Author Archives: Allan Tarp

BundleBundleMath on a BBBoard

Can mathematics be decolonized?
Well of course, since mathematics is a socially constructed essence that will always be a colonization of the natural existence it came from and reduces.

Existence before Essence will decolonize Mathematics, and end the Math Word War. A paradigm-shift from MatheMatism to ManyMath.

BundleBundleMath on a BBBoard sec. 1+2
BundleBundleMath on a BBBoard sec. 1+3
Video: Many before Math, Math decolonized by the child’s BundleBundle-Numbers with units.
Workshop: Flexible Bundle Numbers Develop the Childs Innate Mastery of Many.
This image has an empty alt attribute; its file name is BBBoard-1.jpg
A BBBoard shows that 67 = (B-4)*(B-3) = (10 – 4 – 3)*B + 4*3 = 3B12 = 4B2 = 42

Grade one Class one, in a Decolonized Future
The teacher: Welcome children, I am your teacher in math, which is about the numbers that you can see on this number line, and that is built upon the fact that one plus one is two as you can see here. So …

Showing a V-sign a child says: “Mister teacher, here is one 1s in space, and here is also one 1s. If we count them in time, we can see how many 1s we have by saying ‘one, two’. So, we have two 1s. But only until we add them as a bundle. Then we have one 2s, so 1s plus 1s become 2s, but one plus one is still one when we count it, and not two as you say. The thumb is also one 1s. They cannot be counted since they are not the same. But they can be added to one 3s. So, again one plus one is one. Here is another 3s on the other hand. They are the same, so we can count them as two 3s. And we can add them as one 6s. Or, we can split the two 3s into six 1s and see that two times three is six. So, the counting numbers two and three can be multiplied, but they cannot be added.

Therefore, please forget adding your line-numbers without units. Instead, help us adding the bundle-numbers with units we bring to school, as 2 3s and 4 5s, that we can add next-to as eights, or on-top as 3s or 5s as we can see on a peg board. If we add them next-to, we add plates, which my uncle calls integral calculus. And if we add them on-top the units must be changed to the same unit, which my uncle calls linearity or proportionality. He says it is taught the first year at college, but we need it here to keep and develop the bundle-numbers with units we bring to school, instead of being colonized with your line-numbers without units.

We know that you want to bundle in tens, and in ten-tens, and in ten-ten tens, but we like to bundle also in 2s, in 3s, in 4s, in half-tens, etc. We know that you have not been taught this and that the textbook doesn’t teach it. But don’t worry, we will teach you what we found out in preschool. Or better, instead of you colonizing our ways let us find out together what math may grow from our bundle-numbers with units. My uncle is a philosopher, and he calls it existentialism if we let existence come before essence.

And, when existence comes before essence, we must count the totals before we can add them. We know you say that 8 divided by 2 is 8 split in 2 parts, but to us 8 divided by 2 is 8 counted in 2s. You cannot split 9 in 2 parts, but we can easily count 9 in 2s as 4 bundles and 1 unbundled that becomes a decimal, 9 = 4B1 2s, or a fraction if we count it in 2s also, 9 = 4 ½ 2s. Or, with negative less-numbers we get 5 bundles less 1, 9 = 5B-1 2s. Now, let us begin with the fingers on a hand. You only see the essence, five, but we see all the ways the five fingers may exist.

F01. A total of fingers many exist as five ones, T = 5 1s, or as one bundle of fives, T = 1B0 5s. Also, the fingers may be bundled in 4s as T = 0B5 = 1B1 4s or as two bundles less 3, T = 2B-3 4s. And the fingers may be bundled in 3s as T = 0B5 = 1B2 = 2B-1 3s. And the fingers may be bundled in 2s as T = 0B5 = 1B3 = 2B1 = 3B-1 2s. But 2 2s is also one bundle of bundles, 1 bundle-bundle, 1 BB, so we also have that T = 1BB0B1 2s. Putting two hands together we see, that eight is one bundle-bundle-bundle, 1 BBB, so that ten is 1BBB0BB1B0 2s. And, if we count ten fingers in 3s, T = 3B1 3s = 1BB0B1 3s. Likewise if we count in tens, twelve is 1B2, and forty-seven is 4B7, and 345 is 3BB4B5.

