article: Structural and semiotic diversity in the didactic transition from the natural-number domain to the integers: a study of understanding in the field of additive relativity

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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]