teachers

Penn. Teacher Revitalizes Math Through Culture

Unique Approach Reveals Cross-Cultural Application of Mathematics

“The disconnect between the high school curriculum and students’ lives is all too common, particularly in math, and it frustrates me.”

High school math teacher Gerald Smith is concerned about mathematics instruction in the United States.

Smith’s concerns are shared by others, including the National Council of Teachers of Mathematics. In a May 2024 position statement, the council expressed dissatisfaction with traditional modes of instruction which leave “students feeling a disconnect” and encouraged educators to humanize mathematics, to help students see math as a creative process of exploring and interacting with the world.

Smith has been teaching math for more than 20 years. He currently teaches pre-algebra and geometry at Indiana Area Senior High School in Indiana, Pennsylvania, and has been there for more than a decade. Previously, he taught abroad in Namibia and Eritrea.

In his efforts to help students see math as a vehicle for solving problems, Smith incorporates authentic applications from various cultures into his instruction. By using both local and international examples of mathematics applications, Smith helps students see math as something that is both universal and diverse. Tuva helps him do that.

Missing the Application for the Tools

“Math classes should be about how we use this tool of mathematics to understand the world around us,” explained Smith. “Many state and national exams focus too much on the tool itself, and not how it is used. It’s like being in a carpentry class, and only studying the power drill, not what you can do with it.”

“It’s like being in a carpentry class and only studying the power drill, not what you can do with it.”

This perspective is shared and elaborated upon further in the book Math is a Verb by professors Jim Barta, Ron Eglash, and Cathy Barkley. Their book challenges the perception of math as a set of static rules written in ancient times.

“Across the globe, people who would never be considered mathematicians are engaged with mathematical activities in the work they complete, the artifacts they construct, or the objects they design,” they counter. Furthermore, “mathematics is best understood as we experience its application within the cultures and contexts in which it is applied.”

Going Global

Smith with Karpathos municipal officials Vice Mayor Stathis Galafanakis (L) and civil engineer Jimmy Gorgatsoulis (R)

Smith’s most recent attempts to reveal mathematics as a living, breathing, multicultural discipline brought him to Greece. All teachers in his district are eligible for a partially paid sabbatical after their first 10 years of teaching. In anticipation, he applied for and was awarded a scholarship from the Fulbright Distinguished Awards in Teaching Research Program. Smith spent his six-month sabbatical gathering data in Greece and networking with educators and policymakers who live there.

He returned with a collection of self-made lesson plans. The lessons simultaneously address key mathematical concepts and reveal how communities in Greece are applying math to solve real-world problems. Each of his lessons utilizes authentic data gathered from a municipality or other civic organization in Greece.

Using Linear Regression to Predict Water Supply

Smith has a blog called Mr. Smith’s Mathbox where you can read about his adventures in Greece and access his lesson materials. The link for Lesson 1 will bring you to Tuva and a lesson titled, “Is the rain going to be enough?”

Smith’s “Is the rain going to be enough?” lesson on Tuva.

The lesson confronts students with an issue facing municipal leaders on the island of Karpathos, Greece. Even as a long-anticipated reservoir is being built, rainfall is decreasing and population is increasing. They’re worried the supply of drinking water will not meet demand. Smith challenges students to use linear regression to model rainfall and population levels by 2030 and predict whether or not the reservoir will be adequate.

Finding the Right Tool

Real-world data can be hard to comprehend without the right scaffolding. Smith discovered the Tuva Tools when he was searching for a way to enable his students to actively and independently explore the datasets he’d gathered. He decided it would be a good fit for his project.

“The tool is so powerful, especially for kids who don’t identify themselves as data folks,” he explained.

Smith worked with Tuva to get his datasets added to the Dataset Library. Then, he used the Tuva Activity Builder to create his own lessons.

To create your own activities, find the cranberry-colored Create Activity button next to any dataset in Tuva’s Dataset Library.

Tuva’s Activity Builder enables users to create their own lessons based on datasets in Tuva’s Dataset Library. (Subscribers can create activities using any of the > 400 datasets in the library, and Basic users can create activities using any of the datasets marked “free”.)

