Reversing the Trend: DigiMat

The new book Dumbing Down – The Crisis of Quality and Equity in a Once-Great School System—and How to Reverse the Trend by Magnus Henrekson and Johan Wennström identifies the core reasons for the present crisis in the Swedish school system with falling knowledge levels, inflated grades, increasing differences between student groups, frustration and distress among teachers and students, to be the emerging dominance of  a postmodern social constructivist view of truth and knowledge in combination with a new school market system with both public and private enterprise for-profit schools supported by a tax financed student voucher system unique for Sweden, with the following key message:

• Our assertion that a universal transition to a postmodern social constructivist teaching approach is the main factor explaining the decline in students’ knowledge, as well as the various other problems in the Swedish school system, is supported by the fact that a similar effect can be seen in other countries
• Since the system has impeded schools from competing based on how successful they are at imparting knowledge to their students, competition has steered toward goals other than knowledge acquisition, including generous grading.
• To be clear about our point: “post-truth” schooling and the drive to marketize education are two inde- pendent forces... but they are mutually reinforcing and have in tandem created the negative conditions for teachers and students in Sweden. It was through this marriage with the market system that the aim of the postmodern social constructivist view of knowledge to redirect schools from the purpose of teaching in the classical sense could be fully achieved.

The resolution of the crisis is presented as return to a classical view of objective truth and knowledge in the form of a virtuous circle with the following key elements:

• Good curriculum. 
• A good teacher has deep subject knowledge and uses efficient pedagogical methods.

The subject of mathematics has a special role as a core subject of both the modern world of enlightenment carried by classical school mathematics and of the post-modern digital world asking for a reform of school mathematics. The good curriculum for a school mathematics of today thus is a combination of classical analytical mathematics and new digital mathematics as presented on DigiMat supported by Leibniz World of Math. DigiMat shows a way out of the crisis by combining the best elements of both the modern and post-modern world. DigiMat shows a way of reversing the trend! A return to traditional school mathematics is not  an option.

DigiMat supports both a classical world view of objective generality ultimately expressed by mathematical symbols in mathematical equations and individualistic digital game worlds created by computer code as digital mathematics. DigiMat as tool for simulation of the world is similar to Garageband and Logic Pro X as tool for music production, in that a basic set of digitally supported tools are combined to rich output. 

Återkoppling till Sveriges Ingenjörer.

Hopplös Traditionell SkolMatematik

Ledarredaktionen Podd: Det går att vända skolan med Magnus Henrekson

DigiMat möter Sveriges Ingenjörer i workshop Lidingö skolor 21 April. Watch out!

The main message of the book is that the present school crisis is the result of a take over of post-modern social-constructivist teaching, but is this a correct analysis? Can it be that in fact the crisis is the crisis of a traditional school which no longer delivers in the digital age? If so, then the resolution of the crisis is not a return to the old school, but instead a new synthesis of the best elements from the old system with the tools of new digital world, something like DigiMat?   

   

KVA Talar till Barnen

Kungliga Vetenskapsakademien KVA har givit ut skriften Vetenskapen säger: Om Klimatet författad av bland andra Deliang Chen, professor i fysikalisk meteorologi vid Göteborgs universitet, med syfte att upplysa svenska folket: 

• Syftet är att nå ut med vetenskapssamhällets samlade syn på en fråga som berör oss alla.
• Att forskningen på senare år nått fram till en samsyn om klimatförändringarna tror Delian Chen inte alltid att allmänheten är fullt medveten om. 
• Istället sprids ibland missuppfattningar om att det fortfarande råder oenighet inom vetenskapssamhället om hur det faktiskt förhåller sig.
• Det är viktigt att känna till att det kapitlet är avslutat nu. 
• Det är också viktigt att veta att det inte är för sent att agera och att allt vi gör påverkar klimatet. Ibland hör man att det inte spelar någon roll vad vi gör i Sverige, men det är inte sant. 
• Varje ton koldioxid vi släpper ut har en påverkan.

