Folkemødedebat: Er STEM kun for drenge?

På folkemødet havde Teknologipagten og LIFE organiseret debatten “Er STEM kun for drenge?”

Hermed en opsummering af mine pointer samt et par opfølgende bemærkninger.

Deltagerne var, fra venstre til højre: moderator Agi Csonka, Charlotte Mark, Maiken Lykke Lolck, Martin Exner, undertegnede og Christine Antorini.

Selvbestemmelse og klasseledelse:

  • hos os vælger børnene selv STEM til, som en naturlig del af vores motivationsorienterede pædagogik generelt. Vi har ca. dobbelt så mange piger som drenge, der kommer til STEM-forløbene (Som i parentes bemærket er programmering og elektronik og matematik – områder hvor kønsfordelingen traditionelt er særligt skæv).
  • vi har på Island set, at kønsopdelt undervisning kan være en løsning, men har også erfaring for, at man med struktureret klasseledelse sagtens kan sikre, at pigerne også får plads.
  • slaget mener jeg skal slås på læreruddannelsen, navnlig ved at gøre uddannelsen 5-årig, med en meget stor andel af praktik.
  • i den sammenhæng mener jeg, at det er afgørende at få formidlet en række positive fortællinger om alle de små livsbekræftende mirakler, man naturligt kommer ud for, når man har med børn at gøre. De didaktiske jobs har potentiale for at være verdens mest spændende og udviklende – men vi skal have italesat dem som sådanne!

Autenticitet / relevans

Jeg pointerede, at det at være lige ikke er det samme som at være ens. Vi observerer i det daglige tydelige kønsbetingede forskelle mellem drenge og piger. Det er helt fint – vi ser forskelle og alsidighed som en klar styrke. Til gengæld kræver det at skabe lige vilkår for alle, at vi aktivt forholder os til disse forskelle.

Et praktisk aspekt, jeg ikke fik nævnt, er, at vi prioriterer brugen af fri software meget højt. Den frie software udgør en slags uendeligt ocean af autentiske læringsmuligheder og den intense mentoreringskultur i miljøet en unik katalysator for læring.

Tak til alle deltagerne – publikum inklusive – for en god og relevant debat.

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Discovering Hjallastefnan schools in Iceland

The Hjalli model logo

Gleðilegan miðvikudag <3 – Happy Wednesday. This is what you can read every day when you enter Hjallastefnan schools in Iceland. Schools where happiness and positivity reigns. But they also have another particularity. Hjallastefnan – or the Hjalli model ( – fights for gender equality and counters gender stereotypes. It has now existed for 30 years and gathers 15 kindergartens and 3 primary schools (up to the 4th grade) across Iceland – the number one country when it comes to gender equality.

Here is a little overview of my visit to both a kindergarten and a primary school from the Hjalli model in Reykjavík. As a part of The Danish-French School’s exchange program for teachers, I wanted to discover their methods, get inspired, and use this opportunity to see the different interest in STEM for both genders.

The first impression you get when you read about the model is gender separation and uniforms. This seems a bit old school, but it is anything like that when you see the actual practice.
The uniforms are here to make every kid equal. Whether red or blue, skirt or trousers, it’s all the same, for everyone. Your boy wears a red skirt? No problem.
The gender separation is not strict either, and they get mixed at least once a day. They separate them to work on gender weaknesses and reduce inequalities.

We are all “friends” there. You talk to someone else by using the expression “Dear friend” – “Kæri vinur” for a boy and “Kæra vinkona” for a girl. Even between adults. “Góðan dag kæra vinkona Joséphine!” – the teachers were telling me in the morning. And don’t forget the heart when you write a message. The post-its are heart-shaped too of course.
Messages should also always be turned in a positive way. A child talks too loudly during lunch? Just tell “Dear friend, use your mouth for eating”. Another starts getting violent? “Dear friend, use your words”. And it works. They get used to receive and give positive messages from the youngest age, and train all in a circle to use this kind of formulas.
The atmosphere is also very quiet. Children have an inside voice and an outside voice. They are often in small groups, and they use a meditating position when sitting in a circle. And boys have for example smaller rooms, so it is harder for them to run around and make noise.
Finally, their environment is very simple and natural, so that the children use their imagination during playing time. Only a few games are available, including wood cubes and homemade clay. In the playground, no big structures nor swings. In the kindergarten they have sandboxes, sheds, ropes, big tires and a wading pool for when it rains. In the school, they just use the forest as a playground.

