DEDUCTIVE REASONING follows from rules of logic. It is an "If a then b" type of reasoning. Conclusions are not drawn from experiment or measurement. For example, you could not prove that global warming existed using deductive reasoning. But to prove that 2 odd numbers when added produce an even number it is ideal. The formalization of deductive reasoning goes back to the Greeks. They were disdainful of physical measurements. They started with a few basis assumptions about lines and points on a plane. These were called axioms and were considered to be "self evident." (They were, however, not comfortable with one axiom the parallel postulate and with good reason). Using the axioms one can deduce one proposition from another proposition.

INDUCTIVE REASONING is based on empirical data. Most proofs outside mathematics invoke empirical data. The law of gravity is not a theorem. It is a probabilistic statement based on the fact that historically it has always been the case. It is a physical law.

Inductive reasoning is not the same as mathematical induction.

I decided to post a few more mathematics websites that I use from time to time.

I like mathwords for looking up mathematical terms and definitions.

The Understanding Mathematics website was developed at the University of Utah to offer support to undergraduate mathematics students. Its contents are relevant to mathematics learners at many levels.

This website discusses the story of the number zero, in four dimensions.

The John Handley High School mathematics website has many interesting resources from puzzles, to quotes to lesson plans.

The Vocational Information Center offers a link to many mathematics sites.

Bransford's current project is The LIFE Center. The kinds of questions that Bransford and his colleagues ask are: What do people need to learn about for a high quality life? How do people learn about health care, nutrition, finances, local environmental conditions.

Books that were recommended mentioned during the talk were:
*Fish is Fish by Leo Leonni (A children's picture book that shows how when something is explained to a fish, the fish interprets it in light of what it knows).

Books edited or co-edited by John Bransford
How People Learn
How Students Learn
Preparing Teachers for a Changing World

Books on the changing needs of society in the future
The World is Flat Friedman and Wyman
The Power of Productivity William Lewis
The New Division of Labor Levy and Murnane

A book that describes the intellectual aspects of everyday work:
The Mind at Work by Mike Rose

APOS: A constructivist theory of learning

Using a theory of learning in college mathematics courses

THE EUROPEAN UNION
*European Union (EU) countries have the right to withdraw from the EU unlike US states.
*Unanimity of agreement is required on decisions that relate to crime and security matters within the Union. Qualified majorities are acceptable on other issues. Individual countries have the lead responsibility for matters relating to military involvement and foreign policy whereas the EU has the lead responsibility in matters that relate to cross-border crime, standard setting, commerce and humanitarian issues.
*The EU operates on 7-year budgetary cycles and every country must agree on the budget. The EU cannot borrow and it spends 1% of EU Gross Domestic Product (GDP)

THE EUROPEAN UNION AND THE UNITED STATES
*The EU and the US have 12% of the world's population and 45% of the world's wealth.
*For 1800 of the last 2000 years India and China had relatively greater influence in the world than they have today but India and China were hampered by "European meddling" in their affairs and Europe was boosted by the industrial revolution.
*The level of US investment in the United Kingdom alone is higher than the total level of US investment in Asia.
*A challenge for the US and the EU is how they will deal with an inevitable falling in their percentage of the world's wealth. Will rebalancing take place peacefully or not? The US and the EU need to work together to manage the transition.
*There are huge inequalities in worker pay across the EU. The average worker in Denmark (the highest earners) earns 11 times as much as the average worker in Latvia (the lowest earners). In the US the average worker in Haiwaii (the highest earners) earns twice as much as the average worker in Mississippi (the lowest earners).

IRELAND
*John Bruton disagrees with the Irish requirement where all students must learn what he called a "dead language," the Irish language.
*US companies make 3 times as much profit from investments in Ireland than they do from their investments in China.
*40% of legislation passed in Ireland is build on EU templates and is required by the EU.

She did tell a good story about being at a folk festival in Ireland when she overheard two women debating in the portaloos whether she would sing her biggest hit or not. Her take off of a northern Irish accent wasn't bad!

