STEM Skills- Mathematics Focus Volume 1II

Characterizing skill

As educators/teachers, our mission is not just to teach Math but to inspire a deep and lasting connection with the subject. Today, I want to share with you a powerful tool that can help you achieve this: Characterizing Skill In Math.

Think of characterizing as a way to unveil the magic of mathematics to your students. It is about showing them how to look beyond the surface of numbers and equations and discover the intricate patterns and relationships that lie within.

So, how do we do this? Start by inviting your students on a journey of exploration. Show them that Math is not just about getting the right answer, but about understanding the why behind it. Encourage them to ask questions, make observations, and explore mathematical concepts from different angles. Teach them how to analyze geometric shapes, dissect algebraic equations, and uncover numerical patterns. Show them that every mathematical object has its own unique set of properties waiting to be discovered.

Example 1– Characterizing a Triangle:

Imagine you are teaching a lesson on Geometry, and your students are learning about triangles. You want to illustrate characterizing skill by having them analyze the properties of a triangle.

1. Identifying Attributes: Start by presenting a triangle to your students, either visually or through a diagram. Guide them to identify its key attributes, such as:

·???????? Three sides

·???????? Three angles

·???????? Internal angles summing up to 180 degrees

·???????? Classification based on side lengths and angle measures (e.g., equilateral, isosceles, scalene, acute, obtuse, right)

2. Describing Properties: Encourage students to describe the properties of the triangle they have identified. For instance:

·???????? An equilateral triangle has all three sides of equal length and all three angles measuring 60 degrees.

·???????? An isosceles triangle has two sides of equal length and two angles of equal measure.

·???????? A right triangle has one angle measuring 90 degrees.

3. Exploring Relationships: Prompt students to explore relationships between different properties. For example:

·???????? In a right triangle, the side opposite the right angle (the hypotenuse) is the longest side.

·???????? The sum of the lengths of any two sides of a triangle must be greater than the length of the third side (Triangle Inequality Theorem).

4. Extension Activities: To deepen understanding, engage students in extension activities such as:

·???????? Classifying triangles based on their properties and creating a visual display.

·???????? Exploring the Pythagorean Theorem and its application in finding the lengths of sides in right triangles.

·???????? Investigating the properties of special triangles like the 30-60-90 triangle or the 45-45-90 triangle.

By guiding students through this process of analyzing and characterizing the properties of a triangle, you are helping them develop characterizing skills in geometry. They will not only understand the characteristics of triangles but also learn to apply these skills to analyze other geometric shapes effectively.

Example 2- Characterizing the Fibonacci Sequence:

In this example, we will guide students through characterizing the properties of the Fibonacci sequence, where each term is the sum of the two preceding terms: 1,1,2,3,5,8,13, 21…

1. Identifying Patterns: Start by introducing the Fibonacci sequence to your students and guiding them to identify its key characteristics:

·???????? Each term is the sum of the two preceding terms.

·???????? The sequence starts with 1, 1.

2. Describing Properties: Encourage students to describe the properties of the Fibonacci sequence they have identified. For instance:

·???????? The Fibonacci sequence exhibits patterns in nature, such as the arrangement of petals in flowers, branching in trees, and spiral patterns in shells and galaxies.

3. Exploring Relationships: Prompt students to explore relationships between different properties. For example:

·???????? Investigate how changing the starting values of the sequence affects its progression.

·???????? Explore the relationship between the Fibonacci sequence and other mathematical concepts, such as Pascal's triangle or the Lucas sequence.

4. Extension Activities: To deepen understanding, engage students in extension activities such as:

·???????? Generating Fibonacci-like sequences with different starting values or recurrence relations.

·???????? Exploring applications of the Fibonacci sequence in real-world contexts, such as in finance, art, or architecture.

Overall, characterizing skill in mathematics is not only about understanding mathematical concepts but also about developing critical thinking, problem-solving, and analytical abilities that are essential for success in both academic and real-world contexts.