Papers presented at the CTRAS 2023 June Conference, **C**lassroom **T**eaching **R**esearch for **A**ll **S**tudents

**Artificial Intelligence makes Difference Research more relevant**

Allan Tarp, the MATHeCADEMY.net

Research typically is seen as an example of a top-down or bottom-up lab-lib cooperation where laboratory observations are deduced from or are inducing library concepts. In the top-down version, library theory generates a hypothesis that, validated or falsified in the laboratory, leads to a strengthened or adapted theory. In the bottom-up version, laboratory observations lead to categories, that additional observations may split into subcategories.

Artificial Intelligence has access to the library, but laboratory data will be input. Top-down research thus may be generated very quickly with a quality depending on the reliability of the input, which may be difficult to check.

In contrast, AI is of less help to bottom-up research typically generating new categories not yet present in the library.

Also Difference Research searching for differences making a difference (Tarp, 2018) may now be more relevant since although AI may locate existing differences, it cannot invent new differences. Nor can it examine the difference they make.

Examples of difference research are bundle-numbers with units, operations as icons for counting, re-counting to change unit, per-numbers coming from recounting in two units, integration as addition of locally constant per-numbers, trigonometry before geometry, and mathematism adding numbers without units.

References:

Tarp, A. (2018). Mastering Many by counting, re-counting and double-counting before adding on-top and next-to. Journal of Mathematics Education, 11(1), 103-117.

**Online math opens for a communicative turn in number language education**

Allan Tarp, the MATHeCADEMY.net

“Of course, the goal of mathematics education is to master mathematics before it can be applied to later master Many.” Seeing this as a ‘goal displacement’ making a means a goal, sociology (Bauman, 1990) and difference research (Tarp, 2018) suggests a communicative turn as in foreign language education in the 1970s (Widdowson, 1978): Maybe mastering Many is a more accessible way to later master Mathematics. Likewise, existentialism (Sartre, 2007) holds that existence should precede essence.

Seeing 4 fingers 2 by 2 as ‘2 2s’ shows that preschool children master Many with 2D bundle-numbers with units. In this ‘BundleNumber-math’ adding is preceded by counting, which de-models (Tarp, 2020) division and multiplication as icons for a broom and a lift to push-away the unit-bundles to be lifted as a stack. They combine in a ‘recount-formula’ (Tarp, 2018), T = (T/B)xB, predicting that T contains T/B Bs. Subtraction iconizes a rope to pull-away the stack to find unbundled that are placed on-top as decimals, fractions, or negatives. Addition iconizes adding on-top and next-to.

This allows both school and education students to be guided by the concrete subject on their desktop instead of by an instructor on a screen, as exemplified by the MATHeCADEMY.net.

References:

Bauman, Z. (1990). Thinking sociologically. Blackwell.

Sartre, J.P. (2007). Existentialism is a humanism. Yale University Press.

Tarp, A. (2018). Mastering Many by counting, re-counting and double-counting before adding on-top and next-to. Journal of Mathematics Education, 11(1), 103-117.

Tarp, A. (2020). De-modeling numbers, operations and equations: From inside-inside to outside-inside understanding. Ho Chi Minh City University of Education Journal of Science 17(3), 453-466.

Widdowson, H. G. (1978). Teaching language as communication. Oxford University Press.