Smith has integrated the Tuva tools into three of his other lessons as well. In “Island Hopping” students use data to make a recommendation to the Ios municipality on whether the island can support more swimming pools. (Below, explore the Ios dataset using the Tuva tools.)

Students note trends in how tourists are arriving and where they are lodging in Smith’s “Hypertourism” and “Sleeping in Santorini” lesson sequence. Then they use linear models to predict how many beds will be needed in basic vs. luxury accommodations in the coming years.

Best Understood Indeed

The common denominator in these lessons is context. If, as Barta et al. stated, “mathematics is best understood as we experience its application within the cultures and contexts in which it is applied,” Smith’s students will leave his class with a deeper comprehension of the underlying meaning of mathematics.

Want to Play?

Tinker with Smith’s four Greece datasets on Tuva for free until the end of October.

Engaging Students with Data That Hits Close to Home

In 2023, Minnesota saw an unprecedented 22 air quality alerts in just 52 days. And for one day in mid-May 2024, St. Paul held the unenviable position of worst air quality in the United States.

6th-grade Earth Science Teacher Emily Harer saw potential for authentic science learning in the unfortunate air quality downturn. Air quality issues are a suitably complex issue. Since the publication of the Next Generation Science Standards in 2013, major emphasis has been placed on anchoring science learning in complex phenomena. Even better, it was a phenomenon her students could immediately relate to.

“National curriculum is often focused on things that aren’t local,” she explained. “Having local phenomena is extremely important for students to latch onto.”

Harer, who teaches at Global Arts Plus Upper School in St. Paul, said she wants students to know that science is all around them and that they can contribute to the body of science knowledge through research and data collection. That’s much easier to do if the phenomenon they’re studying is local and relevant.

Putting Local Data into Students’ Hands

During the 2023-24 school year, Harer engaged her students in a month-long air quality unit. Throughout the unit, Harer had her students investigate the myriad factors contributing to air quality. Using historical weather and air pollution data from the National Weather Service and the Environmental Protection Agency, Harer created datasets using all local data. Then she uploaded them into Tuva and embedded them into the lessons on her class website.

Harer’s students can use Tuva tools to manipulate the data right on her class website because she has embedded the datasets on it.

“It was exciting to see students think about experimental setup, drag and drop the attributes, to then find answers to their questions,” said Harer.

Hosting the data in Tuva allowed her students to more easily interact with it and to look for relationships between particulate matter and other variables such as wildfires, rainfall, seasons, and land cover.

Students were able to manipulate the data to determine when wildfire smoke was in the air in Ramsey County in 2023. They saw the daily changes in particulate matter through time and could point directly to when the wildfire happened.

A student uses Tuva to explore the variables that impact St. Paul’s air quality.

The complexity of the phenomenon prompted students to generate new questions as they encountered unexpected findings. For example, when they compared ozone and temperature data in Ramsey County to Voyageurs National Park to the north, they realized that their prediction was actually opposite to what the data showed. Voyageurs National Park had substantially more ozone than Ramsey County in the spring. This cognitive dissonance spurred further inquiry and research.

Outcomes: Engagement and Deep Understanding

The combination of real-world, local data and Tuva tools is one Harer plans to repeat for two reasons: engagement and depth of understanding.

“I don’t usually see people getting that jacked about graphs,” admitted Harer.

Memorable student reactions when playing with the data on Tuva included: “Oh wow! Oh my gosh, I just did that!”, “Whoa! The rain washed that particulate matter out!!” and, “Dang! This is really life… in St. Paul.”

Engagement drove learning. By the end of the unit, students really understood particles in the air and were asking deep questions about weather, topography, vegetation, and air quality – startling high-quality questions. Jason Johnson, chief engineer at TSI Inc., a Minnesota-based company that designs and engineers air monitors for scientific research, visited the class near the end of the unit. During his visit, he projected a graph from his graduate program and was surprised at the students’ insightful observations and questions.

“They are 6th-graders, and they understand this so deeply!” he told Harer.

