Kagenyi David Macharia


The primary objective of the educational process is the development of the thinking of learners. This paper deals with the development of learners' thinking in mathematics, in the transition from the acquisition of calculation algorithms to the acquisition of the algorithmic rules. Algorithmic rules need to be understood and it means the need to change the way of teaching. A substantial change in teaching is the use of question-answer system. This system is described in the paper in terms of pedagogy and psychology, and all these facts lead to comprehensive view of the application of the system in teaching mathematics. In the next part of the article we describe the features of learners thinking. When the method of substitution is taught properly, these features enrich the learners‘ thinking. The method of substitution is the first algorithmic rule.


Article visualizations:

Hit counter



mobile phones; mobile learning; m education, educational outcomes; new learning, new teaching

Full Text:



Alam, S., & Islam, Y. M. (2008, July). Virtual interactive classroom (VIC) using mobile technology at the Bangladesh Open University (BOU). Paper presented at the 5th Pan-Commonwealth Forum on Open Learning. Retrieved from http://wikieducator.org/images/4/45/PID_563.pdf

Batchuluun, B., Ramos, A. J., & Trinona, J. P. (2007). Evaluations of distance-based delivery methods: Report C, mobile technology in nonformal distance education. In J. Baggaley & T. Belawati (Eds.), Distance education technology in Asia (pp. 131-149). Lahore: Virtual University of Pakistan.

Brown, T. (2003, June). The role of m-learning in the future of e-learning in Africa? Paper presented at the 21st ICDE World Conference, Hong Kong.

dela Pena-Bandalaria, M. (2007). Impact of ICTs on open and distance learning in a developing country setting: The Philippine experience. International Review of Research in Open and Distance Learning, 8(1). Retrieved from http://www.irrodl.org/index.php/irrodl/article/view/334/793

Dhanarajan, T. (2009). Education for all in the digital age. In S. Akhtar & P. Arinto (Eds.), Digital review of Asia Pacific 2009-2010 (pp. 45-49). New Delhi: SAGE Publications.

Dighe, A., Hakeem, H., & Shaeffer, S. (2009). ICTs in non-formal education in Asia Pacific. In S. Akhtar & P. Arinto (Eds.), Digital review of Asia Pacific 2009-2010 (pp. 59-66). New Delhi: SAGE Publications.

Donner, J. (2008). Research approaches to mobile phone use in the developing world: A review of literature. The Information Society, 24, 140-159.

Frohberg, D, Göth, C., & Schwabe, G. (2009). Mobile learning projects – a critical analysis of the state of the art. Journal of Computer Assisted Learning, 25, 307–331.

Geddes, S. J. (2004). Mobile learning in the 21st century: Benefits for learners. Knowledge Tree. Retrieved from http://knowledgetree.flexiblelearning.net.au/edition06/download/Geddes.pdf

Islam, Y. M., Ashraf, M., Rahman, Z., & Rahman, M. (2005). Mobile telephone technology as a distance learning tool. Proceedings of the Seventh International Conference on Enterprise Information Systems, Miami, USA, May 25-28, 226-232.

Islam, Y. M., Rahman, Z., Razzaq, S. S., Sayed, M. A., & Zaman, S. (2006). Effect of feedback during lecture style delivery both in a face-to-face classroom & during a distance education television session in a developing country like Bangladesh without the use of Internet. Proceedings of the Sixth IEEE International Conference on Advanced Learning Technologies, 469-471. Available from IEEE Xplore Digital Library: http://ieeexplore.ieee.org/Xplore/guesthome.jsp

John-Harmen Valk, Ahmed T. Rashid, and Laurent Elder

Pan Asia Networking, IDRC, Canada (2010) www.irrodl.org/index.php/irrodl/article/view/794/1487

Kam, M., Kumar, A., Shirley, J., Mathur, A., & Canny, J. (2009). Improving literacy in rural India: Cellphone games in an after-school program. Proceedings of IEEE/ACM Conference on Information and Communication Technology and Development (ICTD ’09), Doha, Qatar, April 17-19. Retrieved from http://www.cs.cmu.edu/~mattkam/publications/ICTD2009.pdf

Keegan, D. (2002). The future of learning: From elearning to mlearning. Hagen, Germany: FernUniversitat. Retrieved from http://www.eric.ed.gov/ERICDocs/data/ericdocs2sql/content_storage_01/0000019b/80/1a/b6/8e.pdf

Kukulska-Hulme, A., & Traxler, J. (2007). Designing for mobile and wireless learning. In H. Beetham & R. Sharpe (Eds.), Rethinking pedagogy for a digital age: Designing and delivering e-learning (pp. 180-192). London: Routledge.

