keywords:
[a certain kind of measure is involved]
[the familiar numerical systems]
[‘relative natural’ numbers]
[five structural differences]
[such differences are also cognitive]
[qualitative meta-analysis]
[proportionality]
[fractions]
[the conceptual field of multiplication]
[directed numbers]
[numerical thinking]
[understanding arithmetic]
[additive conceptual field]
[different types of numerical concepts]
[have coexisted informally]
[principle of permanence of formal laws]
[numerous problems that appear in Mathematics Education]
[an unusual numerical structure]
[based on a verifiable fact]
