Quest

My students swear they can do it.   Many managers ask if their employees can do it, but the fact of the matter is, It can’t be done.  Check out this article The Myth of Multi-Tasking by Christine Rosen. She finds an amalgamation of new research that shows that multi-tasking reduces performance, quality, and drops IQ (in an interesting study). I’m sold, however I would like to the authors of these studies why it seems that some people work better with background music on.

According to Polya:

“The difference between experienced and inexperienced problem solvers is that inexperienced problem solvers don’t know hwat to do when they don’t know what to do.”

He outlined

First principle: Understand the problem

This seems so obvious that it is often not even mentioned, yet students are often stymied in their efforts to solve problems simply because they don’t understand it fully, or even in part. Pólya taught teachers to ask students questions such as:

• Do you understand all the words used in stating the problem?
• What are you asked to find or show?
• Can you restate the problem in your own words?
• Can you think of a picture or a diagram that might help you understand the problem?
• Is there enough information to enable you to find a solution?
• Do you need to ask a question to get the answer?

Second principle: Devise a plan

Pólya mentions (1957) that there are many reasonable ways to solve problems. The skill at choosing an appropriate strategy is best learned by solving many problems. You will find choosing a strategy increasingly easy. A partial list of strategies is included:

• Guess and check
• Make an orderly list
• Eliminate possibilities
• Use symmetry
• Consider special cases
• Use direct reasoning
• Solve an equation

Also suggested:

• Look for a pattern
• Draw a picture
• Solve a simpler problem
• Use a model
• Work backward
• Use a formula
• Be creative
• Use your head/noggen

Third principle: Carry out the plan

This step is usually easier than devising the plan. In general (1957), all you need is care and patience, given that you have the necessary skills. Persist with the plan that you have chosen. If it continues not to work discard it and choose another. Don’t be misled, this is how mathematics is done, even by professionals.

Fourth principle: Review/extend

Pólya mentions (1957) that much can be gained by taking the time to reflect and look back at what you have done, what worked and what didn’t. Doing this will enable you to predict what strategy to use to solve future problems, if these relate to the original problem.

There are 10 key strategies:
-Working backwards
-Finding a pattern
-Adopting a different point of view
-Solving a simpler, analogous problem
-Considering extreme cases
-Making a drawing
-Intelligent guessing and testing
-Accounting for all possibilities
-Organizing data
-Logical reasoning

Here is a link with some good examples:

problem_solving

the-art-of-problem-solving-vienna-2-06

Problems to use these 10 techniques.

Think you have it hard?  Think your job is pretty bad.  There are a lot of bad jobs out there in the world.  Here is a job that I’m pretty sure I couldn’t do at all, in bare feet.  Each brick probably weights 3-4 pounds times 22 is 66-88 pounds, balanced on his head. Yikes!

Here is one more….ever wonder who cleans sewage?

Students love psychology.  Two popular experiements are the power of conformity by Solomon Asche and the power of authority by Stanly Milgram:

Much ado about the state of education in the state of California.

Daily complaints:
Too crowed, not enough funding, charter schools, home schools, over-under legislated, lousy teachers, teacher unions, irrelevant curriculum, no vocational schools, teaching to the test, over testing, lack of parental participation…..the list goes on and on…and on.

Now that I am in the thick of it, I have some comments:
1) The method by which teachers are recruited and then educated is terrible. I have been disappointed with the administration and quality of what I am being taught and am asked to do to “prove” I am “worthy” of becoming a high school teacher. To be clear: we have some very nice, well-meaning, intelligent, and even competent instructors and administrators, but altogether, the system isn’t working well…if at all. I invite comment on this issue from some of my fellow teachers. My gripe list is 40 items long….feel free to send me a note and I add your complaint to mine and then submit it.

2) There is a lack of vocational programs in the schools. Somewhere along the way, decision makers got into their heads that everyone is college bound and therefore we only ought focus on sending students to college. Sure, college is the best way for people to improve their lot. It is however misguided and wrong to take away meaningful opportunities from young people and foist it on the community college system.

3) There is a lot of standardized testing. Why not roll the CaHSEE into STAR testing.
a: We would get better results from the STAR if students knew their graduation would depend on it.
b: We could eliminate days lost due to CaHSEE testing
c: We could eliminate duplicate bureaucracies and expenses saving the state millions a year.

