DEVELOPING MATHEMATICAL THINKING THROUGH ACTIVITY BASED HEURISTIC APPROACH: A CASE OF MAKING CONNECTIONS BETWEEN PATTERNS, SEQUENCES AND GRAPHS
Abstract
Teaching approaches is a key factor that contributes to the improvement of learner achievement. Moreover, learning mathematics through activities helps learners to develop mathematical thinking which is the foundation for development and a basis for sustainable development in mathematics. In this study, 77 third year pre-service mathematics teachers at Makerere University were provided with an experience of utilizing the activity based heuristic approach in making connections between patterns, sequences and graphs with the intention of developing their mathematical thinking. The participants were subjected to a whole-class discussion after which they reflected on the discussion. The whole-class discussion was videotaped and data were collected through observation of the video and making reflective notes. Having used observation narratives and thematic analysis of reflections from the whole-class discussion through the lens of the conversational framework, it was observed that learning mathematics through activities helps learners to develop mathematical thinking which is the foundation for their development and a basis for their sustainable development in mathematics. The learners are engaged in the learning process and besides, develop several other competences like communication, creativity and innovation, presentation and working in a team. From the pre-service teachers’ perspective, the major implication of activity based heuristic approach is the need for an exigent change of the pedagogical training approaches for Makerere University’s pre-service mathematics teachers.
Article visualizations:
Keywords
Full Text:
PDFReferences
Abraham, M. R. (2008). Importance of a theoretical framework for research. ACS Symposium Series, 976, 47-66.
Adams Becker, S., Cummins, M., Davis, A., Freeman, A., Hall Giesinger, C., & Ananthanarayanan, V. (2017). NMC Horizon report: 2017 Higher Education Edition. Austin, Texas: The New Media Consortium.
Adom, D., Emad, K. H., & Adu-Agyem, J. (2018). Theoretical and conceptual framework: mandatory ingredients of a quality research. International Journal of Scientific Research, 7(1), 438-441.
Batiibwe, M. S. K. (2019). Teachers’ pedagogical content knowledge and teaching of Statistics in lower secondary schools in Wakiso District. Journal of Education and Practice, 10(25), 93-101.1096.
Batiibwe, M. S. K., Bakkabulindi, F. E. K., & Mango, J. M. (2018). “How do the constructs of the TPACK framework relate with the use of ICT in pedagogy among teachers of mathematical disciplines in universities in Uganda?” African Journal of Education, Science and Technology, 5(1): 1-11.
Bakker, A., Smit. J., & Wegerif (2015). Scaffolding and dialogic teaching in mathematics education: Introduction and review. ZDM Mathematics Education, 47(7), 1047-1065.
Bonwell, C., & Elison, J. (1991). Active learning: creating excitement in the classroom. ASHE-RIC Higher Education Report. Retrieved from www.oid.ucla.edu/../active.learning-eric on 22 August 2019.
Celik, H. C. (2018). The effects of activity based learning on sixth grade students’ achievement and attitudes towards mathematics activities. Eurasia Journal of Mathematics, Science and Technology Education, 14(5): 1963-1977.
Cox, S. E. (2014). Perceptions and influence behind teaching practices: Do teachers teach as they were taught? All Theses and Dissertations, 5301. http://scholarsarchive.byu.edu/etd/5301.
Churches, A. (2008). Bloom’s digital taxonomy. Retrieved from https://www.researchgate.net/publication/228381038_Bloom's_Digital_Taxonomy Accessed 4 March 2019.
Delima, N. (2017). A relationship between problem solving ability and students’ mathematical thinking. Journal of Mathematics Education, 6(1), 21-28.
Delima, N., Rahmah, M. A., & Akbar, A. (2018). The analysis of students’ mathematical thinking based on their mathematics self-concept. Journal of Physics: Conf Series, 1108, 1-8. Doi: 10.1088/1742-6596/1108/1/012104.
Dolev, S., & Even, R. (2015). Justifications and explanations in Israeli 7th grade math textbooks. International Journal of Science and Mathematics Education, 13(2): 309-327.
D’souza, Q. (2016). Activity based learning. Retrieved from https://www.youtube.com/watch?v=eCXHVTcAS7k on 14 July 2019.
