M.Sc. Lauri Hellsten ( laurihellsten, lauri.k.hellsten@gmail.com)
math and physics teacher in Espoon yhteislyseon upper secondary school
in-service teacher trainer and textbook author
using GeoGebra since 2009 (or was it 2010...)
Examples of the usage of GeoGebra and Google Sheets
CC BY SA naosuke ii
CC BY SA naosuke ii
New national curriculum 2015
Digital matriculation exam (math 2019, chemistry & physics 2018)
Server
Router
Students laptop, booted from an USB-stick
Student can participate in the A-level (10+3 courses) or B-level (6+2 courses) math exam. The structure of the exam is the same in both level exams.
Part | Problems given | Student answers | max. points |
---|---|---|---|
A | 4 | 4 | 48 |
B1 | 5 | 3 | 36 |
B2 | 4 | 3 | 36 |
120 p
math-demo.abitti.fi (opensource)
KCalc
Everything in part A and
Finnish Association of STEM-teachers has been training in-profession teachers from 2015 onward on the new curriculum and digital matriculation exam. There has been approximately 40 training days each semester all over Finland that the Finnish national board of education has financed.
problems given to teachers, students and examples of
interactive materials from digital books
+ Self-assesment during the course
Example problem from MAOL training material; Hellsten, Setälä, Mäkiö
How high is the highest pyramid made of spheres when four have the radius of 1 and one has the radius of 2?
Three circles tangent to one another as seen in the picture below. Centerpoints of the circles are A, B and C and the radius of the circles are 1, 2 and 3. What is the radius of the largest circle inside these three circles?
Example problem from MAOL training material; Hellsten
Hero swims at speed v and monster runs at speed 4v. The hero knows he can outrun the monster if he can get to the shore safely. Can the hero escape?
Example problem from MAOL training material; Hellsten
Radius of the lake is 2 and it's centerpoint is (0,0).
Example problem from MAOL training material; Hellsten
Long story short: What is the max volume when you know the sides but don't know the angle or when you know the angle but don't know the sides?
How does the population of bacteria change over time? Make the necessary assumptions and create a model
From book MAB4: Matemaattiset mallit; Hellsten, Hellsten, Luisto; Tabletkoulu
From book Resonanssi 3: Haapola, Hellsten, Huuska, Viitanen; e-Oppi
From book Resonanssi 4: Haapola, Hellsten, Huuska, Viitanen; e-Oppi
From book Resonanssi 4: Haapola, Hellsten, Huuska, Viitanen; e-Oppi
In-development material from Resonanssi 6: Haapola, Hellsten, Huuska, Viitanen; e-Oppi
Old physics matriculation exam problem solved; Hellsten
The teacher guides the student to identify what the studied topic is about and compare their own perceptions and views on the whole.
Unit 1
Self-assessment
1A
passed
Unit 2
Self-assesment
2A
failed
Self-assessment
2A
failed
passed
passed
Guidelines for the course; Peura, Hellsten
Text
Self-assessment form created with Google Sheets; Peura, Hellsten
Solve the problem.
Evaluate your own solution with the given criteria.
Polku-material; Peura, Hellsten
flippedlearning.fi
polku.opetus.tv
tabletkoulu.fi
e-oppi.fi
eyl.fi
maot.fi
eduhakkerit.fi
bit.ly/fyohjeita