Area: 319 sq.km Population: 38.5 mln Math teachers: 30 000 Masters Degree in math: 95%
Area: 319 sq.km Population: 38.5 mln Math teachers: 30 000 Masters Degree in math: 95%
Winds of change…
Winds of change…
Winds of change…
He must be
really smart
!
Winds of change…
routine non-routine
Winds of change…
routine non-routine
non-routine
machine solved routine – human solved
Winds of change…
Winds of change…
Winds of change…
Conclusions for education
Prepare students to be ready to deal also with non-routine tasks
Prepare students to recognize and deal with lies
Prepare students to be ready to deal also with non-routine tasks
Prepare students to recognize and deal with lies
How to achieve that?
Conclusions for education
Realities
Why do we have to learn mathematics?!
Realities
- Mr. Jones, will I ever use this algebra?
- You won’t, but some smarter kids might!
Realities
Practice patiently – you will see why this makes sense later!
Realities
Practice patiently – you will see why this makes sense later!
Math teaching concept oriented:
Introduce concept nr n
Practice concept n
Test concept n
Time
left? STOP
YES
n=n+1 n=1
NO
„What mathematics do people really need?”
„What do we de-emphasize and remove?”
„What mathematics do people really need?”
„What do we de-emphasize and remove?”
„What literature do people really need?”
„What do we de-emphasize and remove?”
„What mathematics do people really need?”
„What do we de-emphasize and remove?”
„What literature do people really need?”
„What do we de-emphasize and remove?”
Mathematics is, like literature and art,
part of our cultural heritage
Math teaching concept oriented:
Introduce concept nr n
Practice concept n
Test concept n
Time
left? STOP
YES
n=n+1 n=1
NO
Math teaching concept oriented:
Introduce concept nr n
Practice concept n
Test concept n
Time
left? STOP
YES
n=n+1 n=1
NO
process oriented:
Mathematical reasoning and argumentation
Strategic thinking
Mathematical modeling
Conclusions for education
Prepare students to be ready to deal also with non-routine tasks
Strategic thinking
Prepare students to recognize and deal with lies
Mathematical reasoning and argumentation
Polish national curriculum (2008)
New national curriculum
General requirements, Specific requirements
Prove that…
Matura 2014
Matura 2014
Prove that…
Prove that…
Prove that…
Egzamin gimnazjalny 2014
Egzamin gimnazjalny 2014
Internet: I calculated like crazy, while it was enough to think!
PISA – levels of math competences
358 420 482 545 605 668
< 1 1 2 3 4 5 6
6,8%
3,3%
5,0%
2,3%
poniżej poziomu 1 poziom 1 poziom 2 poziom 3 poziom 4 poziom 5 poziom 6
0 5 10 15 20 25 30
2003 2006 2009 2012
PISA – levels of math competences
358 420 482 545 605 668
< 1 1 2 3 4 5 6
20,5%
14,4%
16,7%
10,4%
poniżej poziomu 1 poziom 1 poziom 2 poziom 3 poziom 4 poziom 5 poziom 6
0 5 10 15 20 25 30
2003 2006 2009 2012
Students at level 1 or below in EU (math)
Estonia Finlandia
Polska Holandia
Dania Irlandia
Niemcy Austria
Belgia Łotwa
Słowenia Czechy
W. Brytania Norwegia
Francja Hiszpania
Luksemburg Włochy
Portugalia Litwa
Szwecja Słowacja
Węgry Chorwacja
Grecja Rumunia
Bułgaria 0
5 10 15 20 25 30 35 40 45 50
0 5 10 15 20 25 30 35 40 45 50
2012
2009
Students at levels 5 or 6 in EU (math)
0 5 10 15 20 25
0 5 10 15 20 25
2012
2009
16,7%
10,4%
Mathematical reasononing – the weakest point in 2003
0 10 20 30 40 50 60 70 80 90
OECD 2012 Polska 2012
1 2 3 4 5 6 7 8 9 10
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
Polska 2003 Polska 2012
How to teach mathematical reasoning?
Explain why you can start solving this Sudoku by writing 1 in position *.
How to teach mathematical reasoning?
What is, roughly, the volume of a dollar bill?
Development of the PISA 2021 Mathematics Framework
Mathematical literacy is an individual’s capacity to reason mathematically and to formulate, employ, and interpret mathematics to solve problems in a variety of real-world contexts.
It includes concepts, procedures, facts and tools to describe, explain and predict phenomena. It assists individuals to
know the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive, engaged and reflective 21st century citizens.
Development of the PISA 2021 Mathematics Framework
Mathematical literacy is an individual’s capacity to reason mathematically and to formulate, employ, and interpret mathematics to solve problems in a variety of real-world contexts.
It includes concepts, procedures, facts and tools to describe, explain and predict phenomena. It assists individuals to
know the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive, engaged and reflective 21st century citizens.
25% of items
Development of the PISA 2021 Mathematics Framework
Mathematical literacy is an individual’s capacity to reason mathematically and to formulate, employ, and interpret mathematics to solve problems in a variety of real-world contexts.
It includes concepts, procedures, facts and tools to describe, explain and predict phenomena. It assists individuals to
know the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive, engaged and reflective 21st century citizens.
25% of items
A new subscale reporting the ability to reason mathematically