Playground at Barnaskólinn í Reykjavík

So, how does it work on a daily basis? The children are gathered in groups of the same age and same gender. Each group has its own classroom and teacher. In the corner, a big carpet with a sun in the middle has numbers all around for the children to sit on. They all start the day by singing good morning to the sun, the trees, the flowers, and every single child in the room. The rest of the day is a mix of “hópatímar” – group time – “valtímar” – activity of their choice – and “blöndum” – mixing the genders. Each of these has its own song that the group sing together, like a jingle in a TV show.

  • Hópatímar: The teacher takes the group for some activities or teaching, either in the classroom or outside. The youngest work mostly with countering the gender stereotypes here. The girls work on their strength and power, making some physical exercise, climbing on chairs, and learning to express themselves loudly and clearly. With the boys, it’s a completely different atmosphere. They work on their gentle hands, giving hand massage with lotion to each other, brushing their hair, and putting nail polish on. The groups also do compliment rounds. Girls tell each other “You are strong!” or “You are wonderful!”, while boys are more like “You have a good heart!” or “You have beautiful eyes!”. As the children get older, these group times are more and more used for conventional teaching.
  • Valtímar: One by one, the children choose between different playing or creative activities. This can be Kapla, clay, crochet, Lego, going outside, drawing, or even chess (They start chess lessons from 3 and some 5-year-olds are going to the European championship this summer). The teachers make sure that each activity has 2 or 4 children, so there is always a playmate to be with. When the capacity of children is reached, the activity becomes unavailable for the rest of the group.
  • Blöndum: Boys and girls of the same age get together and do activities in pairs. Because of the gender training that they do separately, they seem to work more easily together as equals. When building a structure with blocks, girls don’t hesitate to take the leadership while boys try to make things pretty. The older they get, the more often the gender are mixed. Blöndum also exists as a multi-age version.

Icebot enjoying the sun at the beach

Let’s talk about STEM. Icebot, a rover from the Dark Side Challenge made by one of our 8-year-old girl and her mom (, was also part of the trip. It has been presented to the 8-years-olds, girls and boys separately. The goal was to see if the two genders have a different interest in robotics. And the answer is yes.
From the girls’ side, they see the robot like a tool that they can control. And they want to be good at it. Trying one by one, they manage to send the rover where they want with the minimum effort and take a picture of their friends. One girl will also stay for the whole time next to the computer to explain to the other ones how it works. They were simply organized and efficient. But they were not so curious about how it works concretely. They saw it as a product that works, and they have fun with it by completing simple goals.
Let’s go to the boys now. They first have many questions about every component and how it works. They use their imagination to have a super robot. One wants to send it to space. Another wants a mechanical arm to bring soda cans. They also want to make it prettier. They see a final product that doesn’t exist yet. Then they try it. It becomes much more chaotic than the girls, and they keep trying the commands without any plan. They just want it to keep moving, for fun. They’d also rather move themselves to take a picture than the robot.
When it came to the feedback, both groups were super enthusiastic and kept asking about having their own (We should hopefully send them one by the end of the summer holidays). If the groups were mixed, I would imagine that the boys would take control and make the robot move constantly, while the girls would let go and lose interest as they won’t have the opportunity to master the commands and find out concrete goals. Separating them can therefore be an advantage to trigger girls’ interest in STEM.

Evaluation of the robotics workshop by the 8 year-old girls – 10/10!

This experience was really enriching, and I hope to collaborate with them again. I’ve met blooming children and welcoming teachers. Have a good day, my friend!

Thank you for the visit, Dr. Stallman

As I got news of RMS visiting Denmark again, it struck me that he might be interested in visiting something as rare as a school clearly affirming that software should be free/libre. We are using the convention free/libre to emphasize that the software is free as in “freedom”, not “free beer”. It is an ambiguity of the English language that has historically caused some confusion, albeit the notions are not mutually exclusive. In fact, software freedom and financial viability have in retrospect turned out to be perfectly compatible.

