Didactic strategies for conceptual understanding and motivation in university mathematics: a systematic review

The conceptual understanding and motivation for learning and teaching math constitute a challenge for didactic research at all levels of education. However, it is essential in higher education levels like the university, where achieving advanced reasoning and connecting the nature of math with professional applications is important. This systematic literature review analyzes peer-reviewed research published between 2000 and 2023, focusing on didactic and instructional strategies applied that enhance comprehension and engagement in undergraduate and higher mathematics education. Following PRISMA guidelines, we get a final analysis of 30 studies where the semiotic representations and gamification strategies are considered key strategies to achieve conceptual and motivated understanding of math in the context of higher education. Semiotic methods from Duval’s theoretical framework emphasize the coordination of symbolic, graphical, and algebraic registers to promote deep conceptual learning. As an active learning method, gamification is highly effective for enhancing student engagement and motivation, helping students overcome their apprehension toward mathematics. While most studies explored these strategies independently, this review identifies gaps in integrative approaches. It highlights the need for further research on their combined impact, especially when representational depth is aligned with motivational design. The 2000–2023 window captures the consolidation of semiotic frameworks and the expansion of ICT and gamification in higher mathematics education.