**ERIC Number:**EJ962496

**Record Type:**Journal

**Publication Date:**2011

**Pages:**7

**Abstractor:**ERIC

**Reference Count:**8

**ISBN:**N/A

**ISSN:**ISSN-0819-4564

To Solve or Not to Solve, that Is the Problem

Braiden, Doug

Australian Senior Mathematics Journal, v25 n2 p7-13 2011

The senior school Mathematics syllabus is often restricted to the study of single variable differential equations of the first order. Unfortunately most real life examples do not follow such types of relations. In addition, very few differential equations in real life have exact solutions that can be expressed in finite terms. Even if the solution can be found exactly it may be far too difficult to be clearly articulated such as those that form an infinite series. In either case, these "real life problems" are well beyond the scope of the secondary student to solve. Does this mean that many of the exciting relationships and models found in the real world cannot be studied by the secondary student? What if the behaviour of the solution was just as important as the solution itself? What device can be so powerful? Enter the "phase plane"--a geometrical device. To understand how the phase plane works, the author first considers the "predator-prey model" defined by Alfred Lotka in 1920 and Vito Volterra in 1926 called the Lotka-Volterra System. Although many mathematical models exist whose solutions are quite complex, this need not prevent students from exploring such ideas. The phase plane method gives the student another tool in their ever expanding "tool box" to explore an exciting area of mathematics. (Contains 3 figures.)

Descriptors: Mathematical Models, Equations (Mathematics), Mathematics Instruction, Problem Solving, Secondary School Mathematics, Secondary Education, Handheld Devices, Graphing Calculators, Foreign Countries

Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office@aamt.edu.au; Web site: http://www.aamt.edu.au

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Secondary Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Identifiers - Location:**Australia