Incorporating Discovery in Developmental Mathematics

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Presentation transcript:

Incorporating Discovery in Developmental Mathematics George Woodbury College of the Sequoias – Visalia, CA georgew@cos.edu

Cycles of Learning Discover Engage Reflect

Discover

Discover Can Developmental Math students really discover this material?

Discover I’m not looking for my students to discover independently.

Discover I do want my students to participate in the discovery.

Discover As I teach I try to lead the discovery.

Discover Involve students

Discover Collaborate, not dictate

Discover Help students to develop that “little voice”

Discover – Example Solve:

Discover Option 1: Clearly explain the steps for solving this new type of equation. Isolate the absolute value. Rewrite as two equations. Solve the equations.

Discover Option 2: “Can anyone find a solution of this new type of equation?”

Discover – Example Solve:

Discover Get students to think. Get students engaged and active, rather than being passive. Get students to explain their reasoning and share their strategies.

Discovery – Strategy 1 The Reversal

Multiply

Multiply

What did I multiply to get an answer of

After covering … Ask …

Graphing Square Root Functions After covering … Graphing Square Root Functions Ask … Here’s a graph. What’s the function?

Solving Quadratic Equations By Factoring After covering … Solving Quadratic Equations By Factoring Ask … Here’s a solution set. What’s the equation?

After covering … Your Turn Ask …

“Wolfram|Alpha” Style Discovery – Strategy 2 “Wolfram|Alpha” Style

Problem: Simplify Answer:

Problem: Simplify Answer:

Problem: Simplify Answer:

Problem: Your Turn Answer:

Using Technology to Develop Graphing Strategies Discovery – Strategy 3 Using Technology to Develop Graphing Strategies

Properties of Graphs Desmos.com Graphing Parabolas Discovery Properties of Graphs Desmos.com Graphing Parabolas

Properties of Graphs Desmos.com Translations (h & k) Discovery Properties of Graphs Desmos.com Translations (h & k)

Flipping the Classroom Discovery – Strategy 4 Flipping the Classroom

Flipping the Classroom Simplifying Radical Expressions Discovery Flipping the Classroom Simplifying Radical Expressions

Flipping the Classroom Graphing Absolute Value Functions Discovery Flipping the Classroom Graphing Absolute Value Functions

Summary

True Learning I believe that true learning only occurs when students are allowed to participate in the discovery of procedures and problem solving strategies, rather than being handed a recipe of steps to follow.

Cycles of Learning Discover Engage Reflect

Feedback Questions? Comments? georgew@cos.edu @georgewoodbury on Twitter