Constructivism

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"What works, works."

If you know how to construct something, you know how it works (at least as far as the level of construction and the levels above is/are concerned). If you know how something works, you might be able to construct it.

how conceivable are mathematics and constructivism? isn't it problematic to assume/infer/conclude just because constructivism is both a construction and learning paradigm from engineering that it is also suitable for mathematics? doesn't a statement like "what works, works" remind me of a statement like "what looks good, is good" or "what looks like that, is or must be like that", just a little bit on one/a higher level, but still being unmathematical?

Isn't the inferring of "what looks like that, is or must be like that" also a main challenge in Gestalt psychology? So would it be possible to "use" or "convert" or "adapt" such a highly problematic and actually completely unmathematical learning paradigm to mathematics? Or more specifically: Some kind of finding out how concepts of mathematics that have very little to do with Gestalt psychology might still be expressed or explained or visually represented by Gestalt psychology so that mathematics can be learned in a better and more (but probably still not mathematically perfectly) appropriate way? A visual or visualized didactic of mathematics? But isn't it impossible even if the best and most advanced and sophisticated (in terms of visual ideas and engineering/technology) visualization ideas and techniques (maybe cutting edge 3D interactive visualization or even like a computer game or maybe even direct neural interfaces in the future) would be used to really "map" or "visualize" or "express" ... just mathematics? Isn't it an intelligence issue and purely an intelligence issue? And isn't pure intelligence ultimately not "mappable" at all even with the most sophisticated visual "didactics and engineering attempts" (or even "struggles"?)? But still try it?

And what about the didactics of engineering and Gestalt psychology? Wouldn't it be easier to apply learning methods from Gestalt psychology at least to engineering but would that matter in terms of the didactics of mathematics?

Would it be a good idea to merge the pages "Constructivism" and Gestalt psychology into a single page? At the moment, there is a redirect from the page "Gestalt psychology" to this page here, but the two terms are actually (in terms of general didactics) not at all the same. But maybe just because mathematics is so complex and almost infeasible to map or visualize might it be that in the special case of pure mathematics teaching, the two different disciplines of didactics might have to combine their efforts so that the effort becomes the same. But would not even the best (and maybe also mathematically to a certain degree talented) engineers be able to sufficiently do that because it is technically unfeasible? But still try it because no other option is available and the compromise with reality requires (demands) it? Therefore, the UMIS would be a constructivist-Gestalt-psychology endeavor for a process that is actually unfeasible and futile because it is not or hardly possible to simply somehow artificially create or develop what actually is true intelligence? Therefore, would intelligence itself be unreachable by any means of technology?

But still, because of a maybe necessary compromise with reality, shouldn't it actually be begun as quickly as possible? But who would do it? When? How? With what kind of technology? In which kind of setting? With which kind of programming languages? Hardware? Interfaces to the eyes and later brain? 3D computer game developers? That would actually be the UMIS, but intelligence is not replaceable. What would be required to develop the UMIS:

  • "very good" (what does that mean?) mathematics knowledge anyway because if you do not know what the subject to be learned is, you cannot develop a learning environment for it at all (and because of this, I would actually already drop out of the selection)
  • just good engineering knowledge too in order to really develop the UMIS technology. but the question if and how much robots might be embedded into the UMIS too remains because at the moment, I imagine the UMIS as some kind of almost "ordinary" computer monitor interface with just very sophisticated 3d computer game and/or also more conventional/static "clickable" or otherwise quite conventionally learning
  • a talent for connecting mathematics and engineering and didactics (constructivism & g ps) in terms of interactive 3d visualization
  • therefore, I am actually really out of the race because I am not a 3d game developer let alone a mathematician and I have not even found out yet how "my" small animals (especially mice and/or rats and/or bats) and maybe also robots (but I have hardly any robotic development experience either there, so not even that) can be meaningfully integrated into the UMIS. But maybe that would be the only place where I might still be somehow meaningfully participate but it would be very difficult and challenging to connect these robots with the UMIS too (but how?) and connecting animals would not be ethical anyway and also hardly make sense and the animals are actually only there in order to facilitate robotics, make it more creative (but that has little to do with mathematics) and prevent that children interact too much with robots and too little with animals. So maybe, the way would go like that: motivate children with animals and robots for mathematics and when they are interested let them learn mathematics in the most sophisticated way as early and as axiomatically as possible with a 3d interactive learning environment which is constantly being improved - but with full knowledge that something like a maximally optimized (in terms of constructivism and Gestalt psychology) UMIS is still not able to allow the learning of mathematics in the most genuine or "appropriate" way because even the best UMIS cannot replace one's own (in many/most cases lack of) intelligence.

And might that be also the reason why constructivism is only (fully? or only partially?) able to explain the layers above and not the layers beyond? and what about the same layer?

But isn't constructivism at least one of the best or even the best teaching method(s) for technology teaching?

Possible topics (old section, but still with a few good ideas for further text):

  • constructivism and (the philosophy and/or foundations of) mathematics
  • constructivism and mathematization
  • What do constructivist learning environments mean for the didactics of mathematics? Is there a constructivist way of learning mathematics?
  • How sustainable are real-world constructivist learning environments?
  • constructivism in the brain vs. constructivism with real parts and hands?
  • constructivism and neural networks
  • constructivism and truth, transparency and honesty
  • constructivism and intransparency, dishonesty and lying
  • constructivism and the "what is outside my body and asynchronous to it" problem (this point would be a good idea for a new page because it is a didactics topic that is relatively unrelated from mathematics but has implications for robotics)

The title of this page here is "constructivism", but the page "Gestalt psychology" also leads to this page here and the two above statements in terms of looks or looking might imply the didactics paradigm of Gestalt psychology relatively precisely too. And it is probably even possible that a visual depiction of Gestalt psychology is objective/appropriate/applicable/true/consistent/congruent in a specific context within the frames/borders of that particular (and certainly non-mathematical) context and its intermediate level, but such a context would certainly not be a (purely) mathematical context. Therefore, if Gestalt psychology is used in the didactics of mathematics (which might even be necessary and justifiable), it is unfortunately not able to objectively/appropriately/... (see the list above) represent mathematics. The human brain as far as its limited abilities have so far discovered mathematics - and even more mathematics itself - is/are too complex (and simple in a deeply mathematical way) to just be visually represented, not even in the most "sophisticated" or "elaborate" way.