F02. Here we counted in space, but we also use bundle as the unit when we count in time. If we count our finger in 3s we cannot say ‘1, 2’, and so on since 1 is not 1 3s. Instead, it is 0 bundle 1 3s, so we count ‘0B1, 0B2, 0B3 or 1B0, 1B1, 1B2 or 2B-1’. Or we may count ‘1B-2, 1B-1, 1B0, 2B-2, 2B-1.’

F03. With sticks we see that 5 1s may be bundled as 1 5s that may be rearranged as one icon with 5 sticks. The other digits may also be seen as icons with the number of sticks they repents, where zero is a looking glass finding nothing. We don’t need an icon for ten since here the total is 1B0 if we count in tens.

F04. The calculations are icons also. If we reduce 8 by 2, subtraction is a ‘pull-away icon’ for a rope so that 8-2 means ‘from 8 pull-away 2’. Now a calculator can predict the result, 8 – 2 = 6. And this creates a split formula ‘8 = (8-2) + 2’ telling that 8 remains if the pulled-away is placed next to, or ‘T = (T-B)+B’ with T and B for the total and the bundle.
If we recount 8 in 2s, division is a ‘push-away icon’ for a broom so that 8/2 means ‘from 8 push-away 2s’. Now a calculator can predict the result, 8/2 = 4. If we stack the 4 2s, multiplication becomes a ‘lift icon’ predicting the result, 8 = 4×2. This creates a recount formula ‘8 = (8/2) x 2’ telling that 8 contains 8/2 of 2s, or ‘T = (T/B) x B’ or ‘T = (T/B)*B’ with T and B for the total and the bundle. If we recount 7 in 2s, subtraction is a ‘pull-away icon’ for a rope so 7 – 3*2 means ‘from 7 pull-away 3 2s’.
Finally, addition is a ‘two-ways icon’ showing that two stacks as 2 3s and 4 5s may be added horizontally next-to as areas using integral calculus, or vertically on-top after recounting has made the units like.

F05. A reversed calculation is called an equation using the letter u for the original unknown number. The split and recount formulas may be used to solve equations.
The reverse calculation or equation ‘u+2 = 8’ asks ‘8 is split in 2 and what?’.
The answer, u, is of course if found by the splitting 8 = (8-2) + 2.
So, u+2 = 8 = (8-2) + 2 predicts that u = 8-2, which is also found by simply pulling-away 2 from 8, u = 8-2.
The reverse calculation or equation ‘u*2 = 8’ asks ‘8 is how many 2s?’.
The answer, u, is of course if found by the recounting 8 = (8/2)*2. So, u*2 = 8 = (8/2)*2 predicts that u = 8/2, which is also found by simply recounting 8 in 2s, u = 8/2.
In both cases we see that we find the solution by moving to opposite side with opposite sign. My uncle says that this follows the official definitions. 8-2 is the number u that added to 2 gives 8, so if u = 8-2 then u+2 = 8.
And, 8/2 is the number u that multiplied with to 2 gives 8, so if u = 8/2 then u*2 = 8. And he warned us against a ‘same on both sides’ method you might want to teach us. A combined equation as ‘3*u + 2 = 14’ may be solved by a song:
(3*u) + 2 = 14; 3*u = 14 – 2 = 12; u = 12/3 = 4. TEST: (3*4) + 2 = 12 + 2 = 14.

Equations are the best we know; they’re solved by isolation.
But first the brackets must be placed, around multiplication.
We change the sign and take away, and only u itself will stay.
We just keep on moving, we never give up.
So feed us equations, we don’t want to stop.


