Don’t pull out the Soviet/French curriculum. We assume the average intelligence walking monkey.
Modern mathematics (for now at least) builds on sets. Of course mathematics is not all about studying sets themselves, but the objects in our mind that manifests as sets in our artificial framework (philosophers calm down). It is about numbers, quantities and geometry.
I would introduce the uninitiated brain first to shapes. In a sense, I don’t introduce shapes to him (gender neutral, I don’t discriminate between genders, in fact please believe that I am unable to) but he picks them up through vision. Now you would say well your ears perform Fourier transform automatically but you don’t know Fourier transform. Please, it’s not the same thing. The human mind is wonderful, and it doesn’t make sense for Richard Borcherds, and for me, how we are able to do mathematics at all, but we can and some of it is even really natural. He (again, gender neutral) would at least intuitively understand the concepts of length, area, shapes, angles, etc.. During this stage, it is crucial for the human mind to explore and obtain the ability to make sense of the world around him. Minimal guidance is needed apart from language aquisition.
After he is able to speak, we can now converse fluently in quantities. Counting then becomes the single target he should pursue. Introducing LEGO. The number of blocks without explicit counting up to 5 would be great. That’s actually my limit but I would assume a toddler to have a better brain than an old man like myself. Then we could consider the binary operation of addition. By arranging the blocks in lattices multiplication can be understood, along with its commutativity.
Now for the introduction of sets. An elementary way to present sets could be sorting the blocks into colours. This should be immediately followed up with combinatorics problems in combinations and permutations, ultimately leading to the inclusion-exclusion principle to show the power of sets. Extensive combinatorics training would greatly enhance arithmetic skills and general mental prowess.
Idk what else to write lol. How should I go about introducing algebra?