Characterizing aspects of reform enacted in Calculus I lessons

Abstract

We investigate aspects of reform enacted in 66 class observations from 18 institutions collected as part of the National Study of University Calculus in the US. We examined four aspects related to how problems were solved in class: the extent of student involvement, the representations and technology used, and specific features of the problems solved. As a whole, we observed low enactment of reform-oriented practices in these lessons, with more variation within rather than across institutions. We describe lessons that illustrate different ways in which reform aspects were enacted and suggest some implications for further studies.

KEYWORDS:

• Calculus
• instruction
• observation instrument
• reform
• post-secondary mathematics

Acknowledgements

Author Note: Portions of this work were presented at the Didactics of Mathematics in Higher Education as a Scientific Discipline conference, in Hanover, Germany, December 2015; in the NCTM Research Conference, in San Francisco, April 2016, and in the 13th International Congress of Mathematical Education in Hamburg, Germany, July 2016. We thank Murat Sümer and Sarah Sobek for contributions to the early analysis of the data, Helen Burn, Ashley Jackson, and the Research on Teaching Mathematics in Undergraduate Settings (RTMUS) for comments on earlier versions of the work. This material is based upon work supported by the National Science Foundation under Grant No. DRL REESE 0910240. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The institutions were classified by the highest mathematics degree awarded: PhD, master’s, baccalaureate, and associate’s degrees. Institutions awarding similar degree were considered peer. See Bressoud et al. (2015).

2 In their study, Freeman and colleagues counted as active learning interventions those that encompassed ‘occasional group problem-solving, worksheets or tutorials completed during class, use of personal response systems with or without peer instruction, and studio or workshop course designs’ (p. 8410).

3 The observers made judgements regarding gender that might be different from self-identification.

4 https://apstudents.collegeboard.org/courses/ap-calculus-ab/calculator-policies.

5 Information extrapolated from two sources, https://www.statista.com/statistics/183996/us-high-school-enrollment-in-public-and-private-institutions/ and https://research.collegeboard.org/programs/ap/data/archived/ap-2018.

6 NExT: https://www.maa.org/programs-and-communities/professional-development/project-next.

7 ACCCESS: https://amatyc.org/page/ACCCESS.

Additional information

Funding

This material is based upon work supported by the National Science Foundation [grant number DRL REESE 0910240].