I asked RMS an got the following answer:

An so it happened that RMS came to visit us last Saturday.

Aware of previous anecdotes about RMS’s supposedly lacking social skills, I was psychologically prepared to make use of the full special educational toolbox. That turned out to be unnecessary.

I first of all experienced RMS as someone who is listening and being razor sharp. He thrives best under a fast pace and needs a planned schedule. He prioritizes clearly and was for instance not interested in seeing the school’s gym. He has a well-developed sense of humor and speaks French and Spanish fluently.

His key issues are clearly defined and he works hard on them, squeezing work out of every minute. One might consider that it isn’t comme il faut to pull out your laptop and start working during the lunch, but objectively speaking it is the rational choice if you have a lot to do.

Different indeed, and thank god for that.

Visit of a legend.

The impression I am left with is that RMS is as relevant as ever. Free software enabled a historical power shift in the (IT) world in the ’00s, illustrated in the ’10s by the IT giants’ overtaking of the scene. Today, free software is everywhere, for instance in billions of Android devices, servers and containers, embedded devices etc. etc. So in a certain sense, it has vanquished.

But the concept is up against some heavy-weight opponents. The fundamental problem is that the companies developing the software have no direct interest in securing its freedom. In fact, they trivially seek to maximize the bottom line, which rarely is aligned with the notion of sharing.

One example is patents, which to a large extent today serve to prevent competitors from taking market shares.

Another example is the move towards on-line services: from a software engineering perspective it doesn’t make much sense to use a browser as the standard platform for running programs, using Javascript as “byte code”. It is an inefficient and limiting middle layer. But it is a means to control the users by hiding away data and logic on faraway servers and within non-free Javascript. I installed the Firefox plugin for LibreJS last Saturday – it shows how few sites out there are running free software.

Finally, it is common practice that teachers in schools and universities encourage the students to use proprietary software, because “the licenses are almost gratis”. In 2019! Talk about the fox guarding the hen house.

In the current state of affairs, free software still critically depends on citizens continuously fighting for it, on developers pushing for their right to use free tools.

At some point we will hopefully see that publicly funded projects will be subjected to the condition of the code being free/libre. After all, denying the tax payers the freedom to fully use the software they have paid for is de facto a scam.

I asked RMS for feedback on the school’s IT policy and ended up with the following version:

When choosing technology for education, we only use free/libre programs, in accord with the school’s fundamental values of freedom and justice. From an IT literacy perspective we consider it essential that the children learn to identify which technological choices will make them dependent and which ones will give them autonomy. This includes explaining the privacy-related consequences of using the typical online services.

The policy has always been very easy to apply, as free/libre solutions exist for every relevant problem we have encountered.

Perhaps surprisingly, we have observed that children are very receptive to traditional text-based programming and do not express any need for simplistic point-and-click interfaces. The more interested pupils participate in managing the school’s servers and infrastructure, learning valuable skills in that process. In practice this establishes an intense exchange and mentoring culture, characteristic of environments where information can be shared freely.

We regularly sponsor free/libre projects that we make use of and consider it the morally right thing to do for an institution.

Computer games, including games on phones and tablets, are not allowed at school during the opening hours, because we have observed that they cause attention deficits and addiction. Generally speaking, screen-oriented activities may only occur if they have a well-defined pedagogical purpose.

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Hacking time!

Model Moms

Our Dark Side Challenge concept keeps spinning off new ideas and concepts. This time, it’s the Model Moms!

It’s not about fashion models.

And just relax – it’s not about being the perfect mother either.

This is about engaging girls in STEM by building models – in wood, metal, plastic, numbers or code… or even trash. And about involving the girls’ primary role model: their mother.

The concept is simply a number of progressions that mothers can explore with their daughters:

  1. building the metal chassis of a rover
  2. assembling the rest of the robot (3D printed parts)
  3. design and 3D print a name tag
  4. adding the electronics parts with the proper wiring
  5. practicing some programming
  6. uploading the program and running the tests
  7. remote controlling the rover in a Dark Side Challenge challenge, where the rover has to explore an unknown terrain without real-time feedback

MWM rover Coquine completed before shipping to Norway.

