Abstract
College algebra has been noted as a critical course in post-secondary institutions because it serves as a gateway for major selection and college completion. Combinatorial topics like repeatable permutations are often overlooked in K-12 and undergraduate curricula. Likewise, students’ achievement and motivation are affected by the type of classroom climate created in the undergraduate mathematics classroom. Inquiry-based mathematical education (IBME) is a viable instructional approach because of its focus on community meaning-making of the mathematical content. However, lecture-style approaches still dominate post-secondary mathematics classrooms even though they have been criticized for their focus on procedural knowledge and disinviting environment. Therefore, the purpose of this quasi-experimental study was to test the effects of instructional approach (i.e., lecture-style vs. IBME) and social support (i.e., absence or presence) on undergraduate student motivation and achievement of combinatorial mathematics. Findings indicated that intentional social support-building – regardless of pedagogical method – had the strongest effects on students’ perceived autonomy-support, competence and achievement. Although no differing pedagogical effects were discovered (most likely due to the one-time implementation of the lesson formats), the findings provide evidence for the necessity of community-building efforts -- an aspect of education that is often overlooked in the undergraduate mathematics classroom.
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This research was supported in part by a Faculty-Undergraduate Student Engagement (FUSE) grant from Western Kentucky University.
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Appendices
Appendix 1
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Name: __________________________.
Summative Evaluation Rubric
Question | Description | Score |
|---|---|---|
Q1 | Give one point for each of the following: -Student uses logic (no formula) to try and find a solution -Student finds correct number of permutations | /2 |
Q2 | Student finds correct number of permutations using the mathematical relationship nr | /1 |
Q3a | Give one point for each of the following: -Student states problem is not a repeatable permutation -Student states that chairs are not repeatable | /2 |
Q3b | Give one point for each of the following: -Student states problem is a repeatable permutation -Student states that order of the numbers matters -Student states that numbers are repeatable -Student identifies n as 6 (or the number of different options on the die) -Student identifies r as 3 (or the number of times the die was rolled) -Student states that solution is 216, or 63 | /6 |
Q3c | Give one point for each of the following: -Student states problem is a repeatable permutation -Student states that order of the numbers matters -Student states that numbers are repeatable -Student identifies n as 10 (or the numbers to choose from) -Student identifies r as 9 (or the number of spaces in the password) -Student states that solution is 109 | /6 |
Total | /17 |
The percentage I got correct is: ____________.
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Duffin, L.C., Keith, H.B., Rudloff, M.I. et al. The Effects of Instructional Approach and Social Support on College Algebra Students’ Motivation and Achievement: Classroom Climate Matters. Int. J. Res. Undergrad. Math. Ed. 6, 90–112 (2020). https://doi.org/10.1007/s40753-019-00101-9
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DOI: https://doi.org/10.1007/s40753-019-00101-9