The graph Jason Johnson shared with Harer’s 6th-graders during his classroom visit, from “Engines and nanoparticles: a review” David B. Kittelson Journal of Aerosol Science. Volume 29, Issues 5–6, 1 June 1998, Pages 575-588

Taking it Even Further

This year, Harer plans to expand the project to include data collected by instruments on the roof of the school buildings. The campus has a weather station. Last year, Harer was able to use grant funding from the National STEM Scholar Program to purchase and install a BlueSky air quality monitor as well. By the time her Air Quality Unit rolls around, she will have a full year of data from these instruments. She anticipates that her hyper-local weather and air quality data will be even more engaging for her students and will help them understand how science fits into their lives.

Emily Harer poses beside the school’s new BlueSky air monitor with Dr. Lucy Rose from the University of Minnesota Department of Forestry Resources. Rose assisted with the project.

“I see science everywhere. When kids do too, that is so exciting” she said. “I want kids to see how cool Minnesota is and that we have a lot to offer here.”

Incorporate Local Data into Your Lessons

Uploading data into Tuva and sharing it with your students is simple. Here are the steps and, in case you need help, links to our associated support pages.

Find data and, if it is not already, put it into a spreadsheet.
Upload the data on Tuva.
Share the dataset by assigning it to your class or embedding it onto your website.

“Why are we learning this?”

Utah Teacher Macy Cook Is Ready With an Answer

Macy Cook is a 6th-grade teacher in Salt Lake City, Utah. Her self-contained classroom at Uintah Elementary School houses 28 11- and 12-year-olds. Like many students on the cusp of adolescence, Cook’s pupils are beginning to chafe at authority and to question the requirements adults place upon them. They want to know, “Why are we learning this?”

Cook doesn’t believe it’s a snarky question, but rather a valid query that deserves a serious response. She vividly recalls hating it when teachers responded, “Because I said so,” and she’s determined to reply thoughtfully when her own students wonder about the importance of a particular concept.

“I want everything to have a reason,” she said. “I want them to know where it will show up in their life, so it has purpose.”

Purpose and Application – A Quick Snapshot of the Research

Cook’s educational philosophy aligns well with national efforts to improve science education and is backed by a substantial body of research. One of the major principles of The Framework for K-12 Science Education is Connecting to Students’ Interests and Experiences.

“In order for students to develop a sustained attraction to science and for them to appreciate the many ways in which it is pertinent to their daily lives, classroom learning experiences in science need to connect with their own interests and experiences.” – The Framework for K-12 Science Education

Multiple studies indicate lack of purpose hinders STEM learning. Interventions that emphasize the utility of science improve outcomes and persistence, particularly for historically underrepresented students. Practitioners have shown when students apply science, such as when they participate in citizen science, it can enhance motivation, interest, knowledge, and communication skills.

Tuva Helps Contextualize Science

Cook was introduced to Tuva this winter when she participated in a professional development series hosted by the Salt Lake City School District and led by Tuva instructional specialists. Cook quickly became a fan and has been frequently using Tuva with her students.

“Tuva has been really amazing for them to see the real-world application of the topics they’ve learned,” said Cook.

Tuva’s Content Library includes 400 curated, real-world datasets and more than 450 applied math and science lessons based on them, which makes connecting to the world outside of the classroom easy.

Recently, Cook’s students have been studying atomic chemistry. Cook said it is hard for sixth graders to wrap their heads around the concept that elements make up molecules and molecules make up everything on Earth.

Cook used Tuva’s Nature of the Elements activity to help her kids grasp the importance of elements.

Tuva’s lesson, Introduction: The Nature of Elements, intentionally pointed out the relevance. One question prompted students to complete the sentence, “A few elements that are important to me are…” Cook expanded the question to include, “What elements do you recognize?” Within moments, students were calling across the room as they encountered familiar terms. “Aluminum- like in aluminum foil.” “Neon signs.” “Oxygen!” “We use chlorine in our pool.”

Understanding the elements’ ubiquity gave purpose to the ensuing exercise. Exploring the trends in the periodic table was transformed from something abstract to something intimately connected to their daily lives.

Another Answer to “Why?’

When Cook was in 6th grade, her math teacher’s response to, “Why?” was, “You are not going to always have a calculator in your back pocket.” Flash forward 20-odd years- Cook grins at me through the Zoom screen and waggles her cell phone. (Psyche!)