From then on the world is open and one can:

  1. use the newly acquired coding skills to model interesting problems with differential equations
  2. improve the program of the robot to make it more autonomous
  3. improve the robot itself to make it do a lot of useful stuff, like virtually visiting the grand-parents or hoovering their house
  4. or just make it more likeable and cute :) Hopefully, getting some girls involved will improve that aspect! (and yes, that appears to be a clearly gender-specific trait. And that’s fine.)
  5. … and much much more – including imagining the stories of teacher-astronaut Aė exploring the darkest corners of the solar system with her pupils and their assistant robots…

Aė and the Dark Side Story

Most of the progressions are very easy, and a few of them less so. Some might require explanations from more experienced makers, some might require a 3D printer or other tools such as a multi-meter. The key here is to function as a group, meaning that there always will be help to get.

Fakta og uddybninger ift. “Debatten: Er der en voksen til stede?”

Som opfølgning på at jeg udtalte mig i Debatten: Er der en voksen til stede?, lader det til, at der er brug for lidt baggrundsinformation og underliggende fakta.

Grunden til at jeg valgte at deltage er, at jeg mener at problematikken omkring børns trivsel og udvikling er det vigtigste, vi som samfund for tiden bør beskæftige os med. Det har jeg ment i nogen tid og det er sådan set derfor, at min medstifter og jeg har brugt de sidste ti år af vores liv på at opbygge Den dansk-franske Skole og Børnehave.

Pædagogerne og lærerne mener jeg er et vidunderligt folkefærd af bundgode, altruistiske og tillidsvækkende mennesker. Roden til problemerne mener jeg er, at fagene savner anerkendelse i befolkningen, hvorfor der kommer for lidt søgetryk på uddannelserne og optagelseskvotienten. Dette udgør en selvforstærkende negativ spiral. Og det mener jeg, at man kan gøre noget ved.

Specifikt i forhold til minimumsnormeringer mener jeg, at det vil være en afsindig dårlig idé: idéen er den sædvanlige “vi-skal-allokere-flere-ressourcer-NU!” knee-jerk reaktion, som desværre sjældent løser noget som helst og, værre end det, flytter fokus væk fra det egentlige problem. I eksemplet her vil en større efterspørgsel på pædagoger kun skabe endnu flere tomme pladser på studiet og forstærke problemet yderligere.

Min rolle i programmet var, ligesom pædagogen Anette Stoltenberg Hansen, at bidrage med praktisk indsigt fra dagligdagen på gulvet. I modsætning til de politiske deltagere i programmet var ingen af os særligt scenevante og vores dagsorden var ikke at få så meget seerfladetid som muligt, hvorfor vi endte med at få forholdsvis få minutters opmærksomhed.

Et af mine budskaber var, at man indenfor almindelige rammer, eller mindre, kan skabe et pædagogisk miljø med høj trivsel hos børn og voksne. Disse rammer er:

Vi har en normering på ca. 1:6 målt ift. hvor mange arbejdstimer, der bliver lagt af personalet (125) vs. hvor mange timer børnene sammenlagt er i institutionen (692). Det er helt korrekt, at vi nogle gange kun er to voksne på gruppen, nogle gange endda kun een. Der er i alt p.t. 10 ansatte, de 3 er på deltid og alle er aktive både i skolen og børnehaven. For tiden har vi een uddannet pædagog, som primært er i børnehaven.

Vi har 9 lukkedage om året og 48 ugentlige åbningstimer, ligesom alle andre i København og omegn. Det står i vores vedtægter.

Vi betaler alt vores didaktiske personale lærerløn, som er højere end pædagogløn (kr. 189,- i timen + 17,3% pension, altså om måneden 35538,- alt inklusive). Alle har 6 ugers ferie og derudover mulighed for 2 ugers betalt og lønnet ophold på en af vores samarbejdsskoler/institutioner (p.t. USA, Schweitz, Norge, Island, Frankrig). Derudover afsætter vi væsentlige midler til videreuddannelse, som til gengæld foregår udenfor arbejdstiden.

