How We View the World:

And Why We Should Find Other ViewsR. Redekopp, U of Manitoba

And the Survey Says:

The first question is: Where did real math The first question is: Where did real math begin?begin?

Comments can be made at Comments can be made at todaysmeet.com/OldsApril3

Math is NOT a Science

It is a philosophical systemIt is a philosophical system

A system of logic based on assumptionsA system of logic based on assumptions

A good system but it directs the way we thinkA good system but it directs the way we think

Assumptions and Problems

When does 1+ 1 <> 2? When did 1+1 = 2.5?When does 1+ 1 <> 2? When did 1+1 = 2.5?

When does 1 = 1.034?When does 1 = 1.034?

When is the shortest distance between two When is the shortest distance between two points not a straight line?points not a straight line?

Let’s Count!

BinaryBinary

HexadecimalHexadecimal

VigesimalVigesimal

Who uses this? French has a weird variation of Who uses this? French has a weird variation of thisthis

Mayans and Aztecs did, Yoruba, Africa does, Mayans and Aztecs did, Yoruba, Africa does, Bhutan does and there are others.Bhutan does and there are others.

The Gods Must Be Crazy

What to look for?What to look for?

A Coke bottle as a technology. A Coke bottle as a technology.

Something that can’t be sharedSomething that can’t be shared

Primitive vs civilized – who’s happier?Primitive vs civilized – who’s happier?

Is ‘time’ really such a great thing?Is ‘time’ really such a great thing?

Who works harder?Who works harder?

Survey 2

What is more important, the group or the What is more important, the group or the individual?individual?

What assumptions are you making?What assumptions are you making?

Math Problems

Why do textbook problems seem irrelevant?Why do textbook problems seem irrelevant?

Because they are.Because they are.

They (and the math culture) think that you can:They (and the math culture) think that you can:

Ignore the situation – people and feelingsIgnore the situation – people and feelings

Work with only a tiny part of the problem by itself.Work with only a tiny part of the problem by itself.

Be happy when you solve almost nothing!!!Be happy when you solve almost nothing!!!

A lame math joke

Three men are in a hot-air balloon.  Soon, they find themselves lost in a Three men are in a hot-air balloon.  Soon, they find themselves lost in a canyon somewhere.  One of the three men says, "I've got an idea.  We canyon somewhere.  One of the three men says, "I've got an idea.  We can call for help in this canyon and the echo will carry our voices far.”can call for help in this canyon and the echo will carry our voices far.”

So he leans over the basket and yells out, "Helllloooooo! Where are we?" So he leans over the basket and yells out, "Helllloooooo! Where are we?" (They hear the echo several times).(They hear the echo several times).

15 minutes later, they hear this echoing voice: "Helllloooooo! You're 15 minutes later, they hear this echoing voice: "Helllloooooo! You're lost!!”lost!!”

One of the men says, "That must have been a mathematician.” Puzzled, One of the men says, "That must have been a mathematician.” Puzzled, one of the other men asks, "Why do you say that?” The reply: "For three one of the other men asks, "Why do you say that?” The reply: "For three reasons.  (1) he took a long time to answer, (2) he was absolutely reasons.  (1) he took a long time to answer, (2) he was absolutely correct, and (3) his answer was absolutely useless."correct, and (3) his answer was absolutely useless."

Math Problems

No context – eliminate all factors except one No context – eliminate all factors except one or two.or two.

One solution – in 3 minutes or lessOne solution – in 3 minutes or less

Other ways of viewing a problemOther ways of viewing a problem

Munir Fasheh – examples from the Middle EastMunir Fasheh – examples from the Middle East

Problem Interpretation

Manir FashehManir Fasheh

I came to believe that the main objective of [doing] I came to believe that the main objective of [doing] mathematics (or any other subject) in developing mathematics (or any other subject) in developing countries, is to doubt, to inquire, to discover, to see countries, is to doubt, to inquire, to discover, to see alternatives, and, most important of all, to construct alternatives, and, most important of all, to construct new perspectives and convictions. (p. 276)new perspectives and convictions. (p. 276)

http://site.ebrary.com/lib/umanitoba/Doc?http://site.ebrary.com/lib/umanitoba/Doc?id=10064652&ppg=262id=10064652&ppg=262

Problem Interpretation

Powtoon - http://www.youtube.com/watch?Powtoon - http://www.youtube.com/watch?v=E2XlhcSK63Mv=E2XlhcSK63M

Lying With Statistics

Math never lies – if you ignore the Math never lies – if you ignore the assumptionsassumptions

What is deceptive about the next graph?What is deceptive about the next graph?

