cycles of learning george woodbury college of the sequoias – visalia, ca [email protected]
TRANSCRIPT
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Cycles of Learning
Discover
Engage
Reflect
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Discover
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Discover• Can Developmental Math students
really discover this material?
• I’m not looking for my students to discover independently.
• I do want my students to participate in the discovery.
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Discover• As I teach I try to lead the discovery.
• Involve students
• Collaborate, not dictate
• Help students to develop that “little voice”
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Self Discovery
The Reversal
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• Multiply
8 5x x
6 9x x
2 6x x
10 4x x
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• Multiply
28 5 13 40x x x x
26 9 15 54x x x x
22 6 4 12x x x x
210 4 6 40x x x x
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• What did I multiply to get an answer of
2 15 54x x
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• After covering …
• Ask …
5 4 32 3 7 5x x x
2 4 3 23 ? 6 9 33x x x x
2 5 4 3? 5 12 8 40 96x x x x x
4 3 2? ? 6 15 27x x x
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• After covering …
Graphing Square Root Functions
• Ask …
Here’s a graph. What’s the function?
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• After covering …
Solving Quadratic Equations By Factoring
• Ask …
Here’s a solution set. What’s the equation?
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• After covering …
Your Turn
• Ask …
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Self Discovery
“Wolfram|Alpha” Style
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• Problem:Simplify
• Answer:
2
2
10 21
5 14
x x
x x
3
2
x
x
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• Problem:Simplify
• Answer:
2 2
2 2
8 15 16
12 12 35
x x x
x x x x
4
7
x
x
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• Problem:Simplify
• Answer:
7 5 2
2
8 28 4
4
x x x
x
5 32 7 1x x
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• Problem:Your Turn
• Answer:
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Self Discovery
Properties of GraphsDesmos.com
Graphing Parabolas
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Self Discovery
Properties of GraphsDesmos.com
Translations (h & k)
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Self Discovery
Flipping the Classroom
Graphing Absolute Value Functions
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Engage
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Reflect
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Reflect• Give students a chance to …
• Summarize what we have done
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Reflect• Give students a chance to …
• Explain concepts in their own words
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Reflect• Give students a chance to …
• Compare (and contrast) current topics to previous topics
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Reflect• Give students a chance to …
• Think about the “big picture”
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Reflect - Example• Compare and contrast the process
for solving a linear equation with the process for solving a simple linear inequality.
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Reflect - Example• Which technique would be most
efficient for graphing the following lines – graphing by intercepts or graphing by slope? Why?
8 5 80x y 3
54
y x
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Reflect - Example• Give an example of a system of
linear equations that would be better solved by using the substitution method than the elimination method.
• Give an example of a system of linear equations that would be better solved by using the elimination method than the substitution method.
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Reflect - Example• Compare the process of finding the
intercepts of a parabola to finding the intercepts of a line.
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Reflect – In Class• Reserve the last 5 minutes of class to
…
• Summarize that day’s materials
• Ask reflective questions
• Ask students to share their observations
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Cycles of Learning
Discover
Engage
Reflect
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Summary
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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.
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Active Learning• Students learn more when they are
actively engaged and participating in the process, taking responsibility for their own learning.
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Reflection• I believe that students must be
constantly encouraged to reflect upon what they have learned.
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Reflection• By understanding the differences and
commonalities between the current concept and previous concepts helps students develop a true understanding of the material.
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Cycles of Learning
Discover
Engage
Reflect