Technology has and will continue to evolve rapidly. Cook predicts our rapidly changing world will require today’s students to have stronger data literacy skills.

“The future of what the kids are going to do is probably going to be computer-based, so learning how to manipulate and read data is really important. Even if it’s not something the average adult does now, it will be.”

Experts agree. Harvard Data Science Review estimated there will be more than 150,000 U.S. job openings requiring data analysis skills by 2025. The U.S. Bureau of Labor Statistics reports higher-than-average job growth in data-related careers by 2032. Graduates with strong data skills will have an advantage, not only in data science but also in diverse fields such as agriculture and real estate that increasingly rely on data.

What’s Obvious to Us, Isn’t to Them

The reasons for providing a rigorous education in science and data literacy are obvious to adults. Not so for kids. Cook’s intentional focus on purpose and application, combined with the baked-in relevance of real-world data, ensures that her students are never left wondering, “Why am I Iearning this?”

Math Teacher Delivers Personalized Learning at Scale

Math teacher Chad Boger prepares 30 different lesson plans per week. Increasingly, he’s using Tuva to make that formidable feat more manageable.

Boger is a teacher at Fusion Academy, a private school that offers one-on-one, personalized learning. The school serves students who thrive in a non-traditional setting. Fusion Academy promotes its program as specifically advantageous for twice-exceptional students and neurodivergent students, such as those with ADD, ADHD, or anxiety.

Boger said he enjoys working with kids at Fusion because he “gravitates” toward kids with special learning needs. He added that the one-on-one nature of his work is a boon because he gets to know each student well.

The Challenges of Condensed Class Time

That said, the one-to-one approach presents unique challenges for instructors. In a typical high school course, a student is in the classroom with their teacher for an average of 3 hours and 45 minutes per week. Fusion Academy teachers, in contrast, get just two 50-minute sessions.

Because instruction is condensed, they must be efficient with their face-to-face time. Boger is always looking for resources to help him optimize instruction time. After stumbling across Tuva this fall, Boger has used it frequently.

“Tuva is super intuitive, and it is going to save me so much time,” he said

This year, Boger’s caseload is primarily composed of juniors and seniors learning statistics. He found that teaching students to use spreadsheets was inefficient.

“It felt like a lot of wasted time when the goal was data analysis,” he explained.

This fall most of his pupils are working on descriptive statistics. Boger appreciates how easy it is to examine qualitative and quantitative data in Tuva. With the click of a few buttons, students can quickly separate the data into categories, make a box plot or histogram, and compare the spread and median of each category of data.

“Doing the same tasks with a spreadsheet,” he noted, “would have taken so much longer.”

Boger’s students use Tuva to efficiently make data displays like this one.

Never the Same Lesson Twice

Fusion Academy is not just one-to-one; it’s also personalized. Personalized learning is an approach whereby student interests and learning styles guide content and approach.

“We know that every child learns differently,” Boger said. “In a mentorship/teacher relationship, you can learn about each student’s preferences and tailor your lessons and instruction style to your learner’s needs.”

“We know that every child learns differently.”

A preliminary study by RAND Education and the Bill and Melinda Gates Foundation suggests personalized learning can help improve outcomes for a broad range of students¹. But it’s a heavy lift for educators. Unlike in a traditional classroom, instructors cannot plan a lesson and reuse it for all of the other sections of that course. Each lesson must cater to the unique interests and needs of the student. But how do you do that when you are planning 30 lessons a week?

Boger personalizes his statistics course by allowing students to select a topic they’re interested in and find a related dataset. Interests have ranged widely- from music to nutrition and book genres to Supreme Court data. Regardless of their chosen data, Boger has students upload it into Tuva for easy exploration.

Last semester, Boger uploaded the dataset that was used to make this visualization about crime rates. Users can upload up to five datasets to Tuva for free. Try it!

Passionate About Data Literacy

Teaching statistics is Boger’s job, but that’s not all it is. It’s also his mission. Boger believes that by getting kids invested in learning statistics, he is preparing them with the data literacy skills they need to thrive in the information age.

