Mathematics
What is it and how do I get some?
How do we use it?
mathematics concerned with quantity, shape, space and
change
used to create models in the natural and human sciences
the possibility of a mathematical treatment is taken by many
to be the sign of intellectual rigor
possesses qualities such as beauty and elegance
seems to be broadly universal and not tied to a particular
culture
How much do you love
math?
Math SL, split into Advance Algebra and
Algebra 2
Once in those 2 groups, line up by “who loves
math most”.
We will put you in groups 1 ,2, 3, 4, 5.
In groups 1-5
Discuss and prepare to share your ideas with the
larger group of the following:
What is meant by mathematical
knowledge and how do we
acquire it?
Make notes in your journal
With whole class …
What is meant by mathematical knowledge and
how do we acquire it?
How does the math class you are in
and/or how much you like math
define how you perceive
mathematical knowledge?
Divide up, evenly into
the following groups:
Sense Perception
Language
Reason
Emotion/faith
Imagination/intuition
Does Math Exist?
Watch this.
New group task
Discuss and share you thoughts on the following:
Does math exist for us to
find/discover? Or is it something
people have created?
Which Ways of Knowing do we use to
“know”math? All to the same degree?
Justified, true, belief …
Do you KNOW?
Can you trust your eyes?
For the next two figures , decide
which horizontal segment is
longer.
Which segment is longer: AB or AC?
Can you trust your
intuition?
Xeno’s paradox – I’m trying to
leave the room. I go to the
halfway point, then I have to go
through the ¼ way point, then
the 1/8 of way point, … . Do I
get out the door?
Your reasoning?
A clock strikes 6-o’clock in 5
seconds. How long will it take
to strike 12?
Your business
reasoning?
A fruit vendor sells apples 2 for 5rmb and
oranges at 3 for 5rmb. He decides keeping
track is too much trouble and puts all the
apples and oranges in a bin and sells them
at 5 pieces for 10rmb. Then he realizes he
can just sell everything at 1 for 2rmb.
Is this reasonable?
Does culture limit how
we KNOW?
HOMEWORK
• Read the article: Living without
Numbers or Time
• Journal: How did you answer: is math
discovered or invented? How would
the Piraha people answer that
question? Does culture limit our
mathematical knowledge?
References
Butterworth, Brian - What happens when you can't
count past four?
Kline, Morris – Mathematics and the Search for
Knowledge
ToK Guide
Von Bredow, Rafaela - Living without Numbers or
Time