Critical Thinking in Mathematics & Sciences

By Dr. Amina Eladdadi, Department of Mathematics

As a mathematician, I am trained to think critically since critical thinking is the “quintessence” for doing mathematics. As a Bio-mathematician, I am trained to be a multidisciplinary critical thinker with collaborative skills so that I can communicate – mathematically speaking – with my colleagues in the biological and medical disciplines, where I apply mathematical and computational theories.

Being able to think critically is one thing, but teaching others to think critically is another matter. Critical thinking calls for many skills and abilities, and so does teaching it! I believe that teaching critical thinking in mathematics or for that matter any other discipline is essential in the development of successful students because critical thinking is becoming “the critical skill” that is highly sought after by all employers.

The ability to “think critically” is always listed as one of the main outcomes of undergraduate education. Some instructors teach this skill, together with the content of their discipline. However, most of the time the teaching of critical thinking skills is done so “indirectly” that students do not even pick up the signals of the “critical thinking skills” being taught implicitly.  The question then becomes, “how much of critical thinking skills should be taught directly along with the discipline content rather than implicitly with the content being taught? This brings up many other questions about teaching critical thinking skills that I briefly mention (though not answered) in the next sections of this blog.

I must say that it is not an easy task for me to promote critical thinking skills in my mathematics courses, even though mathematics is all about logic and evaluating arguments. Similarly, students seem to find it difficult to cultivate critical thinking abilities during their learning process; that is if they know at all that they are being taught something called “Critical Thinking.” So why is it so hard to teach critical thinking? Are instructors trained to teach critical thinking to their students? Does critical thinking vary from one discipline to another? These were a few of my pedagogical questions that I set out to explore during my 2013-14 Provisions Fellowship on Critical Thinking.

In this first blog, I focus on the last question that is: “does critical thinking vary from one discipline to another?” This is of great interest to me because I work on biological and medical problems where I utilize my mathematical and computational knowledge to solve some of the pressing health issues such as cancer. My interdisciplinary experiences taught me that biological/medical scientists and mathematicians think critically of course, but differently about the same phenomena despite that the common objective is to solve a problem, such as curing cancer.

In the field of mathematics, critical thinking and problem solving go hand in hand. In other words, the students must learn how to think critically for them to be able to acquire mathematical knowledge through problem solving. So, what is critical thinking? There are many definitions of critical thinking depending on which field you come from. As a Mathematician, where logical inquiries and deductive reasoning govern everything we do, I would interpret critical thinking simply as a “logical and active approach of thinking.”  This is only my interpretation of critical thinking within my field of mathematics. I am sure you will be able to find your own interpretation as well within your field. Try it!

Curious to learn more about how critical thinking is perceived by and used in other disciplines, I delved into the book titled “A Practical Guide to Critical Thinking: Deciding What to Do and Believe,” by David Hunter (Wiley Publisher, 2009).  First, I choose this book because it was sitting on my bookshelf for a quite sometime, and secondly, because it presents an interdisciplinary approach to critical thinking across disciplines which is of great interest to me. This book is primarily a textbook, which can be used for college courses on critical thinking and logic.

The author presents an interdisciplinary approach to critical thinking by giving examples from various subjects and fields of research such as business, education, and the physical and biological sciences. I found Hunter’s book to be well organized. Chapters include several sections discussing some aspects of critical thinking, summaries, examples, and exercises. Each chapter ends with four sections: from theory to practice, thinking critically – about ourselves, in the classroom and the workplace. As I was reading this book, I reflected on many aspects of critical thinking that I briefly summarize in this blog.

Hunter defines critical thinking, as “a reasonable and reflective thinking aimed at deciding on what to believe and what to do.” I don’t know why, but he starts every chapter with this same sentence. I did ask him and will let you know in my next blog if I ever hear back from him! He explains that for the critical thinking to be “reasonable thinking”, one must have reasons for their beliefs based on adequate epistemic reasons, which in turns requires reflection on the meaning of the concepts and claims.

Additionally, Hunter shows how different disciplines might approach the same phenomena using different conceptual frameworks. He explains that thinking critically within a given discipline necessitates reflecting on that particular discipline’s frameworks. He also describes that mastering a discipline requires mastering its key concepts, sources of evidence, and primary modes of reasoning in this order. For example, Hunter describes that while geologists and physicists are both interested in earthquakes, they think about this phenomenon differently.  Similarly, sociologists and psychologists are interested in family dynamics, they use different tools to describe, explain and investigate the family life. Another example is cancer and how it can be conceived by different disciplines.

In summary, this book was worth reading and definitely gives the readers many strategies that can help them to think critically at home, at work, in the classroom, and in life in general. The book ends with two appendices: one on mistakes that a good critical thinker should avoid, and the other on practical strategies the critical thinker should embrace in order to be more reflective and reasonable.


One Response

  1. Hi, Amina–thanks so much for your post–very engaging! I’m really intrigued by the question of whether–in its essence?–critical thinking varies from field to field, discipline to discipline, or whether there’s a kind of core set of moves common to “critical thinking” regardless of discipline. (Does the repeated first sentence indicate–implicitly, if not explicitly–a kind of “sameness” across chapters/approaches)?

    I also like your observations on how seldom it is to (critically) make our thinking–it’s assumptions/steps, etc.–“visible” to students–how often critical thinking is, as it were, assumed. Wish I could say, more; have to come back to this when I have more energy (or: caffeine). 😉


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