The Use of Digital Technology in Extending Mathematical Problem Solving Reasoning

Abstract

Abstract. The incorporation of digital technologies (both multiple purpose and mathematics action technologies) in mathematical learning environments can foster and extend discussions among learners and teachers even beyond class time. That is, learners not only keep reflecting on mathematical ideas or problems; but also they can review or consult related online resources. Similarly, the use of dynamic geometry systems provides affordances to construct dynamic models of tasks where learners can analyse how objects move within the configuration and formulate mathematical relations. In this report, we discuss three exemplars to characterize ways in which the use of technology extends mathematical reasoning in problem solving approaches. This information becomes important for teachers to value and frame the incorporation of technology in learning environments. At the end, some limitations of this approach are discussed.

Improving Students’ Mathematical Reasoning in Geometry Using Adobe Flash Learning Media

“…The possible misleading perception of a triangular prism could be overruled and do not interfere with their activity to reason and answer triangular prism questions. This notion is supported by questionnaire and interview results in which the students stated that the use of the media helped them understand geo- (Zembat, 2008) and heightens mathematical reasoning activity by making implicit dynamism of a mathematical object (Santos-Trigo et al, 2015). Further, mathematical reasoning depends on spatial perception, and to reason mathematically involves learning to overrule potentially misleading perception (Goldstone et al, 2017).…”

“…The importance of mathematical reasoning has inspired educators to improve and to develop students' mathematical reasoning, for example, by understanding how students conduct mathematical reasoning activity (Francisco and Maher, 2010;Mata-Pereira and da Ponte, 2017), by designing instructional methods embedded with metacognitive strategies (Kramarski and Mevarech, 2003;Mevarech and Fridkin, 2006), or by designing practical tasks assessment (Boesen, Lithner, and Palm, 2010). Improvement via technology such as computer program application in learning settings have also used in mathematics education research (Foletta and Leep, 2000;Kramarski and Zeichner, 2001;Zembat, 2008;Huscroft-D'Angelo, Higgins, and Crawford, 2014;Santos-Trigo, Reyes-Martínez, and Aguilar-Magallón, 2015;Higgins, Crawford, Huscroft-D'Angelo, and Horney, 2016;Goldstone, Marghetis, Weitnauer, Ottmar, and Landy, 2017). Technology-integrated mathematics curricula can help students develop mathematical concepts and procedures in a meaningful way (Zembat, 2008).…”

“…Technology-integrated mathematics curricula can help students develop mathematical concepts and procedures in a meaningful way (Zembat, 2008). The use of technology heightens mathematical reasoning activity by making implicit dynamism of a mathematical object (Santos-Trigo et al, 2015). Goldstone et al (2017) further revealed that reasoning depends on spatial perception and learning to reason mathematically involves learning to overrule potentially misleading perception.…”

An exploration of preservice teachers’ use of educational technologies as visualization tools when teaching mathematics.

“…Sherman (2014) posits that teachers' effective use of specialized educational technologies -such as dynamic geometry software (DGS) and graphing calculators -has the potential to deepen students' mathematical subject knowledge while supporting their mathematical thinking and discourse. Santos-Trigo, Reyes-Martínez, and Aguilar-Magallón (2015) found that the use of digital educational technologies in mathematics teaching extends mathematical thinking when dealing with problem-solving. Dubinsky and Tall (2002) also claim that computers can be utilized as a tool to complement the development of advanced mathematical thinking in many ways.…”

“…Several scholars (Pea, 1987;Symons & Pierce, 2019;Yao & Manouchehri, 2019;Jacinto & Carreira, 2021) have also established that, when utilized appropriately, digital technologies (which they refer to as 'cognitive technologies/computing') prompt mathematical thinking development as a means of problem-solving. Although Santos-Trigo et al (2015) caution that the use of technology for the development of mathematical thinking has some limitations, it appears that the correct use of educational technologies can assist in the development of mathematical thinking among students. For example, Joshi (2017) points out that, to a certain extent, the use of educational technology for the development of mathematical thinking presents an opportunity for better visualization of mathematical problems.…”