# An Evaluation of ULTRA; an Experimental Real Analysis Course Built on a Transformative Theoretical Model

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## Abstract

Most prospective secondary mathematics teachers in the United States complete a course in real analysis, yet view the content as unrelated to their future teaching. We leveraged a theoretically-motivated instructional model to design modules for a real analysis course that could inform secondary teachers’ actionable content knowledge and pedagogy. The theoretical model and designed curriculum launches the study of advanced mathematics content, in this case, real analysis, via authentic 7–12 classroom situations, abstracts the secondary mathematics, and uses that content to motivate the presentation of the advanced mathematics content. Subsequently, the curriculum then reconnects to practice, asking the teachers to translate ideas from real analysis in ways that are appropriate for teaching high school content to students. This study evaluated the success of the curriculum in terms of the students’ proficiency with real analysis, challenging secondary mathematics content, and the use of that content in teaching situations via both written post-tests and interviews and showed the viability of the model and experimental curriculum.

## Keywords

Secondary teacher preparation Advanced mathematics Real analysis Pedagogical practice## Notes

### Acknowledgements

This material is based upon work supported by the National Science Foundation under collaborative grants DUE 1524739, DUE 1524681 and DUE 1524619. Any opinions, findings, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

### Compliance with Ethical Standards

### Conflict of Interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

## Supplementary material

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