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Keith Devlin’s Thoughts About a Modern Mathematics Education

Keith Devlin has long been a world class math educator. This IAE Blog entry discusses his recent article, All the Mathematical Methods I Learned in My University Math Degree Became Obsolete in My Lifetime (Devlin, 01/01/2017). Quoting Devlin:

When I graduated with a bachelor’s degree in mathematics from one of the most prestigious university mathematics programs in the world (Kings College London) in 1968, I had acquired a set of skills that guaranteed full employment, wherever I chose to go, for the then-foreseeable future—a state of affairs that had been in existence ever since modern mathematics began some three thousand years earlier. By the turn of the new Millennium, however, just over thirty years later, those skills were essentially worthless, having been very effectively outsourced to machines that did it faster and more reliably, and were made widely available with the onset of first desktop- and then cloud-computing. In a single lifetime, I experienced first-hand a dramatic change in the nature of mathematics and how it played a role in society. [Bold added for emphasis.]

Now, in 2017, we can look back and ask what progress undergraduate math education has made in light of the observation by Devlin and many others. During this time, computer hardware, software, and connectivity have continued to make rapid progress. This progress has greatly changed how colleges graduates solve the problems and accomplish the tasks in the disciplines they have studied. Of course the amount of change varies considerably from discipline to discipline.

Just for the fun of it, I examined the current requirements in the undergraduate math program of study at Kings College London. From the material I found on the Web, it is clear that this is a very challenging and rigorous program of study. But, I saw no mention of computers in the program description, nor any requirements in the field of Computer and Information Science. Clearly, the faculty in this program believe that rigorous math is good math, and is what a bachelor’s degree in math is all about.

The bachelor’s degree in mathematics at my alma mater, the University of Oregon, requires less courses in mathematics than does the Kings College London, and requires more breadth of study outside of mathematics. In addition, it offers a joint Math/Computer Science degree (University of Oregon, 2016). Quoting from this document:

Are you fascinated by the challenges and excitement of computer and information science? Do you also have a consuming interest in mathematics? With this major, you can explore the realm of computer and information science while developing a mathematics anchor. If you want to gain knowledge in both fields, but don’t initially want to specialize in either, this may be the major for you.

The knowledge you gain in this major is hugely practical in the real world. Computer science offers the challenge and excitement of a dynamically evolving science, the discoveries and applications of which affect every aspect of modern life. You will choose classes from areas such as programming languages, modeling and simulation, human-computer interaction, and artificial intelligence. [Bold added for emphasis.]

The Fourth R: Reasoning/Computational Thinking

Reading, writing, and arithmetic (math)—the three Rs—are considered to be the basics of education. At the PreK-12 level, students are required to take year after year of coursework in these areas. If students go on to college, they typically are required to take additional coursework in one or more of these areas. Indeed, a great many students entering college do so poorly on placement exams that they are required to start their college work with remedial courses that do not carry credit toward their degree (ACT, 2015). Quoting from the ACT article:

The ACT (2015) provides data annually on the percentages of students going on to college who were “qualified” in English, Reading, Mathematics, Science, and All Four Subjects. The site referenced above provides data for the past five years. During that time, the percentage qualified in all four areas went from 25% to 28%. English, Reading, and Math showed modest declines, and science showed a modest increase. In summary, the situation has not improved much over the past five years, and over 70% of students entering college need to take remedial coursework in one or more of the basic subject areas.

We live at a time when a fourth R (Reasoning/Computational Thinking) has emerged. See my recent free book, The Fourth R (Moursund, 12/23/2016). The 4th R makes use of both human brain and computer brain to answer questions, represent and solve problems, and accomplish tasks.

My short book recommends that the fourth R be thoroughly integrated throughout the PreK-12 curriculum in each discipline area students study during their many years in school. In higher education, I recommend that the four Rs be treated equally, thoroughly integrated into each course students take. The emphasis on each of the four Rs should, of course, be appropriate to the specific discipline a course is covering.

My major thesis is that it takes years and years of study and use to develop an appropriate modern level of competence in each of the four Rs. Currently there are two major movements in computer education. The first is to teach some computer programming to all precollege students, and the second is to require some computer science coursework at the college level.

Both of these approaches have merit. However, both are weak in that they do not focus on integrating Information and Communication Technology (ICT) knowledge and skills into the new knowledge and skills the students are gaining as they progress through their PreK-12 and further education. This integration requires that all teachers have the computer knowledge and skills appropriate to the level and disciplines they teach, and that all curriculum content reflect “modern” use of ICT.

Kelsey Sheehy’s article, Computer Science Transitions from Elective to Requirement, presents some of the ICT progress being made in higher education (Sheehy, 4/3/2012). She quotes Geoffrey Bowker, professor of informatics at the University of California—Irvine:

"Yes, [computer science] absolutely should be [required]," says Geoffrey Bowker, professor of informatics at the University of California—Irvine. All aspects of our personal lives and our work lives are affected by computers. We need to know about the tools that we're working with."

"Getting a flavor of science is great," he says. "But computer science is not a flavor; it's a staple." [Bold added for emphasis.]

Bowker’s point is consistent with my point of view. ICT is both a discipline of study and a tool useful across the curriculum. It is a “staple” in a modern education.

What You Can Do

No matter what your current level of informal and formal education, you are living at a time of very rapid pace of change in your world. This is likely to affect your own future and the future of many people you care about. Think carefully about what you are going to do to help yourself and others to deal with these changes. Perhaps start with an analysis of what you are currently doing. If you are not fully satisfied with your analysis, start to become more proactive. Set some learning and teaching goals for yourself. Then, “Make it so.”

References and Resources

ACT (2015). ACT [American College Testing] 2015 condition of college & career readiness. Retrieved 11/16/015 from

CCSS (n.d.). Common Core State Standards initiative. Retrieved 1/28//2017 from

Devlin, K. (01/01/2017). All the mathematical methods I learned in my university math degree became obsolete in my lifetime. The Huffington Post. Retrieved 13122017 from

Devlin, K. (n.d.). Keith Devlin at Stanford University. Retrieved 1/18/2017 from

Moursund, D. (12/23/2016). The Fourth R. Eugene, OR: Information Age Education. Download the Microsoft Word file from Download the PDF file from Access the book online at

Sheehy, K. (4/3/2012). Computer science transitions from elective to requirement. US News. Retrieved 1/29/2017 from

University of Oregon (2016). Joint mathematics and computer science degree program. Retrieved 1/30/2017 from

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