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To invest in the future of mathematics education is to invest in our future teachers. Equipping such individuals should be the utmost priority, for they will communicate mathematics to our students. Research shows that the way we work with and explain mathematics is consequential to our proof scheme; that is, the proof schemes we hold are the proof schemes we will inevitably teach. This study explores the possible proof schemes and mindsets held by ten university students studying mathematics education at Lee University--six enrolled in a geometry course and four in an algebra course. Through interviews and critical thinking exercises, we analyzed the future students' proof schemes and views on mathematics. Our analysis found that participants who had encountered proof-based mathematics courses had a tendency to approach problems analytically, which implied the existence of an association between their definitions of proof and methods of problem-solving. This relationship perhaps has implications about teacher preparation and development prior to entering the classroom, thus revealing its significance to student success.


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19 Jul 2022
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  • Alternative title
    • Mathematics Background and Proof Schemes

  • Journal title
    • Papers & Publications

  • Volume
    • 6

  • Issue
    • 1

  • Date submitted

    19 July 2022

  • Keywords
  • Additional information
    • Acknowledgements:

      Dr. Laura M. Singletary and Dr. Debra L. Mimbs

      Author Biography:

      Amanda Akin is a fourth-year undergraduate student at Lee University. She is currently pursuing a Bachelor’s of Science in Mathematics and anticipates graduating in May of 2017. During her time at Lee, she has collaborated with staff and colleagues to research mathematics education and complete two pilot studies. After graduation, Amanda hopes to enroll in a PhD program for mathematics education and pursue a career in research. Allison Bernhard is a fourth-year undergraduate student at Lee University. Currently, she is working to receive a Bachelor’s of Science in Mathematics Education while fulfilling the requirements for a degree in Mathematics. She has spent extensive time researching mathematics education with her advisor, Dr. Laura Singletary. Following graduation in December of 2017, Allison seeks to teach secondary mathematics at the high school level and obtain her Master’s Degree in Mathematics Education. Casey McGrath graduated from Lee University with her Bachelor’s of Science in Mathematics in May of 2016. She is currently working towards a M.Ed. in secondary education for mathematics at Vanderbilt University while also working towards her teaching certification. Additionally, she is working with her advisor, Dr. Tesha Sengupta-Irving, on a new project involving mathematical argumentation. Upon graduation, Casey hopes to teach high school mathematics in lower income schools. Elizabeth Rawson is a third-year undergraduate student at Lee University. She is currently pursuing a Bachelor’s of Science in Mathematics while simultaneously working towards meeting all requirements for a Secondary Mathematics Teaching Certificate. Upon graduation in May of 2018, Elizabeth plans to obtain a teaching career in secondary education, pursue a Master’s Degree in Mathematics Education, and further research in the field.

      Graduation Date:

      December 2017