Skriften stödjer detta budskap på följande sätt: 

1. Det är obestridligt att människans påverkan, främst genom utsläpp av växthusgaser, har orsakat en global uppvärmning och andra förändringar i klimatsystemet.
2. Klimatsystemet tar emot energi från solen genom att fånga upp solstrålningen, och blir av med nästan lika mycket energi igen genom att sända ut infraröd strålning (värmestrålning) till rymden. För närvarande är den infraröda utstrålningen runt 0,8 W/m2 mindre än solinstrålningen. Det är denna strålningsobalans som leder till den pågående globala uppvärmningen.
3. De senaste 160 åren har den globala medeltemperaturen stigit med 1,1 grader. Det finns ingen annan vetenskapligt förankrad förklaring till detta än de ökande halterna av växthusgaser, främst koldioxid.
4. Ofta beskrivs växthuseffekten, väldigt förenklat, som ett växthus där solstrålning lätt kan ta sig in medan värmen inne i växthuset har svårt att ta sig ut igen. Det medför en ökad temperatur i växthuset, se följande förklarande figur:

 

Kommentar: 

1. Att påstå att något är obestridligt är inte ett vetenskapligs argument. I vetenskap kan allt bestridas och ändras om nya fakta tillkommer, till skillnad från religion eller juridik.
2. Noggrannheten i mätning av in och utstrålning är inte tillräcklig för att avgöra en skillnad på 0.8 W/m2 när maximal instrålning är ca 1366 W/m2. 
3. Noggrannheten av mätning av global medeltemperatur är inte mindre än 1 C (avläs en typisk termometer) varför påståendet om 1.1 C höjning saknar mening. Höjningen kan lika gärna vara 0.5 C eller 0.1 C dvs utan signifikans. Att säga att koldioxiden är orsaken till den eventuella höjningen, eftersom man inte vet någon annan förklaring, är inte heller något vetenskapligt argument eftersom säkerheten i påståendet verkat öka ju mindre man vet. Och vad är egentligen innebörden av global medeltemperatur?
4. Bilden som ser ut som en barnteckning med sin eviga sol i övre hörnet ger en helt felaktig bild av jorden + atmosfären som ett växthus med tak som verkar reflektera (återstråla) både högfrekvent solstrålning och lågfrekvent infraröd strålning från jorden. Varför ger KVA en fysikaliskt helt felaktig missvisande beskrivning av den s k växthuseffekten? 

Sammantaget ger skriften intryck av att ha skrivits för förskolan. Varför riktar sig KVA till barnen med sin ovetenskapliga skrämselpropaganda? Jag har bett KVA om svar, som kommer att rapporteras.

Här kan vi jämföra KVAs teckning med en riktig barnteckning som illustrerar Solen, det Svenska Samhället samt Hotet från Koldioxidutsläpp:

Back Radiation: Algebraic Fiction or Physical Reality? 2

This is a continuation of the previous post with focus on the unphysical nature of back radiation as expressed in Schwarzschild's two-stream model of radiative heat transfer taking the following form in a setting of a horisontal atmospheric layer connecting the Earth surface to outer space with $z$ a vertical coordinate representing optical distance:

• $\frac{dU}{dz}=-U+B,$
• $\frac{dD}{dz}= D-B,$

where $U$ is upwelling radiation and $D$ is downwelling radiation and $B(T)$ is upward/downward emission of radiation according Stefan-Boltzmann's law with $T$ temperature depending on $z$. Subtracting the equations, we have

• $\frac{d(D-U)}{dz}=D-2B+U.$  (0)

We see a balance at a certain level $z$ between U as incoming radiation from below, D as incoming radiation from above and -2B as emission upward and downward. Discretizing $z$ into discrete levels/nodes $z_i=i*h$ with $h$ a mesh size and $i=0,1,2...$, the balance of upward and downward radiation involves  

• $B_{i+1}-2B_i+B_{i-1}$    (1)

with $B_i=B(T(z_i))$, if we set $B_{i+1}=D(z_{i+1})$ and $B_{i-1}=U(z_{i-1})$. 

We will now compare (0)-(1) with the following discretised heat equation for a temperature $T(z,t)$ with $t$ a time coordinate:

• $dT_i/dt = (T_{i+1}-2T_i+T_{i-1})*\frac{1}{pow(h,2)}$   (2)

where $T_i=T(z_i,t)$, which is a discretisation of $\frac{\partial T}{\partial t}=\frac{\partial^2 T}{\partial x^2}$. We know that the heat equation is a stable physical model subject to perturbations $p$ of (2) of the form

• $dT_i/dt = (T_{i+1}-2T_i+T_{i-1})*\frac{1}{pow(h,2)}+p$.    (3)

while perturbations $P$ of (1) would have the form

• $B_{i+1}-2B_i+B_{i-1}+P$.    (4)

We see that introducing a perturbation $P$ of the form (4) in (2) would correspond to a perturbation $p=\frac{P}{pow(h,2)}$ which would be big since $h$ is small. We thus see a fundamental difference as concerns stability between a heat equation of the form (2), which is stable, and a two-stream model of radiative transfer of the form (0). 

