• Sofia Shireen N. K. Ali Ph.D. Research Scholar, (Fiji), Mangalore University
  • Dr. (Mrs.) Flosy C. R. D’Souza Associate Professor and Research Guide St. Ann’s College of Education, (Autonomous) Mangalore India


LSI –Learning Style Inventory, ATM-Achievement Test in Mathematics, Geogebra, Cognitive Apprenticeship model, Geometry


Mathematics plays a significant role in accelerating the social, economic, and technological development of a nation. It is evident in the developing countries, as the nations are rapidly moving towards globalization in all aspects. The world of today tends more profoundly on science and technology demands with additional mathematical knowledge on the part of its people. Thus it is necessary to prepare the child with a strong base of Mathematical knowledge to face the challenges of the modern technological society. This study was conducted to scrutinize the effects of Cognitive Apprenticeship model with GeoGebra and its Effect on Academic Achievement in Geometry of on year eight rural school students. This study was conducted with eighty in two intact classes in Lautoka District in Fiji. The school was selected randomly using the lottery method. After selection the students were classified into two groups one as ICTCAM group and the other as CI group. There were 40 students in each group, and intelligence was kept as Covariate. It was an experimental study of Two by three factorial design was used. The students were also classified into three types of learners according to their standards of learning styles through the LSI Ali.sofia&Dsouza.Flosy (2017).As a pretest, both the groups were tested for Achievement through the ATM prepared by Ali.sofia&Dsouza.Flosy (2017), which was designed according to the Geometry syllabus of year eight. Data was collected, and then treatment was done with 40 lessons of one hour using the instructional package developed by the investigator and validated by experts with the ICTCAM Group, while the CI group was taught with 40 lessons with a duration of 45 mins using the CI instructional Package. The data was collected for the post-test of ATM. The pre and post-test were developed using the new revised Bloom’s Taxonomy of Verbs, which had a total of 60 multiple-choice questions. Two way ANCOVA was used for data analysis.

This study proves that there were significant differences in the Achievement in Mathematics of year eight students of rural schools after partialing out the effect of Intelligence. According to the findings of this study, it was recommended that Cognitive Apprenticeship model with GeoGebra supportive teaching methods should be adopted and used in teaching Geometry in year eight level as it develops the high order and low order thinking skills of new revised Bloom’s Taxonomy of verbs and improves the Achievement results in Mathematics.


I. Battista, M. T. (2008). Development of the Shape Makers Geometry Micro-world: design principles and research In M. K. Heid & G. W. Blume (Eds.), Research on Technology and the Teaching and Learning of Mathematics: Cases and perspectives (Vol. 2, pp. 131-156). Charlotte, NC: Information Age.

II. Clements, D. H., Sarama, J., and DiBiase, A. M. (Eds.). (2004). Engaging young children in mathematics: Standards for early childhood mathematics education. Routledge.

III. Collins, A., Brown, J. S., & Newman, S. (1989). Cognitive Apprenticeship: Teaching the Crafts of Reading, Writing, and Mathematics. In Resnick, L. B. (ed.), Knowing, Learning, and Instruction: Essays in honor of Robert Glaser. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc, pp. 453-494.

IV. Collins, A., Brown, J. S., & Holum, A. (1991).Cognitive apprenticeship: Making thinking visible. American Educator: The Professional Journal of the American Federation of Teachers, 15(3), 6-11, 38-46.

V. Tharp, R. (1993). The institutional and social context of educational reform: Practice and reform. In E. A. Forman, N. Minnick, & C. A. Stone (Eds.), Contexts for learning: Sociocultural dynamics in children’s development (pp. 269–282). New York: Cambridge University Press.

VI. Tharp, R., & Gallimore, R.(1988). Rousing minds to life: Teaching, learning, and schooling in a social context. Cambridge: Cambridge University Press.

VII. Trouche, L., Drijvers, P., Gueudet, G., & Sacristan, A. I. (2013).Technology-driven Developments and Policy implications for Mathematics Education. In M. A. Clements, A. J. Bishop, C. Keitel, J. Kil-Patrick, & F. K. S. Leung (Eds.), Third international handbook of mathematics education SE-24 (Vol. 27, pp. 753–789). New York, NY: Springer. DOI: 10.1007/978-1-4614-4684-224.

VIII. Gallimore, R., & Tharp, R. (1990).Teaching mind in society: Teaching, schooling, and literate discourse. In L. C. Moll (Ed.), Vygotsky and education: Instructional implications and applications of sociohistorical psychology. New York: Cambridge.

IX. Geogebra. Free Mathematics Software for Learning and Teaching. Retrieved from

X. Goodwin, K. (2008). The impact of interactive multimedia on kindergarten students’ representations of fractions. Issues in Educational Research, 18(2), 103-117.

XI. Gutiérrez, A., and Boero, P. (Eds.). (2006). Handbook of research on the psychology of mathematics education: Past, present, and future. Sense publishers.

XII. Harris, J., Mishra, J. & Koehler, M. (2009). Teachers ‘Technological Pedagogical Content Knowledge and learning activity types: Curriculum-based technology integration Reframed. Journal of Research on Technology in Education, 41(4), 393-416.

XIII. Hohenwarter, M. (2002). GeoGebra - a software system for dynamic geometry and algebra of the plane (English: GeoGebra - a software system for dynamic geometry and algebra in the plane). Master's thesis, University of Salzburg.

XIV. Martín-Caraballo, A. M., and Tenorio-Villalón, Á. F. (2015). Teaching Numerical Methods for Non-linear Equations with GeoGebra-Based Activities. Mathematics Education, 10(2), 53-65.

XV. Olive, J., Makar, K., Hoyos, V., Kee Kor, L., Kosheleva, O., & Sträße, R. (2010).Mathematical knowledge and practices are resulting from access to digital technologies.In C. Hoyle & J. B. Lagrange (Eds.), Mathematics Education and Technology Rethinking the terrain (Vol. 8, pp. 133-177).

XVI. Pitta-Pantazi, D., Gray, E., and Christou, C. (2004). Elementary school students’ mental representations of fractions. In Proceedings of the 28th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 41-48).

XVII. Ramatlapana, K. A. (2016). Prospective Mathematics Teachers ‘circle geometry technological content knowledge of teaching in a GeoGebra-based. In W. Mwakapenda, T. Sedumedi, and M. Makgato. (Eds.) Proceedings of the 24th Annual Conference of the Southern African Association for Research in Mathematics, Science and Technology Education (SAARMSTE), 12 – 15 January 2016, (pp. 208 - 220). Pretoria, South Africa.

XVIII. The National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author.

XIX. Thambi, N., and Eu, L. K. (2013). Effect of Students’ Achievement in Fractions using GeoGebra. SAINSAB. 16. 97-106.

XX. Van Heiele,P.M.(1986).Structure Insight: A theory of Mathematics.Orlando,Fla: Academic Press.

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How to Cite

Sofia Shireen N. K. Ali, & Dr. (Mrs.) Flosy C. R. D’Souza. (2019). COGNITIVE APPRENTICESHIP MODEL WITH GEOGEBRA AND ITS EFFECT ON ACADEMIC ACHIEVEMENT IN GEOMETRY OF ON YEAR EIGHT RURAL SCHOOL STUDENTS. International Education and Research Journal (IERJ), 5(10). Retrieved from