View from the Classroom

Fostering Systems Thinking in the Middle Grades

Foley Teaches Complexity Using Multivariate Graphs

Downpours in Uruguay, but drought in Peru. Enormous blizzards in the northeast, but steeply climbing worldwide temperatures. Climate science can be confusing… especially if you’re only 14 years old. Without an understanding of complex systems, it can seem downright contradictory.

That’s why Maura Foley, an earth and climate science teacher at the Hopkins School in Connecticut, devotes significant energy to helping her students investigate systems interactions.

“Today’s problems are complex problems, so we need thinking that is going to reach outside of these discrete zones of understanding,” said Foley.

Foley admits that understanding complexity is part of higher order, abstract thinking – an easier task for her high school students than her middle school students. However, she believes it’s essential to begin building the idea of complexity in the lower grade bands. In her middle school courses, the process of building that understanding starts with noticing how one thing affects another, which affects another, and so on.

“Today’s problems are complex problems, so we need thinking that is going to reach outside of these discrete zones of understanding.”

“What’s great about Tuva is being able to blow through looking at a whole bunch of variables quickly,” explained Foley. “They don’t need to be a spreadsheet expert to quickly go ahead and make 10 graphs.”

Foley uses Tuva activities and datasets consistently throughout her Surface to Space class in 8th-grade. Each dataset includes multiple, interconnected variables that students can drag and drop onto the axes to explore correlations.

October Weather in US Cities Datset Image — New England Ice-Out Dates, Global Change and October Weather in US Cities are a few Tuva datasets Foley’s students use to explore complex earth and climate systems.

When students first use Tuva, she said there tends to be some oohs and aahs as they watch the dots rearrange themselves. Then, Foley starts to hear students verbalizing the patterns they observe.

“Those observations are able to keep going and going because it’s not like I’ve handed them a simple graph,” said Foley.

Graph Showing Positive Relationship Between Humidity and Particulate Matter — This graph, created by an 8th-grader in Foley’s class, investigated the relationship between particulate matter and humidity.

Foley has observed that once students notice one relationship, they begin to wonder if other variables are related. Tuva allows them to quickly and easily satisfy their curiosity. It starts a deeper conversation in which students begin to comprehend the complexity of Earth’s systems.

In addition to middle school science, Foley teaches a high school elective: Engineering Nature. In this higher level class, Foley expects her students to apply their understanding of interconnectedness to tackle pressing issues, such as climate change. Last year her students made biogeochemical terrariums and tracked CO₂ concentrations over time. Then they geoengineered the terrariums to reduce the CO₂ concentrations.

Foley’s emphasis on interconnected systems when these students were in the middle grades prepared them to take on this rigorous geoengineering challenge. In the long term, Foley‘s students will be prepared to face the complex problems of a complex world.

Stats Teacher Drives Engagement with Authentic Data

Relevance Prompts Annie Pettit’s Students to Dive Deeper

Annie Pettit has taught a variety of different high school math courses during her 18-year career, but her self-professed passion is statistics. She gravitates toward stats because it provides multiple opportunities to use real-world data.

“As much as possible, I try to get data that relates to the kids, data they are excited about or that they can relate to,” Pettit said.

histogram comparing points scored/season by Kobe Bryant, LeBron James and Michael Jordan — Engagement is high when the data is relevant to kids, such as the NBA statistics this student analyzed to determine the GOAT (greatest of all time).

Pettit designs her statistics course at Des Moines Christian School so that assignments earlier in the year are more supported. First, she acquaints students with the Tuva graphing tools using a premade Tuva activity with step-by-step directions. Then, she assigns a simple comparison project in which students can use these tools to create dot plots and box plots about data that’s personally meaningful. Students select a topic independently. DC Comics vs Marvel Comics profits, passing yards from last season’s football season, viewership for The Office vs. Friends, the US women’s national team vs the men’s national team – the topics are as varied as Pettit’s students.

Pettit continues to ratchet up the rigor throughout the year, so that by quarter four students are ready to “do stats like a statistician does” using large datasets and lots of variables.