Note that the idea of two-stream radiative heat transfer with upwelling/outgoing (longwave) radiation OLR and downwelling (long wave) DLR is firmly implanted in the discussion of the GHE through the two-stream Schwarzschild model. In particular, the existence of DLR is supposedly being demonstrated experimentally with the help of a pyrgeometer, which however is a ghost detector. 

Back Radiation: Algebraic Fiction or Physical Reality?

The physics of a "greenhouse effect" (GHE) resulting from "back radiation" from a colder atmosphere with "greenhouse gases" (GH-gases) to a warmer Earth surface, is still a subject of active discussion. A recent contribution is Verification of the Greenhouse Effect in the Laboratory by Hermann Harde and Michael Schnell published in Science of Climate Change, presenting the following main points:

• The impact of the different greenhouse gases (GH-gases) on our climate is not really well understood and even under experts this repeatedly leads to doubts about its existence and its influence on our climate.
• This article summarizes the theoretical background of the GHE and presents first quantitative measurements of this effect with an advanced experimental set-up. 
• For our studies we use an experimental set-up, which consists of two plates in a closed housing, one plate heated to 30 C, the other cooled to -11.4 C. 
• ...the set-up...uses a heated plate as radiation source and simultaneously as sensitive detector for the back-radiation from GH-gases. We measure the increasing temperature of this plate or, alternatively at stabilized temperature, the energy saving due to the back-radiation.
• We measure the additional warming of a pre-heated plate due to back-radiation of the greenhouse gases carbon dioxide, methane and nitrous oxide as a function of the gas concentration, and we derive from the observed warming the radiative forcing of these gases.
• Our studies also demonstrate that contrary to the often-misinterpreted 2nd law of thermodynamics a warmer body can further be heated by absorbing the radiation from a colder body, here the radiation from the cooled plate and a GH-gas.
• In addition and independent of the temperature measurements is the back radiations of the GH gases directly recorded as reduced electrical heating of the upper plate.
• These measurements clearly demonstrate that contrary to the often misinterpreted 2nd law of thermodynamics a warmer body can further be heated by absorbing the radiation from a colder body, here the radiation from the cooled plate and a GH-gas.
• The presented measurements and calculations clearly confirm the existence of an atmospheric GHE, but they also demonstrate the only small impact on global warming with increasing GH-gas concentrations, which in any way are apperently dominated by natural emissions. So, there is no reason for panic and climate emergency.

The article claims to give the first verification of GHE in a laboratory setting with measurements supported by theory in the form of Schwarzschild's two-stream equation for radiative heat transfer. GHE is viewed to be an effect of back radiation with a warmer plate absorbing radiation from a colder plate, yet without violation of the 2nd law of thermodynamics. 

I have agued (see also video) that back radiation with two-way radiative heat transfer is unphysical and should be replaced by one-way transfer from warm to cold, with recent detailed follow up by Joseph Reynen. The presence of back radiation is directly connected to Schwarzschild two-stream model, which is described as follows in standard treatise Atmospheric Radiation: Theoretical Basis by Goody and Yung: 

• While it sets the pattern of the formalism used in radiative transfer problems, its physical content is very slight.
• The Schwarzschild-Schuster approximation is now of historical interest only.

The key issue concerning back radiation and Schwarzschild's two-stream equation is as follows: Stefan-Boltzmann's equation (SB) for one-way radiative heat transfer $Q$ between two bodies $B_1$ and $B_2$ of temperatures $T_1$ and $T_2$ with $T_2>T_1$ takes the form

• $Q =\epsilon\sigma (T_2^4-T_1^4)$      (1)

with $\sigma$ Stefan-Boltzmann's constant and $0<\epsilon \le1$ a coefficient depending on the nature of the bodies with $\epsilon =1$ for black bodies. Algebraically the SB equation can formally be written 

•  $Q = \epsilon\sigma T_2^4 - \epsilon\sigma T_1^4$    (2)

expressing two-way transfer with $\epsilon\sigma T_2^4$ heat transfer from $B_2$ to $B_1$ and $\epsilon\sigma T_1^4$ heat transfer from $B_1$ to $B_2$.  We see that (1) expresses $Q$ as net transfer from warm to cold, which in (2) is formally written as the difference between two gross transfers back and forth between warm and cold. 

