Mathematical Development: Magnitudes and Numbering

Variables in Didactic Rankings

The didactic nature of the attributes or properties involves the degree of abstraction of the material, the possible conjunction or disjunction of attributes, the use of denial, the size of the collection, and the number of property values.

Key Milestones in Measurement

Consideration and Magnitude Perception

One must consider and perceive magnitudes; there are quantities that are very obvious, such as length. Regarding weight (mass), to perceive and consider it, children can perform activities such as weighing with their hands or using a balance. They often choose "higher" even if it is within.

Conservation of Magnitude

If I have a ball of dough and squash it, it changes shape, but not weight.

Magnitude Management and Social Contacts

Magnitude given regarding management is intrinsically a classification. The establishment of social contacts between the magnitude and the number (being able to measure) involves the choice of a pattern (unit), which then leads to the legal units that we know. Example: one folio is a pattern, but if I need to measure the mass, two folios might be needed for location. Activities for students should be conducted without attempting to accelerate the pace of development of different stages.

The Nomenclature of Numbers

The oral numbering system is more complex than the written one; it is a system that is not positional (one does not say "ten and one"). The writing system is positional decimal (0-9). There are fewer terms in the oral system. For the numbering learning process, the number goes through three phases:

Phases of Learning Numbers

• Overall Approach: The most important phase, involving early representations of the number.
• Algorithmic Phase: The student begins to discover regularities and rules of the written numerical series. Appropriation of the rules starts by writing and using the algorithm. System regularities result in written and oral irregularities beginning to be known.
• Grouping Decimal: In groupings, there are changes and variations in the figures.

Constitution of the Unit

• Lack of unity: This occurs as one starts to compare.
• Object-Unit: This is closely linked to the object to be measured. Example: If they measure a pencil, they will take a smaller pencil.
• Situational unit: Still linked to the object, but the student tends to select small objects to measure small things, adapting to the situation.
• Figural Unit: Linked to the situational unit, but the dependency on the object to be measured will be missing.
• Unit itself: Free, independent, and common for all.