Vi bruger ikke vikarer og har 6,0 fraværsdage per medarbejder per år, hvoraf de fleste er barns første sygedag. Een outlier øger tallet fra 3,2 til 6,0.

En plads i børnehaven koster 2500,- og vuggestuen 3600. Det svarer til de kommunale priser fra 2014, dengang vi begyndte at få tilskud. Vi får derudover ca. kr. 5500,- fra komnunen, og har altså ialt 8000,- per barn per måned til at betale løn, husleje, madordning og diverse driftomkostninger. Mit gæt er, at det er mindre end hvad kommunale institutioner har at gøre godt med (som lader til at være 9500,-).

Vi har en stor andel af børn med ikke-vestlig baggrund – meget nørrebrosk. I forhold til antal børn med vanskeligheder ligger vi p.t. indenfor norm, men plejer at ligge over norm. I skolen ligger vi langt over norm.

Mine kolleger havde opfordret mig til at nævne vores lidt originale “4K” feedback-kultur som et afgørende element i vores organisation, men det fik jeg ikke gjort. Den er meget tillidsbaseret og lyder som følger:

Vi opfordrer personalet til at give indbyrdes feedback og ser til at feedbacken er:

  • kontant: sørg for, at alt der skal siges, bliver sagt. Også selvom det kan virke ubehageligt.
  • konstruktiv: sørg for at anlægge et perspektiv på tingene, så modtageren kan bruge det til noget.
  • kærlig: garantér, at feedbacken gives ud fra gode intentioner. Kvalificeret feedback er noget nær den største gave, man kan give et andet menneske.
  • klodset: især negativ feedback har det med at blive akavet. Sådan er det og det er ok – det må i hvert fald ikke være til hinder for, at tingene bliver sagt.

Så hvad kan vi gøre? Jeg vil foreslå:

  • at man gør pædagog- og læreruddannelsen til kandidatuddannelser med en meget stor andel af praktik (f.eks. 50%), eventuelt at man slår de to uddannelser sammen.
  • brand’er uddannelsen som en all-round lederuddannelse og får skabt præcedens for at man kan skifte til og fra faget sent i karrieren (“livslang læring”)
  • italesætter funktionen som den nok mest afgørende for samfundets udvikling og vækst
  • generelt fokuserer på at få skabt positive, autentiske, praksisbaserede fortællinger om, hvordan man kan udvikle sig personligt, fagligt og socialt i et didaktisk miljø

First Week On The Dark Side

Last week we embarked on a new venture – The Dark Side Challenge.

The eventual goal of the challenge is to build a robot that can autonomously navigate through a terrain where radio contact is sporadic or even impossible – just as if it were on the dark side of the Moon or somewhere even farther away.

While achieving that goal, the challengers are learning to program and debug embedded devices and sensors, to imagine, reason and persevere, understand how to properly balance machine intelligence with human interaction. The youngest ones are even learning the alphabet – both in capital and small letters!

The first steps are all about teaching fundamentals, but soon we hope to remotely program robots at the other end of the planet and invite others to do the same with the ones we have in our classroom.

The first session was about… sewing. In order to protect their small computer, the children needed to manufacture a small protective pouch. Once they had sewn the pouch, they were given an Uno R3 board (Arduino clone) together with a printed sticker with their name on. The board is personal, it’s theirs, as we believe that the sense of ownership will spur motivation.

As a part of the session, the children were explained what the board can be used for: sensing things such as light, heat, humidity. They learned about ultra-sound and distance, motors and drivers and about hacking remote controls.

Some of the boys had converted a wooden vegetable box from Årstiderne to a rover with four motorized wheels. The robot could move autonomously after being fed a program consisting of a sequence of the letters w, s, a, d (forward, back, left, right) via the Uno’s serial interface. This was done using a program written by one of the older pupils.

The second session was about actual programming. The children were handed a sheet with a short program that would make the Uno’s built-in LED blink. For the small ones (aged 5-6), just finding the (capital) letters on the keyboard was a challenge, and even more so were the parentheses, curly braces and semi-colon.

