## Monday, April 22, 2013

### Teaching/Learning Mathematics

## Monday, April 1, 2013

### Resurrecting California’s Public Universities

Quoting from the editorial:

"The same California State Legislature that cut the higher education budget to ribbons, while spending ever larger sums on prisons, now proposes to magically set things right by requiring public colleges and universities to offer more online courses. The problem is that online courses as generally configured are not broadly useful. They work well for highly skilled, highly motivated students but are potentially disastrous for large numbers of struggling students who lack basic competencies and require remedial education. These courses would be a questionable fit for first-time freshmen in the 23-campus California State University system, more than 60 percent of whom need remedial instruction in math, English or both.

"The story of how the state’s fabled higher education system got to this point is told in a troubling analysis by the Public Policy Institute of California, a nonpartisan think tank."

## Sunday, March 31, 2013

### Stephen Wolfram at SXSW

It is impossible to listen to him talk and not come away excited and with many ideas to pursue.

### The 100th Annivsary of Paul Erdos' Birth

## Tuesday, August 21, 2012

### New GeoGebra Routines

## Sunday, October 16, 2011

**, and a line, the**

*focus***.**

*directrix*The September 2011 issue of The College Mathematics Journal (published by MAA) contains an article by Dan Joseph, Gregory Hartman and Caleb Gibson titled Generalized Parabolas (available online if a member/subscriber or through jstor: http://www.jstor.org/pss/10.4169/college.math.j.42.4.275 if you have access to jstor). In their article they investigate what happens if you change the directrix in the definition above to a general curve, for example, a parabola (see example 3 below). The authors took an analytical approach, using Mathematica to find the equation of each generalized parabola.

I recognized GeoGebra could be used for a purely geometrical investigation. Go to http://www.burke-consulting.com/GeneralizedParabolas.html to see some way cool examples and then try it out for yourself IMNSHO.

John

## Monday, August 1, 2011

### Is mathematics invented or discovered?

I often tell students when introducing new (to them) concepts that when mathematicians hit a brick wall in pursuing some investigation, they invent something to knock down the wall. Mathematics is purely an invention of the human mind.

Another way of looking at the same thing is that the tool to knock down the wall was there all along just waiting for someone with the need to discover it. All of mathematics exists as a fundamental part of the universe independent of us.

In thinking about this, I realized that I use the terms “invent” and “discover” interchangeably when talking about mathematics, and yet they are not the same.

Theoretical astrophysicist Mario Livio has an article in the August Scientific American titled “Why Math Works” where he examines both sides of this philosophical argument … and comes down squarely in the middle.

The article is at www.sciam.com; however, I think you need to be a subscriber to read the whole article (unless the college has a site license).