Roadmap to Glory: Scaffolding Real Analysis for Deeper Learning

In this paper, we explain changes made in an introductory Real Analysis classroom that address common challenges and that may allow for all levels of students to meet a high standard of learning and written work. We aim for this goal by fusing elements of a hybrid course with scaffolded collaborative work to improve student learning. The hybrid structure allows students to engage new material at their pace, while the scaffolding allows for more challenging coursework and models for students some typical arguments in analysis. As a result, students that initially submitted proofs needing significant improvement in coherence and organization show positive gains in self-confidence and are enabled to progress quickly to submitting mathematical writing of a high calibre. Our case study occurred at a large institution serving many underrepresented and non-traditional student populations. The approach may be effective at schools with similar goals and challenges.