Eko, Y. S., Prabawanto, S., & Jupri, A. (2018). The role of writing justification in mathematics concept: The case of trigonometry. Journal of Physics: Conference Series, 1097012146.
Festus, A. B. (2013). Activity-based learning strategies in the mathematics classrooms. Journal of Education and Practice, 4(13), 8-15.
Fuson, K. C. (2019). Relating math words, visual images and math symbols for understanding and competence. International Journal of Disability, Development and Education, 66(2): 119-132.
Goodman, M. S., Li, Y., & Tiwari, R. C. (2011). Detecting multiple change points in piecewise constant hazard functions. Journal of Applied Statistics, 38(11): 2523-2532.
Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., & Altman, D. G. (2015). Statistical tests, p values, confidence intervals, and power: A guide to misinterpretations. European Journal of Epidemiology, 31: 337-350.
Guba, E. G., & Lincoln, Y. S. (1994). Competing paradigms in qualitative research. In N. K. Denzin and Y. S. Lincoln (Eds.), Handbook of Qualitative Research. (pp. 105-117). Thousand oaks, CA: Sage Publications Inc.
Hudson, B., Henderson, S., & Hudson, A. (2014). Developing mathematical thinking in the primary classroom: Liberating students and teachers as learners of mathematics. Journal of Curriculum Studies, 47(3): 374-398.
Kargar, M., Tarmizi, R. A., & Bayart, S. (2010). Relationship between mathematical thinking, mathematics anxiety and mathematics attitudes among university students. Procedia Social and Behavioral Sciences, 8, 537-542. doi: 10.1016/j.sbspro.2010.12.074
Karigi, M. W., & Tumuti, S. (2015). Students and teachers attitude factors contributing to poor performance in mathematics in K. C. S. E in selected public secondary schools in Kiambaa Division of Central Province, Kenya. The Strategic Journal of Business & Change Management, 2(58): 317-332.
Laurillard, D. (2002). Rethinking university teaching: A conversational framework for the effective use of learning technologies. London: Routledge Falmer.
Laurillard, D. (2008). The teacher as action researcher. Using technology to capture pedagogic form. Studies in Higher Education, 33(2): 139-154.
Laurillard, D. (2012). Teaching as a design science: Building pedagogical patterns for learning and technology. New York, NY: Routledge.
Li, N., Mok, I, A, C., & Cao, Y. (2019). The evolution of mathematical thinking in Chinese mathematics education. Mathematics, 7(297), 1-18. Doi: 10.3390/math7030297.
Linchevski, L. (1995). Algebra with numbers and arithmetic with letters: A definition of pre-algebra. The Journal of Mathematical Behavior, 14(1): 113-120.
Mafabi, D. (2018). Malpractice in national examinations killing the quality of education in Uganda. http://www.pmldaily.com/news/education/2018/11/malpractice-in-national-examinations-killing-the-quality-of-education-in-uganda.html
Nabatte, P. (2019). Maths teachers urged to adopt modern methods of teaching to enhance students’ abilities. https://news.mak.ac.ug/2019/01/maths-teachers-urged-adopt-modern-methods-teaching-enhance-students-abilities
Nangonzi, Y. (2019). Students failing Museveni’s science dream. The Observer, March 7, 2019.
National Curriculum Development Centre (2018). O level curriculum. https://www.ncdc.go.ug/content/o-level-curriculum. Accessed 2 May 2019
Nepal, B. (2016). Impact of gender and location on mathematical thinking and mathematics achievement. Journal of Advanced Academic Research, 3(3), 11-21.
Ng’ambi, D., Gachago, D., Ivala, E., Bozalek, V., & Watters, K. (2014). Emerging technologies in South African Higher Education Institutions: Towards a teaching and learning practice. https://vula.uct.ac.za/access/content/group/8ff4f1d3-4a8... Retrieved on March 18, 2014.
Ngware, M., Hungi, N., Mahuro, G., Mutsiya, M., & Abuya, B. (2016). The Quality of Education in Uganda: A Case of Iganga and Mayuge Districts. Graphic Version, Nairobi: APHRC.
Pashler, H., McDaniel, M., Rohrer, D., & Bjork, R. (2008). Learning styles: Concepts and evidence. Psychological Science in the Public Interest, 9(3): 105-119.
