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

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