developing prospective mathematics teachers in mexico

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Developing prospective mathematics teachers in Mexico: A lesson on the relationship between integration and differentiation Juan Carlos Ponce Campuzano Faculty of Educational Sciences University of Colima

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Presentation for the Delta 2013 Kiama, Australia.

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Page 1: Developing prospective mathematics teachers in Mexico

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

Page 2: Developing prospective mathematics teachers in Mexico

Mexico

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Mexico

• Population: 117 million

(World rank: 11th).• Language:

Spanish (92%) & Native languages (8%).

Mexico City

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Mexico City

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20 million population(Mexico city + Metropolitan area)

≈ Australian population

Page 6: Developing prospective mathematics teachers in Mexico
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Page 8: Developing prospective mathematics teachers in Mexico

Developing prospective mathematics teachers in Mexico:

A lesson on the relationship between integration and differentiation

Page 9: Developing prospective mathematics teachers in Mexico

Teachers of mathematics in Mexico

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Where are they trained?

• For basic education:• Normales (Teachers Colleges) and Universities• For High School and Higher Education:• Universities

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General information about Education in Mexico

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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

Page 13: Developing prospective mathematics teachers in Mexico

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

Page 14: Developing prospective mathematics teachers in Mexico

Phases of Education in MexicoBasic:Ages: 5 to 15 years

Average: Only 9 years of education

Mandatory

Page 15: Developing prospective mathematics teachers in Mexico

Phases of Education in MexicoHigh School:Ages: 15 to 18 years

Higher: Ages: 18 to 29 years

Page 16: Developing prospective mathematics teachers in Mexico

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

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Issues in Mexico

• Educational• Economical• Lack of jobs• Corruption• Political• Violence

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There is hope!

• Mexican authorities and Universities have been working together for improving education at all levels.

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University of Colima

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* Colima

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Faculty of Educational Sciences

• Programme for training mathematics teachersfor basic and high school level.

Page 24: Developing prospective mathematics teachers in Mexico

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

Page 25: Developing prospective mathematics teachers in Mexico

A lesson on the relationship between integration and differentiation

Page 26: Developing prospective mathematics teachers in Mexico

The Fundamental Theorem of Calculus

Page 27: Developing prospective mathematics teachers in Mexico

Fundamental Theorem of Calculus

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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

Page 29: Developing prospective mathematics teachers in Mexico

Fundamental Theorem of Calculus

Page 30: Developing prospective mathematics teachers in Mexico

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

Page 31: Developing prospective mathematics teachers in Mexico

Fundamental Theorem of Calculus

• Applets• Geogebra

Page 32: Developing prospective mathematics teachers in Mexico

Example 1

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Time

Velo

city

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Example 2

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x

a

df t dt f x

dx

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What can you say about the car?

Page 43: Developing prospective mathematics teachers in Mexico

Another example

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• Intuitive idea of the Fundamental Theorem of Calculus.

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• Use of technology• Dynamic interaction and visualization• Theory• History of mathematics• …

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Thanks

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