Here are the examples that I found for constructivism:
http://www.thirteen.org/edonline/concept2class/constructivism/demonstration.html
This link is a collection of examples, but I found the first one to mirror a lot of the ENC 1101/ENC 1102 (freshman english) courses that the libraries teach. The instructor usually asks the student to choose a controversial topic and to take a side and find evidence from articles/books in favor of the side taken. It allows the students to choose what topic they want to learn about.
Another example of constructivism is from one of the engineering professors that I work with in Mechanical Engineering. He asked his students to take a real-life structure that has failed (such as a building collapsing or bridge buckling) and had them research why it had failed and determine what should have been different in the original structure design.
Another example of constructivism is from one of the engineering professors in Nuclear and Radiological Engineering who made his students develop their own radiation shielding device for whatever radiation facility that wanted to work with, whether it be an x-ray lab, nuclear reactor facility, or a nuclear power plant. They had to research their particular facility and then determine what degree of radiation they had to protect against and then determine what materials would help to create that protection.
In an article that I read this weekend, I found another example of constructivism that had to do with an accounting course that was offered with a web application that presented real-world tax problems that accounting graduates would face once they left their program.
Here are the examples that I found for Schema Theory:
When I was in high school, my geometry teacher made drawings on the board to make us remember what he was talking about. For example, for us to remember how a trapezoid looked, he said that there was this animal called a "ZOID" and that he was going to trap it. For some odd reason, I have neither forgotten that shape nor the story behind it.
Another example from my friend's history class in high school would be when her teacher asked the students to play on different sides of the Civil War and develop their political policy according to what their textbook said. She said it was effective because in her mind it's a framework for the past that she wouldn't have learned if she had just read it from the book alone.
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