Implicit in (2) is Kirchhoff's Law expressing that absorptivity is equal to emissivity since in (2) the coefficient $\epsilon$ has both the role of emissivity and absorptivity depending on the interpretation of (2) as both heat balance for $B_1$ absorbing heat from $B_2$ while emitting heat to $B_2$, and heat balance for $B_2$ absorbing heat from $B_1$ while emitting heat to $B_1$. 

Algebraically (1) and (2) are formally the same but the physics is different with one-way net heat transfer in (1) and two-way difference of gross heat transfer in (2). Now comes the key observation: From stability point of view (1) and (2) are not the same: A percentagewise small perturbation of net transfer will result in a small change of net transfer, while a small percentagewise perturbation of gross flow may result in a big perturbation of net transfer. 

One can now argue that physics must be stable to persist over time and so two-way radiative heat transfer as expressed by Schwarzschild's two-stream equations is unphysical and that is also what Goody and Yung says. 

It thus remains to find a mathematical model for one-way radiative heat transfer and here the stack model studied by Reynen is a first step. In a next post I will exhibit the crucial aspect of stability in a simple example comparing from stability point of view Schwarzschild's unphysical two-stream equations with a physical heat equation. 

Energy Power Politics: China vs US/EU

A basic postulate of Mearsheimer's offensive realism expressed in The Tragedy of Great Power Politics says that states attempt to maximise their power at the expense of other states with survival as ultimate goal.

Great power politics is played with economical and military force both ultimately resting on supply of energy. 

China is now increasing its energy production with a new coal plant opened every week.

All 27 EU Member States are committed to turning the EU into the first climate neutral continent by 2050.

President Biden is pledging to reduce U.S. greenhouse gas emissions by at least 50% by 2030.

This is the set-up for the UN Climate Change Conference COP26 in Glasgow starting next week: China will continue to build economical and military power from fossil energy, while EU/US will phase out fossil energy without possibility to compensate by new nuclear energy.

From an offensive realist point of view with survival as ultimate goal, this does not look good at all for EU/US. Clearly EU/US politicians do not listen to Mearsheimer, only Xi.     

Styrs Skolan av Läromedelsföretagen?

Statistik från Läromedelsföretagen visar att Skolan till Läromedelsföretagen betalar 500-1000 kr (snitt 650 kr) ca 0.5% av totalkostnaden per år och elev. Det ger en stor läromedelsmarknad om minst 650 miljoner kr att dela mellan läromedelsjättar som Gleerups, Studentlitteratur, Liber och Natur och Kultur. 

För huvudämnet matematik skulle då kanske varje elev per år få tillgång till läromedel för 200 kr. Hur mycket lärdom kan det rymmas inom en sådan ram? Räcker det? Inte i alla skolor tydligen, eftersom många lägger det dubbla, förmodligen för att det krävs. Men kanske inte ens det räcker för att ge alla elever tillgång till rikt material för utveckling och förkovran.

Skolans undervisning verkar styras av läromedelsföretagen som producerar och säljer läromedel med speciellt funktionalitet som gör att läraren i detalj kan övervaka varje elevs prestation uppgift för uppgift minut för minut, vilket då kan bli lärarens huvuduppgift eftersom det utmärkta läromedlet sköter själva undervisningen. Matematikämnet är särdeles lämpat för denna övervakade detaljstyrda utbildning. Men kanske är det inte det bästa för vare sig elev eller lärare.

Här erbjuder Leibniz World of Math ett alternativ i form av konkret realisering av den nya läroplanen i matematik+programmering i form av:  

• open textbook fritt tillgänglig utan kostnad,
• ny skolmatematik som konstruktiv matematik för en digital värld,
• sammanhållet rikt program från förskola till högskola där eleven själv bygger matematik 
• utvecklat av högsta akademiska kompetens.

Som Rektor, testa vad Leibniz WoM kan ge Dina Lärare.

Som Lärare, testa vad Leibniz WoM kan ge Dina Elever.

Som Elev, testa vad Leibniz WoM kan ge Dig själv.

Nobel Prize in Physics to Climate Models which Do Not Model Climate

The Nobel Committee in Physics has as an act of scientific political correctness today given half of the Nobel Prize in Physics in 2021 to Syukuro Manabe and Klaus Hasselmann for the physical modelling of Earth's climate quantifying variability and reliably predicting global warming.

In other words, the Prize has been given to Climate Models which Do Not Model the Climate, as is shown in the following graph of Global Warming over time comparing Climate Model predictions with Real World observations (second image from Roy Spencer Global Warming) : 

These graphs must have been unknown to the Committee. What is the meaning of "reliably predicting global warming" when the prediction has nothing to do with the actually observed absence of observable global warming (0.2 C over 40 years)? Is the "reliability" that all climate models show too much warming, or that the spread is so big that even virtually no warming is included in the predictions?

