Principles of Math Teaching and Learning

Teaching and Learning Concepts

Concrete Bases (Teaching)

Convert mathematics into something concrete. Create recognizable contexts to which children can assign their own meanings.

Construction (Learning)

Learning is a constructive activity, contrary to the idea that children simply absorb knowledge presented to them.

Models (Teaching)

To achieve progress, students must have tools at their disposal that enable them to establish a link between informal and formal mathematics. Models and materials are important.

Raising the Level (Learning)

The learning process occurs at different levels of formality. Changes can be sudden and create discontinuity in the learning process.

Time for Reflection (Teaching)

The teacher has to find time to include reflection on the kind of mathematics being taught.

Reflection (Learning)

Learning is stimulated by reflection; this is the engine that drives progress and advancement in level.

Interactive Math Lessons (Teaching)

Interaction should be natural in a mathematics classroom.

The Social Context (Learning)

Children learn most often with adults or other children, not alone. Shared mathematical concepts and procedures are discussed, generating ideas collectively. They express different views and need to persuade others or listen to their arguments.

Weaving the Threads of Learning (Teaching)

The teacher should base their teaching on real-world situations (horizontal mathematization). On the other hand, vertical mathematization allows connections among mathematical ideas.

Structure (Learning)

New knowledge is incorporated into existing cognitive structures (assimilation), or the whole structure is adjusted to accommodate new ideas (accommodation).

Objectives of Mathematics Education

1. Represent facts and real or simulated situations of everyday life with symbolic mathematical models to understand, evaluate, and produce information and messages using correct language and specific vocabulary of the subject.

2. Evaluate the role of mathematics in everyday life, enjoy its use, and acknowledge the contributions of diverse cultures to the development of mathematical knowledge.

Mathematics Content Blocks

• Numbers and Operations

  1. Single-digit natural numbers.
  2. Memorization of pairs of numbers that sum to 10 for use in addition and subtraction with order changes.

• Measurement: Estimation and Calculation of Magnitudes

  1. Length, weight/mass, and capacity.
  2. Using the most common conventional measurement units:
     • meter, centimeter, kilogram, and liter.

• Geometry

  1. Plane and solid shapes.
  2. Intuition of point, line, and plane as geometric elements.

• Information Processing, Chance, and Probability

  1. Statistical graphs.
  2. Conducting surveys whose answers have two or more possibilities.