So that’s the obvious stuff

Mathematics carries a bias within it (all those Mathematics carries a bias within it (all those assumptions).assumptions).

It has been built (most recently) by rich, white, It has been built (most recently) by rich, white, male, European/North American, military male, European/North American, military interestsinterests

Bias is not bad – but we need to be aware of Bias is not bad – but we need to be aware of it!!it!!

Assumptions?

Faster is betterFaster is better

Efficient is betterEfficient is better

Progress is inevitable and betterProgress is inevitable and better

Anything can be made into an abstract objectAnything can be made into an abstract object

Problems are just a bunch of little piecesProblems are just a bunch of little pieces

Emotions are irrelevantEmotions are irrelevant

Everything is merely a number

What happens when we ‘number’ or quantify What happens when we ‘number’ or quantify people and animals?people and animals?

Some people think this can be immoralSome people think this can be immoral

BibleBible

African cattleAfrican cattle

YouYou

Efficiency

• Mass production is better because it is more Mass production is better because it is more efficientefficient

• Better for who?Better for who?

– Business, farmers, workers, consumers, chemical Business, farmers, workers, consumers, chemical companiescompanies

• Efficiency is challenged in the next videoEfficiency is challenged in the next video

Food, Inc. clip (5:29)

• What to watch for:What to watch for:

• Math / Numbers say large scale production is Math / Numbers say large scale production is better.better.

• This farmer says large scale is inefficient, inhuman, This farmer says large scale is inefficient, inhuman, inhumane and just creates bigger problemsinhumane and just creates bigger problems

• Does this influence how we view each other (and Does this influence how we view each other (and other cultures)?other cultures)?

Efficiency

• XL FoodsXL Foods

• Spinach recallSpinach recall

• Turkey recallTurkey recall

• Disregard for living things – people and Disregard for living things – people and animalsanimals

Progress

• What is progress?What is progress?

– More stuff?More stuff?

– More free time?More free time?

– No famines or starvation?No famines or starvation?

– Cleaner environment?Cleaner environment?

– World peace?World peace?

Progress

• We can’t stop progressWe can’t stop progress

• BUT we can re-define it!!!BUT we can re-define it!!!

• We need to learn about other points of view We need to learn about other points of view and other valuesand other values

• We need to think differently, and we can’t do We need to think differently, and we can’t do that without learning new and different things.that without learning new and different things.

Multicultural value

• Math origins are in Africa, India and ChinaMath origins are in Africa, India and China

• The great Greeks (Euclid, Pythagoras) The great Greeks (Euclid, Pythagoras) mathematicians studied in Egypt firstmathematicians studied in Egypt first

• The Pyramids, Great Wall and Mayan The Pyramids, Great Wall and Mayan monuments are not accidentsmonuments are not accidents

Multicultural value

• We made these little gray houses of logs that We made these little gray houses of logs that you see, and they are square. It is a bad way you see, and they are square. It is a bad way to live, for there can be no power in a square. to live, for there can be no power in a square. You have noticed that everything an Indian You have noticed that everything an Indian does is in a circle, and that is because the does is in a circle, and that is because the Power of the World always works in circles and Power of the World always works in circles and everything tries to be roundeverything tries to be round

Multicultural value

• Do more than ‘respect’ other points of viewDo more than ‘respect’ other points of view

• Find out more about how people relate to each Find out more about how people relate to each other and the earthother and the earth

• Be prepared to changeBe prepared to change

• Think about what kind of world you want in 30 Think about what kind of world you want in 30 yearsyears