Espoon yhteislyseon lukio

Upper secondary school

M.Sc. Lauri Hellsten (      laurihellsten)

math and physics teacher (9 years in the profession)

working in the University of Helsinki regarding assessment and in-service teacher training

updating education in ICT, curriculum and assessment


  • School building was built in 1968 and renovated in 2007
  • Espoon yhteislyseo = lower and upper secondary school. 
  • About 280 students in the lower secondary school and 350 students in the upper secondary school
    • Special football programme for gifted athletes (approx. 15 students).
  • Located near Kauklahti next to the train station,
  • Emphasises entrepreneurship, global citizenship, sustainable development and social skills for the future.
  • Lot of international projects (CERN course, Model UN course, Swedish language course, German history course, Shanghai-exchange)
    • Students learn to understand cultural differences and they learn valuable lessons on how to live in a globalised world.
  • Open minded and innovative teachers developing new teaching methods 

About our school

CC BY SA naosuke ii

 1. Upper Secondary Schools Act

 2. National core curriculum

  • 300 pages altogether

  • 13 pages math curriculum

  • 5 pages physics curriculum

 3. Local curriculum (mostly same as #2)

 4. Matriculation exam



What guides the teacher?

CC BY SA naosuke ii

What's new?

New national curriculum 2015

  • Focus on assessments for learning.
    • Emphasis on the formative assessment.
  • Student must show diverse knowledge on the contents and goals of a course for the courses assesment.
  • Specific ICT skills as goals in STEM-courses.


Digital matriculation exam (math 2019, chemistry & physics 2018)

  • Use of programs (GeoGebra, LoggerPro, etc.) in STEM-courses.
  • New type of problems involving large scales of different type of digital materials (real life data, videos, simulations, etc.) that couldn't be done in the paper exam.

Upper secondary school in Finland

1. semester

2. semester

3. semester

1. period

2. period

3. period

4. period

5. period

min. 75 courses and usually 3 years 

usually 6 + 1 weeks

5 - 7 courses,

1 course = 3 x 75 min per week

Matriculation exam at the end, min. 4 exams

Lauri's schedule

  • Finnish and literature: 16 courses / semester
  • Swedish: 19 courses / semester
  • Math, Physics, Chemistry, Arts, Music: 20 courses / semester 
  • Religion, Philosophy, Psychology, Ethics, Biology, Geography, History, Civics, Health education: 21 courses / semester
  • Guidance councelor, Crafts, Domestic science: 22 courses / semester
  • Gymnastics: 23 courses / semester

Course amounts per teacher

Law & assessment 

"A student´s assessment is to guide and encourage learning and develop the student's capacity for self-evaluation."

- Basic Education Act and the Upper Secondary Schools Act of 1998 (translated)

Formative assessment is emphasized in the law and curriculum.

Self-determination theory







Daniel H. Pink The Surprising Truth About What Motivates Us



comes with


Digital matriculation exam

The digital exam system (



Students laptop, booted from an USB-stick




All of the programs in the exam system

Digital matriculation exam in mathematics (2019)

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

Tools for answering in part A (opensource)


Tools for answering in part B1 and B2

Everything in part A and

  • LibreOffice Calc
  • wxMaxima
  • Texas Instruments TI-Nspire CAS
  • Casio ClassPad Manager
  • Logger Pro
  • GeoGebra
  • 4f Vihko (finnish program)

Answers from A-level math course 6 exam

B2-problem from A-level math course 3 exam

B2-problem from A-level math course 4 exam

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.

  • 2015 - 2016 New upper secondary school curriculum
  • 2016 - 2017 ICT in upper secondary school courses
  • 2017 - 2018 Digital materials in STEM

Teacher training


problems given to teachers, students and examples of
interactive materials from digital books

+ Self-assesment during the course

Modeling and solving problems using multiple representations

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?

Modeling and solving problems using CAS

Example problem from MAOL training material; Hellsten

Creating new type of problems involving material

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).

Creating new type of problems involving material

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?

Visualizing math in different ways and creating open/closed assignments

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

Visualizing atomic level interactions

From book Resonanssi 3: Haapola, Hellsten, Huuska, Viitanen; e-Oppi

From book Resonanssi 4: Haapola, Hellsten, Huuska, Viitanen; e-Oppi

Visualizing forces and interactions

From book Resonanssi 4: Haapola, Hellsten, Huuska, Viitanen; e-Oppi

Visualizing forces and interactions

Visualizing atomic level interactions

In-development material from Resonanssi 6: Haapola, Hellsten, Huuska, Viitanen; e-Oppi

Creating and analyzing graphs from a given or acquired data set.

Old physics matriculation exam problem solved; Hellsten

Messing around with GeoGebra spreadsheets

“The use of ICT changes the role of the teacher, who will be more of a facilitator guiding the students' learning processes than a knowledge provider. The time allocated for the teacher and the pupil to meet in is too valuable to be spent solely on information distribution. The teacher is required to command new skills and to adapt a new approach, which in turn generates pressure on the basic and continuing education of teachers.”

Finnish National Board of Education review, 2011 (translated)



ICT in Learning

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




Unit 2




















Guidelines for the course; Peura, Hellsten


Self-assessment during the course

Self-assessment problems

Solve the problem.

Evaluate your own solution with the given criteria.

Polku-material; Peura, Hellsten

"No technology has an impact on learning on its own; it all depends on how it is used. (Nesta, 2012)"