## Improving the Teaching of Threshold Concepts in Introductory Logic Courses

Grant recipient: Nicolas Fillion, Department of Philosophy

Project team: Bradley Zurcher and Marissa Bennett, research assistants

Timeframe: January 2015 to March 2017

Support provided: \$10,000

Course addressed: PHIL 110 Introduction to Logic and Reasoning

Final report: View Nicolas Fillion's final report (PDF)

Interim report: View Nicolas Fillion's interim report (PDF)

Description: Philosophy 110 helps students acquire better reasoning skills and is a quantitative requirement. This material is challenging for students to learn. We find the course has a multi-modal grade distribution. That is, students tend to cluster into at least two levels of grade performance. This suggests a large number of students fail to properly acquire the core notions of logical methodology. Specifically, they may not have been able to learn critical threshold concepts regarding logic.

In the Fall 2013 semester, we used an innovative methodology developed by R. Arthur in his new text-book Natural Deduction. Preliminary results suggest threshold concepts have been more effectively assimilated using this methods and this bimodality, reduced. However, pedagogical material targeted for SFU students needs to be developed to supplement Arthur's book. An important difficulty lies in the fact that English Second Language (ESL) students have struggled with the dense explications and with the literary examples used in this book.

We aim to study the trends in student performance we have observed, and use this information to support the development of additional pedagogical material to support the use of this innovative methodology at SFU. We will prepare a document containing supplementary explanation of the threshold concepts with examples formulated in a more accessible language and solved exercises to provide practice in applying the core concepts of logical methodology in practical applications.

• What typical learning process do neophytes undergo to become proficient in formal logic?
• What are the relations between grade distribution statistics, students learning, and teaching effectiveness?
• How can we adequately measure the bimodality (or multimodality) to indicate difficulties with the acquisition of threshold concepts?
• How robust is the phenomenon of bimodality in grade distribution?
• Is the bimodality caused by a differential involvement with the course?
• How to measure the quality of a method to teach threshold concepts?
• How can the findings support the design and development of new pedagogical materials that will enable us to more efficiently implement and improve student learning?

Dissemination: The project has led to the following presentation about the theoretical framework enhanced and applied to formal logic as a discipline:

Fillion N. & Zurcher B., Threshold concepts in formal logic, Canadian Society for the History and Philosophy of Science, Ottawa, 2015.

A component of the project was to produce a set of exercises that would supplement the textbook, specifically designed to help the many students whose first language is not English. This is now available:

Fillion N. (2016). Introduction to Logic Exercises: 694 supplemental exercises for “An Introduction to Logic” by R.T.W.~Arthur, Broadview Press, distributed online for free with book purchase.

Over the course of this project, we have also reviewed the first edition of the textbook used in this course:

Fillion, N. and Zurcher, B. (2014). Review of Richard Arthur's “Natural Deduction: An Introduction to Logic with Real Arguments, a Little History, and Some Humour”, Dialogue. 51(1), 190-192.

Finally, the author of the textbook, Richard Arthur, has just published the second edition of the textbook. We have been very active in giving him feedback on what works and what doesn’t work for us, and he has modified the book significantly to accommodate our needs. This is reflected in the authors Acknowledgements to the second edition: “But my main debt of gratitude is to Nic Fillion of Simon Fraser University, BC, for all his constructive remarks and many detailed suggestions for this new edition.” (p. xx)

We have had success with the theoretical part of the project, with the curricular development component, and with the development of pedagogical material to help students (especially, ESL students). However, we had less success with the data analysis. Our attempt to track the progress of students using their quiz and exam scores and to detect implicit effects of threshold concepts using factor analysis has not led to a corroboration of our hypotheses. More work using a different methodology will be done the next few times I teach the course.

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