Category Archives: CupCount

Journal of Mathematics Education 11:1

Mastering Many by Counting, Re-counting and Double-counting before Adding On-top and Next-to

Allan Tarp, The, Denmark, March 2018

Observing the quantitative competence children bring to school, and by using difference-research searching for differences making a difference, we discover a different ‘Many-matics’. Here digits are icons with as many sticks as they represent. Operations are icons also, used when bundle-counting produces two-dimensional block-numbers, ready to be re-counted in the same unit to remove or create overloads to make operations easier; or in a new unit, later called proportionality; or to and from tens rooting multiplication tables and solving equations. Here double-counting in two units creates per-numbers becoming fractions with like units; both being, not numbers, but operators needing numbers to become numbers. Addition here occurs both on-top rooting proportionality, and next-to rooting integral calculus by adding areas; and here trigonometry precedes geometry.

2017 Articles on Math Education

Articles from 2017 on Mathematics and Education and Research
A collection of articles about Mathematics Education written in 2017

  1. Does Europe really need Compulsory School Classes?
  2. Mathematics, Banality or Evilness
  3. CupCounting and Calculus in Early Childhood Education
  4. Fifty Years of Research without Improving Mathematics Education, Why?
  5. A 1year pre-engineer course for Young migrants, a job for critical or civilized math education
  6. Online Teacher Training for Curing Math Dislike: Cup&Re-Counting & Multiplication Before Addition
  7. Debate on how to improve mathematics education
  8. Poster: MigrantMath as CupCounting & PreSchool Calculus
  9. A Heidegger View on How to Improve Mathematics Education
  10. Count and Multiply Before You Add: Proportionality and Calculus for Early Childhood and Migrants
  11. The Simplicity of Mathematics Designing a STEM-based Core Math Curriculum for Outsiders and Migrants
  12. The Simplicity of Mathematics Designing a STEM-based Core Mathematics Curriculum for Young Male Migrants
  13. Math Competenc(i)es – Catholic or Protestant?
  14. The ‘KomMod Report’, a Counter Report to the Ministry’s Competence Report
  15. Twelve Proposals for 1day Skype Seminars
  16. Difference-Research Powering PISA Performance: Count & Multiply before You Add
  17. Reflections from the CTRAS 2017 Conference in China
  18. Sixteen Proposals for the 8th ICMI-East Asia Regional Conference on Mathematics Education
  19. Plenary PowerPointPresentation at the CTRAS 2017 July Conference in China
  20. Math Dislike
  21. Migrant Math 01
  22. Mathematics Predicts, PreCalculus with a TI-82 or TI-84

MADIFpapers 2000-2018

MADIFpapers 2000-2018

Killer-Equations, Job Threats and Syntax Errors
Student-mathematics versus teacher-Metamatics
Mathematism and the Irrelevance of the Research Industry
The 12 Math-Blunders of Killer-Mathematics
Mathematics: Grounded Enlightenment – or Pastoral Salvation
Discourse Protection in Mathematics Education
Golden Learning Opportunities in Preschool
Calculators and IconCounting and CupWriting in PreSchool and in Special Needs Education
Grounding Conflicting Theories
The Simplicity of Mathematics Designing a STEM-based Core Mathematics Curriculum for Young
Male Migrants
Math Competenc(i)es – Catholic or Protestant?

Posters 2018 Biennale in Sweden

Math Biennale 2018 Posters

Posters at the 2018 Swedish Biennale Stand
●Math Dislike Cured by 1 Cup & 5 Sticks
●Migrant Math for STEM Teachers/Engineers
INTRO: Saving the Princess with BundleNumbers
Good Math: MANY-Math, Tales about Totals
Bad Math: SET-Math, Tales about LineNumbers
Evil MATH: Fraction-Math, Tales about Operators
Good Math: Icons, Bundling, ReCounting & PerNumbers
Core Math from Childhood
Grand Theory in Math Ed Research & Difference Research
Math Dislike CURED by 1 Cup & 5 Sticks
Improving Schools in Sweden
Migrant-Math making migrants STEM-Teachers or Engineers
Count before you Add
Kids own Math
1Year online CATS-Course
1Week STEM-Course
Is Math True always or sometimes? Is Mathematics well-defined?
Beware of Institutions & Teachers & Research & Forced Classes
Good & Bad & Evil Education
Rejected Research Papers
Research Paper: The Simplicity of Mathematics Designing a STEM-based Core Mathematics Curriculum for Young Male Migrants
(STEM: Science + Technology + Engineering + Mathematics)