“If you put data in front of them that interests them… they actually want to find out the answer instead of doing it to get it done.”

Last year she gave her statistics students five options of datasets to choose from for their final project: electric cars, basketball statistics, baseball statistics, state crime rates or movie production budgets. Pettit noted that real-world data motivates students at all different levels – those to whom math comes easily, and those who have to work a bit harder to master statistical concepts.

“If you put data in front of them that interests them or if they get to pick their own data, they actually want to find out the answer instead of doing it to get it done.”

A few graphs from one student’s final project about electric car performance.

The depth and insight shown in her students’ work is a testament to their level of engagement. For example, a student investigating electric car performance reflected that statistical analysis often challenges our assumptions, and variables that seem like they would be correlated don’t correlate at all.

Pettit prefers to have students analyze these authentic datasets in Tuva where they can focus on justifying their conclusions instead of on the logistics of making the graphs.

“Tuva makes statistics come alive!” Pettit said. “Tuva allows my students to be statisticians. They are able to analyze big datasets and draw conclusions from data they find relevant to their lives.”

Accentuating the Power of Shared Data

California Teacher Spiri Bavelas Trains her Students to Know Their Way Around Messy Data

Working with data becomes second nature to students in Spiri Bavelas’ science classroom. Whenever they are completing an experiment in her class, students collect their own data and put it into a shared, class-wide spreadsheet. Then, Bavelas uploads the data into Tuva where students can manipulate and explore it. When Bavelas uses larger, messy datasets, she’s drawing from her years as a research assistant before she began teaching.

“You never are going to look at just five numbers in the real science world.”

“When I started, students collected four or five numbers and were supposed to come up with a big conclusion, but you never are going to look at just five numbers in the real science world,” she said.

Bavelas has worked in a handful of different schools throughout California, but recently took a position at R. Roger Rowe Middle School in Rancho Santa Fe. Wherever she has been, Bavelas has engaged her students with large data sets.

One of the lessons she hopes to impart to her students is that people can use data to make better decisions. Bavelas used a popular mining simulation to illustrate this concept during an environmental resources unit. Students placed cookies on grid paper and mined the chocolate chips, keeping track of expenses and income. Afterward, she instructed them to measure damage to the environment based on the number of grid squares where crumbs landed. By analyzing all of the data pooled from Bavelas’ classes, students gained insights into which mining strategies caused minimal harm, enabling them to develop new, environmentally-friendly, yet still profitable, methods of extraction.

Bavelas’ students use Tuva to generate graphs that include data from all of their classmates.

Bavelas also showcased the utility of collective data during an annual egg drop competition at one of her former schools. Engineering teams were awarded points for landing crafts that had a slow descent, hit the target, and kept the egg safe. Bavelas had been collecting egg drop data over multiple years. Students used the data from prior years to inform their design decisions. For example, the data revealed that a light lander is advantageous, but only up to a point. If the device is too light, it drifts off target.

“Data analysis is not just something you can do in one class,” Bavelas said. “Data can be a thing on a larger scale where you can collaborate with people that are not right next to you.”

Bavelas also wants her students to be aware that data displays can be manipulated to suggest certain conclusions. For example, she explained, if you look at a bar graph and zoom in on the differences it might look like the more massive car travels down a ramp faster. However, when you look at it on a larger scale, the difference is tiny, and calculations reveal there is no statistical correlation between mass and speed.

Whether it’s understanding the importance of sample size, utilizing data to make good choices, or being savvy enough to detect deceit, Bavelas hopes the lessons students learn in her science class will serve them well in whatever path they choose.

“I want the skills students obtain in science class to be a vehicle for better understanding and functioning in the entire world.”

Rural Math Teacher Uses Real-World Data to Promote Equity

Nate Sebold Champions Authentic Data to Surface Social Justice Issues and Boost Inclusion

One of the things Putney, Vermont, teacher Nate Sebold loves about middle school students is that they are full of questions. He considers it his job to “harness” those questions and give kids the tools they need to answer them. For Sebold, that means having students interact with data.

