Sunday, August 26, 2007

Parallel lines and optical illusions

Look at the 2 lines above, are they parallel or bent?

Look at the diagonal lines above, do they look parallel?
Optical illusions occur in everyday life. Sometimes things do not look as what they are supposed to be. It is important to illustrate this point to students learning geometry, that one should not assume some properties of the object by visual inspection.

In short, for questions not drawn to scale, one should not make unnecessary assumptions. So if you're given two lines, how can one determine whether they are parallel?

Saturday, August 25, 2007

Mathematics and Careers

In the book "Careers for Number Crunchers and Other Quantitative Types" (VGM Career Books) , Rebecca Burnett explores various careers that require a certain aptitude in mathematics. Here is a list from the book:

Tracking of financial records
  1. Accountants
  2. Book keepers
Managing Money and Cash flow
  1. Chief Finance Officer (CFO)
  2. Office Manager
  3. Bank Teller
Guiding Investments
  1. Mortgage Officer
  2. Financial and Securities sales representative
Buying in the workplace
  1. Purchasing Manager
Marketing and Selling in the Workplace
  1. Sales Service Representative
  2. Insurance agent
  3. Marketing
Quantitative Thinking Careers
  1. Engineers
  2. Computer System analysts
  3. Calculating Risks and Probabilities
  4. Actuaries
  5. Operation Research Analyst
  6. Statistician
Research in Natural Sciences
  1. Biological scientist
  2. Meteorologist
  3. Physicist
  4. Mathematician
  1. Teacher
The book also lists some real life examples of the responsibilities in each career. For instance, for an actuarial analyst such as Brian, he uses computers to do mathematical analysis on databases to help him make recommendations about raising and lower insurance rates and changing policy coverages for insurance companies.

For an operations research analyst, one must apply quantitative thinking to help refine and solve work flow problems in a company. For example, an analyst in a manufacturing facility might deal with modifying production lines for new products, while an analyst employed by a hospital might monitor the use of pharmaceutical and laboratory services. They also also employed by airlines to help build a system for scheduling airline staff.

A good book to read for those who are interested in a career that deals with numbers.

Friday, August 03, 2007

ThinkQuest Website on Mathematics

The following thinkquest website is well worth visiting. It contains abundant information on Algebra, Geometry, Calculus and Trigonometry. This will prove handy in O level mathematics.

Wednesday, August 01, 2007

Java Applet on Algebraic Tiles

A useful online algebraic resource can be found in the website highlighted below:

Go to yr 9-12>Algebra>Algebra Tiles

Accompanying the java applet are instructions and activities that can be used in class to teach algebra. This java applet can be used to illustrate many algebraic techniques including expansion and factorisation.