Devlin's Angle

January 2000

Johnny might not be math-challenged; his problem could just be that he's an auditory learner

"I'm not stupid, I'm auditory," was how one student reacted after taking the learning-styles diagnostic test developed and administered by Diablo Valley College, a public, two-year community college outside San Francisco, California. "I realize there's nothing 'wrong' with me; I just process information differently," was another student's comment.

These are just two of several success stories cited by Diablo Valley College mathematics instructor Suzanne Miller in a report on the test she gave at the California Mathematics Council meeting in Monterey, CA, last month.

The diagnostic is based on Miller's research into learning styles, and was written by the college's learning disability specialist Catherine Jester. It comprises 32 multiple-choice questions designed to ascertain a student's natural learning style, and has been freely available on the Web since January 1998. It takes just a few minutes to complete, and the result -- a profile of the student's learning style along with specific suggestions of how best to study -- is available immediately. To date, over 10,000 students from Diablo Valley College and elsewhere have used it to overcome math anxiety and improve their performance in mathematics.

Miller's initial analysis of the data generated by the test indicate that there may be a good reason why so many people find learning math so difficult. Among males aged between 18 and 25, Miller found, just 17% are suited to learn through reading text. For the remaining 83%, the standard college textbook is little more than dead weight to carry around in their bag! The figure for women in the same age group is a bit higher: just under 35% can learn from textually presented information.

These figures contrast with those for students aged 35 or over -- a substantial population in today's community college community. In this age-group, 27% of males and over 42% of females find it natural to learn from reading. But that's still less than half the student population. Miller does not know whether the difference between the two age-groups is a direct consequence of growing older, or is a reflection of changes in the environment in which today's under 25s grew up. The answer to that question will have to await a follow-up study she hopes to carry out when today's younger respondents grow older.

By far the most powerful method of learning among all age-groups is visual nonverbal: diagrams, tables, illustrations, pictures, and video. Among the 18-25 age-group, 48.1% of males and 36.2% of females favor this method of learning. The figures for the over-35s are almost identical: 46.0% and 38.8%. Half a century after the dawn of the television age, these results are perhaps not surprising. But the vast majority of mathematics courses are still structured around the traditional college textbook.

At a time when many people are taking college courses on the Internet, it is worth taking note of another of Miller's findings: that a surprisingly high proportion of people learn best from listening. In the 18-25 age-group, 38.0% of males and 31.3% of females are predominantly auditory learners; among the over 35s, 35.2% of males and 25.7% of females. If providers of Internet-based education want to reach those individuals, they had better provide instruction by voice as well as text, illustrations, and video.

Among Miller's own online math students is a married couple with a 4 month old child. The husband is visual non-verbal, draws pictures and can then 'see' the answer to the problem. His wife is a reader who works step by step. As Miller remarks, "They have not been able to collaborate because his way confuses her and vice versa."

The fourth group of learners Miller's study has identified are those who learn best in a tactile or kinesthetic fashion, by manipulating objects or gesticulating with their hands. Among the younger age-group, 20.2% of men and 20.7% of women learn best in this fashion; among the older students, the figures are 14.1% and 13.1%, respectively. Don't expect those individuals to succeed unless they are free to stand up and move around.

Creating even more of a challenge for teachers, between 20 and 24% of students do not fall cleanly into one particular category, but exhibit a hybrid learning style that spans two or more of the four categories.

I took the test myself. It diagnosed me (correctly) as primarily suited to learning by reading and secondarily by visually presented information (diagrams, graphs, tables, etc.). Among the seven specific suggestions to improve my learning, my diagnostic report said I should "Write out sentences and phrases that summarize key information obtained from your textbook and lecture", that I should "Make flashcards of vocabulary words and concepts that need to be memorized," and that "When learning information presented in diagrams or illustrations, write out explanations for the information." I did all of these when I was a student. Indeed, the only suggestions I did not use are those involving computers, which were not available in my own student days. Looking back, I was lucky that my learning style fitted so well into the educational system prevalent at the time. I did well. Many are not so fortunate.

In her presentation at Monterey, Miller observed that "The project has made faculty more aware of the importance of understanding diverse learning styles and designing course work to reach the broadest possible spectrum of styles." Perhaps more significant, she says, "It helps students by identifying their strengths, encouraging them to become active managers of their educational resources and to take responsibility for their learning."

Miller's study had 3,596 males and 2,998 females in the 18-25 age-group and 707 males and 1,480 females aged 35 and over. The learning styles survey is available on the web at: .

Devlin's Angle is updated at the beginning of each month.
Keith Devlin ( is Dean of Science at Saint Mary's College of California, in Moraga, California, and a Senior Researcher at Stanford University. His latest book InfoSense: Turning Information Into Knowledge, which shows how a mathematical approach to information can help us to understand information flow and manage it more efficiently, was published by W. H. Freeman last August.