“If I can at least expose them to these things and help them think more critically—is it coming from a reliable source? Is it someone trying to push their agenda? That’s what I am trying to get across—not just can you calculate a formula.”

Pane, John F., Elizabeth D. Steiner, Matthew D. Baird, Laura S. Hamilton, and Joseph D. Pane, How Does Personalized Learning Affect Student Achievement? Santa Monica, CA: RAND Corporation, 2017. https://www.rand.org/pubs/research_briefs/RB9994.html. ↩︎

This Teacher Wishes Her Content Wasn’t Relevant

The Unique Challenges of Teaching About Environmental Injustice to Students Who Are Living It

Satina Ciandro’s environmental science students have experienced environmental injustice firsthand, which, paradoxically, makes it harder to teach about climate change.

On the one hand, it’s personal- offering baked-in relevance. On the other hand… it’s personal. Which means it’s also emotionally fraught.

“It took me 23 years of teaching science to really teach about climate change. Not just mention it, really teach it,” admitted Ciandro.

A Student Body Familiar with Inequity

Ciandro teaches science at Watsonville High School, located in a small city in the Monterey Bay Area of California. 96% of her students are Hispanic. 88% of her students are economically disadvantaged.

“Most of my students are students of color and they understand injustice very well,” said Ciandro.

In fact, many of her students were directly impacted last March when the Pajaro River Levee was breached, flooding homes in a low-income community primarily inhabited by migrant workers and their families. Needed repairs on the levee had been deferred by the Army Corps of Engineers when their cost-benefit analysis concluded the low home values in the area didn’t warrant prioritizing levee repairs.

Getting Past the Paralysis

The breach is just one example of environmental injustice Ciandro’s students have faced. A 2021 Environmental Protection Agency study indicated, “…the most severe harms from climate change fall disproportionately upon underserved communities who are least able to prepare for, and recover from, heat waves, poor air quality, flooding, and other impacts.” Racial and ethnic minority communities are particularly vulnerable, they stated.

Ciandro’s hesitancy to really go deeply into climate change stemmed in part from recognition that discussing yet another example of environmental injustice would be triggering for her students. She worried her lessons would be all doom and gloom.

Ciandro also worried about her lack of perspective. How could she teach about an experience she had not had?

“I am a white lady… I don’t know what they are living through,” she said.

Getting it right felt insurmountable.

Over the past few years, Satina has picked up a few trauma-informed strategies that help her feel more comfortable delving into the science of climate change and all of its messy ramifications. She’s learned that providing time and space for students to process things that are emotionally triggering is imperative. Ciandro incorporates art, journaling, and other forms of reflection into her science instruction.

She’s also learned that focusing on solutions helps reduce the doom and gloom factor.

“You can’t just point out the injustice and not do anything about it,” Ciandro said.

A recent study revealed 59% of young people ages 16-25 were “very” or “extremely” worried about climate change, a phenomenon increasingly known as eco-anxiety. Some eco-anxiety can spur people to action; too much eco-anxiety can have the opposite effect, leading to despair and inaction.

Having students take steps to help solve the problem can be empowering and can reduce anxiety. She cautioned, however, that you need to explore solutions in a way that does not put all the burden on the students to figure it out.

“That’s the point of the whole lesson- not to make you feel bad, but to consider what are the solutions, and how are we going to do the things to fix it?”

Striking the Balance with Urban Heat Islands

Recently, Ciandro applied these trauma-informed strategies in an urban heat islands unit. Ciandro was inspired to take this angle by Dr. Tammie Visintainer when she participated in her National Science Foundation-funded Climate Justice Action Research Summer Program at San Jose State University. The cohort of participating educators are all using urban heat islands as a lens to investigate climate justice with their students.

Urban centers tend to be hotter than surrounding rural areas. Materials like brick and pavement absorb and hold onto more heat than vegetation. This creates “islands” of heat. As the climate changes, heat-related deaths have also increased. Heat-related deaths in the United States spiked 59% between 2018 and 2022 according to the National Center for Health Statistics. People in cities are at higher risk of heat-related ailments.

Ciandro knew from her program that even within the cities, however, the effects of heat are not felt equally. Urban areas with fewer trees get hotter. Urban areas with lower tree density usually have two other things in common: high minority populations and historical subjection to redlining. Redlining was a practice carried out by lenders to create policies around who they would lend money to.