SECTION I, FINDING a New Paradigm, BundleBundleMath

  1. Grade one Class one in a Decolonized Future
  2. Valid Always or Sometimes,? Mathema-tics or -tism?
  3. From Many to Bundle-numbers with Units, for Teachers
  4. Micro Curricula, for Learners
  5. Many before Math may Decolonize Math, a Video
  6. Math Dislike Cured with BundleBundle Math
  7. Bundle-counting and Next-to Addition Roots Linearity and Integration
  8. Research Project in Bundle-counting and Next-to Addition
  9. CATS: Learning Mathematics through Counting & Adding Many in Time & Space
  10. The ‘KomMod Report’, a Counter-report to the Ministry’s Competence Report
  11. Word Problems

    SECTION II, REFLECTING on the New Paradigm
  12. A short History of Mathematics
  13. What is Math – and why Learn it?
  14. Fifty Years of Research without Improving Mathematics Education, why?
  15. Postmodern Enlightenment, Schools, and Learning
  16. Can Postmodern Thinking Contribute to Mathematics Education Research

    SECTION III, SPREADING the New Paradigm
  17. ICME Conferences 1976, 1996-2024
  18. The Swedish MADIF papers 2000-2020
  19. The Swedish Mathematics Biennale
  20. The MES Conferences
  21. CERME Conferences
  22. The Catania Trilogy 2015: Diagnosing Poor PISA Performance
  23. CTRAS Conferences
  24. The 8th ICMI-East Asia Conference on Mathematics Education 2018
  25. ICMI Study 24, School Mathematics Curriculum Reforms 2018
  26. NORMA 24
  27. Curriculum Proposal at a South African teacher college
  28. Celebrating the Luther year 1517 with some Theses on Mathematics and Education
  29. Invitation to a Dialogue on Mathematics Education and its Research
  30. MrAlTarp YouTube videos
    Two-level Table of Contents

Bundt-Bundt tal på et Bundt-Bundt bræt

Bundt-Bundt tal på et BBBræt, barnets egen matematik

Et BBBræt, der viser, at 67 = (B-4)*(B-3) = (10 – 4 – 3)*B + 4*3 = 3B12 = 4B2 = 42

Matematik: MatemaTisme, eller MangeMatik med barnets 2D BundtBundtTal på etBBBræt?

Matematik blir så let hvis Mange mestres først med MangeMatik. MATERIALE, se senere.

MangeMatik respekterer, at MANGE beskrives med barnets egne BundtBundt-tal med enheder – i stedet for at få påtvunget falsk WOKE-identitet som linjetal uden enheder, der blir matematisme ved at påstå, at 2+1 er 3 altid, til trods for at 2dage+1uge er 9dage.

MangeMatik ses ved at spørge en 3-årig “Hvor mange år næste gang?” Svaret er 4, med 4 fingre vist. Men holdt sammen 2 og 2, indvender barnet “Det er ikke 4, det er 2 2ere.” Barnet ser således, hvad der findes i rum og tid, bundter af 2ere i rummet, og 2 af dem i tid, når de tælles. Så det, der eksisterer, er totaler, der kan optælles til (gen)forening (algebra på arabisk) i rum og tid, som fx 2B1 2ere.

MangeMatik bygger på filosofien eksistentialisme, der anbefaler, at eksistens går forud for essens, der ellers vil kolonisere eksistensen. Det eksternt eksisterende går altså forud for interne ’essens-regimer’ som bør dekonstrueres & demodeleres så eksistensen afkoloniseres

BundtTal med enheder: 8, 0B8, 1B-2, eller 1B0 8ere. Og 87, 8B7, 9B-3.


MangeMatik med BundtBundt-tal, folder og ark

Matematik er bare så let, YouTube video.

Børn forbliver tal-kyndige med deres egne BundtBundttal med enheder, arbejdshæfte på engelsk og dansk

Flexible Bundle Numbers Develop the Childs Innate Mastery of Many, workshop på engelsk.

MrAlTarp YouTube videoer, fx ‘Fysik er svært, eller er det? og Linjeopdelt eller blokopdelt skole

Frisæt skolen og matematikken, stand på Lærfest 2024

Many before Math, Math decolonized by the child’s own BundleBundle-Numbers with units, en YouTube video.

