Promoting flexible mathematical thinking with growth mindset, deliberate practice, and serious games

Abstract

Adaptive expertise is a greatly appreciated, yet rarely achieved, goal of mathematics curricula because it is considered to typify high-level mathematical thinking. Adaptive expertise demonstrates knowledge and skills that can be dynamically implemented in uncommon situations, not just within highly defined tasks or sufficiently prepared contexts. To achieve adaptive expertise, students must be given occasions to practice solving open-ended mathematical tasks in unfamiliar circumstances, allowing them to contemplate, analyze, and explore different connections and alternative solutions to develop their emerging skills and knowledge structures. Traditional math classrooms are often equipped with textbooks and instructional approaches that focus on isolated, routine exercises, or drill-andpractice, which encourage students to master isolated procedural techniques to find the most or only efficient solution. Math teachers, therefore, employ teaching methods that emphasize speed and accuracy using these materials. The idea of mathematics as a “fixed” subject, which is full of rigid and absolute rules, unintentionally continues to be reinforced.
This doctoral dissertation aims to investigate design principles for learning environments that support flexible mathematical thinking in mathematics education. This thesis focuses on two objectives: first, it aspires to understand how adaptive expertise can be promoted with deliberate practice, and whether it can be done by using a mathematical game-based learning environment called the Number Navigation Game (NNG). The nature of deliberate practice is demanding and occurs just beyond one’s abilities. It necessitates deep engagement, continuous efforts to enhance performance, and a positive attitude towards challenges—traits synonymous with a growth mindset. Given the association between a growth mindset and persistent learning behavior, the second objective explores ways to cultivate growth mindset in mathematics classrooms. This is vital for integrating game-based learning into conventional mathematics instruction and realizing the goal of adaptive expertise in mathematics.
This dissertation is divided into two parts, encompassing three sub-studies. Part one, comprising Studies I and II, focuses on the Number Navigation Game (NNG). Study I explores game experiences during the NNG development process and examines how different design choices influence students’ gaming experiences. The results provide insights into the iterative design process of a research-based serious game, shedding light on students' interactions with both learning and gaming components and their relation to novel mathematical learning objectives. Study II delves into various game performance profiles using gaming analytics and investigates the diverse ways students engage with the NNG. Utilizing log data from game performances in the energy mode, combined with measured mathematics learning outcomes, math interest, perceived challenge, and experienced flow during gameplay, Study II offers evidence on promoting adaptive expertise through deliberate practice, game-based learning environments, and learning outcomes. In essence, Studies I and II highlight how the NNG serves as a supportive platform for presenting students with novel contexts, challenging tasks, and immediate feedback, making it a viable tool for traditional classrooms.
Part two (Study III) investigates the current state of growth mindset interventions in mathematics education through a systematic review. The results show that when implicit theories of intelligence interventions were conducted specifically in the math domain, positive results were reported, whereas general implicit theories of intelligence interventions yielded mixed results. This indicates that to make the necessary behavioral changes based on changed beliefs, participants need to engage with mathematical content at a deeper level than the surface level. Most importantly, the learning environment must be embedded with elements that support struggle and mistakes, encourage effortful practices, and make progress visible to students. In this way, students will be provided with evidence of the development of their own mathematical skills as a result of practice.