Making the invisible visible

Cultured bacteria colonies taken from hands.  When one becomes many, their secret existence is revealed.

Cultured bacteria colonies taken from hands. When one becomes many, their secret existence is revealed.

In the midst of reading Macbeth, engaging in mock trials, dissecting mathematical arguments, and tackling epidemiology, students have experienced a fundamental challenge for learners: trying to understand the things that do not readily reveal themselves.  How do we make the invisible visible?  Through stories?  Through trials and deliberations?  By pulling apart mathematical arguments? Yes, yes, and yes!  In science we’ve had to make the infinitesimal a little more tangible, and had to design experiments to test our ideas.

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Testing Assumptions

Some of the most important work students are undertaking in geometry this year involves constructing and critiquing mathematical arguments. Since an argument is always based on underlying premises or assumptions, it is important to recognize and examine those assumptions. In the unit on quadrilaterals and area that they are wrapping up this week, students have looked not only at how to use area formulas, but also at their derivations. Students are familiar with the formula for the area of a triangle, but why does that formula work? To answer this question, we had to make a few assumptions.

One of these assumptions is that dissecting and rearranging parts of a shape does not change the area.

square to triangle

The areas of the square and triangle shown are equal because the triangle is created by rearranging parts of the square.

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Epidemiology and Criminology

The Broad Street Pump:  Once a source of London's cholera and now a symbol of modern public health

The Broad Street Pump: Once a source of London’s cholera and now a symbol of modern public health

The 9th Grade Academy recently wrapped up a unit on epidemiology that took students from 19th-Century London to 21st-Century West Africa. Along the way we learned about the “father of modern epidemiology,” John Snow, as well as some of the processes that epidemiologists use to solve outbreaks to this day. We compared the history of cholera in London to a modern outbreak in Haiti, and then focused on Ebola as the primary example of a modern epidemiological challenge. We talked about causes, complications, solutions, and effects of public health problems, and considered the roles that various parties play in contributing to a healthier world for all people.

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