Certain districts were “redlined”. Mortgage lenders marked them in red on the maps, which meant they were coded as “hazardous.” Banks would not give mortgages to people buying homes in redlined districts. The rationale listed for assigning a specific neighborhood rating often cited race.

In nearby San Jose, California, for example, agents specifically noted one of these two reasons: “inharmonious racial concentration” or “heterogeneous” for five of 12 districts rated “hazardous.”

“When I went through history class in my white suburban school, I never learned about redlining. I did not know that it was on purpose and that it was systemic. I didn’t know. I know it’s not an excuse, but I’m learning with them,” said Ciandro.

Ciandro wants to make sure her students do learn about redlining. She designed a two-month long, project-based unit around the urban heat island phenomenon. Within the course of her unit, she wanted her students to discover the temperature differences; do some experiments to determine what factors affect temperature in our built environment; uncover the correlation between the 1930s neighborhood ratings and heat; and to take action to make a change.

How Tuva was Able to Help

Ciandro found that premade graphic visualizations about urban heat islands are easy to find, but she wanted students to be able to explore and manipulate the raw data themselves. Discovering a relationship on your own as you tinker with data makes a bigger impression than observing it on a premade graph. Ciandro’s go-to program for data exploration is Tuva. Ciandro has been a loyal Tuva user for many years and uses at least one Tuva activity per unit in her environmental science course.

Ciandro immediately went to Tuva in search of a relevant dataset but was disappointed to find we did not have one. After a conversation with us this summer during which she expressed a need for a dataset about urban heat islands and redlining, Tuva team member Annette Brickley curated one. She located a 2020 research paper by Hoffman, Shandas and Pendleton from Groundwork USA. When Brickley reached out to ask for permission to use the data on Tuva, Hoffman generously shared their complete dataset. Tuva’s dataset pulls out data from seven of the U.S. cities included in Hoffman’s paper.

Later, Ciandro used Tuva’s Activity Builder to create a lesson that would help her students explore the dataset and discover relationships between neighborhood grade, tree canopy, impervious surfaces and temperature. The story the data tells is pretty bleak, but Ciandro manages to infuse hope at the end of the activity.

Box plot showing that neighborhoods given ratings of C and D in the 1930s are hotter today than those that were rated A or B.

“Imagine you are a city planner and your job is to allocate funds for a major climate action grant,” she writes. “How will you distribute the funds to each type of neighborhood? Justify your answer using data.”(We liked her activity so much, we published it. Access it here.)

Ciandro’s students also collected data across the Watsonville High School campus. Each group selected two spots, collected surface temperature data once per week, and entered the data on Tuva. Through this exercise, they observed locations near concrete were consistently hotter than green spaces.

Student Empowerment

As the unit neared its end, four of Ciandro’s students – Jazmyn, Mario, Rocio and Anail- gathered around a Zoom meeting to tell me about their learning experience.

“I did not realize how impacted our little city is because it is so based on concrete,” noted Anail. “My (part of the) city is in the red line,” she added.

The other students agreed with Anail that the last few months have been eye-opening. Until this unit, they did not know urban heat islands existed let alone that extreme heat is worst in areas that were historically redlined. The other thing they agreed on was that everyone else in Watsonville should be made aware of the problem too. Jazmyn laid out her hopes for her community.

“I want them to get a better idea of how it actually affects us in our daily lives, I want them to not feel negative because there are solutions to it, and I want them to come together as a community to plant more trees,” she said.

As a culminating project, student teams created podcasts to help educate their community. The podcasts, which they plan to submit to the KQED Youth Media Challenge, played the dual role of helping students process injustice and giving them a way to fight back against it. (Want a sneak peek before they’re live? Listen to Jazmyn and Mario’s submission here.)

Teaching Tough Topics: “Something We Need”

Ciandro says teaching tough topics helped her grow as a teacher.

“It helped me as an educator to teach something that is tough to teach. It is a different way of teaching, and it’s something we really need,” said Ciandro.“You have to do your best and hope you are going to do more good than harm.”