Digital Tools and Paper-and-Pencil in Solving-and-Expressing: How Technology Expands a Student’s Conceptual Model of a Covariation Problem

Abstract

This study aims at understanding the role of the tools chosen throughout the processes of solving a non-routine mathematical problem and communicating its solution. In assuming that problem-solving is a synchronous activity of mathematization and expression of mathematical thinking we take our proposed Mathematical Problem Solving with Technology (MPST) model to analyze the processes of solving-and-expressing-problems. Resorting to qualitative methods for data collection and analysis, we report on the case of an 8th grader working on a covariation problem to examine the role that paper-and-pencil and digital tools play in the development of a conceptual model of the situation. We found that the resources used throughout the solving-and-expressing activity influenced the depth of the conceptual model developed, within a process of progressive mathematization. Whereas paper-and-pencil led to the emergence of a conceptual model based on exploring particular cases, the digital transformation of the solution was triggered by the process of communicating its mathematical justification and expanded the previous model. Moreover, the complexity of this activity is evidenced by its multiple sequences of processes. Finally, the integration process seems crucial as the concomitant use of technological and mathematical resources precedes major advancements in the expansion of the conceptual model.

Covid-19 Effect on the Assessment of the Use of Smartphone Apps in STEM Learning

“…The current study is largely in line with the research by Jacinto and Carreira (2021), showing that STEM tasks should be completed in the app and on paper to promote learning success. Solving problems in this fashion contributes to better understanding of the problem and a variety of ways to solve it, as well as activates students' thinking.…”

“…Based on the results of teacher surveys, it can be concluded that educational applications provide numerous opportunities for learning, which is confirmed by the data obtained by Ahmed et al (2021), Jones et al (2013), Lindsay (2016), Olszewski and Crompton (2020). However, these apps should not completely replace the ability to actually complete tasks, as argued by Jacinto and Carreira (2021). The results of the conducted survey confirm that the so-called "forced" turn to distance learning should be in harmony with the traditional needs of students (e.g., live sintering, doing exercises by hand).…”

Analysis of Co-Construction and Sharing Mechanism of Digital Education Resources based on Digital Information Encryption Technology

“…. x n 􏼈 􏼉 is a set composed of one character, (A, •) is a postexchangeable quasi group defined on A, and A + is a set composed of all nonempty character declarations in set A [31,32]. e character declaration transformations E and D. Based on the operation, ⊙ are defined as follows as equations ( 5) and ( 6):…”

Knowledge for teaching mathematical problem-solving with technology: An exploratory study of a mathematics teacher’s proficiency

“…We note that, although the processes are clearly defined, appear in a sequential list, and have seemingly distinct boundaries, in fact as admitted by the original models, in the MPST model they are rather flexible. For instance, while in studies with middle grade students the process communicate would emerge throughout the activity (Jacinto & Carreira, 2021), it is expected that it will not be patent in the activity of the participant in this study, due to the nature of the research setting (online observation of individual activity).…”

“…Actual mathematical problem-solving seldom occurs in a linear, straightforward way; instead, as shown with young or adult problem solvers, the process takes place in a cyclic way (Carlson & Bloom, 2005). This is also the case when problem solvers make use of digital tools in carrying out the process (Carreira & Jacinto, 2019;Jacinto & Carreira, 2021;Rott et al, 2021). However, the role of technology in triggering this cyclic activity and pushing the solver to move forward is still insufficiently understood.…”