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Copy of Mathematics
Mathematics
Compare/Contrast
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PV=nRT
Hai-lin Yeh & Cindy Tjia
also known as "theoretical math"
- number theory
- topology
- To what extent can teaching math in different ways affect our knowledge and understanding?
- How do we determine what type of math should be taught?
- To what extent should mathematics determine our accessibility to higher education?
"The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics"
-G.H. Hardy
No real life application or representation
Main Idea
Example: 3x2=6
Mathematics is the study of pattern that puts concepts in a relationship to each other, expressed as a system and solved using reason.
They show up in the physical world and consists of equations and numbers invented by us.
Like other areas of knowledge, mathematics
is shared knowledge.
- An example of truth is the Euclidian geometry.
- was considered both valid and true
- The Riemann system was also both valid and true
- leads to recognition of alternative systems
- truth within a system
First
Third
Second
Individual mathematicians contribute their work
to a communal pool
If it is found reliable, they build on the theory by
doing further work and in turn, contribute to a
collective pool.
Other mathematicians, in process of peer review,
scrutinize the work for errors.
COMMON CORE and UC Requirements
: TOK ISSUE?
UC Requirements
Common Core (Applied Math)
Old Way (Pure Math)
AP or IB examination:
Score of 3, 4 or 5 on the AP Statistics Exam satisfies elementary and intermediate algebra.
Score of 3, 4 or 5 on the AP Calculus AB or Calculus BC Exam satisfies three years.
Score of 5, 6, or 7 on the IB Mathematics HL exam.
NOTE: All students must complete a geometry course or integrated math with geometry content; neither AP Calculus AB/BC nor IB HL Mathematics exam will satisfy the geometry requirement.
- Mathematics can be applied to the WOK language
- precise, straight to the point, and can be manipulated without losing its meaning
- Mathematics can also be applied to WOK reason
- way of working and justifying conclusions
Relation to WOK
Methods: Shared Knowledge
Pure Math
includes fields such as:
- algebra
- analysis
- geometry
Mathematical
Truth
Related Knowledge Questions
Applied Math
Applied math is using math tools we learn from pure math in order to enhance research and connect them with the other areas of knowledge and the real world