A part of the lesson consisted of installing the Arduino IDE – a simple apt-get install arduino on the Linux machines and a download from the Arduino software page for Windows and Mac. The page is somewhat hard to find, as Arduino unfortunately now seem to be promoting their web-based IDE.

The older ones (6-8) did the exercise at varying speeds, most of them in groups of 2-3 and we needed to improvise some follow-up exercises:

  • make the blinking faster. This is achieved by decreasing the delays (and not increasing them). Suggested values could be 500ms, 50ms, 25ms.
  • make the LED blink an SOS, like the Titanic sent just before sinking.
  • shorten the code in the SOS exercise by using for loops.

In the programming session, 9 girls and 5 boys participated.

In the next session we have planned that they will be adding another LED to the board and have both LEDs blink. In that context they will get the opportunity to fry a LED by connecting it directly to a battery (without a resistance) – motivating why it’s relevant to understand Ohm’s law (V=RI) and the power law (P=VI).

Progress of the project can be followed on

Documents rédigés par nos stagiaires

À L’école franco-danoise nous accueillons souvent des stagiaires, cela dans le but de contribuer à former les futures générations d’enseignants, de fare connaître notre façon de travailler et finalement d’avoir une vue fraîche et indépendante sur notre fonctionnement.

Voici ci-dessous un extrait des documents rédigés par nos stagiaires au fil des années

Octobre 2017: Les accords par Daphnée Beaulieu-Turenne

Juin 2018: Synthèse de stage par Noélise Floc’h

Mars 2019: Observation d’une skovbørneheave par Camille Busillet et Noëmi Foureyzon

Avril 2019: Retour sur 17 principes Noëmi Foureyzon

Avril 2019: Retour sur les 17 principes Camille Busillet

The top 3 math-didactical fails. Ever.

It was back towards the end of last century, and most of us didn’t really grasp what we were supposed to make of it. It didn’t seem to be of any concern whether the teaching was motivating or not, nor whether the time the children invested in the learning eventually was worth it. In the math lessons we were told that…

1. the cosine is used to calculate the length of the edges in a triangle…

… which no-one really has done for ages.

What you actually do use the cosine and sine for is to describe circular movements: cos(t) and sin(t) are respectively the x and the y coordinate of a point having moved t length units along the unit circle. From a practical perspective that can be used for instance to write a program that displays a clock.

Playing around with the code in line 7 and 8 gives a good hands-on understanding of the parameters in the expression

C + A·cos(ωt + φ),

i.e. the meaning of:

  • the amplitude A: the length of the hands of the watch
  • the frequency ω: the speed at which they rotate (one of them is 12 times faster than the other) ¹
  • the phase φ: at what time they start (in this case 12 o’clock, at -90°)
  • the offset C: where the center of the clock is.

Pushing it a little further, the concept can be used to convey an understanding of signals, frequencies and spectra, be it sound signals, light waves, simple alternating currents, rotating wheels and much more.

Interestingly, the kids are quite receptive to the notion of a (Fourier) spectrum. For instance, the spectrum of an F major chord on our piano looks like this:


You can also explain the children what a low-pass filter is by playing a high-pitched tone (~13kHz) on a computer: the kids will hold their ears in pain while most adults won’t be able to hear it at all. Very funny!

2. a function is something involving a graph…

…something with “ax+b”, which is not completely wrong per se, but nonetheless a serious under-statement of the importance of the concept of a function.

Indeed, considering functions as the fundamental building blocks of modeling – the Swiss army knife of abstract thinking so to speak – completely changes the perspective. A function associates an output with an input, no more, no less. When you have formulated your function – your model – you have identified what is relevant, and discarded what was irrelevant. That can be unfathomably important:

From then on you will begin to see relations of causality, predict events and progress, compare the predicted with the observed, chain functions together, understand what is happening, act intelligently, adapt and improve, share your understanding with others.

Within the natural sciences the concept is omnipresent. Physicist tend to refer to it as operators.

Large organizations are barely manageable without it nowadays. In business language functions are often referred to as processes.

A great tool for introducing the concept of a function to children (4+) is the function builder, a tool allowing to visually build and play with functions that transforms an input (on the left) to an output (on the right):


At the school we sometimes organize a function-Pictionary:

“If the input is… [drawing] a bread, and the output is… [drawing] slices, then the function is probably… a knife!”

