Understanding Math Learning and Teaching in Children

Posted on Feb 26, 2025 in Other university degrees and diplomas

Cognitive, Functional, and Instrumental Objectives

• Cognitive Objectives: Promote, encourage, and develop cognitive abilities.
• Functional Objectives: Focus on skills and procedures that the child is capable of performing. Enables basic skills and procedures.
• Instrumental Objectives: Serve as tools to formalize and conceptualize. Provide sustenance or support for the child to learn (math and study areas).

Teaching and Learning Approaches in Math

• a) Direct Instruction: The goal of teaching math is for learning to be transmitted directly, and students repeat it as it is told.
• b) Discovery Education: Begins with the students’ background knowledge. For cognitive development, students must acquire new knowledge. All answers are valid because students have thought of them and have discovered new concepts through logical reasoning. They learn through experience. Math is the subject of learning as they assimilate.

Conservation of Area

Involves the ability to perceive that an amount does not change regardless of the changes occurring in its total configuration.

• Genesis (Up to 5 years): The conservation of quantity is not present; thought is rigid and subject to direct perception.
• Preparation (5 to 6 years): Begins to appear but does not generalize.
• Mastery (6+ years): The notion of conservation is fully developed.

Correspondence Term by Term

Associating the elements of two sets by taking one element from each and forming pairs.

1. Global Comparison and Lack of Correspondence: The child is *not* capable of generating a set with the same elements as another.
2. Correspondence, Non-Equivalent Term by Term: Creates a set with the same elements as one given by one-to-one correspondence among the elements of the set.
3. Term by Term Correspondence with Equivalence: Ability to develop a set of objects with the same amount as another without any doubt.

Serialization

Operating capacity by establishing comparative relations between elements of a set and ranking them according to their differences.

• Global Serialization: Builds series without regard to the characteristics of the objects.
• Intuitive Serialization: Completes series based on the relationship between objects.
• Operational Serialization: The child anticipates the series and performs it using a methodical approach.

Inclusion of the Part to the Whole

Perceiving the qualities of things and distinguishing similarities and differences by grouping them according to properties.

• Genesis (4-5 years): Do not have this notion.
• Transition (5-6 years): Answers are contradictory.
• Achievement (6+ years): Have acquired this notion.

Quantifiers

Words that distinguish aggregate quantities. Quantify in an inaccurate or implied way. Designate non-numerical quantities.

• Formation of the concept: It is the logical and primary classification. Classify the existing universe into two sub-concepts.
• Dichotomy: It brings together all elements of a concept in two sub-concepts. Each sub-concept is an initial concept. The two sub-concepts have an attribute different approach.
• Division initial concept: This is an extension of the dichotomy that in some cases the results are not satisfactory and successful divisions. It brings together elements from 2 or more subsets. All this subset is an element of the initial concept.

Contexts

• Sequence: The first ability exercised in children, using numbers in their usual order without referring to any entity or object.
• Counting: An activity that takes place when counting things.
• Cardinal: A natural number that describes the total amount of elements of a well-defined set.
• Ordinal: Describes the relative position of an element within a totally ordered discrete set, with a chosen initial element.

Measurement

An act that children cannot do easily and spontaneously. The measurement process begins with the perception of the quality being measured, using words like “more than,” “less than,” “as much as,” etc.

• Anthropometric Measurement: Measures that depend on each individual, using the student’s body parts as a resource.