“How to interpret data, how to question data sources, how to investigate data – these are increasingly important for today’s 13-year olds. Data is going to be such a huge part of their lives,” said Sebold.

According to Sebold, contrived data won’t cut it. He prefers to use real-world data. His reasons are twofold: social justice and classroom inclusivity.

Surfacing Social Justice Issues with Data

Sebold experienced an aha moment at a National Council of Teachers of Mathematics conference. The presenter pointed out that teachers make a choice when they place a graph in front of students. The graph can be about something socially relevant, or not. Since then Sebold selects data carefully with an eye to surfacing important social justice issues. For example, Sebold regularly uses the Tuva activity Incomes of Men and Women in the US: Comparing Groups with Box Plots. Sebold said that introducing relevant data, like this dataset, in the classroom creates a space for students to ask questions and increases classroom dialogue.

Boosting Inclusion by Helping Student Connect Personally to Data

Another advantage of real-world data, Sebold said, is that it benefits students with learning differences.

Before taking the job at Putney Central School in 2022, Sebold spent a number of years as math department head at the Greenwood School, a small college preparatory school for students with learning differences. He and his science colleague noticed a real difference in conceptual understanding of data when students had collected it themselves.

“When they would sort it… they would say, ‘there’s my point in the midst of all the others!’ The data meant something.”

Sebold explained that when students saw that the graphs were not just randomly created, but made up of points of data they had collected, it helped them comprehend that all graphs are made up of individual data points. Data visualizations became more concrete.

In one project, Sebold’s students entered their own demographic data into Tuva. Sebold notes students’ comprehension of graphs increases when they help with the data collection process.

“When we pulled the data up on Tuva, they would try to find their own response, their data point. Then, when they would sort it or organize it, they would say, ‘there’s my point in the midst of all the others!’ The data meant something,” Sebold said.

Inspired? Surface social justice with these resources.

Tuva Lessons and Datasets About Current Social Issues

Starting the Year with Data Literacy

Science Teacher Margo Murphy Does Science From Day One

When most people think “back to school,” it conjures images of students seated at a desk, their heads bent over their computers and papers. In Margo Murphy’s Earth Systems Science classroom, though, “back to school” has a different meaning. Murphy jumps right into doing science. That means the first days back find her students outside in their Rockport, Maine schoolyard collecting data.

At first, the content of the investigation doesn’t matter; what matters is if observational data can be gathered to answer the question. Each group picks a question that sparks their interest. For logistical purposes, Murphy limits them questions they can answer on campus. For example, one group of students might be measuring the length of white pine needles to see how variable they are while another is documenting the brands, models and colors of vehicles in the school parking lot. The purpose?

“It gives kids the idea that you can have highly variable data but still see trends,” Murphy explained. This is fundamental in her Earth Systems course, she elaborated. “You are going to have messy data if you are going to work in the earth sciences.” Murphy and her Earth Systems colleagues at Camden Hills Regional High School consider data literacy so essential to the earth sciences that they devote a significant portion of the first quarter helping their students master it.

“They don’t have to focus on getting it ‘right’ the first time, so they can iterate.”

Once students have collected data, they upload their data on Tuva and begin to explore it. Murphy’s students always enjoy the “playground aspect” of Tuva, being able to bring data in and look at it in a variety of ways. To capitalize on this engagement, Murphy builds in time for her students to “play”.

“[With Tuva] they don’t have to focus on getting it ‘right’ the first time, so they can iterate,” Murphy said.

Murphy scaffolds learning using Tuva’s graph choice chart.

As students are becoming conversant with analyzing complex data, Murphy scaffolds the learning process using Tuva resources like the graph choice chart.

The time and energy devoted to data literacy pays dividends later in her course as students grapple with complex earth systems core ideas such as weather and climate, topics which Murphy considers vitally important.

Two scatter plot graphs showing a strong correlation between CFC levels and ozone hole area. — Murphy introduces data skills early, preparing students to apply them to projects like this one later in the course.

“I want kids to understand that there is change on the planet, that this change is rapid, and how they can find evidence and understand that evidence to understand these changes and ask good questions.”