3. differential equations are solved using obscure rules learned by heart…

… and aren’t of much use after all, as most people who learned about them in high-school will recall (hint: “coefficients in a complex-valued function”). What should have been the great epiphany concluding 13 painful years on the school bench ended up as a complete anti-climax for the vast majority.

But in reality it’s quite simple: once you have formulated your model using functions, you generally want to know how it behaves under different circumstances (inputs). The interesting models are often so complex that simply entering the input into a formula won’t work – one has to work out the final result in small pieces at the time. These small different pieces (differences) are added up (integrated) into a solution, nowadays in practice always using a computer.

From a pedagogical perspective the classical Euler method is quite suitable and can be used from age ~6 and up, see the first order example (x’ = ±1) below²:


In the example, the velocity v=1 of the cloud is constant until the cloud reaches sufficiently far out on the right (x>250), after which the velocity changes sign until it reaches sufficiently far left (x<150), after which it changes sign and so forth. In each iteration of the draw loop, v is added to the position x, giving the new position ³.

The slightly older children can use differential equations to answer truly relevant questions, such as calculating the time it takes a space ship to travel to Mars:


In most of the examples above, one skill has turned out to significantly leverage the fun and relevance of math: programming. And so it turns out that math can be easy after all!


So stop whining.

Start coding :)




¹ Strictly speaking, ω is the angular frequency, i.e. ω=2πf where f is the frequency expressed in Hz.

² The example isn’t actually a true first order differential equation (DE), since there doesn’t exist a function f such that x’=f(x), since for a given value of x ∈ [150, 250], x’ can take on two values, 1 and -1. As it would often be the case when solving actual real-world problems, we are cheating a little: here we are using an extra variable (v) to store more information than what a first order system can hold. In order to solve the problem within a strict DE framework, one would need a second order equation involving Dirac delta functions, as in the flying pig example (code here).

³ Formally, rather than adding v we would need to add Δx, the distance traveled during a short time Δt, i.e. Δx=v·Δt. Here it works because we assume Δt=1.

Lærer i de humanistiske fag søges

Lilleskole søger engageret og frisindet underviser til dansk, engelsk, historie, samfundskundskab o.l.

Til besættelse af deltidsstilling og på sigt heltidsstilling søges snarest en underviser med mod på at prøve sine grænser af og undervise under usædvanlige vilkår.

Om skolen

Den dansk-franske Skole og Børnehave kendetegnes ved at:

  • anvende en Freinet-inspireret pædagogik i et aldersintegreret setup
  • inddrage det omgivende samfund, også fagligt, i form af en aktiv støttegruppe
  • undervise på fransk allerede fra børnehaven

Visionen med skolen er at skabe et fagligt og personligt udviklingsmiljø, hvor den enkelte har mulighed for og forventes at realisere sit fulde og alsidige potentiale.


Den dansk-franske Skole søger en lærer der:

  • kan personificere en dygtighedskultur og ønsker at indgå i et intenst, krævende og udviklende livslangt læringsforløb
  • kan arbejde selvstændigt og kreativt, en ildsjæl
  • anerkender barnets vilje til egenudvikling og formår at udnytte barnets og gruppens egen motivation til at drive læringen
  • er bekendt med og ønsker at praktisere en Freinet-lignende pædagogik
  • er i stand til at indse og udnytte synergien mellem faglig og social udvikling
  • er fagligt og tværfagligt meget velfunderet, og er dygtig til at arbejde i et tætknyttet team


  • besidder en kandidatgrad og/eller er pædagog/læreruddannet (evt. under uddannelse)
  • kan flydende dansk, helst på modersmålsniveau
  • er interesseret i at lære fransk eller kan det i forvejen, gerne på modersmålsniveau


Skolens personale består af en håndfuld højtuddannede og engagerede undervisere og gør ikke brug af vikarer. Den tæller ~40 elever fra 0. til 9. og en børnehave med ~20 elever.

Alle undervisere varetager børnehaven mindst ca. 1 dag om ugen.