Fra Mange til bundt-tal med enheder, for lærere
Mikro-læseplaner for lærende
ML01. Cifre som ikoner i rummet, IIIII = 5
ML02. Styk-tælling i tid, = IIII I
ML03. Bundt-tælling i tid med enheder: 0B1, …, 0B5 eller 1B0, 3 3ere = 1BB
ML04. Fleksibel bundt-tælling i rum med over- og under-læs, 5 = 1B3 = 2B1 = 3B-1 2ere
ML05. Opdeling, 8 = (8-2) + 2
ML06. Omtælling, 8 = (8/2)x2
ML07. Omtælling af de ubundtede, 8 = (8/3)3 = 2B2 = 2 2/3 = 3B-1 3ere
ML08. Omtælling i kvadrater, 6 4ere = 1 BB ?ere
ML09. Omtælling til et andet ikon, 3 4ere = ? 5ere
ML10. Omtælling fra ti’ere til ikoner, 2 ti’ere = ? 7ere
ML11. Omtælling fra ikoner til ti’ere, 6 7ere = ? ti’ere
ML12. Omtælling til en anden fysisk enhed skaber per-tal, 3kr/5kg
ML13. Med samme enhed bliver per-tal til brøker, 3kr/5kr = 3/5
ML14. Omtælles en staks sider giver trigonometri, højde = (højde/bund)bund = tanA*bund
ML15. Plusning vandret eller lodret, T = 2 3ere + 4 5ere = ? 8ere; T = ? 3ere; T = ? 5ere
ML16. Minus og plus med etcifrede tal, 8 + 6 = 1B2 + 1B0 = 2B2 6ere
ML17. Plusning af per-tal og brøker er integralregning
ML18. Plusning af Bundt-Bundt kvadrater
ML19. Plusning af ukendte bogstavtal
ML20. Ændring i tid
ML21. Bundt-tal i et koordinatsystem
ML22. Spil-teori og skade-kontrol
ML23. Enkle brætspil
Fakta og fiktion og fup, de tre genrer i tal-modeller
Modellering og de-modellering
Tre fodnoter
Hvor forskellig er forskellen?
Oversigt over forskellen mellem Essens- and Eksistens-matematik
Kronikker og læserbreve om matematik 2023-2024
Matematik-skandalen: Skolens matematisme berøver barnet dets tal-sprog og talsans
Fra katolsk til protestantisk matematik, fra bevis til beregning
Foredrag for skolebørn om min matematikbog på BogForum 2023
Coronatiden, krise eller skandale, hvad med en høring?
Ny matematik og ny skole nu, ellers uddør vi
Afkoloniser tal-sproget nu
Lær dit barn at matematikke før skolen gør det
Kan matematikken afkoloniseres ved at ombytte essens med eksistens?

Avisindlæg om matematik 23-24


Foredrag til forskningens dag

Corona-skandalen, hvad hindrede en civilsamfundsborger i at hindre den?

Er eksperterne talblinde?

Matematik-skandalen: Skolens matematisme berøver barnet dets tal-sprog og talsans

Fra katolsk til protestantisk matematik, fra bevis til beregning

Foredrag for skolebørn om min Matematikbog på BogForum 2023

Coronatiden, krise eller skandale, hvad med en høring?

Ny matematik og ny skole nu, ellers uddør vi

Afkoloniser tal-sproget nu

Lær dit barn at matematikke før skolen gør det

Kan matematikken afkoloniseres ved at ombytte essens med eksistens?

Frisæt MATEMATIK, lad børn beholde deres egne Bundt-Bundt tal med enheder, på et 2D Bundt-Bundt Bræt

