The Reflective Educator

Education ∪ Math ∪ Technology

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Day: August 12, 2011

Geogebra simulations in math

I love using Geogebra! Take a look at the diagram below (use the slider to change the value of n) and then think about how difficult this one simple interactive diagram would be to recreate without the technology.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

For more Geogebra resources, either check out the official Geogebra website (http://www.geogebra.org/) or the awesome resources shared below to get a feel for what you can do with Geogebra.

http://www.ualberta.ca/~urban/Projects/Math/Tech%20in%20Math.htm by @stefras

http://mrhonner.com/2011/06/19/pendulum-animation/ by @MrHonner

http://www.geogebra.org/en/upload/index.php?&direction=0&order=&directory=english/Daniel_A_Kaufmann by @dak721

 

Explain Constructivism in 140 characters

This video of Michelle Bachmann complaining about Mathematics education is just wrong. 

 

My take-away from this video is that Michelle Bachmann has a fundamental misunderstanding of what constructivist teaching is. She doesn’t get it. To be honest though, when you look at educational materials which are shared with parents, they very rarely, if ever, define the purpose behind the pedagogy in language that is accessible to people outside of the field of teaching.

My thought is that we need to define some of the terms we use in language which makes sense for the average person. For example, the definition of Constructivism on Wikipedia is:

Constructivism is a theory of knowledge (epistemology) that argues that humans generate knowledge and meaning from an interaction between their experiences and their ideas.

This definition is problematic, not because it is inaccurate, but because it is incomprehensible to a non-academic. It comes across as knowledge is arbitrary.

A few weeks ago, I asked people to attempt and define constructivism themselves (in 140 characters or less) via Twitter. Here are some of the definitions.

A belief that knowledge exists in and is constructed by the mind of the learner, not transmitted from outside. @MathEdNet and @Wedaman

Making meaning and building understanding starting from what you already know. @josieholdford

Learning is the result of our individual experiences & the social support given around those experiences. @delta_dc

Making meaning and building understanding starting from what you already know. @pwacmdh

Learning is the result of our individual experiences & the social support given around those experiences. @mssandersths and @bonzimmer

While these meanings may not be enough to explain constructivism to parents in enough detail, they are more comprehensible to the average person, and a much easier place to begin a conversation about what the impact the Constructivist learning theory has on how we should approach education.

A problem with averages

This xkcd comic demonstrates a big problem with averages.

The problem with average ratings

 

By the way, this same problem occurs when you average grades as well.