Alice McGill closed the evening by reminding the audience that the human voice is the most powerful instrument. On a few occasions during the evening she got the audience to sing reminding us of proverbs from Zimbabwe that claim that if you can talk you can sing and if you can walk you can dance. She opened her presentation by telling us that her story was herself and convinced us of that by telling lively and engaging stories of her homesickness in college and her becoming a teacher and about Brer Rabbit's attempt to marry the king's daughter.

The evening reminded me of what a powerful medium storytelling can be for educating and how knowledge of generations have been passed on by generations (such as McGill's story of how Africans used to be able to fly - lore which could not, in the past, be shared with bakras). The underlying human element of storytelling was highlighted by Alice McGill when early in her session she asked for the house lights to be put up because when she tells stories she likes to be able to see the whites of her listeners' eyes

The film deals with many issues including ageing, living your dreams, bending the rules and being frugal. But the sum of the movie is not about issues it's just about being human and being alive. Part of it is like a road trip across the United States of the 1960's. There are some great quotes such as when the old man tells the young boy that if you don't follow your dreams you might as well be a vegetable. "What vegetable?" "A cabbage." My only gripe with the movie is the soundtrack which is a bit tedious and too close to American Beauty for my liking. Definitely a 9 out of 10 for me.

Now I'm going to read about it on http://www.imdb.com/title/tt0412080/

The restaurant was also known for its cheap prices. The decor resembled Beweley's in Dublin and even the waiting staff were dressed in black and white. "I have been coming here since I was in my twenties and now I'm in my seventies" explained one woman to a waiter. Another customer who seemed to be much older claimed that he had been coming here every Friday for as long as he remembers. All the waiting staff knew him by name. But, now the restaurant was closing because the family no longer wish to continue the tradition.

Why did people seem so sad to be losing a restaurant when there are many other good restaurants in Chicago? We discussed this and the best reason we could think of is that people are tired of predictable food from menus of franchised and chain restaurants. Berghoff's seemed to offer genuine, distinctive food and what it lacked in presentation it compensated for in wholesomeness. In a world rushing to conformity of taste, Berghoff's offered an alternative. We need more Berghoff's and that is why it is sad to see it closing.

They introduced me to a way of running that is really simple:
*Getting good running shoes, fitted by someone who has experience doing this; a heart-rate monitor and suitable running gear.
*Doing 80% of your running at aerobic maximum heart rate (calculated by subtracting your age from 180.)
*Doing a 'lactic threshold' run once a week (where you raise your heart rate by 20 beats per minute)
*Doing interval training
*Doing stretches and other running exercises.

A good friend, Richard, was interested in doing this type of running too so I promised him that I would search out some information on the web. I haven't found that much but this pdf page seems to be quite good: http://www.denison.edu/human_res/payroll/Level25k.pdf. Please add a comment if you can suggest more suitable online materials.

"It is a mistake to assume that creativity and rote learning are incompatible. Some of the most original scientists ... have been known to have memorized music, poetry, or historical information extensively...Educational reformers at the start of the twentieth century claimed that 'rote learning' was not an efficient way to store and acquire information. As a result...rote learning was phased out of the schools...If you decide what you would like to have in memory...the whole process of learning by heart will become a pleasant task."

www.boards.ie
This website has links to discussions on a wide range of topics, all from an Irish perspective.

www.imdb.com
A great site to go to for reviews, trivia, summaries and other details about every film you ever saw or wanted to see.

www.jumptheshark.com
This is a discussion about (mainly but not exclusively U.S.) TV programmes and when (if) they passed their peak.

Staying in Club Quarters, a hotel that I got on www.priceline.com for $80 a night. It's situated in The Loop. Went to the John Hancock observation tower yesterday and to the Museum of contemporary art http://www.mcachicago.org/. Look out for the big baby and the small Hitler exhibits in this museum.

What I found out today, though, was that you can get a City Pass book of tickets for around $50 which gives entry to The Art Institute of Chicago, the Shedd Acquarium, the Planetarium, the Field Museum (though you have to pay extra for the Pompeii exhibition), the Museum of Science and Industry and the Hancock Observatory.