Matematik, MatemaTisme eller MangeMatik med barnets 2D BundtBundtTal på BBBræt

BogForum 2023

MateMatik Miraklet 2030

MateMatik Miraklet 2030,
Brug Barnets BundtTal med enheder
For matematik er bare så let

e-bog af Allan Tarp,

Mange er det første vi møder, overalt i rum og tid, som fingre og som åndedrag, osv. Og Mange er indlejret i sproget som ental og flertal, som bundt-tal og tælle-tal, og som styk-tal og per-tal.
Hvor barnet har sin egen naturlige forståelse af Mange, har skolen en helt anden kunstig forståelse af Mange. Som kaldes matematik, men som i stedet er en selvskabt kunstfærdig ’matematisme’ uden enheder, altid sandt inde i skolen, men sjældent uden for skolen, hvor der altid er enheder.
Men hvorfor skal skolens kunstige intelligens påtvinges barnet, så det mister sin naturlige intelligens?
Så dette er fortællingen om barnets eget tal-sprog, der bruger fleksible bundt-tal med enheder i stedet for skolens stive linje-tal uden enheder.
At et barn har sit eget tal-sprog ses ved at spørge en 3årig ”Hvor mange år bliver du næste gang?”. Svaret kommer straks med fire finger løftet i vejret. Men barnet protesterer, hvis man viser fire fingre samlet to og to: ”Det er ikke fire, det er 2 toere.”
Barnet ser, hvad der eksisterer i rum og tid, bundter med to i rum, optalt til to i tid. Så barnet skelner mellem eksistens og essens. < fortsættes i e-bogen>

Matematik-skandalen: Skolen underviser i matematisme, der berøver barnet sit tal-sprog og medfødte talsans. 1
Hvad er matematik – og hvorfor skal vi lære det? 4
Matematik er bare så let 7
Lær MangeMatik på et BundtBundtBrædt 11
Giv de unge deres egen skole 24
Drop matematik og genindfør regning 26
Foucault og matematiksvaghed 28
Matematikmodel, forenkling eller forudsigelse 30
Kontingensforskning i matematik 32
Drenge – ingeniører eller bistandsslaver 37
Bevisgale matematiklærere på afveje 38
Invitation til en matematikduel 40
Sådan består alle matematik B 41
Nytænk begyndermatematikken 42
Stop folkeskolen efter 7. klasse 42
Fra matematismus til matematik 43
Naturen drukner i meta-matisme 45
Katolsk matematik, og protestantisk 46
Matematik, banalitet eller ondskab 48
Drop dog munkematematikken og dens mundtlige eksamen 51
Da grammatikken invaderede matematikken 53
I matematik er brug bedre end beviser 55
Regnemodeller, fakta eller fiktion 56
Normal afstand og hygiejne, og lidt kortere tid 59
Mystiske tal og formler bag nedlukningen 61
Lær matematik af dit barn 61
Matematisme skabte coronakrisen 62
Tal TAL til de unge, så de forstår situationens alvor 63
Seruminstituttets matematik-misbrug forhindrer genåbning 63
Matematik-skandalen: Skolens matematisme berøver barnet dets tal-sprog og talsans 65
Alle skolens problemer forsvinder med en amerikansk highskole 68
Corona-skandalen 2020-22, den fortiede Bergamo-hypotese 71
Om brug og misbrug af corona-matematik 72
KOMMOD-rapporten 74
Fleksible Bundt-tal respekter og udvikler børns egen matematik 79
Piaget: Først gribe, så begribe 83
Forsøgsansøgning 1978 matematik C 84
Kvantitativ kompetence i gymnasiet, forsøgsansøgning 2002 86
Matematik Fællesfag 87
Matematik Tilvalgsfag 89
Med CAS kan alle bestå matematik C 92
Med per-tal består alle matematik B 96
KerneMatematik C 100
Projekter til Matematik C 105
Bundles Bring Back Brains from Exclusion to Special Education 127

ICME 15 Sidney

ICME-15: Come and be counted!

What is the 15th International Congress on Mathematical Education?

The International Congress on Mathematical Education is the largest international conference on mathematics education in the world. This quadrennial event is organised under the auspices of the International Commission on Mathematical Instruction and explores current global trends in mathematics education research and mathematics teaching practices at all levels.

The 15th International Congress on Mathematical Education (ICME-15) will take place 7-14 July 2024 at International Convention Centre in Sydney, Australia. ICME-15 promises to be an innovative congress that builds on the well-established ICME program, showcasing established and emerging thought leaders from around the world.


