Let Kids teach teachers teach MatheMatics as ManyMath, a natural science about MANY using flexible bundle-numbers with units to count and recount before adding on-top and next-to; the CATS approach: Count & Add in Time & Space
Math decolonized by the child’s own BundleBundle-Numbers with units.
The Mathematics Education for the Future Project A Symposium on New Ways of Teaching & Learning The Historic City of Bologna, Italy, August 6-10, 2024
Project Home Pages: https://sites.google.com/view/alan-rogerson-home/home
And, https://sites.unipa.it/grim/21project.htm Organising Committee:Alan Rogerson,Jasia Morska and Simone Brasili Local Organisers: Chiara Chiarini and Alan Rogerson In Cooperation with: Budapest Semesters in Mathematics Education, Hong Kong Institute of Education, MUED, DQME3, MAV, AWM, ATM, AAMT, Wholemovement, MACAS, AIMSSEC, Mathematics Education Centre, Institute for Mathematics, Faculty of Sciences, Eötvös Lóránd University, Budapest, International Symmetry Association and WTM-Verlag.
OUR PROJECT and OUR CONFERENCES
The programme for the Symposium is 5 nights B&B, Aug 6-10, 2024 Aug 6: Arrival ONLY & Registration: NO meals, NO sessions (B&B only) Aug 7-10: 4 work Days with presentations and lunch Aug 7: Welcome Reception at 6.15pm – cocktails/snacks Aug 10: Gala Dinner 7pm in Hotel Restaurant Aug 11: Departure ONLY with check-out after breakfast
Bologna is a city full of history. Its medieval center is among the largest in Europe and its forty-two kilometers of porticoes, and the medieval towers, give Bologna its unique character. Bologna University was founded in 1088 and is the oldest university in the world! (yes.. older even than “the other two places” in the UK!) Bologna has an international airport and is also well served by High Speed Trains that run the whole length of Italy with frequent connections to Milan, Firenze, Rome, Naples etc.
(1) If you are interested in attending please fill in and send the registration form below. (2) If you you wish to present a paper or workshop please send NOW a formal doc x ABSTRACT (up to 12 lines max) following CLOSELY the format guidelines attached. To help you do this page 2 of the guidelines is a doc x template which is already FULLY formatted for you to enter your abstract.
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. A BBBoard shows that 67 = (B-4)*(B-3) = (10 – 4 – 3)*B + 4*3 = 3B12 = 4B2 = 42
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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.
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CONTENTS Abstract Introduction
● SECTION I, FINDING a New Paradigm, BundleBundleMath
Grade one Class one in a Decolonized Future
Valid Always or Sometimes,? Mathema-tics or -tism?
From Many to Bundle-numbers with Units, for Teachers
Micro Curricula, for Learners
Many before Math may Decolonize Math, a Video
Math Dislike Cured with BundleBundle Math
Bundle-counting and Next-to Addition Roots Linearity and Integration
Research Project in Bundle-counting and Next-to Addition
CATS: Learning Mathematics through Counting & Adding Many in Time & Space
The ‘KomMod Report’, a Counter-report to the Ministry’s Competence Report
Word Problems
● SECTION II, REFLECTING on the New Paradigm
A short History of Mathematics
What is Math – and why Learn it?
Fifty Years of Research without Improving Mathematics Education, why?
Postmodern Enlightenment, Schools, and Learning
Can Postmodern Thinking Contribute to Mathematics Education Research
● SECTION III, SPREADING the New Paradigm
ICME Conferences 1976, 1996-2024
The Swedish MADIF papers 2000-2020
The Swedish Mathematics Biennale
The MES Conferences
CERME Conferences
The Catania Trilogy 2015: Diagnosing Poor PISA Performance
CTRAS Conferences
The 8th ICMI-East Asia Conference on Mathematics Education 2018
ICMI Study 24, School Mathematics Curriculum Reforms 2018
NORMA 24
Curriculum Proposal at a South African teacher college
Celebrating the Luther year 1517 with some Theses on Mathematics and Education
Invitation to a Dialogue on Mathematics Education and its Research
MrAlTarp YouTube videos Two-level Table of Contents
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.
Many before Math, Math decolonized by the child’s own BundleBundle-Numbers with units, en YouTube video.
INDHOLD Sammendrag Oversigt 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 Algebra-tavlen Fakta og fiktion og fup, de tre genrer i tal-modeller Modellering og de-modellering Tre fodnoter Læreruddannelse Hvor forskellig er forskellen? Oversigt over forskellen mellem Essens- and Eksistens-matematik Konklusion Referencer 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?
MateMatik Miraklet 2030, Brug Barnets BundtTal med enheder For matematik er bare så let
e-bog af Allan Tarp, www.MidSummer.dk
Forord 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>
INDHOLD Forord INTRODUKTION: MATEMATIK, LET ELLER SVÆRT 1 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 KRONIKKER OM MATEMATIK, MATEMATISME OG MANGEMATIK 24 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 LÆSEPLANER 74 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 UNDERVISNINGSMATERIALE 100 KerneMatematik C 100 Projekter til Matematik C 105 WEB-BASERET LÆRERKURSUS PÅ MATHeCADEMY.net 119 AN ENGLISH ARTICLE 127 Bundles Bring Back Brains from Exclusion to Special Education 127
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
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
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.
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, https://sites.google.com/view/norme/home, 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