Kritik av Skolverket i Ny Avhandling om Matematik+Programmering

Peter Vinnervik ger Skolverket svidande kritik i sin avhandling om den nya kursplanen med programmering som del av matematikämnet, vilket tas upp i artikeln Forskare: Skolverket är otydliga om programmering i Läraren:

• Skolans styrdokument ger inte lärarna tillräckligt bra stöd för hur de ska undervisa i programmering.
• Man talar om att eleverna ska lära sig programmeringens grunder, men vad de består av kommuniceras väldigt kortfattat i kursplanerna, framför allt för ämnet matematikbudskapet om programmering kommuniceras via flera olika texter. 
• Man är väldigt otydlig med vad det är för kunskaper som eleverna ska lära sig. 
• Lärarna upplever budskapet som väldigt luddigt.
• Det behövs ytterligare en revidering av kursplanerna för att göra det tydligare för lärarna hur de ska arbeta med programmering i undervisningen.

Peter Vinnervik går så långt att han föreslår att programmering skall överföras till teknikämnet, eftersom reform av matematikundervisningen förefaller vara utsiktslös. 

Vi får se om Skolverket kan lyssna på denna kritik. Skolverkets syn uttrycks av undervisningsråd Johan Falk, som i Läraren uttrycker Skolverket: Ge mattelärare tid att fortbilda sig i programmering:

•  Studiematerial och tillfällen till fortbildning i programmering finns. 
• Flaskhalsen är tid och den är det bara skolhuvudmännen som kan skapa för sina lärare.

Innebörden är att Skolverket inte anser att Skolverket kan göra något mer än det som redan gjorts. 

Det skall bli intressant att se om Skolverket är kapabelt att lyssna på något av den svidande kritiken från Vinnervik. Det är inte säkert. Som Skolverkets Generaldirektör Peter Fredriksson urskuldande brukar säga: "Matematik är inte Sveriges bästa gren".

From Vinnervik's Abstract:

The results show that teachers face several intrinsic and extrinsic challenges during the process of integrating programming in their teaching. A perceived lack of professional knowledge and understanding of programming among the teachers emerged as a prominent challenge both prior to and more than two years into the reform. Additional challenges are related to teaching materials, time for preparation and professional development. In technology education, teachers mainly see programming as a medium to explore and understand technological systems and construction work. They are uncertain of what programming means in terms of practices and concepts, and about learning progression and assessment. The results further reveal that the curriculum texts are sparse on details about what programming knowledge entails. Important strategic decisions are left entirely to the teachers without any clear guidance. In addition, the results indicate that many technology teachers work in isolation and that interdisciplinary work around programming, as intended in the curriculum, is generally lacking. It is concluded that there is a risk of inequality among schools and that the children’s experience of programming becomes fragmented, despite good intentions. The current implementation model needs to be improved, and this thesis presents two possible actions.

New Math Education Site: Leibniz World of Math

I have changed the name of my mathematics education project to Leibniz World of Math from the previous DigiMat Encyclopedia. Take a look! 

Euler Was Right, Prandtl Was Wrong II

I am working on a new article to be expanded to a book with the title Euler Was Right, Prandtl Was Wrong  which can be seen as a summary of my work on fluid dynamics for 30 years together with former students Johan Hoffman, Johan Jansson and Anders Szepessy. In short, our work shows that the following prophetic declaration by Euler from 1755, indeed is fully correct:

• My two equations contain all of the theory of fluid mechanics. It is not the principles of mechanics we lack to pursue this analysis but only Analysis (computation), which is not sufficiently developed for this purpose...We have to wait until the age of the computer to solve the equations.

And yes, we now live in the age of the computer and then Euler's two equations as a parameter-free model can be solved in the form of Euler CFD (Computational Fluid Dynamics) and so open a whole new world of turbulent flow to prediction, analysis and control, without any further need of mathematical modeling with parameter fitting. 

Euler CFD is to be compared with Prandtl CFD as the Standard CFD developed during the 20th century based on Prandtl's boundary layer theory including complicated wall and turbulence models with many parameters, which does not offer true predictive computation, as the legacy of the declared Father of Modern Fluid Mechanics. 

Take look and see what you think. This post directly connects to the discussion in recent posts with Doug McLean representing Standard CFD. See also previous post.