What Cognitive Science Can Tell Us about Learning Logic

Debby Hutchins, new coauthor on The Art of Reasoning, discusses how her experiences in the classroom and studying cognitive science informed how she approached working on an introductory logic book

“I get the rules, but where do I start?”

As a graduate student working the logic help desk at Texas A&M, I came to expect this question. Learning to construct proofs is the most important task in a symbolic logic class. A proof starts with given premises and derives a specified conclusion through a series of steps, each of which must be justified by a rule. Teachers of introductory logic have generally taken the same basic approach: learn the rules of inference; learn a few tips for proof strategy; put them together and do some proofs. This process is how most of us learned logic.

Yet a large number of the students who came to us for help seemed to find the process opaque, unnatural, and awkward. They seemed to be putting in the effort and following all the standard advice. They used flashcards, learned the rules, studied all the tips in the book, and attended class. They had excellent teachers. The logic faculty at Texas A&M was, in my opinion, one of the best in the world. And I didn’t form that opinion merely on hearsay or reputation: they were my teachers, too. So why weren’t these kids learning?

I had been out of school for several years when I started at A&M. Consequently, I needed a logic refresher.  So I sat in on a few classes, alongside some of the very students I was tutoring. I realized that I needed to figure out what made my experience of logic different from theirs. I decided to become my own student and figure out how I know what to do.

Have you ever tried to catch yourself in the act of reasoning? To watch the process as an observer? It’s not easy, but it is revealing. The next time a student asked where to start, I had an answer. “Look at the conclusion and find it in the premises.” I had stumbled into a strategy like many before me—the strategy of backward reasoning. And although I didn’t realize it at the time, I had started a journey toward a lifelong preoccupation with questions about how students learn or, more importantly, fail to learn logic.

The A&M faculty taught me logic, and Aggie students forced me to reflect on the process. But it was my students at Boston College who taught me how to teach logic in a classroom setting. My classroom at BC was a living laboratory for learning how to put my ideas into practice. The students there are generally bright, responsible, and interested in learning—a joy to teach. But it was the students who genuinely struggled that helped me the most. They taught me a very important lesson: lead with strategy and let the rules tag along. Most students mistakenly believe that the primary key to successful proofs lies in memorizing the rules. Though students need to understand and learn the rules, the ultimate goal in symbolic logic is successful proof discovery. We should all focus more on the process (I would even say, the art) of planning proof strategy from the beginning.  I realized that backward reasoning shouldn’t be reserved for remediation; it should be taught, in class, beginning with the very first proof.

My next lesson came from students at Fitchburg State. There I learned that many students genuinely have problems recognizing substitution instances of rules, whether in symbolic logic or natural language reasoning. They can, perhaps, understand the rationale of rules in isolation and recite the basic form  (e.g., “If p, then q. p, therefore q ”), but they can’t seem to recognize those patterns when we replace p and q with more complex statements or, in some cases, even with other statement letters.  In an attempt to figure out why, I began researching findings from cognitive science, particularly deduction studies, and learned about pattern recognition deficiencies.

Learning that David Kelley shared my interest in cognitive science was a huge motivating factor in deciding to work on The Art of Reasoning with him. From the beginning, our discussions have centered on the question “How can we integrate our knowledge of this research with the experience of teachers to build a better logic book?” We let that goal guide our writing. Let me mention a few things we’re particularly proud of:

1. In the symbolic chapters, we’ve increased the focus on proof strategy as a process. Research confirms what many of us discover in the classroom: novices are most successful when they use backward reasoning. Not only do we explain this process to the students, but we have designed exercises to lead them through it step by step.

2. I believe that the reasons some students struggle to see substitution instances are varied and complex. But research and classroom experience reveal that weakness in pattern recognition is at least one contributing factor. One way to improve this recognition is to tie new patterns to more familiar ones. We’ve used both shapes and colors in introducing the rules of implication. But we also put these tools directly into the students’ hands, by explaining how they can implement these strategies for themselves.

3. Even if students master critical thinking and logic, we are increasingly learning about the psychological and social factors that interfere with reasoning. That’s why we’ve devoted a whole chapter to cognitive bias. We hope that by teaching students about our common susceptibility to bias—and teaching them to mitigate its effects—we can help them be not just successful logic students, but genuinely better thinkers.

My journey began with a question. Could any beginning be more natural for a philosopher? My hope for The Art of Reasoning is that it takes that journey to the next level. We want our new edition to be a resource that confirms and assists the practical wisdom of experienced logic teachers. We also hope it serves as a foundation for the next generation of logic teachers to succeed in the classroom, launch their own instructional inquiries, and join the conversation to shape the logic pedagogy of the future.

2 thoughts on “What Cognitive Science Can Tell Us about Learning Logic

  1. Charles Hogg

    These are some excellent insights. I also try to “game-ify” some aspects of proofs, like taking an expression and trying to use equivalence rules to see how there are many ways to see the same material.

  2. Frank Fair

    Hi, Debby. I just wanted to say congratulations on the book, and I really appreciate your sharing your own journey toward integrating perspectives from cognitive science into logic pedagogy. I’ve used Tom Gilovich’s How We Know What Isn’t So in my critical thinking classes to introduce students to some of the relevant issues, and I’ve gotten a number of very interesting responses to reflection pieces assigned over several of the chapters. Keep up the good work!

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