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Grant program: Teaching and Learning Development Grant (TLDG)

Grant recipient: Karen Yeats, Department of Mathematics

Project team: Sophie Burrill, Esma Emmioglu, and Cameron Morland, research assistants

Timeframe: January 2013 to July 2016

Funding: $5,000

Final report: View Karen Yeat's final report (PDF)

Description: MACM 201 (Discrete Mathematics II) is a smorgasbord course that covers elementary counting, probability, classic enumeration, and graph theory and trees. Topics prior to graph theory can all be broadly considered enumeration, which is the area of investigation in this project.  Many students find the course very difficult and many don’t pass.  Other students simply don’t see what the point is.  The course generally feels disjointed, and as such can be frustrating for both students and instructors. 

My hope is to strengthen the cohesion of the course by developing a new approach that will be compared with the standard approach.  In the new approach, each student will be assigned one of several combinatorial objects (i.e. binary rooted trees, partitions, and binary strings) at the start of the term for use during in-class discussions and exams related to enumeration.  Lecture meetings will have one of three formats.  Some lectures will be traditional lectures introducing course material.  In other lectures, students will be in homogeneous groups studying the same combinatorial object and working on problems applied to the course topic with the object. In the third format, students will be in heterogeneous groups with all objects represented to present what they have found and acquire some familiarity with other combinatorial objects.  In addition, assignments and exams will have questions using the assigned object. There will also be a question on an object no students have been exposed to in order to evaluate how well students can generalize their knowledge and integrate new but related concepts. Exams will be analyzed at the individual question level to determine performance on each question.  Surveys of student engagement and course cohesion will be used to examine differences between the standard- and new-approach experience.  My hope is that this new approach will (1) show students how course topics are interrelated, (2) give students a chance see the beauty in parts of the combinatorial objects, (3) let students be more self-directed within a rigid curriculum, and (4) lead to better student performance in MACM 201.

Questions addressed:

• Can we increase the sense of coherence in MACM 201?

• Can we increase the depth of engagement and the depth of learning of the students?
• Do students in the new approach feel there is more coherence in MACM 201 as compared with students in the standard approach?  Do students in the new approach feel more engaged with the course content as compared with students in the standard approach?
• Does the new approach improve student performance? Is there improved performance in weaker and stronger students?
• Does the new approach improve a student’s ability to transfer or apply their knowledge
in new circumstances?  Does the new approach let students integrate new related ideas more effectively?

Knowledge sharing: Results and findings will be presented at a mathematics departmental meeting. 

Yeats, K., Burril, S. Emmioglu, E., & Morland, C. (2016, July). Depth of experience in MACM 201. Poster session presented at Celebrating 10 years of Teaching and Learning Research at ÓÈÎïÊÓƵ,ÓÈÎïÊÓƵ, Burnaby, BC.