# Didactics of mathematics

The didactics of mathematics is crucial for allowing as many people/entities learn as much as possible about mathematics during their existence in the real world. In case of human babies (whether and how animals and animal babies can also participate is another topic), robotics is the best way to begin. Babies and toddlers are hardly able to understand or learn mathematics, but they are able to intuitively understand robots. By already beginning in early childhood with robotics, the scaffold for all later mathematics learning efforts can already begin to be developed soon after birth.

Generally, robotics has ten crucially new aspects (components) that conventional school learning environments of nowadays unfortunately only have to a limited degree:

- learning gratitute and respect towards what exists (including mathematics) and restriction of oneself in the context of knowledge, mathematics and one's own amibitions
- socially embedded: new knowledge is learned developed together with other people (humans) and sometimes (often) additionally with animals and robots
- movement-oriented (for a more healthy lifestyle, back to the nomadic roots of homo sapiens)
- outdoor-oriented can and should indeed be at least partially (and increasingly) performed outdoors in natural environments (also a more healthy lifestyle, also back to the nomadic roots of homo sapiens)
- individually adapted: individually adapted learning environments adapted to the cognitive and learning abilities and motivations of each baby, toddler and child individually
- autonomous (see the next point "intrinsically motivated")
- intrinsically motivated: Toddlers and children like to move and if they can learn the concepts of mathematics and especially pure mathematics by moving around, they are intrinsically more motivated to learn these fundamental concepts compared to when learning while sitting and standing still. The onset of learning mathematics and robotics can be much earlier because already toddlers are intrinsically motivated to move (and babies are curious towards new stimuli like a robot) and there is a continuation of intrinsically learning from birth.
- multimodal learning: Doing, constructing (see also the next point "constructivism), thinking: activity of one's own body and body parts, hands, several senses at the same time (vision, hearing, touch, smelling, possibly tasting, equilibrium), emotions and thinking. And not just seeing and possibly listening while sitting or standing still.
- constructivism (learning by constructing things)
- Gestalt psychology (learning by having things explained well)

Furthermore, software can help to improve the didactic of mathematics in three ways now and in the near-term future:

- software in order to learn mathematics from early childhood that is also the precursor of a possible universal mathematical information system#Learning and Didactics of mathematics
- classic mathematics software from simple calculators up to complex mathematical software packages
- "universal" mathematical software, see universal mathematical information system, that is something in between the two above software types and increasingly incorporates both types of the above software

Mid-term future (not yet now, because it is unsafe and/or technically infeasible at the moment):

- direct neural interfaces for learning mathematics and robotics and interacting with "computers" (respectively their successors) in the middle-term future when the stage of the beginning technological singularity approaches, the sharp distinction between software and hardware decreases
- ultimately, because of increasingly perfect mathematization, "everything" increasingly becomes mathematics and the distinction between software and hardware disappears

For the didactics of pure mathematics, see also the following pages:

- conveying the full complexity of mathematics as early as possible in an individually adapted way
- how can the mathematical imagination of a child be preserved and enhanced?
- list of URls for the didactics of mathematics
- more ideas are appreciated very much, especially for the didactics of pure mathematics, please write me an e-mail to moc.liamg -ta- rennatrigsakul if you have an additional idea