajtm.v12i1.160
Fuadiah, N. F., Suryadi, D., & Turmudi. (2016). Some difficulties in understanding negative numbers faced by students a qualitative study applied at secondary schools in Indonesia. International Education Studies, 10(1), 24-38. doi:10.5539/ies.v10n1p24
Khalid, M., & Embong, Z. (2019). Sources and possible causes of errors and misconceptions in operations of integers. International Electronic Journal of Mathematics Education, 15(1). doi:10.29333/iejme/6265
Khun-Inkeeree, H., Omar-Fauzee, M. S., & Othman, M. K. (2016). Students’ attitude towards achievement in mathematics: A cross sectional study of year six students in Songklha province, Thailand. European Journal of Education Studies, 2(4). doi:10.5281
Koh, E. T., & Owen, W. L. (2000). Descriptive research and qualitative research. Introduction to Nutrition and Health Research, 221-222.
Lalian, O. (2019). The effects of using video media in mathematics Learning on students’ cognitive and aspects. AIP Conference Proceedings. Retrieved from https://doi.org/10.1063/1.5061865
Lamb, L. C., & Thanheiser, E. (2006). Understanding integers: Using balloons and weights software. Algebraic Thinking, 2, 163-164.
Makonye, J. P., & Fakude, J. (2016). A study of errors and misconceptions in the learning of addition and subtraction of directed numbers in grade 8. doi:10.1177?2158244016671375
Mejias, S., Muller, C., & Schiltz, C. (2019). Assessing mathematical school readiness. doi:10.3389/fpsyg.2019.01173
Nunez, R., & Lakoff, G. (2013). The metaphorical structure of mathematics: Sketching out cognitive foundations for a mind-based mathematics in mathematical reasoning. 29-98.
Nurnberger-Haag, J., Kratky, J., & Karpinski, A. C. (2022). The integer test of primary operations: A practical and validated assessment of middle school students’ calculations with negative numbers.
Pandey, B. D. (2017). A study of mathematical achievement of secondary school students. International Journal of Advanced Research, 12(5). doi:10.21474/IJAR01/6165
Permata, D., Wijayanti, P., & Masriyah. (2019). Students’ misconceptions on the algebraic prerequisites concept: Operation of integer numbers and fractions. The Sixth Seminar Nasional Pendidikan Matematika Universitas Ahmad Dahlan 2018. doi:10.1088/1742-6569/1188/1/012059
Purwaningrum, J., & Bintoro, H. (2019). Miskonsepsi matematika materi bilangan pada mahasiswa calon guru sekolah dasar. Prosiding Seminar Nasional MIPA Kolaborasi, 1(1), 173-180.
Rosyidah, A. N., Maulyda, M. A., Jiwandono, I. S., Oktaviyanti, I., & Gunawan, G. (2021). Misconceptions and errorss integer operations: A study in preservice elementary school teachers (PGSD). Journal of Physics: Conference Series. doi:10.1088/1742-6596/1779/1/012078
Rubin, R., Marcelino, J., Mortel, R., & Lapinid, M. C. (2014). Activity-based teaching of integer concepts and its operations. Paper presented at the DLSU Research Congress 2014 De La Salle Unversity, 1-16.
Sadler, J. T. (2012, July). The positives about negatives: A study of errors and misconceptions with integer operatios in adult education. Retrieved from http://hdl.handle.net/20.500.12648/221
Setyawati, R. D., & Indiati, I. (2O18). Analysis misconceptions of integers in microteaching Activities. Journal of Physics: Conference Series. doi:10.1088/1742-6596/1013/1/012146
Cite this article:
Harun, N.J., Cuevas, K.A., Asakil, O.I., Alviar, J.V. & Solon, L.V. (2023). Assessing students’ mastery and misconceptions in the fundamental operations on integers. International Journal of Science, Technology, Engineering and Mathematics, 3 (3), 36-55. https://doi.org/10.53378/353000
License:
This work is licensed under a Creative Commons Attribution (CC BY 4.0) International License.
Find this article in:
Most read articles in this journal
- Analysis of the inventory management system towards enhanced university service delivery
- Street food’s microbiological load and vendors’ food hygiene and safety practices compliance in the schools of Cebu City
- Assessing students’ mastery and misconceptions in the fundamental operations on integers
- Leafina: Potency of Kakawate leaves, fishbone meal and saba banana peel compost soil amendment to the water holding capacity of loam soil
- Problem-based learning strategies and critical thinking skills among pre-service teachers
- Eating habits, nutrition literacy, and mathematics performance of junior high school students
- Effectiveness of project COUNTS in improving students’ numeracy skills
- Exploring students’ procedural fluency and written adaptive reasoning skills in solving open-ended problems
- Compressive strength and cost analysis of concrete hollow blocks with upcycled plastics as replacement for choker aggregates
- Transforming SME operations with real-time mobile POS and Firebase integration