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

Phuong Pui

Mastering mathematics is not just about memorizing formulas; its about flexible thinking and applying knowledge in new contexts. This is termed adaptive expertise. Yet, traditional math classrooms often focus on rote learning and quick recall, which can make math seem rigid with only one “correct” solution. There is a need for more complex forms of practice in mathematics classrooms, especially deliberate practice, an approach proven to foster exceptional growth in various fields. In math, this means providing students with intricate practice opportunities that challenge and build their skills, rather than just repeating known exercises.

This doctoral dissertation investigates design principles for learning environments, with the overarching goal of fostering and supporting flexible mathematical thinking. It explored the promotion of adaptive expertise in mathematics through deliberate practice via a serious game called the Number Navigation Game (NNG), a game-based learning environment designed to advance students’ (aged 10 to 13) mathematical skills with whole-number arithmetic, focusing especially on flexibility and adaptivity. Within the game, students face tailored challenges, receive real-time feedback, and are encouraged to explore various solutions. The games design ensures that students not only learn but also refine their skills and deepen their understanding, aiming for better performances.

Furthermore, the research explores the growth mindset concept, the idea that with dedication, skills can grow. Especially in math, adopting a growth mindset can drive students to tackle challenging problems persistently. The study found that for mindset interventions to be effective in math education, they must be tailored specifically to the subject. Engaging deeply with mathematical content is vital. The right learning environment is essential, one that promotes effort embraces mistakes, and encourages non-routine problem-solving. Such an environment can show students the fruits of their efforts, fostering genuine mathematical growth.