Modeling Eased by Demodeling and Rerooting, paper for Topic Study Group 3.4, accepted as poster

A Text-Free Math Education Found by Difference Research for Protection Against Alien Artificial Intelligence, paper for Topic Study Group 5.10, apparently rejected?

Decolonizing mathematics when demodeling it by using the child’s uncolonized 2D bundle-numbers with units, workshop

Decolonizing mathematics, can that secure numeracy for all, and be protected from AI?, discussion group, reejcted

Abstracts on the ICME15 website 15

Digital poster for TSG 3.4: De-colonizing mathematics by de-modeling & re-rooting.

Many before Math, Math decolonized by the child’s own BundleBundle-Numbers with units, a YouTube video

Calculus across disciplines

How do biologists, chemists, economists, engineers and physicists understand and use calculus concepts in their disciplines? And what does that imply for the teaching and learning calculus in their disciplines? This conference seeks to explore these complex questions by bringing specialists from these disciplines together with mathematics educators. 

Rejected paper: As operators, per-numbers are multiplied before adding as areas

NORSMA7 2023

NORSMA 7 addresses important issues for mathematics and special education policy and
practice in Nordic countries. Theories, empirical results, and experiences from practice are
presented. Both results from development and research already finalized, experiences from
on-going work, and ideas for future collaboration are welcomed. We also welcome theoretical contributions to fundamental issues as what is meant by special needs education in
mathematics and as how to characterize being in difficulties in mathematics.

Rejected proposal: Bring Back Brains with Woke Math

Prepared paper: Bundle- and Per-numbers Replacing the Number Line will Free the Magic of Numbers from its ‘No-unit’ Greenhouse


NORMA 24 – Interplay between research and teaching practice in mathematics education

NORMA 24, The Tenth Nordic Conference on Mathematics Education will take place in Denmark from the 4th to the 7th of June 2024 at Aarhus University, Campus Emdrup in Copenhagen.

The NORMA conferences are organized in collaboration with NoRME​- the Nordic Society for Research in Mathematics Education,, NoRME is open for membership from national societies for research in mathematics education in the Nordic and Baltic countries.

The NORMA conferences offer forum for discussions and constructive interactions among researchers, teachers, teacher educators, graduate students and others interested in mathematics education research in the Nordic context. NORMA are small-scale conferences that emphasize interaction between participants and interplay between scientific and social activities. 


From a colonized to a decolonized mathematics, from 8 to 2 competences, from non-unit to unit-numbers
Respecting the child’s innate number sense, is that Woke-math?
To master or not to master math before Many, that is the question
A rejected proposal for a symposium

Bundle-Bundle-Numbers with Units

Many before Math, Math decolonized by the child’s own BundleBundle-Numbers with units, a YouTube video, and a PDF version.

Flexible Bundle-numbers Develops Children’s Innate Mastery of Many workshop, YouTube video

Flexible Bundle Numbers Workshop Web, PDF-version

Bundle-Bundle-numbers with Units may make Children stay Numerate, booklet

Many-Math, sheet

Many-Math, folder

Apparently, we have 2 Mathematics Paradigms, one without Units, and one With Units

• an inside ‘no-unit-math’ paradigm, where 1 plus 2 is 3 always despite 1week + 2days is 9days, and
• an outside ‘unit-math’ paradigm, where 1 plus 2 depends on the units

The ‘unit-math’ paradigm builds on the philosophy, EXISTENTIALISM, where EXISTENCE precedes ESSENCE
So, unit-math describes real existence, and neglects institutionalized essence

The outside, ‘unit-math’ paradigm, provides the same mathematics, as the inside, ‘no-unit-math’ paradigm, only in a different order. And, the ‘unit-math’ paradigm, avoids the inside paradigm’s ‘mathema-tism’, with its falsifiable, addition-claims.

So, to become a full science, mathematics should leave, its 1 plus 2 is 3, ‘no-unit-math’ greenhouse, and accept that, of course, numbers cannot add, without units.

It should teach the outside ‘counting-before-adding’, ‘unit-math’, paradigm, where Numbers and operations are icons, linked directly to existing things, and actions