Abstract
In this paper, we propose some organizing principles that can be useful for high schools or bachelor mathematics teachers when designing technology-based instructional tasks. It is widely accepted that tasks are the most important aspect to promote students’ mathematical understanding, since tasks offer opportunities to attain relevant sensorial experiences fostering the construction of mental images as sources of meanings for mathematical concepts. In this vein, we reflect on the work developed by three bachelor mathematics teachers who participated in a problem solving seminar. The main points identified during task design involved recognizing how mathematical concepts are structured around the task, and which are needed to approach it, and proposing a hypothetical learning trajectory in which technology plays a role as amplifier and reorganizer of cognitive processes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Watson, A., Minoru, O.: Themes and issues in mathematics education concerning task design: Editorial introduction. In: Watson, A., Ohtani, M. (eds.) Task Design in Mathematics Education: An ICMI Study 22, pp. 3–18. Springer, Cham (2015)
Schoenfeld, A.H.: Mathematical Problem Solving. Academic Press, Orlando (1985)
Naaranoja, Marja, Uden, Lorna: Eight R’s – case study. In: Uden, L., Liberona, D., Welzer, T. (eds.) LTEC 2015. CCIS, vol. 533, pp. 67–76. Springer, Heidelberg (2015)
Pea, R.D.: Cognitive technologies for mathematics education. In: Schoenfeld, A. (ed.) Cognitive Science and Mathematics Education, pp. 89–122. Erlbaum, Hillsdale (1987)
Jensen, E.: Teaching with the Brain in Mind, 2nd edn. Association for Supervision and Curriculum Development, Alexandria (2005)
Beard, C., Wilson, J.P.: Experiential Learning: A Handbook for Education, Training and Coaching. KoganPage, London (2013)
Zull, J.A.: The Art of Changing the Brain: Enriching the Practice of Teaching by Exploring the Biology of Learning. Stylus, Sterling (2002)
Vygotsky, L.S.: Thought and Language. MIT Press, Cambridge (1962)
Vygotsky, L.S.: Mind in Society: The Development of the Higher Psychological Processes. Harvard University Press, Cambridge (1978)
Santos-Trigo, M., Reyes-Rodriguez, A., Espinosa-Perez, H.: Musing on the use of dynamic software and mathematics epistemology. TEAMAT 26(4), 167–178 (2007)
Polya, G.: How to Solve it. Princeton University Press, Princeton (1945)
Leung, A., Bolite-Frant, J.: Designing mathematics tasks: the role of tools. In: Watson, A., Ohtani, M. (eds.) Tasks Design in Mathematics Education, pp. 191–228. Springer, Cham (2015)
Santos-Trigo, M., Reyes-Rodriguez, A.: The use of digital technology in finding multiple paths to solve and extend an equilateral triangle task. Int. J. Math. Educ. Sci. Tech. 47(1), 58–81 (2016)
Santos-Trigo, M.: La Resolución de Problemas Matemáticos: Fundamentos Cognitivos. Trillas, México (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Barrera-Mora, F., Reyes-Rodriguez, A. (2016). Designing Technology-Based Tasks for Enhancing Mathematical Understanding Through Problem Solving. In: Uden, L., Liberona, D., Feldmann, B. (eds) Learning Technology for Education in Cloud – The Changing Face of Education. LTEC 2016. Communications in Computer and Information Science, vol 620. Springer, Cham. https://doi.org/10.1007/978-3-319-42147-6_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-42147-6_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42146-9
Online ISBN: 978-3-319-42147-6
eBook Packages: Computer ScienceComputer Science (R0)