Den ugentlige arbejdstid er 37 timer og 6 ugers årlig ferie.

Praktisk information

Ansøgningsfrist: 24. september 2018

Ansættelse iht. lærernes overenskomst.

Skolen ligger på Tagensvej 188, København NV, med gode transport- og udflugtsmuligheder.

For yderligere information se skolens hjemmeside

Ansøgning sendes til

Den stærke gymnasieelev

Det er oftest elevernes faglige udvikling der vægtes højst når forældre skal vælge den helt rigtige skole til deres børn, men vi burde måske vægte personlig og social udvikling lige så højt?

Hvert år i august har jeg fornøjelsen af at lære en ny gruppe søde og unge 1. g’ere at kende. Det er typisk en blanding af elever fra forskellige baggrunde, som alle på hver deres måde bidrager til klasserummet, men som alligevel ikke befinder sig på samme niveau hverken fagligt, personligt og socialt. Mit fornemmeste job som lærer er derfor at finde et fagligt udgangspunkt hvor alle kan være med, og hvor alle ligeledes bliver udfordret både fagligt og personligt. 

Det burde ikke være noget større problem, da alle elever i gymnasiet jo forinden er blevet erklæret “uddannelsesparate”, og alle har derfor et fagligt minimumsniveau og ligeledes nogle personlige og sociale forudsætninger for at kunne gennemføre en ungdomsuddannelse. Drømmesceneriet er selvfølgelig at eleverne er stærke på alle tre punkter, men da det sjældent er tilfældet, er der visse kvaliteter jeg som lærer sætter større pris på end andre.

Det er klart at et meget højt fagligt niveau faciliterer en rigtig god opstart, men hvis eleven hverken er selvstændig i sit arbejde, motiveret for at lære endnu mere eller tager ansvar for at opsøge ny viden og ikke kan samarbejde med andre, bliver overgangen mellem 9. klasse og 1.g en del sværere. 

Forventningen til eleverne er jo at de kan arbejde selv, selvstændigt opsøge ny viden, arbejde i grupper og dermed også lære af hinanden, og hvis alle disse kompetencer allerede er der fra start, er det ikke en lige så stor udfordring at opnå de faglige mål i gymnasiet.

Jeg oplever ofte at de elever der kommer fra skoler med undervisningsmetoder som bunder i en tro på menneskets vilje til at lære, og en tro på at eleverne bør være aktive i læringsprocessen, er mere selvstændige, ansvarlige og motiverede. Disse elever besidder, udover de intellektuelle minimumskrav, en stor samarbejdsevne, kreative kompetencer og er gode til at tænke projekt- og procesorienteret, hvilket gør at de er selvstændige i deres stillingstagen. De er både lydhøre, men formår også at tænke kritisk og at være initiativrige. Mange elever der kommer direkte fra folkeskolen har et fint fagligt niveau, men har  også svært ved at træffe valg, at arbejde selvstændigt og er meget resultatorienterede. Det lærer de selvfølgelig i løbet af gymnasietiden, men det er måske et unødvendigt benspænd.

Det er på baggrund af min erfaring med mine gymnasieelevers styrker og svagheder, at jeg har valgt en alternativ skolegang for mine børn. Her lærer de at fordybe sig i emner der interesserer dem, at reflektere, at tage ansvar og at være vedholdne. De bliver dagligt støttet i deres lyst til læring gennem trygge relationer og tillid, hvilket ikke kun styrker deres faglighed men i høj grad også de sociale og personlige kompetencer som jeg værdsætter hos mine gymnasieelever. Jeg er overbevist om at frihedsbaseret læring, som vi netop ser på Montessori-, Steiner- og Freinetskolerne spiller en stor rolle i elevernes udvikling. Friheden til arbejde, udvikling og vækst indenfor nogle klare grænser i et sundt miljø, hjælper eleverne til at kende deres styrker og svagheder, at samarbejde og at udvikle deres selvdisciplin og koncentration. Disse selvstændige elever med stor selvindsigt er, efter min mening, langt bedre rustet til ungdomsuddannelserne og i endnu højere grad også til de videregåendeuddannelser.

Mette Blicher, gymnasielærer