DifferenceResearch Powers PISA

Difference-Research Powering PISA Performance: Count and Multiply before you Add

To explain 50 years of low performing mathematics education research, this paper asks: Can mathematics and education and research be different? Difference-research searching traditions for hidden differences provides an answer: Traditional mathematics, defining concepts from above as examples of abstractions, can be different by instead defining concepts from below as abstractions from examples. Also, traditional line-organized office-directed education can be different by uncovering and developing the individual talent through daily lessons in self-chosen half-year blocks. And traditional research extending its volume of references can be different, either as grounded theory abstracting categories from observations, or as difference-research uncovering hidden differences to see if they make a difference. One such difference is: To improve PISA performance, Count and Multiply before you Add.

Difference-Research Powering PISA Performance, a 31 page article

Dalian Talk 2017, a 30 minutes PowerPoint keynote Presentation of the above article


STEM-based Core Math for Migrants

The Simplicity of Mathematics Designing a STEM-based Core Math Curriculum for Outsiders and Migrants

Swedish educational shortages challenge traditional mathematics education offered to migrants. Mathematics could be taught in its simplicity instead of as ‘meta-matsim’, a mixture of ‘meta-matics’ defining concepts as examples of inside abstractions instead of as abstractions from outside examples; and ‘mathe-matism’ true inside classrooms but seldom outside as when adding numbers without units. Rebuilt as ‘many-matics’ from its outside root, Many, mathematics unveils its simplicity to be taught in a STEM context at a 2year course providing a background as pre-teacher or pre-engineer for young male migrants wanting to help rebuilding their original countries.

Core STEM Math

Migrant Math in twenty 1page Sheets



  1. From Sticks to Icons
  2. Counting-sequences in Icons
  3. CupCount in Icons
  4. CupCount with Dices
  5. ReCount in the Same Unit
  6. ReCount in a New Unit
  7. ReCount in BundleBundles
  8. ReCount in Tens on Squared Paper or an Abacus
  9. ReCount from Tens
  10. ReCount Large Numbers in Tens
  11. DoubleCount with PerNumbers
  12. DoubleCount with Fractions and Percentages
  13. ReCount PerNumbers, Fractions
  14. Add OnTop
  15. Reversed Adding OnTop
  16. Add NextTo
  17. Reversed Adding NextTo
  18. Add Tens
  19. Reversed Adding Tens
  20. Recounting Solves Equations

12 Proposals for 1day Skype Seminars

Twelve proposals for Skype seminars

01) The Root of Mathematics, Many, dealt with by Block-Numbers, Cup-Counting and Preschool Calculus.
02) 12 Luther-like Theses about how ManyMath can Improve Math Education
03) Curing Math Dislike with one Cup and five Sticks
04) DoubleCounting rooting Proportionality – and Fractions and Percentages as PerNumbers
05) Algebraic Fractions made easy by Block-Numbers with Units
06) Algebra and Geometry, always Together, never Apart
07) Calculus in Middle School and High School
08) Mathematics, the Grammar of the Number-Language. But why teach Grammar before Language?
09) Quantitative Literature also has three Genres: Fact and Fiction and Fiddle
10) Distance Teacher Education in Mathematics by the CATS method: Count & Add in Time & Space
11) 50 years of Sterile Mathematics Education Research, Why?
12) Difference-Research, a more Successful Research Paradigm?

Heidegger Improving Math Education


After 50 years of research, mathematics education still has learning problems as witnessed by the PISA studies. So, a suspicion arises: Can we be sure that what has been undertaken is mathematics and education and research? We seek an answer in philosophy by listening to Heidegger that, wanting to establish its meaning, finds two forms of Being: that what is, and how it is. In a Heidegger universe, the core ingredients are I and It and They, where I must neglect the gossip from They to establish an authentic relationship to It. Bracketing mathematics’ gossip will allow its root, Many, to open itself and disclose a ‘many-matics’ as a grounded natural science different in many ways from the traditional self-referring set-based mathe-matics. So to improve its educational sentences, mathematics should bring its subjects to the classroom, but leave its gossip outside.

MES9 Contributions with Reviews

MES9 Contributions with Review 

A 1year pre-engineer course for young migrants, a job for critical or civilized math education
Online teacher training for curing math dislike: cup&re-counting & multiplication before addition
Debate on how to improve mathematics education
Migrant-math: cupcounting & preschool calculus

Review paper
Review project
Review symposium
Review poster