The aim of this dissertation was to explore how game-based learning can be used to develop primary school students’ adaptive number knowledge. The dissertation comprises five studies that explore the Number Navigation Game’s (NNG) development, testing and effects in enhancing primary school students’ adaptive number knowledge and related mathematical skills and knowledge. The studies use different methodologies and ask varying questions through the process of development and testing of the NNG. However, as a common thread, each study explores the relationship between game mechanics and mathematical content, and the relationship between game-based training and learning-outcome measures.
Study I tested the NNG’s first working prototype from a user experience point of view and investigated instances of adaptive number knowledge in the game’s context. The game was tested in two sessions, with one student (age 11) playing individually and two students (ages 9 and 11) using the game collaboratively. Data were collected using video-recorded observations, gameplay screen capture and open-ended interview questions regarding the game experience. Results showed that already, the NNG prototype triggered players’ active engagement with different number combinations and numerical relations as well as reflection and discussion about these numerical relations. This suggested that gameplay with the NNG could trigger the type of mathematical thinking and problem solving which was expected to help enhance students’ development of adaptive number knowledge.
Study II comprised three sub-studies (fifth-graders, n = 55; university students, n = 55; and sixth-graders, n = 22) and aimed to develop and test the Arithmetic Production Task, a paper-and-pencil measure of adaptive number knowledge. Individual differences in the Arithmetic Production Task and the relation between adaptive number knowledge and other mathematical skills and knowledge were explored. Results showed similar patterns of individual differences across the different samples and age groups. Adaptive number knowledge was found to be related to arithmetic fluency and conceptual knowledge of arithmetic. Results suggest that the Arithmetic Production Task was able to capture how participants recognise opportunities to use numerical features in their arithmetic problem solving, which can be used as an indicator of their adaptive number knowledge.
Study III was the first attempt to test the NNG’s effects and examine the relationship between game performance and adaptive number knowledge. The study used a quasi-experimental pre-test/post-test design. Participants were 11 pairs of sixth-grade students (11 females, age range: 11-13) from one classroom who played the NNG over a seven-week period. Results showed improvement in participants’ performance in adaptive number knowledge and math fluency. Game performance was found to be a predictor of students’ post-test performance on the multi-operational aspect of adaptive number knowledge.
Study IV provides a detailed overview of game design decisions in the NNG, which are based on theory and the results from previous pilot studies using the NNG (Studies I and III). Another game-development phase followed Study IV, resulting in the final NNG prototype used in Study V.
After the initial pilot and development stages, Study V aimed to test the NNG’s effects in the classroom and on a larger scale across different grade levels. Study V explored how training with the NNG affects the development of primary school students’ adaptive number knowledge, arithmetic fluency and pre-algebra knowledge at different grade levels; and how students’ performance on the NNG affects the development of the mathematical learning outcomes. A pre-test/post-test randomised control design was used, in which the experimental group played the NNG for 10 weeks during math class, and the control group received regular math instruction. Results showed significant overall improvement in the experimental group compared with the control group on all measured mathematical learning outcomes. Game performance was related to the experimental group’s post-test scores even after controlling for pre-test scores and grade. Additionally, results showed that the NNG develops different aspects of adaptive number knowledge, math fluency and pre-algebra knowledge across grade levels.
Overall, the present dissertation’s findings show that the NNG can provide efficient and novel training opportunities for developing primary school students’ adaptive number knowledge and related mathematical skills and knowledge. The game-based format allowed for a large amount of open-ended practice with various number-operation combinations, which usually is difficult to achieve in regular mathematics classrooms. The dissertation’s results provide empirical evidence for the theoretical model of adaptive number knowledge as a component of adaptivity with arithmetic. Additionally, a new and scalable measurement and novel training of adaptive number knowledge were developed. The results also highlight the importance of an iterative design process in educational game development, with the following guiding principles: integration of educational content and game features, measurement questions and application of trainin
