Wathall Synthesis Chapter 3 by Anthony Giliberto

Generalizations

agiliber — 2025-02-20 22:49:00 UTC

Gives teachers explanations of why and what we want our students to comprehend in terms of the relationship between two or more concepts.
the overriding ideas we would like our students to understand and transfer that may contain a qualifier such as may or can
generalizations are statements of two or more concepts that transfer through time, cultures, and across situations in the context of mathematics
help provide goals when planning a unit

Why Generalizations?

agiliber — 2025-02-20 22:55:14 UTC

Gets students to answer the question, "Why am I learning this and what is the point beyond this example?"

Overarching Generalizations

agiliber — 2025-02-20 22:56:14 UTC

are understandings beyond the specifics of a unit
are larger and transferable insights we want students to acquire over year long programs

Difference Between Principles and Generalizations

agiliber — 2025-02-20 23:01:17 UTC

Summed up perfectly in this quote from the text: "Generalizations are understandings that transfer through time, across cultures, and across situations. Generalizations contain no proper nouns, past tense verbs, or pronouns that would associate the idea with a particular person or group . . . . Generalizations are truths supported by factual examples, but they may include a qualifier (often, can, may) when the idea is important but does not hold in all instances” (62).

Topical Generalizations

agiliber — 2025-02-20 23:02:25 UTC

Focus on a particular insight was wants students to take from a specific topic or subject

Principles vs Generalizations

agiliber — 2025-02-20 23:04:43 UTC

In simpler terms: a principle" refers to a fundamental, established truth or rule that applies broadly across different situations, while a "generalization" is a statement that identifies a pattern or relationship based on observed specific cases, essentially taking a concept from a limited set and applying it to a wider range of scenarios

Examples of Generalizations

agiliber — 2025-02-20 23:09:06 UTC

1) The quadratic formula determines the zeros of a function, the roots of a function, and the x intercepts graphically

2) The scaler product between vectors represents the angle between the vectors and magnitude of the vectors

Level One Generalization

agiliber — 2025-02-20 23:12:41 UTC

Should begin with: "Students will understand that... "

This helps focus on what students should UNDERSTAND as opposed to what students will know and do in terms of skills

Why Level One Generalizations are Weak?

agiliber — 2025-02-20 23:14:59 UTC

do not help learners fully understand what and why they are learning
often include "no,no" verbs such as is, are , have, impact, affect, etc.

WE want students to ask questions HOW? and WHY? to make it to the next level

Level Two Generaliztions

agiliber — 2025-02-20 23:17:30 UTC

clearly address the HOW or WHY of a concept
provide strong, clear statements of conceptual understanding and includes key concepts and skills

FOCUS OF TEACHING IS FOR STUDNETS TO BE AT LEVEL TWO GENERALIZATIONS

Level Three Generalizations

agiliber — 2025-02-20 23:19:47 UTC

Address the question.. "So what is the significance or effect? and allows us as teachers to scaffold further and extend students understanding

Can be used to express the real world value of math or to be more specific towards conceptual understanding

TARGET FOR STUDENTS: Instruction Focused

agiliber — 2025-02-20 23:20:18 UTC

Approaches and Examples of How I Give Students Opportunities to Communicate Conceptual Understanding

agiliber — 2025-02-20 23:23:21 UTC

Inductive

agiliber — 2025-02-20 23:28:21 UTC

Learning experiences through WRITING about math

Ex) Graphic Organizers - such as a concept map in which students include the concepts they have learned and how they are connected with statements explaining them
EX) Have students devise a headline that summarizes the key ideas or concepts from a unit or lesson
Ex) Have students complete I understand that..... statements after a unit/lesson/week

Deductive

agiliber — 2025-02-20 23:30:00 UTC

EX 1) Give students the concepts you are going to go over or went over and ask them to connect the statements in a way that reflects the purpose of the unit we are in

Ex 2) Give students a choice of a few statements sand ask them to choose one and give the big idea from it and to justify why