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Results from a Survey of Abstract Algebra Instructors across the United States: Understanding the Choice to (Not) Lecture

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Abstract

In the United States, there is significant interest from policy boards and funding agencies to change students’ experiences in undergraduate mathematics classes. Abstract algebra, an upper division undergraduate course typically required for mathematics majors, has been the subject of reform initiatives since at least the 1960s; yet there is little evidence as to whether these change initiatives have influenced the way abstract algebra is taught. We conducted a national survey of abstract algebra instructors at Master’s- and Doctorate-granting institutions in the United States to investigate teaching practices, to identify beliefs and contextual factors that support/constrain non-lecture teaching practices, and to identify commonalities and differences between those who do and do not lecture. This work provides insight into how abstract algebra is taught in the United States, factors that influence pedagogical decisions, and avenues for how to approach and better support those are interested in implementing non-lecture teaching approaches.

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Notes

  1. Interested readers can see a version of the survey at: pcrg.gse.rutgers.edu/algebra-survey

  2. See www.maa.org/cspcc for more information about the CSPCC project and a copy of the surveys

  3. Here completed means that a participant viewed, but not necessarily responded to, each survey item. When looking at individual survey items, the number of responses varies between 110 and 129. For each survey item in the results, we report the number of responses analyzed.

  4. These models were conducted on a reduced data set (n = 69/55 for Have you ever…? and Would you ever…? respectively), as only respondents that answered each survey item under consideration could be included.

  5. The correct interpretation of these odd rations would be to infer, for instance, that the model was 27 times more likely to predict Non-Lecturer status for a very satisfied instructor as compared with a dissatisfied instructor, assuming other factors held constant – a prediction the model accurately made 57.9% of the time.

  6. Three of the Cronbach’s Alphas are below the oft-cited .70 threshold (Nunnally 1978). However, one would expect a deflated alpha due to the small number of items per factor. Additionally, as this is an exploratory factor analysis where we explored our responses ex post facto with an eye towards dimension reduction for our regression model (as opposed to a confirmatory factor analysis in a psychometric situation where prudent instrument design dictates assessment building around multiple items per construct), we decided these levels were satisfactory enough for us to proceed.

  7. Missing cases were handled using listwise deletion when performing the factor analysis. This resulted in a sample size (n = 78) smaller than expected. Model predictions however can be made for any participant who answered the response items, even if some individual predictor items were missing. In the case of these models, predictive accuracy was based on sample sizes of n = 117/97 for the Have you ever…? and Would you consider…? items, respectively.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Virginia Tech, 460 McBryde Hall, 225 Stanger Street, Blacksburg, VA, 24061-0123, USA

    Estrella Johnson

  2. School of Education, Virginia Tech, 226 War Memorial Hall, Blacksburg, VA, 24061-0123, USA

    Rachel Keller

  3. College of Education, Temple University, Ritter Hall 444, 1301 Cecil B. Moore Ave, Philadelphia, PA, 19122, USA

    Timothy Fukawa-Connelly

Authors
  1. Estrella Johnson
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  2. Rachel Keller
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  3. Timothy Fukawa-Connelly
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Corresponding author

Correspondence to Estrella Johnson.

Appendices

Appendix 1 – Logistic Regression Details

Response 1: Have you ever taught in non-lecture format? [0 = no, 1 = yes]

Response 2: Would you ever consider teaching in a non-lecture format? [0 = no, 1 = yes]

TeachingExp [3 levels]

AAExp [3 levels]

For these 2 variables, the reference group was the last (most experience)

Satisfaction [3 levels] *Removed ‘other’ responses

Reference group was first (dissatisfied)

FollowUpcourse [3 levels]

Reference group was ‘yes - required for math majors’

TerminalDegree [0 = Phd, 1 = Masters]

WorkInGroups [0 = Never, 1 = Sometimes]

GivePresentations [0 = Never, 1 = Sometimes]

LectureisBest [0 = Disagree, 1 = Agree]

LectureIsOnly [0 = Disagree, 1 = Agree]

MathWork [0 = Disagree, 1 = Agree]

EnoughTime [0 = Disagree, 1 = Agree]

AATeachingInterest [0 = weak, 1 = strong]

AALearningResearch [0 = weak, 1 = strong]

AAResearchInterest [0 = weak, 1 = strong]

TandLResearch [0 = weak, 1 = strong]

PandTSupport [0 = no, 1 = yes]

TravelSupport [0 = no, 1 = yes]

CourseFreedom [0 = no, 1 = yes]

DeptPressure [0 = no, 1 = yes]

TimeforClassPrep [0 = no, 1 = yes]

CoveragePressure [0 = Disagree, 1 = Agree]

FailRate [0 = <20%, 1 = >20%]

ExtInf [0 = weak, 1 = strong] (cutpoint is 5)

StudentExperience [0 = weak, 1 = strong]

TeacherExperience [0 = weak, 1 = strong]

TalktoColleagues [0 = weak, 1 = strong]

(Weak combines ‘not at all’ and ‘somewhat’, Strong = ‘very’)

Appendix 2 – Details on Statistical Conclusions

Table 1. Reported Teaching Practices Pairwise Comparisons
Full size table
Table 2. Reported Beliefs Pairwise Comparisons
Full size table

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Johnson, E., Keller, R. & Fukawa-Connelly, T. Results from a Survey of Abstract Algebra Instructors across the United States: Understanding the Choice to (Not) Lecture. Int. J. Res. Undergrad. Math. Ed. 4, 254–285 (2018). https://doi.org/10.1007/s40753-017-0058-1

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