Too often students see the math that they're learning in school as disconnected from life, impotent to have real meaning and purpose outside of its own confines. After my last introductory post on the reasons to implement a Badging system, I want to take you through a couple of opportunities I've given my students to see math work in a civic sense. These badges I've collected fall under a heading I've entitled Math, Equity, and Culture and show mathematics used in powerful ways to those students interested in societal issues.
First, I took an old ABC news article about the Electoral College written by mathematician John Allen Paulos and I asked students to consider the numbers behind how Presidential elections work in the United States. Students who may be more interested in politics and social issues than mathematics can see how individuals who fall on both sides of the Electoral College debate (pro and con) can use mathematics to defend their cases. In defending their own beliefs about the Electoral College, students also see their own need for a stronger mathematical understanding and vocabulary. This provides a greater buy-in to "ordinary" math classes.
Here is a sample student response from the Electoral College badge:
"If the Electoral College was extinct then everyone’s vote would be completely equal in value and the election would be decided by what the majority of the people want, and the state they live in would have no effect on the outcome of the election."
Note the mathematical concepts that the student is wrestling with in this relatively simple sentence: equality, majority, outcome effects, etc. Middle School students aren't equipped to handle some of these mathematical concepts on a formal basis...yet. But, importantly, this student now has a sense for how those topics are important outside of a math textbook and how her current work in a middle school math classroom might be a stepping stone to that formal understanding.
Another badge example uses mathematician Vi Hart's interactive cartoon called The Parable of the Polygons, an object lesson on diversity and segregation in populations. I asked students to read the cartoon and play with the interactives included and then reflect on their experiences.
Look at what some Middle School students said about this activity:
"How small individual biases translate into large collective biases is like making a mistake in a long division problem. When you make one small arithmetic error, the magnitude of the mistake grows larger and larger as you complete the problem, giving you an answer which could be off by a couple million!"
"As the bias accumulates, it gets larger and larger. Soon enough, you have a large collective bias."
"Understanding how mathematics represents biases in a community is essential to solving this societal problem."
There are years of mathematical study necessary to really understand the numeracy concepts underlying those statements. But these students now have a better grasp for the necessity of those mathematical studies and why they are important to help our society advance.
In this Badge section, I have also given students the chance to think about Gerrymandering (thanks to the work of Olivia Walch), and a unique interpretation of the United States Constitution (elucidated by Kurt Gödel as he immigrated in the early 1900s). I also have profiles of mathematicians from diverse populations to allow all students to see mathematicians of different genders, cultures, and backgrounds doing important work (though the absolute best resource for these types of profiles is Annie Perkins' Mathematicians Project).
Any teacher is of course welcome to use any of my Math, Equity, and Culture badges. But what I'd really love is for many more Middle School teachers to find other resources and create their own learning opportunities for students to use. I recently found this new interactive post from Matt Lane about Income Inequality. Let's see what we can come up to help our Middle Schoolers engage with this idea!