Chapter 3 by Treyci Alonzo

Generalizations

tealonzo — 2024-02-20 03:11:22 UTC

Are "big ideas" in math. An example is "Utilizing algebraic tools such algebraic multiplication, subtraction, and division allow highly complex problems to be solved and displayed" (Wathall, p.63, 2016).

Principles

tealonzo — 2024-02-20 03:12:59 UTC

Are more specific. They are theorems, formulas, and things that hold true no matter the situation. They are specific (not general).

Why understand?

tealonzo — 2024-02-20 03:20:47 UTC

So that student's understand that principles have meaning, they are not just to be remembered they should be understood thoroughly
To create structure and flo in a lesson plan, a natural building off of ideas
For collaboration between teachers and students, so that working together the teacher can provide opportunities of showing understanding

Level 1 Generalization

tealonzo — 2024-02-20 03:25:38 UTC

"Students will understand..."

Perhaps the Pythagorean theorem is used to find the hypotenuse of a right triangle!

Level 1 is only naming a topic, we want the students to understand WHICH CONCEPT

Level 2 Generalization

tealonzo — 2024-02-20 03:28:23 UTC

"How or why?"

Building off the last concept, howww is the Pythagorean Theorem used to find the hypotenuse of a right triangle?

Level 2 explains more about the methods used like in this case, we use the 2 legs of a triangle, we use operations

Level 3 Generalization

tealonzo — 2024-02-20 03:31:27 UTC

"So what? What is the significance"

So we understand the methods used, nut do we understand why it works? Here we can show examples of why things work, like using Geogebra to show how if you really square the 2 side lengths the area of the squares add up to the area of the big square.

Opportunities to show understanding

tealonzo — 2024-02-20 03:43:02 UTC

(Wathall, p.81, 2016).

References

tealonzo — 2024-02-20 03:45:23 UTC

Wathall, J. T. (2016). Concept-based mathematics: Teaching For deep understanding In secondary classrooms. Corwin. ISBN-13: 978-1506314945 ISBN-10:1506314945