“Logico-mathematical knowledge” is a term invented by Piaget, the renowned educational researcher. He wanted to make the distinction between different kinds of knowledge, based on their sources.
Piaget identified “physical knowledge,” which can be discerned through the senses (the dog is brown, the sun is warm, the cake is sweet), and he pointed out that physical knowledge is different from “social knowledge,” which can’t be discovered through the senses but which must be told to us by other people (Thanksgiving is on the fourth Thursday of November, my name is Leigh, in the US we drive on the right).
Then there is logico-mathematical knowledge, which is constructed inside the brain. Logico-mathematical knowledge is the knowledge of relationships, and relationships don’t exist until we make them. It’s the sort of knowledge only humans (and perhaps some very intelligent animals to a limited degree) can make. Logico-mathematical knowledge is “real magic”!…the creation of “something” where there used to be “nothing.” Relationships include all abstract nouns, “mathematical” or not: number, area, length, equal…as well as fairness, love, peace, justice…
Logico-mathematical knowledge is horribly difficult to talk about, because once you create “something” out of “nothing,” that “something” exists for you just as surely as if it existed “out there” in Nature. But another person may not have yet created the same “something” in their head as you did in yours, so communicating with them about “something” may be impossible.
For example, try this question: Are there more people in the world, or more women?
This seems so obvious it’s silly, right?Adults know that of course there are more people in the world than there are women, even though they have never counted all the people and all the women, nor has anyone specifically told them this fact. Adults are surprised to find that young children (under the age of five) do not yet have this knowledge and have trouble thinking about groups (people) and parts of the group (women) simultaneously. Young children who have not yet constructed the part-whole relationship in their brains often guess that there are more women than people in the world. (This is because young children often encounter more women than men in their lives , and because they haven’t yet constructed the part-whole relationship, they can only “hear” the question as “Are there more women or more men in the world?” And as far as they can see, there are more women.)
Another problem is that once you have created a “something” in your head it is real to you, and you can’t now recall what it was like before you made the “something.” You very likely believe that the “something” was always there, that it exists in Nature, and that either you discovered it or someone taught it to you. In fact, you created it. In the current ed-psych parlance: You “constructed” it. (educational psychologists, neuroeducators, etc, often use words from architecture: construction, scaffolding, circuitry…)
So. Logico-mathematical knowledge is constructed by each individual, inside his or her own head. It doesn’t come from the outside. It can’t be seen, heard, felt or told. It develops as each person makes logical connections. Schooling and other experiences stimulate the development of logico-mathematical knowledge, but the actual neural connections which represent this knowledge are built from the inside.