Category Archives: CupCount

Core Papers 2018

Core Papers 2017-2018
This selection contains four papers written in 2017 and 2018
01. The Simplicity of Mathematics Designing a STEM-based Core Math Curriculum for Outsiders and Migrants.
This article is due to be published in the next number 34 of Philosophy of Mathematics Education Journal.
The abstract says that 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 migrants wanting to help rebuilding their original countries.

    02. Addition-free migrant-math rooted in STEM re-counting formulas
    A short version of the article above was sent to the Topic Working Group 26 on STEM mathematics at the CERME 11 conference. It was rejected as a paper, so it was redrawn.
    The abstract says that a curriculum architect is asked to avoid traditional mistakes when designing a curriculum for young migrants that will allow them to quickly become STEM pre-teachers and pre-engineers. Typical multiplication formulas expressing re-counting in different units suggest an addition-free curriculum. To answer the question ‘How many in total?’ we count and re-count totals in the same or in a different unit, as well as to and from tens; also, we double-count in two units to create per-numbers, becoming fractions with like units. To predict, we use a re-count formula as a core formula in all STEM subjects.
    03. Mastering Many by Counting, Re-counting and Double-counting before Adding On-top and Next-to
    This article was published in the Journal of Mathematics Education, March 2018, 11(1), 103-117.
    The abstract says that 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.
    04. A Twin Curriculum Since Contemporary Mathematics May Block the Road to its Educational Goal, Mastery of Many
    This article was accepted at the conference ICMI Study 24, School Mathematics Curriculum Reforms: Challenges, Changes And Opportunities, in Tsukuba Japan, 26-30 November 2018. The abstract says that mathematics education research still leaves many issues unsolved after half a century. Since it refers primarily to local theory, we may ask if grand theory may be helpful. Here philosophy suggests respecting and developing the epistemological mastery of Many children bring to school instead of forcing ontological university mathematics upon them. And sociology warns against the goal displacement created by seeing contemporary institutionalized mathematics as the goal needing eight competences to be learned, instead of aiming at its outside root, mastery of Many, needing only two competences, to count and to unite, described and implemented through a guiding twin curriculum.
    **Counting before Adding, The Child’s Own Twin Curriculum, Count & ReCount & DoubleCount before Adding NextTo & OnTop
    This is a Power Point Presentation made from the article above.

AdditionFree Math

Addition-free migrant-math rooted in STEM re-counting formulas
Paper for the STEM working group at the CERME 11 conference
A curriculum architect is asked to avoid traditional mistakes when designing a curriculum for young migrants that will allow them to quickly become STEM pre-teachers and pre-engineers. Typical multiplication formulas expressing re-counting in different units suggest an addition-free curriculum. To answer the question ‘How many in total?’ we count and re-count totals in the same or in a different unit, as well as to and from tens; also, we double-count in two units to create per-numbers, becoming fractions with like units. To predict, we use a re-count formula as a core formula in all STEM subjects.
AdditionFree Math

The Child’s Own Twin Curriculum

A TWIN CURRICULUM SINCE CONTEMPORARY MATHEMATICS MAY BLOCK THE ROAD TO ITS EDUCATIONAL GOAL, MASTERY OF MANY
Count & ReCount & DoubleCount before Adding NextTo & OnTop
Mathematics education research still leaves many issues unsolved after half a century. Since it refers primarily to local theory, we may ask if grand theory may be helpful. Here philosophy suggests respecting and developing the epistemological mastery of Many children bring to school instead of forcing ontological university mathematics upon them. And sociology warns against the goal displacement created by seeing contemporary institutionalized mathematics as the goal needing eight competences to be learned, instead of aiming at its outside root, mastery of Many, needing only two competences, to count and to unite, described and implemented through a guiding twin curriculum.

A Twin Curriculum in Counting & Adding PPP
A Twin Curriculum in Counting & Adding Paper

2018 Articles on Math Education

Articles from 2018 on Mathematics and Education and Research

A collection of articles about Mathematics Education written in 2018, July version

  1. Posters at the 2018 Swedish Biennial stand
  2. Migrants Master Many by Re-counting in Block- & Per-numbers – Short
  3. Migrants Master Many by Re-counting in Block- & Per-numbers – Long
  4. Math: Useful Abstractions or an Undiagnosed Compulsory Cure? Conflicting Theories in Mathematics Education – Short
  5. Math: Useful Abstractions or an Undiagnosed Compulsory Cure? Conflicting Theories in Mathematics Education – Long
  6. A STEM-based Mathematics without Addition – Short
  7. A STEM-based Mathematics without Addition – Long
  8. Cure Math Dislike with 1 Cup & 5 Sticks: New Meanings to Numbers, Counting, Operations & Fractions – Short
  9. Curing Math Dislike with 1 Cup & 5 Sticks: New Meanings to Numbers, Counting, Operations & Fractions – Long
  10. Good Math & Goofy Math, which is Truer? – Short
  11. Good Math & Goofy Math, which is Truer? – Long
  12. A Core STEM Curriculum for Young Migrants – Short
  13. A Core STEM Curriculum for Young Migrants – Long
  14. Fifty Years of Ineffective Math Education Research, Why? Oops, Wrong Numbers, Sorry
  15. Rethinking Line-Number Arithmetic as Block-Number Algebra
  16. A Count-before-Adding Curriculum for Preschool and Migrants
  17. Difference-research Saving Dropout Ryan with a TI-82 Calculator
  18. Conflicting Theories Help Teachers Improve Mathematics Education
  19. Addition-free Core STEM Curriculum for Late Learners along the Silk Road
  20. Good, Bad & Evil Mathematics – Sociological Imagination in Math Education
  21. Remedial Math MicroCurricula – When Stuck in a Traditional Curriculum
  22. Mastering Many by Counting, Re-counting and Double-counting before Adding On-top and Next-to
  23. Good, Bad & Evil Mathematics – Tales of Totals, Numbers & Fractions
  24. The Simplicity of Math reveals a Core Curriculum
  25. Good, Bad & Evil Mathematics – Tales of Totals, Numbers & Fractions, PPP
  26. The Simplicity of Math reveals a Core Curriculum, PPP
  27. A Twin Curriculum Since Contemporary Mathematics May Block the Road to its Educational Goal, Mastery of Many
  28. Addition Free Migrant-Math Rooted in STEM Re-Counting Formulas

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 MATHeCADEMY.net, 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

Content
Introduction
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
Post-Constructivism
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
LEFT
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
MIDDLE
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
Activities
RIGHT
1Year online CATS-Course
1Week STEM-Course
Is Math True always or sometimes? Is Mathematics well-defined?
PYRAMIDeDUCATION & Material
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)