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.