Transformations

Danny Stock

Math in the Time of Corona


Across our distance-learning program, we see examples of teachers striving to make visible our mission and values. Here, we put a spotlight on Middle School math and their efforts to dig into the transformations and learn from them.
 

Geometric Transformations

In 8th grade Geometry, students are studying cultural elements that have stood the test of time, using them to reflect on that old adage, “math is everywhere!” Searching online, students collected symbolic, historical, and culturally significant artifacts and examined each item through a mathematical lens, reflecting on the use of space, arrangement, and patterns and gaining an appreciation of mathematical contributions made by a variety of cultures. 

Students observed geometric transformations (repeated reflection, rotation, translation and/or dilation—enlargement—of shapes in a composition) and symmetry in mosaics, textiles, pottery, sculpture, paintings, murals, dance, architecture, and other engineering designs (like machinery or other man-made objects) from many cultures and traditions, including Islamic, Christian, Buddhist, Native American, Mexican, Greek, Roman, Russian, Korean, Japanese, Indian, and Haitian.

“You often don't even realize a piece of art is geometric until you look closely,” said one student. Another added, “You start to learn that...math is essential in making art.”

“A lot of popular designs in many cultures are mathematically complex,” said Rachel. “I even found transformations on everyday objects that I had seen multiple times in my own home.” 

Mark reflected, “I saw how different people and cultures used math to make art look more interesting and satisfying to look at. It shows how math is an international concept.”

“I began to view cultures differently when observing their use of math in art because different cultures use different transformations,” Leo said.

As students looked ahead to one day visiting a museum in person again, they noted a heightened awareness of the relationship between math and art. One 8th grader said, “I will also share this knowledge with my family when we visit together.”
 

Coronavirus Algebra

Using an interactive module developed by GDS Middle School teachers in Desmos (an online graphing calculator), 8th grade Algebra students used exponential functions to test the effects of different initial numbers of infections on growth rates from the first few weeks of the Coronavirus outbreak in the United States and worldwide. 

“In this way,” explained Middle School math teacher Angie Errett, “students built models based on mathematical equations [they’ve been learning] to mimic real data, discern growth rates, and make statistical and scientific observations and predictions. The activity led students to think about how data collection and biases impacted the quality of the data and how the inclusion of unreliable data can lead to consequences in decision-making and predicting short- and long-term outcomes.”

After refining their models by eliminating faulty or questionable data, students worked backward to predict when the outbreak actually may have begun in the United States—an outbreak that ultimately transformed the way they are learning now. They also considered the impact on public health in scenarios where protective measures were put in place earlier in the outbreak.

Priya explained, “If the numbers at the beginning are unreliable, then the equation will take longer to find, the graph will end up being unreliable, [and that will leave] the coronavirus numbers unpredictable.”

“If your curve is inaccurate in the slightest,” added Jordan, “you may not be prepared for an influx (or decrease) in cases.”

“This could [also] lead to different procedures and failures in experiments,” finished Luke. 

In short, students have developed the ability to engage thoughtfully—and mathematically—in the current national discussion on our transformed communities and how to scale back social distancing responsibly.


Caring Enough to Listen

At the start of class each week in our transformed classrooms, Middle School teachers check in on their students with various developmentally targeted wellness icebreakers. Student voices are encouraged and space is given to talk through how students are experiencing everything from friendships-at-a-distance, coronavirus worries, and GDS distance learning. “I feel like this commitment is part of what defines our team,” explained Middle School math teacher Lauren Thompson. “We have students start by answering in the [Zoom call] chat and then some share out loud. It’s a way to include more voices and offer students multiple ways of engaging.”

Teachers have used appealing graphics for prompts such as “Describe how you are feeling in terms of a weather forecast” and “What instrument would capture your current mood?” The check-ins align with department goals (and the GDS mission) to “promote equity in the math classroom and keep community central to our work,” Lauren said.

As you navigate these tough times with your family, take a lesson from Middle School math and hold firmly to those things you value as a member of the GDS community. Keep caring, keep striving, and keep learning.





 

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