https://padlet.com/lbaraja6/o4x6xsd4exn1yi77 Chapter 3 en-us 2022-11-03 22:43:05 UTC 2023-03-15 23:57:03 UTC hello@padlet.com lbaraja6 https://padlet.com/lbaraja6/o4x6xsd4exn1yi77/wish/2369205473 2022-11-03 22:45:29 UTC https://padlet.com/lbaraja6/o4x6xsd4exn1yi77/wish/2369205473 lbaraja6 https://padlet.com/lbaraja6/o4x6xsd4exn1yi77/wish/2492057905

They summarize what we want our student's to take away after a unit

They are defined as two or more concepts stated as a sentence of relationship

They are truths that are supported by factual examples

They provide goals within a unit to help learners make connections.

Overarching generalizations are understandings beyond a specific unit 

Topical generalizations are specific to a topic 

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Principles are the math facts/ foundational truths which hold all the attributes of generalizations.

They never contain qualifiers such as "may, can, often" which can be included in generalizations

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They provide a clear focus for curriculum and instruction

Allowing opportunities to generalize is crucial to learning math

Writing generalizations should be a collaborative process 

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Level 1: Students will understand that 

• They are weak and do not allow the learner to understand what and why they are they are learning.
• Include no-no words like "is, are, have, impact, affect, and influence"

Level 2: How or why?

• These two questions help scaffold a generalization to the next level by providing clarity and conceptual specificity for depth of understanding

Level 3: So what is the significance/effect.

• Allows for further scaffolding
• Not always necessary as level 2 can express critical understanding and level 3 be used to express the real world value of math

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Achieved through inductive inquiry from which teachers provide students with examples to draw generaliations

Rather than telling students the generalizations and then asking them to work through examples (deductive), students instead discover generalizations and principles for themselves

It is crucial students be given the opportunity to form conceptual understandings by writing in math. 

writing in math encourages students to organize, understand, analyze, and reflect on new learning

Another way to draw out generalizations is graphic organizers 

Learning experiences overall should draw out conceptual understandings using the correct mathematical terminology

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