Mathematical Problem Solving Beyond School: Digital Tools and Students’ Mathematical Representations

Abstract

By looking at the global context of two inclusive mathematical problem solving competitions, the Problem@Web Project intends to study young students' beyond-school problem solving activity. The theoretical framework is aiming to integrate a perspective on problem solving that emphasises understanding and expressing thinking with a view on the representational practices connected to students' digital mathematical performance. Two contextual problems involving motion are the basis for the analysis of students' digital answers and an opportunity to look at the ways in which their conceptualisations emerge from a blend of pictorial and schematic digital representations.

Increase Representation in Mathematics Classes: Effects of Computer Assisted Instruction Development with Hippo Animator

“…Creating a visual representation in maximizing thinking skills in mathematics learning is important as an effort to develop students' mathematical concepts (Schoenfeld, 2013). This finding is in line with the findings of previous studies stating that describing problems visually can increase students 'conceptual and procedural knowledge (Rittle-Johnson & Star, 2007), expressing students' thinking (Carreira, 2015), able to facilitate students to recall previous mathematical knowledge (Pape, 2004), and assist students in integrating various new information presented (Abdullah et al, 2012).…”

“…The research findings show that CAI can be used to visualize abstract mathematical concepts, but must be supported through the concept of multimedia development with communicative, interactive, comprehensive, integrated, coherent, and providing feedback to students. Digital media can refine mathematical objects more than just expressions, algorithms, or mathematical symbols by conceptualizing and developing situations based on images, schematic representations, languages, letters, and available iconic elements (Carreira, 2015). In the perspective of ICT-based learning, other researchers conclude that ICT can involve the active role of students in learning (Oktavianingtyas, Salama, Fatahillah, Monalisa, & Setiawan, 2018).…”

“…Based on this fact, the development and use of representation deserve serious attention in learning. Several previous studies that focused on developing mathematical representations have been carried out, such as the use of digital tools (Carreira, 2015), problem based learning (Tandiling, 2015), developing instruction materials based on joyful problem based learning (Minarni & Napitupulu, 2017), think-talk-write model (Supandi, Waluya, Rochmad, Suyitno, & Dewi, 2018), eye tracking method (Andrà et al, 2009), thinking strategy approach (Abdullah, Zakaria, & Halim, 2012), project-based learning (Widakdo, 2017), and RMEbased progressive mathematization (Warsito, Darhim, & Herman, 2018). Based on previous research, it is known that the cause of the weakness of mathematical representation ability is because it is difficult to bridge representation and change from one representation to another (Yerushalmy, 1997), there are three types of errors that explain students' weaknesses during the translation process: misinterpretation, implementation, and preservation (Adu-Gyamfi, Stiff, & Bossé, 2012).…”

Mathematics Education Students’ Experiences during Lockdown: Managing Collaboration in eLearning

“…Recent literature [19,[45][46][47][48][49][50] concerning twenty-first-century learning approaches such as edutainment, game-based learning, eLearning, blended or flip learning, and learning using dynamic mathematical software (e.g., GeoGebra) provide evidence that digital technologies help foster not only problem-solving skills, but more advanced skills such as critical-creative thinking skills [50]. Borba et al [51] consider that eLearning allows the development of important skills such as computational skills, independent study, searching for information, problem-solving, collaborative learning, personalization, and lifelong learning.…”

“…In particular, the ubiquitous features of MT devices enable the coordination of collaborative activities because students can move with the device to work with other students at different locations [37]. Recent literature [8,45] indicates that digital tools including online communication platforms offer problem solvers a set of affordances, which they can use to orchestrate activities (explore, (re)-construct, explain, and communicate) during collaborative mathematical problem-solving. The affordances offered by the Internet, digital gadgets, and smart devices are critical in augmenting problem solver's understanding of mathematical concepts beyond formal settings [44].…”