Misusing the term quantitative reasoning (#1388)

Topics/tags: Rants, Grinnell

In discussing a strong liberal (or perhaps liberal arts) education, Grinnell builds upon what it calls the Elements of a Liberal Education [1]. The elements appear n paragraph form, without labels. Nonetheless, the College regularly presents them as six short names: Writing and Communication, Language Study, Natural Sciences, Quantitative Reasoning, Human Behavior and Society, and Creative Expression.

I have a lot of things to say about the paragraphs, the labels, and other aspects of how we present them. But those will form another musing, perhaps multiple musings. For now, my muse compels me to write about our use of the term Quantitative Reasoning.

Quick! Think to yourself. What does the term Quantitative Reasoning suggest to you?

That’s right. It has to do with reasoning about quantities.

Here’s what a few other institutions have to say about quantitative reasoning.

Quantitative Reasoning is the ability to manipulate, analyze, and/or evaluate numbers and numerical data. It may involve calculation and/or analysis, and interpretation of quantitative information derived from existing databases or systematic observations, and may be based in a variety of disciplines, not limited to mathematics and the natural and physical sciences George Mason University

A mathematical way of thinking, more broadly referred to here as quantitative reasoning, is widely used, for example, to justify data-based decisions, encode and protect information, manage the treatment of disease, provide a unified understanding of the forces of nature, and formulate government and international policies. As such, it represents several distinct modes of thinking, which can broadly be classified as analysis, logic, probability and statistics, and modeling. From each of these derive techniques that are applicable to specific classes of problems. Often, a combination of different quantitative techniques is necessary to approach specific situations. Notre Dame

This category may potentially encompass any discipline that uses quantitative methods or formal logic, with an emphasis on courses that demonstrate how such methods can be used to explain reality and achieve meaning. Because these courses address both quantitative reasoning and critical thinking, they should locate mathematical skills and reasoning in a context of explaining or solving complex problems. University of Northern Iowa

As I said, it’s reasoning about quantities. I also appreciate one of The University of North Carolina’s expected QR learning outcomes.

Summarize, interpret, and present quantitative data in mathematical forms, such as graphs, diagrams, tables, or mathematical text.

Ooh! It’s not just reasoning. It’s also about presentation.

Now, let’s consider Grinnell’s paragraph.

Quantitative reasoning, with emphasis on mathematical models and methods above the secondary-school level, aids in the expression of hypotheses, processes, and theoretical relations. A course in statistics can be helpful for all students, and particularly for those who might work in the social and behavioral sciences. Studies in computer science offer valuable exposure to principles of logic and problem-solving paradigms.

From my perspective, this paragraph isn’t so much about quantitative reasoning as it is about three ways of approaching ideas: A graduate should be able to apply techniques of mathematics, techniques of statistics, and techniques of computer science. And, while these have many similarities, they also represent different approaches.

While mathematics can involve the study of numbers, it may also explore other abstractions. Topography, set theory, and more may involve counting, but may also involve only abstractions. I think of mathematics as providing an understanding of abstraction and precision as much as it provides a way to model quantities.

Statistics, in contrast, emphasizes not just numbers, but also approximation and mechanisms for handling incomplete information. And, like mathematics, it provides precise mechanisms. A statistician doesn’t just say this is likely to happen; they’ll give you odds and error bars.

Then there’s my field, computer science. We strive to teach our students two forms of thinking: algorithmic thinking and computational thinking. Algorithmic thinking, in short, focuses on how you develop, represent, and demonstrate the correctness of algorithms (unambiguous sets of instructions for performing tasks). Computational thinking, a term coined by Jeanette Wing, is a bit more complicated to describe; Wing spends more than a page describing different aspects. In short, it’s the various ways of thinking that computer scientists employ. But there are a lot of them. Here are just two of Wing’s paragraphs.

Computational thinking is thinking recursively. It is parallel processing. It is interpreting code as data and data as code. It is type checking as the generalization of dimensional analysis. It is recognizing both the virtues and dangers of aliasing, or giving someone or something more than one name. It is recognizing both the cost and power of indirect addressing and procedure call. It is judging a program not just for correctness and efficiency but for aesthetics, and a system’s design for simplicity and elegance.

