Concrete Pictorial Abstract Approach Use in Teaching Mathematics on Secondary Students’ Participation in Six Selected Schools in Kicukiro District, Rwanda

Rozata Umuhoza; Theoneste Hakizimana

doi:10.51867/ajernet.5.4.102

Authors

Umuhoza Rozata
umuhosette@gmail.com
University of Rwanda
Hakizimana Theoneste University of Rwanda https://orcid.org/0009-0005-2566-174X

Keywords:

Abstract, Concrete Materials, Students’ Participation, Pictorial

Abstract

Mathematics is pivotal in science and technology, serving as a gateway discipline. Effective teaching should foster positive attitudes by engaging students with real-world examples. The SPECIFIC objective of this study was to investigate how the use of Concrete-Pictorial -Abstract approach in mathematics subject affects students’ participation in selected schools in Kicukiro District. This study was based on investigating the use concrete pictorial abstract approach in teaching mathematics on secondary students’ participation in selected ordinary secondary schools in Kicukiro district. The population targeted in this study was all 2520 senior two students, 51 mathematics teachers and 36 directors of studies and the sample size comprised 540 students, 6 directors of studies and 6 mathematics teachers. This study applied constructivism theory. A qualitative research approach was used since the topic for research requires an in-depth study in a real situation together with descriptions which can be done better in words than in numbers. Instruments used in data collection in this research are interview and observation. To analyze the data obtained during interview and observation, this study used content analysis. Content analysis is a technique utilized for organizing spoken or written materials into predetermined categories with similar meanings. Findings reveal that when teachers use the CPA approach in teaching mathematics, students participate in lessons through manipulating concrete materials. The stage of pictorial use enables students to develop critical thinking by transitioning from concrete to abstract concepts. This final step involves students using numbers and symbols. At this step the findings show that the students try to make general rule by using numbers and symbols though students seem less active than during the steps of using concrete and pictorial. Conclusion, learners participate in learning mathematics and improve their performance through the usage of concrete pictorial abstract approach, by using tangible materials and visuals aids. This research will help the teachers who teach mathematics to involve the students in order to make the class active and stick on the learner centered approach, by engaging the students in all levels, and it will help both teachers and students to understand that mathematics concepts are tangible by using the materials, and this will attract students’ interest and participation which lead to performance.

Author Biography

Hakizimana Theoneste, University of Rwanda

A masters degree student at mount Kenya University.

Dimensions

REFERENCES

Alvares, B., Gillies, J., & Biadsher, M. (2009). Beyond basic education: Secondary education in the developing world. Washington, D.C.: World Bank.

Arends, R. (2021). Activities for Teaching Creativity and Problem Solving (3rd ed.). San Francisco: Pfeiffer.

Ban, Y. (2021). Teaching Mathematics Through Pictorial Representation (2nd ed.). London: Adventure work place.

Belhu, H. S. (2017). Factors Affecting Learning Mathematics in the Case of Assosa University Collage of Natural Science. International Journal of Education, Culture and Society, 2(1), 6-12. https://doi.org/10.11648/j.ijecs.20170201.12 DOI: https://doi.org/10.11648/j.ijecs.20170201.12

Black, J. B., Segal, A., Vitale, J., & Fadjo, C. L. (2012). Embodied cognition and learning environment design. In Theoretical foundations of learning environments (2nd ed., pp. 26). Routledge.

Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (4th ed.). Pearson.

Dachi, H. A., & Garrett, R. M. (2003). Child labour and its impact on children's access to and participation in primary education: A case study from Tanzania (Education Research Paper No. 48). Department for International Development (DFID). https://ageconsearch.umn.edu/record/12848.

Iliev N., & D'Angelo F. (2014). Teaching Mathematics through Multicultural Literature. Teaching Children Mathematics, 20(7), 452-457. https://doi.org/10.5951/teacchilmath.20.7.0452 DOI: https://doi.org/10.5951/teacchilmath.20.7.0452

Delaney, S. (2020). Number in the senior primary classes: Commissioned research paper. Dublin: National Council for Curriculum and Assessment (NCCA).