I am very fortunate to teach where I do. I feel as if I make a difference everyday. I have great co-workers, administrators, and students. But I got lucky, others are struggling, and some have already left…

In teaching begining geometry I must aid students in understanding some rudimentary concepts of logic.  For example showing valid and invalid arguments, inductive and deductive reasoning, as well as how to disprove an argument.

If it rains, then I get wet
It rains,
———
I get wet

If it is a bird, then it flies
My pet is a bird
————-
My pet flies

If I don’t pay my bill, I get a fine
I don’t get a fine
————-
I paid my bill

These are just some example. However, I noticed that common knowledge impairs their ability to determine whether or not they can disprove an argument or statement. For example, some of my students did not know that all birds don’t fly. Some thought sharks are not fish and whales are fish. Only one knew that a bat is a mammal. Coupled with weak vocabulary skills, this lack of common knowledge makes formulating simple syllogisms difficult and frustrates them.

I enjoy a good optical illusion. There is a lot of math behind them and they frequently take advantage of people’s overconfidence in their perception. Here is a good one from Mindfake. If you think you know give me a comment!

When I was young I played futbol (soccer).  Our team was strong.  We worked well together, and I was having a great season.  I remember playing this one team, where I was having a game of games.  I scored from a corner kick, I scored on a long shot from mid field, and scored after out maneuvering defenders.  We were in zone.  By the end of the game we demolished the other team 5-0.  It was a sound victory and then something surprising happened.  The other team invited us over for drinks and fruit.  This was beyond the usual hand-shakes and see you laters.  This was sportsmanship at its best.  I made some good friends that day.  In fact looking back 25 years later, I am still in contact with people who were on both sides of that game.
With this in mind, it is with great dismay that I look upon the state of sportsmanship in youth sports today.  It seem nearly monthly there is some brawl amongst the players, the parents, the fans, or all of them.  Take a search on youtube of the news for youth violence in sports and you’ll find stunning results.  Dramatic up ticks are changing the focus of the game.  What message does that send to the leaders of tomorrow?

I took this picture behind Cathedral of San Idelfonso. First, the cathedral is the oldest in North America. It was built with stones from Mayan Ruins. The plaza mayor in front is impressive, but what about behind it.? Here is a different slice of Meridian life. Two old men try to get some extra pesos for Christmas, which is in two days from when this photo was taken. One man, plays trumpet. Now Europeans are familiar with this instrument, but so are the Maya. .

The tune he plays is not the sound of a mariachi, it is more basic and sincere. It isn’t loud or boisterous and it can barely be heard over the shopping melee across the street. It sounds old, respectful, and resonates off the walls of the ancient stone.

The other man is dressed in a Tommy Hilfiger shirt. His hat ready for handouts. His seems tired, beat by the heat, and worn by time.

Some of what is old survives and some of what is old adapts. Some fades in to distant memory and some fades altogether. Travel affords us the opportunity to see others, but also see ourselves in a different light.

I’m amazed that Spirit and Opportunity are still going. I remember when they landed and I watched the pictures they sent back nearly every day. I forgot about them for awhile, but found this image of a dust devil on Mars. Stop and think a moment. You are watching images from a remote control device, still running on solar power (5 years and going strong), that is roaming our neighboring planet.

It was just last year that
Voyager left the solar system. It was launched in 1977. It’s still going and we receive transmissions from time to time.

Although I teach Math, I bring these facts up every one in a while. Making something to last is important. Sloppy work leads to expensive mistakes. For this I provide an example of the Martian Lander that crashed into Mars because the two departments used different systems of measurement.

Now we are in the digital age – the age of communication, multi-media, and multi-tasking. It seems a great many things are ephemeral. Dot com here today and gone tomorrow. Unwanted and embarrassing pictures and stories seem to persist to the chagrin of many party-goers who now want gainful employment. But beyond that the landscape changes quickly. I wonder as we forge forth into the digital age, what will our new digital offspring build that will last. Are they up to the challenges of colonization of another planet? Can they save this one? I hope so, for my daughter’s sake.