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What are generalizations in mathematics? What is the difference between a principle and a generalization in mathematics?

Why do we wish our students to understand principles and generalizations in mathematics?

What is the difference between Level 1, 2, and 3 generalizations?

What opportunities do you provide for your students to demonstrate and communicate their conceptual understanding?

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What are generalizations in mathematics? 

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What are generalizations in mathematics? 

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Generalizations give us explanations of why and what we want our students to comprehend in terms of the relationship between two or more concepts. Known as enduring understanding, essential understanding, or big ideas of the unit.

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What is the difference between a principle and a generalization in mathematics?

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What is the difference between a principle and a generalization in mathematics?

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Generalizations are two or more concepts stated as a sentence of relationship. They are the overriding ideas that students need to understand that can include a domain or qualifier.

A principle is a law or foundational truth that holds all the attributes of generalizations and commonly describes real-life situations. Principles are also known as Theorems. They do not contain qualifiers.

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What is the difference between Level 1, 2, and 3 generalizations?

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What is the difference between Level 1, 2, and 3 generalizations?

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Level 1: Students will understand that...

This helps put the focus on what students should understand as opposed to what students will know and do.

Level 2: How or Why?

This demonstrates the critical understanding of what is happening in the mathematical process.

Level 3: So what? What is the significance or effect?

This level of generalization demonstrates a depth of understanding by addressing the questions "So what is the significance or effect?" This helps to express the real-world value of mathematics.

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Why do we wish our students to understand principles and generalizations in mathematics?

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Why do we wish our students to understand principles and generalizations in mathematics?

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It is essential for students to understand the principles, aka the theorems and laws of mathematics. These understandings enable the students to then create generalizations for these mathematical concepts. The practice of generalizations enables the student to deepen and demonstrate their understanding of the principles, which enables them to always understand those concepts.

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What opportunities do you provide for your students to demonstrate and communicate their conceptual understanding?

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What opportunities do you provide for your students to demonstrate and communicate their conceptual understanding?

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Inductive Inquiry

Provide specific examples that enable the students to draw generalizations.

During inductive approaches, students need to be given opportunities to form conceptual understandings from their learning experiences by writing in mathematics.

Graphic organizers can give students a visual representation of how the concepts are related, and then be able to form generalizations.

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Opportunities for students to generalize concepts.

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Opportunities for students to generalize concepts.

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Giving students the opportunity to generalize

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Giving students the opportunity to generalize

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Making generalizations in mathematics - Mathematics for Teaching

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Making generalizations is fundamental to mathematics. Developing this skill and making it part of the students’ mental disposition or habits of mind…