## Is it better to teach pure math instead of applied math?

- Entry #74
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"Is it better to teach pure math instead of applied math?" That is the question used as a title for a column by Jill Barshay, of *The Hechinger Report: Covering Innovation & Inequality in Education.*

The column begins,

"Abstract, pure math — solving disembodied equations filled with x’s and y’s — can often seem boring. Creative math teachers commonly try to come up with concrete, real-world examples to motivate students and make math relevant to adolescents.

"But a new report [*PISA - Equations and Inequalities: Making Mathematics Accessible to All*] from the Organization for Economic Cooperation and Development (OECD) finds that applied-math instruction, or the way it is actually taught in classrooms, may not be serving students well. Furthermore, it found that teachers were often using a watered-down, applied-math approach in classrooms of low-income students, while giving higher income students much more exposure to pure math."

The report says, ". . . many teachers who take a more applied approach aren’t giving their students complex, multi-step problems that require problem-solving and deep thinking.

" `The problem comes when students are asked to mechanically learn simple mathematical procedures and are then given lots of practical problems to apply these,' he said. `And there is a lot more of this kind of instruction going on in classrooms than you imagine.' "

The report is an (proper in our opinion) indictment of algorithmic teaching of algorithmic mathematics in the guise of applications of mathematics and the key phrase about teaching with applied mathematics is "the way it is actually taught in classrooms."

At SIMIODE we are not suggesting students "mechanically learn simple mathematics procedures," but rather we are posing realistic situations in which students need to do complex tasks while assembling the mathematics of differential equations for themselves.

So while we do not see our approach as problematic, it is important to understand the misconceptions and simplistic approaches and perceptions found in what may pass for using applications to teaching mathematics using applications. We believe such reports are attempting to get at the problem of just how difficult it might be to use applications to teach mathematics. Such studies, therefore, merit our attention.

### About the author

#### Brian Winkel

Brian Winkel earned his degrees in mathematics (BS, MS, PhD) in 1964, 1967, and 1971, respectively, with his PhD from Indiana University in Noetherian Ring Theory. While teaching in his first position (liberal arts college Albion College, Albion MI USA) he developed an interest in applications of mathematics to biology and while teaching in an engineering setting (Rose-Hulman Institute of Technology, Terre Haute IN USA, United States Air Force Academy, USAFA CO USA, and United States Military Academy, West Point NY USA) he developed a strong interest in engineering applications of mathematics. With sabbatical experiences at Michigan Technological University, Houghton MI USA and Brown University, Providence RI USA he strengthened his commitment to teaching mathematics using applications to introduce and drive the learning process.

Along the way he founded and edited three journals *Cryptologia *(1977 - Present), *Collegiate Microcomputer* (1982-1993), and *PRIMUS - Problems, Resources, and Issues in Mathematics Undergraduate Studies* (1990 - Present).

Upon retirement from the United States Military Academy in spring 2011 he committed time, energy, and resources, and together with many very talented colleagues who possessed the same vision of teaching modeling first differential equations he founded SIMIODE.