Pokhrel, T. R. (2018). Activity Based Mathematics Instruction: Experiences in addressing the21st century skills. Journal of Mathematics Education, 11(1): 46-61. http://doi.org/10.26711/007577152790020.
Polya, G. (1973). How to solve it: A new aspect of mathematical model. (2nd ed.). Princeton, New Jersey: Princeton University Press.
Reisman, A., Kavanagh, S. S., Monte-Sano, C., Fogo, B., McGrew, S. C., Cipparone, P., &
Simmons, E. (2018). Facilitating whole-class discussions in History: A framework for preparing teacher candidates. Journal of teacher Education, 69(3), 278-293. doi: 10.1177/0022487117707463
Schwandt, T. A. (1994). Constructivist, interpretivist approaches to human inquiry. In N. K. Denzin and Y. S. Lincoln (Eds.), Handbook of Qualitative Research. (pp. 105-117). Thousand oaks, CA: Sage Publications Inc.
Sharples, M., de Roock, R., Ferguson, R., Gaved, M., Herodotou, C., Koh, E., Kukulska-Hulme, A., Looi, C-K, McAndrew, P., Rienties, B., Weller, M., & Wong, L. H. (2016). Innovating Pedagogy 2016: Open University Innovation Report 5. Milton Keynes: The Open University.
Siemens, G. (2005). Connectivism: A learning theory for the digital age. International Journal of Instructional Technology and Distance Learning, 2(10): 3-10.
Simpson, A. (2003). Teaching and assessing skills in mathematics. The Edinburgh Building, Cambridge, UK: Cambridge University Press.
Singh, P., Teoh, S. H., Cheong, T. H, Rasid, N. S. M., Kor, L. K., & Nasir, N. A. M. (2018). The use of problem-solving heuristics approach in enhancing STEM students’ development of mathematical thinking. International Electronic Journal of Mathematics Education, 13(3), 289-303.
Staples, M. E., Bartlo, J., & Thanheiser, E. (2012). Justification as a teaching and learning practice: Its (potential) multifaceted role in middle grades mathematics classrooms. The Journal of Mathematical Behavior, 31: 447-462.
Stern, R., Kalech, M., & Felner, A. (2012). Finding patterns in an unknown graph. Al Commun, 25: 229-256.
Taylor, S. J., & Bogdan, R. (1998). Introduction to qualitative research methods: A guidebook and resource (3rd Ed). Hoboken, NJ: John Wiley & Sons Inc.
Uganda Technology and Management University. (2016). Curriculum review report on lower secondary teacher education. Uganda Technology and Management University. Kampala: Author
Uwezo. (2016). Are Our Children Learning? Uwezo Uganda 6th Learning Assessment Report. Kampala: Twaweza East Africa.
Yorulmaz, A., Altintas, S., & Sidekli, S. (2017). Investigation of the effects of mathematics thinking states of form teachers on their mathematics teaching anxieties. European Journal of Educational Research, 6(4), 485-493.
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
Zhu, Y., Yu, W., & Cai, J. (2018). Understanding students’ mathematical thinking for effective teaching: A comparison between expert and non-expert Chinese elementary mathematics teachers. EURASIA Journal of Mathematics, Science and Technology Education, 14(1), 213-224.
DOI: http://dx.doi.org/10.46827/ejes.v0i0.2889
Refbacks
- There are currently no refbacks.
Copyright (c) 2020 Marjorie Sarah Kabuye Batiibwe
This work is licensed under a Creative Commons Attribution 4.0 International License.
Copyright © 2015-2023. European Journal of Education Studies (ISSN 2501 - 1111) is a registered trademark of Open Access Publishing Group. All rights reserved.
This journal is a serial publication uniquely identified by an International Standard Serial Number (ISSN) serial number certificate issued by Romanian National Library (Biblioteca Nationala a Romaniei). All the research works are uniquely identified by a CrossRef DOI digital object identifier supplied by indexing and repository platforms. All authors who send their manuscripts to this journal and whose articles are published on this journal retain full copyright of their articles. All the research works published on this journal are meeting the Open Access Publishing requirements and can be freely accessed, shared, modified, distributed and used in educational, commercial and non-commercial purposes under a Creative Commons Attribution 4.0 International License (CC BY 4.0).