Computational thinking is using abstraction and decomposition when attacking a large complex task or designing a large complex system. It is separation of concerns. It is choosing an appropriate representation for a problem or modeling the relevant aspects of a problem to make it tractable. It is using invariants to describe a system’s behavior succinctly and declaratively. It is having the confidence we can safely use, modify, and influence a large complex system without understanding its every detail. It is modularizing something in anticipation of multiple uses or prefetching and caching in anticipation of future use.

As I said, these are only two of many paragraphs. At some point, I’m going to review the literature to see the different ways in which educators have summarized these concepts. For now, I’ll just observe that computational thinking overlaps with, but is different from, quantitative reasoning, mathematical thinking, statistical thinking, and algorithmic thinking.

We’ve briefly explored five ways of thinking. As you might expect, I consider it inappropriate to use the name of only one of them to describe all five. What we do as computer scientists is not quantitative reasoning. What mathematicians do may contribute to quantitative reasoning, but mathematical reasoning is much more than reasoning about quantities. Statistical thinking falls much more clearly within the term quantitative reasoning; still, I’d prefer to think of it as precise reasoning under uncertainty.

Perhaps that’s one way to describe a commonality between the types of reasoning: All are precise, and all are formal. A liberally educated student should be able to reason precisely and formally, using the tools of mathematics, statistics, computer science, and philosophical logic.

Of course, a liberally educated student should also be able to reason about the world using the tools of mathematics and statistics. To comprehend and contribute to the modern world, one must be able to read graphs, tables, numeric data, and more.

I will admit that it would be politically complicated to divide that one paragraph into two different elements of the liberal arts. Nonetheless, there are two very different kinds of knowledge represented in that one paragraph, perhaps even five different kinds.

In any case, it’s time for a change.

Postscript: Our use of the term quantitative reasoning has concerned me for almost as long as I’ve been at Grinnell. When we started tagging our courses with the shorthand terms, I found myself particularly concerned. While the paragraph that starts Quantitative reasoning includes computer science, the term itself does not. Hence, I was never comfortable tagging my classes as such.

The issue came to a head, at least from my perspective, at last spring’s all-faculty retreat to discuss the liberal arts. At the retreat, we received an edited [2] version of the six elements. Here’s what the paragraph we’re considering looked like [3].

Quantitative reasoning, with emphasis on mathematical models and methods above the secondary-school level, aids in the expression of hypotheses, processes, and theoretical relations. A course in statistics can be helpful for all students, and particularly for those who might work in the social and behavioral sciences.

When I read that, I lost it. I complained to the President, the Dean, the Chair of the Faculty, others [4]. None of them seems to have understood why I was so upset.

To be clear: Having your subject completely removed from the College’s definition of liberal education feels like an attack. Having the bowdlerized version of that definition prented as if it were the actual one compounds the damage.

After the retreat, an administrator (one I normally respect highly) sent me an apology. In doing so, they noted that other department names were also removed from the definition. They failed to understand my concern: It’s not that my department’s name was removed; it’s that the modes of thinking computer scientists teach were removed. That’s inappropriate. Highly inappropriate.

Here’s an analogy. Let’s suppose our section on language learning also included separate reasons to learn a modern language, a classical language, and a logographic language [5]. If a version of our elements of a liberal education kept the sections on modern languages and classical languages, but left out the logographic languages, someone teaching such a language would likely feel slighted. Similarly, if our section on the creative arts retained studio art, creative writing, theatre, dance, and performance studies, but left out music, our musicians would appropriately feel slighted [6].

We need to do better.

[1] Will this URL continue to work? Who knows.

[2] Perhaps bowdlerized.

[3] This is an approximation. I no longer have the sheet.

[4] Perhaps that was overkill.

[5] Wouldn’t it be great if all Grinnell students studied three different languages? At least two?

[6] I have undoubtedly forgotten categories of languages and elements of creative arts. I apologize to colleagues in any disciplines I missed. However, I’m not presenting an official document.

Version 1.0 of 2025-12-19.