Motlik, S. (2008). Mobile learning in developing nations. International Review of Research in Open and Distance Learning, 9(2). Retrieved from http://www.irrodl.org/index.php/irrodl/article/view/564/1071

Nyiri, K. (2002, August). Towards a philosophy of m-learning. Paper presented at the IEEE International Workshop on Wireless and Mobile Technologies in Education, Vaxjo, Sweden. Retrieved from http://21st.century.phil-inst.hu/eng/m-learning/nyiri_m-learn_philos.htm

Orbicom (2007). Emerging development opportunities: The making of information societies and ICT markets. Ottawa: IDRC.

Pouezevara, S. L., & Khan, R. (2007a). Learning communities enabled by mobile technology: A case study of school-based, in-service secondary teacher training in rural Bangladesh. In Innovative information and communication technology in education and its potential for reducing poverty in the Asia and Pacific region (Appendix 11). Asian Development Bank. Retrieved from http://www.adb.org/Documents/Reports/Consultant/39035-REG/appendix11.pdf

Ramos, A. J. (2008). Final report for sub-project #2, Project MIND: The viability of mobile SMS technologies for non-formal distance learning in Asia. Philippines: Molave Development Foundation, Inc.

Ramos, A. J., & Trinona, J. P. (2009). Mobile technology in nonformal distance education. In J. Baggaley & T. Belawati (Eds.), Distance education technology in Asia (pp. 231-56). Lahore: University of Pakistan.

Sharples, M., Taylor, J., & Vavoula, G. (2005, October). Towards a theory of mobile learning. Paper presented at 4th World Conference on mLearning, Cape Town, South Africa. Retrieved from http://www.mlearn.org.za/CD/papers/Sharples-%20Theory%20of%20Mobile.pdf

Sharples, M., Taylor, J., & Vavoula, G. (2007). A theory of learning for the mobile age. In R. Andrews & C. Haythornthwaite (Eds.), The Sage handbook of e-learning research (pp. 221-247). London: Sage Publications.

Samarajiva, R., & Zainudeen, A. (Eds.). (2008). ICT infrastructure in emerging Asia. Ottawa: IDRC.

Traxler, J. (2007). Defining, discussing and evaluating mobile learning: The moving finger writes and having writ . . . The International Review of Research in Open and Distance Learning, 8(2). Retrieved from http://www.irrodl.org/index.php/irrodl/article/viewArticle/346

Traxler, J., & Dearden, P. (2005). The potential for using SMS to support learning and organisation in Sub-Saharan Africa. Retrieved from http://www.wlv.ac.uk/PDF/cidt-article20.pdf

United Nations. (2008). The Millennium Development Goals Report. New York: UNDESA. Retrieved from http://mdgs.un.org/unsd/mdg/Resources/Static/Products/Progress2008/MDG_Report_2008_En.pdf#page=14

van Weert, T. (2005). Lifelong learning in knowledge society: Implications for education. In T. J. van Weert (Ed.), Education and the knowledge society: Information technology supporting human development (pp. 15-25). Boston: Kluwer Academic Publishing.

Visser, L., & West, P. (2005). The promise of m-learning for distance education in South Africa and other developing nations. In Y. L. Visser, L. Visser, M. Simonson, & R. Amirault (Eds.), Trends and issues in distance education: International perspectives (pp. 117-129). Greenwich, CT.: Information Age Publishing.

Wagner, D., & Kozma, R. (2005). New technologies for literacy and adult education: A global perspective. Paris: UNESCO Publishing.

World Bank (n.d.). Country groups. Retrieved from http://web.worldbank.org/WBSITE/EXTERNAL/DATASTATISTICS/0,,contentMDK:20421402~pagePK:64133150~piPK:64133175~theSitePK:239419,00.html


DOI: http://dx.doi.org/10.46827/ejoe.v0i0.2397


  • There are currently no refbacks.

Copyright © 2016-2023. European Journal of Open Education and E-learning Studies (ISSN 2501-9120) is a registered trademark of Open Access Publishing GroupAll 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 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).