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Presentation for the Delta 2013 Kiama, Australia.
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Developing prospective mathematics teachers in Mexico:
A lesson on the relationship between integration and differentiation
Juan Carlos Ponce CampuzanoFaculty of Educational Sciences
University of Colima
Mexico
Mexico
• Population: 117 million
(World rank: 11th).• Language:
Spanish (92%) & Native languages (8%).
Mexico City
Mexico City
20 million population(Mexico city + Metropolitan area)
≈ Australian population
Developing prospective mathematics teachers in Mexico:
A lesson on the relationship between integration and differentiation
Teachers of mathematics in Mexico
Where are they trained?
• For basic education:• Normales (Teachers Colleges) and Universities• For High School and Higher Education:• Universities
General information about Education in Mexico
Phases of Education in Mexico
Mandatory
pre-K, grades 1-9 grades 10-12 UndergraduatePostgraduate
Basic:Ages: 5 to 15 years
High School:Ages: 15 to 18 years
Higher: Ages: 18 to 29 years
23 years studying
Phases of Education in MexicoBasic:Ages: 5 to 15 years
High School:Ages: 15 to 18 years
Higher: Ages: 18 to 29 years
Average: Only 9 years of education
Mandatory
Phases of Education in MexicoBasic:Ages: 5 to 15 years
Average: Only 9 years of education
Mandatory
Phases of Education in MexicoHigh School:Ages: 15 to 18 years
Higher: Ages: 18 to 29 years
Phases of Education in MexicoHigher: Ages: 18 to 29 years
Average: Only 13 in every 100 students finish the university
Only 3 in every 100 studentswill continue with a post grade
Issues in Mexico
• Educational• Economical• Lack of jobs• Corruption• Political• Violence
There is hope!
• Mexican authorities and Universities have been working together for improving education at all levels.
University of Colima
* Colima
Faculty of Educational Sciences
• Programme for training mathematics teachersfor basic and high school level.
Mathematics curriculum
High SchoolBasic
(1) number sense and algebraic thinking
(2) shape, space and measurement;
(3) data analysis; (4) attitudes toward
the study of mathematics.
Algebra, Analytic geometry, Trigonometry,Calculus,Probability and Statistics
A lesson on the relationship between integration and differentiation
The Fundamental Theorem of Calculus
Fundamental Theorem of Calculus
Fundamental Theorem of Calculus
b
a
f t dt F b F a x
a
df t dt f x
dx
Inverse relationship betweenintegration and differentiation
Fundamental Theorem of Calculus
Fundamental Theorem of Calculus
b
a
f t dt F b F a x
a
df t dt f x
dx
Inverse relationship betweenintegration and differentiation
Fundamental Theorem of Calculus
• Applets• Geogebra
Example 1
Time
Velo
city
Example 2
x
a
df t dt f x
dx
What can you say about the car?
Another example
• Intuitive idea of the Fundamental Theorem of Calculus.
• Use of technology• Dynamic interaction and visualization• Theory• History of mathematics• …
Thanks
