Career opportunities after the PhD degree in
mathematics:
to be a secondary school teacher
Young Mathematician Colloquium, Vrije Universiteit Brussel
Koen De Naeghel
Onze-Lieve-Vrouwecollege Brugge
Content
1 About myself
Studies, work and location
2 About the job
The money The challenge
Teaching concepts and methods An example
What is teaching? Act of commitments
Studies, work and location
1996-2000 Universiteit Gent 2000-2006 Universiteit Hasselt Universiteit Antwerpen Vrije Universiteit Brussel 2006-2007Kindsheid-Jesu Hasselt 2007-20XY
Onze-Lieve-Vrouwecollege Brugge 2008-2009
The money
paid as master
diploma pedagogical competence (dpc) years of service (yos)
yos no dpc dpc
0 e 1550 e 1800
4 e 1710 e 1960
6 e 1790 e 2040
16, 75 e 2520
First thing to do?
Validate the years of doctoral employment!
Second thing to do?
The challenge
Teaching concepts and methods
function polynomial logarithm
angle matrix complex number
sequence limit asymptote
derivative probability integral
dot product normal distribution stochastic variable
What: see curriculum government
What: mathematical correctness
What: conventions
What: common sense
How: see. . . ? Why: see. . . ?
Making choices while keeping in mind:
Teaching concepts and methods
How can I explain things as good as possible?
Ancient times: start with definitions and theorems
Ancient times: examples come afterwards
Modern times: start with examples
Trend: use examples to explore definitions, properties etc.
Trend: to make them self-evident
Personal belief: every mathematical concept has a
An example
Preliminary definite integral as a signed area
Objective relation between integrals and derivatives Option 1 prove Z b a f (x) dx = F (b) − F(a) where F 0(t) = f (t) a b y x y = f (x) Z b a f (x) dx
An example
Option 2 what is the rate of change of A(t) = Z t
a f (x) dx A0(t) ∼ f (t) a t b y x y = f (x) A(t)
Historisch draagvlak
http://vimeo.com/48768091
What is teaching?
(1) Teaching is giving opportunity to the students to discover
things by themselves.
(2) First guess, then prove.
(3) Finished mathematics consists of proofs, but mathematics
Act of commitments
Three basic rules:
(1) Make pupils trust you. . .
by confirming them when they got it right.
(2) Make pupils experience succes. . .
by responding their questions with simpler questions.
(3) Make pupils like math. . .
by being passionate about math yourself. Tell them math stories!
Ex.1 The odds to win the lottery is 1/C6
45 = 1/8 145 060.
So, are these odds really that small?
How long is one million seconds? . . . about 12 days
The odds to win lottery ∼ one second out of . . . 3 months How long is one billion seconds? . . . 32 years
Act of commitments
Three basic rules:
(1) Make pupils trust you. . .
by confirming them when they got it right.
(2) Make pupils experience succes. . .
by responding their questions with simpler questions.
(3) Make pupils like math. . .
by being passionate about math yourself. Tell them math stories!
Ex.2 Last time, I had dinner with eight colleagues.
In order to serve the main course, our plates were taken off the table and brought to the kitchen.
What were the odds that no one got back his own plate? 36, 78 . . . % n→+∞−→ 1
Act of commitments
Three basic rules:
(1) Make pupils trust you. . .
by confirming them when they got it right.
(2) Make pupils experience succes. . .
by responding their questions with simpler questions.
(3) Make pupils like math. . .
by being passionate about math yourself. Tell them math stories!
Ex.3 Climate change according to math? PROVED!
So far, 2016 is the warmest year on record.
What are the number of record years since 1880? expected value
| {z } ↔ actual frequency| {z } 1 + 12 + 13 + · · · + 1371 = 5, 50 . . . 23
To be a secondary school teacher is. . .
(A) Asking yourself how to explain things as good as possible?
(also: natural, self-evident, correct, realizable, meaningful)
(B) Willing to know more about math yourself
content history
teaching methods
(C) Giving the opportunity to pupils
to discover things by themselves
