Effective Math Teaching Strategies for Deeper Understanding

Equivalence of Decimals

Decimals are the expression of decimal fractions. We can obtain equivalent fractions by multiplying the numerator and denominator by 10, 100, etc. To compare two decimal numbers, it is sufficient to compare their corresponding decimal fractions.

Equivalence of Percentages

For example, 2/5 is equivalent to 40/100 (or 40%). Frequent problems involve scenarios where an object's price is increased or decreased, asking for:

• The original price
• The final price after the rebate
• The percentage of the discount

The Measurement Problem in Math Education

The traditional learning of mathematics has often been rigid. This proposes a new method that stimulates thought through trial and error. Learning to measure magnitudes is often identified with simply learning the metric system. It is thought that objectives are met when a student can perform conversions quickly and accurately. However, it is common to see errors in problem results because the conversion often takes place as an act of chance rather than reflection. This leads the student to automation without a guarantee of understanding.

Although our metric system is clear, allowing for perfect division and ease of comparison, it also requires cognitive development from the individual. What is offered, therefore, is a learning method based on direct observation and manipulation.

Using Everyday Objects for Learning

It is convenient to use everyday objects to learn these concepts:

• Length: strings, Cuisenaire strips, etc.
• Capacity: bottles of different sizes and shapes, etc.
• Mass: balance scales
• Surface Area: tangrams
• Geometry: geoboards
• Time: heartbeat, timer, etc.
• Volume: cubes, boxes, etc.

Characteristics of Learning Activities

Level 0: Identification and Description

• Activities focus on the classification, identification, and description of varied forms.
• Use large quantities of physical models that can be manipulated by children.
• Provide a variety of examples in different ways so that irrelevant features are not seen as important.
• Provide opportunities for students to build, draw, compose, or decompose shapes in various ways.

Level 1: Analyzing Properties

• Begin to focus more on the properties of simple figures than on their identification (e.g., define, measure, observe).
• Solving problems that involve the properties of shapes is an important aspect to consider.
• Continue using concrete models, as in Level 0, but use models that allow for the exploration of various properties of the figures.
• Classify shapes using their properties and names.

Level 2: Deductive Reasoning

• Continue using the properties of shapes, but with a focus on defining those properties.
• Start using informal deductive language, such as all, some, and none.
• Investigate the validity of inverting certain relationships.
• Use models and drawings as tools for thinking, and start looking for generalizations and counterexamples.
• Encourage the development and testing of hypotheses.