Dietrich, C., Lichtenberger, E., & Kamalludeen, R. (2017). Predicting community college outcomes: Does high school CTE participation have a significant effect? Journal of Career and Technical Education, 31(1). https://doi.org/10.21061/jcte.v31i1.1506 DOI: https://doi.org/10.21061/jcte.v31i1.1506

Fan, W., & Williams, C. M. (2010). The effects of parental involvement on students' academic self-efficacy, engagement, and intrinsic motivation. Educational Psychology, 30(1), 53-74. https://doi.org/10.1080/01443410903353302 DOI: https://doi.org/10.1080/01443410903353302

Fleming, C. M. (2019). Teaching: a psychological analysis (1st ed.). London: Routledge press.

Hidayah, I., Suriato, & Dwijanto. (2016). The Role of Manipulatives Usage in Mathematics Learning of Primary Education with Scientific Approach towards the Students' Thinking Ability. International Journal of Applied Business and Economic Research, 11(3), 649-662.

Fraenkel, J., Wallen, N., & Hyun, H. (2011). How to design and evaluate research in education (60th ed.). McGraw-Hill.

Jennifer, L. (2021). The Role of Mathematic Manipulatives in the mathematics Classroom. Northwestern College, Iowa, 2(1), 1-16.

Kothari, C. R. (2004). Research methodology: Methods and techniques. New Age International.

Kurniawan, H., Budiyono, Sajidan, & Siswandari. (2020). Concrete-pictorial-abstract approach on student's motivation and problem-solving performance in algebra. Universal Journal of Educational Research, 8(7), 3204-3212. https://doi.org/10.13189/ujer.2020.080749 DOI: https://doi.org/10.13189/ujer.2020.080749

Maniraho, J. F. (2017). The pedagogical content knowledge (PCK) of Rwandan grade six mathematics teachers and its relationship to student learning. African Journal of Educational Studies in Mathematics and Sciences, 14, 223-234.

Terry, M. (2008). The effects that family members and peers have on students' decisions to drop out of school. Educational Research Quarterly, 31(3), 26-38.

Park, J., Emily, B. C., & Marisa, F. H. (2021). Using the virtual-representational-abstract with overlearning instructional sequence to students. The Journal of Special Education, 2(1), 39-52. https://doi.org/10.1177/0022466920912527 DOI: https://doi.org/10.1177/0022466920912527

Schoenfeld, A. H. (2019). Learning to think mathematically: Problem Solving, Metacognition, and Sense-Making in mathematics. Handbook for Research on Mathematics Teaching and Learning, 3(1), 334-370.

Sarama, J., & Clement , D. H. (2016). pysical and virtual manipulatives: what is "concrete". International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives, 2(1), 71-93. https://doi.org/10.1007/978-3-319-32718-1_4 DOI: https://doi.org/10.1007/978-3-319-32718-1_4

Sung, W., Ahn, J. A., & Black, J. (2017). Introducing computational thinkling to young learners. ResearchGate, 2(1), 443-463.

https://doi.org/10.1007/s10758-017-9328-x DOI: https://doi.org/10.1007/s10758-017-9328-x

Ukobizaba, N. M. (2019). Insights of teachers and students on mathematics teaching and learning. African Journal of Educational Studies in Mathematics and Science, 2(1), 24-36.

UNESCO. (2015). Educatuion For All: Achievement and Challenges. Paris: Unesco.

Watt, D. T., & George, L. (2021). Investigating the Impact of Using Manipulatives on students' performance. Caribbean Journal of Education, 42(2), 192-230.

Willingham, D. (2018, October 10). How do Manipulatives Help Students Learn. Retrieved October 28, 2022, from National Centre for Excellence in the Teaching of Mathematics: http:www.ncetm.org.uk