Digital games have become part of childhood and adolescence. The debate has moved from should teenagers play digital games to how to gain benefits from this gameplay. Researchers predict that technology-enhanced learning will increase with educational computer games (serious games) playing an important role. Although serious games are often built on established educational theories, they can also appear boring and struggle to engage the learner. Analyses of serious games demonstrate that many do not offer an entertainment experience comparable to or even recognizable as relatives of the entertainment games familiar to many players. However, a high level of engagement by the learner is viewed as necessary to provide a strong learning environment. The long-term aim of this study is to explore how digital games can support a more engaging and effective mathematics learning experience. This first stage has taken a qualitative grounded theory approach to explore the engagement factors of digital games among young people (aged 7 – 16 years). Analyses of data gathered through a combination of surveys and interviews have led to a framework of engagement factors. This provides a basis for designing serious games that are effective by being both engaging and educational.