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Some tools and examples of uses in making generalizations

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Tools for Inquiry and Drawing generalizations

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Tools for Inquiry and Drawing generalizations

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It is helpful for students to have examples that they relate to and that relays prior knowledge.

It is also helpful for studnets to have a graphic organizer to keep track of their thoughts and connections that they see within the mathematics.

Having students summarize or go back and ask what they did within a lesson and a unit may also help for students to create a synthesis of the information and create their own generalization.

It is also important when teaching the concepts to use the correct mathematical terminology so that the students have a grasp of the mathematics that is occuring.

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How can we draw out these generalizations in students??

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How can we draw out these generalizations in students??

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We want to move away from the traditional approach that tells the students the generalization and then works problems based on that.

Students will learn the generalizations through inductive processes to see the concepts and generalizations for themselves.

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This a comparison of the structure of knowledge and process, highlighting where generalizations come into play.

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We want to make sure that our generalizations are not too vague and unclear, but are not too specific that they appear to be facts.

There is a three-step approach to this that helps to avoid vague language.
1. Students will understand that
2.  How or why?
3. So what is the significance or effect of this knowledge?

When we create generalizations we want to avoid level one generalizations and be sure to explain how or why this knowledge is important.

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Principles in Structures of Knowledge and Process are laws or foundational truths that hold all the attributes of generalizations and commonly describe real-life situations.

These can be seen as mathematical theorems such as Pythagorean's theorem, these do not have qualifier statements and are accepted as facts.

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An example of a generalization that allows for understanding within the concept of quadradic equations.

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Provide goals for understanding, unit planning, and creating connections and are often discovered through the questioning of why am I learning this and how will this extend beyond the example.

Overarching generalizations are the generalizations made that can transfer beyond a unit of study.
Topical generalizations are generalizations that provide clarity within a topic or field of study.

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A generalization is two or more concepts stated as a sentence of relationship, this understanding transfers through time understanding and cultures.
A principle

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The goal of the understandings that we would like our students to achieve at the end of a unit or study on a topic.
This can be seen as the why and what of our students ideal conceptions about mathematics.