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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.

Elementary Educator Gives All of Her Students Sugar Cubes

…and deeper learning ensues

On the surface, giving 5th-graders sugar cubes seems like a terrible idea. But BJ Barrie, a math and science teacher at Euper Lane Elementary School in Fort Smith, Arkansas had her reasons. Chief among them was Barrie’s goal to help students realize they’re capable of making sense of the world on their own.

Barrie was in the midst of a unit on matter. She’d challenged her students to investigate how temperature affects solubility (hence the sugar cubes). Instead of giving the students step-by-step instructions for carrying out the experiment, she left it open-ended, giving them occasional prompts to keep them thinking as they figured out what would work on their own.

**The Challenges of Doing Science in Elementary School**

At the beginning of the year, Barrie’s students often asked her to explain why things happened, expecting that they’d just be told. They didn’t trust themselves to figure out the phenomenon; they didn’t know the steps to take to do so. Barrie says this insecurity likely resulted from limited exposure to hands-on science.

“Some of the early elementary teachers have not had the time to hone in on science as much as they would like to,” explained Barrie.

They’re not alone. A 2021 report from the National Academies of Science, Engineering and Medicine revealed the average elementary student spends less than 20 minutes per day on science.

Science and social studies are often squeezed out of the elementary curriculum due to time pressures from other subjects. Increasingly rigorous and frequent standardized testing in English language arts and mathematics results in these subjects being prioritized.

Some school systems attempt to address the dearth of science instructional time by having students read non-fiction texts about science during their literacy block. Passive methods of relaying content information, like reading and watching videos, fall short of teaching students science practices, however.

**“Why Do You Think That Happened?”**

Barrie’s goal is to graduate 5th-graders who know how to apply the science practices to make sense of phenomena on their own. Hence her mantra: “Why do you think that happened?” This short phrase both turns her students’ attention back to the investigative process and imparts her trust in their ability to figure it out.

“With hands-on experiments, students directly observe phenomena and manipulate variables,” explained Barre. “They develop a deeper understanding of scientific principles by seeing how theories apply in real-world situations.”

Data plays a key role in helping Barrie’s students generate claims in response to her oft-asked question, “Why do you think that happened?” When no one is giving them the “answer”, they need to turn to the data to find out what might be going on. (Ahem- sort of like professional scientists do.)

For example, during the sugar cube experiment, there were three people who dissolved the cube in less than a minute. Barrie encouraged her students to look closely at the class-wide data. What was the difference?

Tuva Jr. Helps Elementary Students Make Sense of Their Data

When sensemaking happens through hands-on experimentation, students must be equipped with the skills necessary to interpret and analyze the resultant data. Like other skills, data literacy must be taught. In Barrie’s classroom, students have built up these data literacy muscles using Tuva Jr., Tuva’s new program designed for kids in grades 3-5. Barrie participated in the Tuva Jr. pilot program earlier this school year and has been a regular user since.

Barrie said she loves Tuva Jr. because “students not only learn data analysis but also discover the power of curiosity and critical thinking.”

Barrie said the playful nature of the Tuva Jr. tools appeals to her students. Like Tuva, the graphing interface uses interactive drag-and-drop technology, making it easy for students to choose which attributes (variables) they want to explore. Students can also choose from a menu of graph types. These are our tried and trusted features that place students in the driver’s seat in a way that can’t happen with static data tables and graphs.

But Tuva Jr. also has unique features. It opens in “Play View” where each case is represented by a playing card, and when users switch to the “Plot View” the data points retain a playful shape, such as that of a football or a koala. Additionally, to prevent overwhelming younger students, the toolbar is simplified and the overall number of attributes and cases is smaller.

Relevance is another strong suit of Tuva Jr., according to Barrie.

“I like how Tuva has content about different things that would be interesting to my students,” said Barrie.

So far, her kids’ favorite Tuva Jr. activities include Comparing Candy and Beach Cleanup. While the candy-themed activity was a fan favorite for obvious reasons, the litter dataset prompted their intellectual curiosity. Knowing that this data was real deepened the conversation. Beach Cleanup launched a wide-ranging discussion about what is considered junk, how certain items could have found their way to the beach, and how plastic never really goes away. Barrie’s students were surprised by how much junk was found on the beach and were inspired to think of strategies for preventing plastic waste that can be carried by wind or water to the water’s edge.

The Case for Giving 10-Year-Olds Sugar Cubes

Our world is a complex place. There’s an unspeakable complexity in nature- in the structure of a glucose molecule or in the creation of a cumulus cloud, for example. And there’s immense complexity in the world’s latest problems, like garbage islands and nanoplastic pollution. When our kids are all grown up and tackling their own generation’s conundrums, they’ll need to ask themselves, “Why do we think that happened?”, and they’ll need to have the capability to gather and analyze data to help them get closer to the answer. That capacity does not just suddenly emerge at a certain age; it has to be built up gradually.

While the potential short-term consequences of giving a room full of 5th-graders sugar cubes loom large, the consequences of not entrusting them with decision-making power while we still have the opportunity to nurture and direct those powers is far greater. BJ Barrie has the long game in mind.

“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?”

How Can Tuva Support the Shifts in the California Math Framework?

In July, California passed an updated Mathematics Curriculum Framework, which outlined major shifts in how the state expects schools and districts to approach math instruction. Our math team is excited about the new emphases of the framework and how Tuva is uniquely positioned to support them.

“We look forward to building on our ongoing substantial work with California educators to dedicatedly support the state’s math teachers, schools, and districts as they look to adapt and update their existing math instruction to teach data literacy and data science to their students,” says our co-founder, Harshil Parikh.

We’ve outlined below some of the major shifts and additions, and highlighted ways our work can support California math educators to be prepared for what’s to come.

Data Literacy and Data Science Emphasized

The California math framework is clear: data literacy and data science should be emphasized throughout the K-12 math ecosystem. In fact, the framework dedicates an entire chapter (Chapter 5) to Mathematical Foundations for Data Science.

“Students should have equitable access to data literacy and introductory data science at the K–12 level to facilitate equitable participation in a data-driven world as adults.” (Chapter 5, Page 5)

The chapter lays out how data science fits into each grade band, as well as thematic topics within the California CCSS-M that directly support data science. Topics like: understanding variability, the data collection process, and comparing and finding associations between variables.

As an organization founded on the belief that data literacy skills are crucial for students’ success in school and beyond, we’re excited to see California join a growing number of states in recognizing the importance of data literacy and data science throughout the K-12 pipeline.

We also know that teaching data literacy skills can be daunting. To support teachers in understanding where their students should be in their data literacy skill-progression across grade bands, we’ve developed a comprehensive data literacy framework that outlines the major skill areas students should progress through as they deepen their data literacy skills.

Data is a Vehicle Through Which Math Content is Applied

In this iteration of the framework, California has introduced Content Connections, which “embody the understandings, skills, and dispositions expected of high school graduates (Chapter 1, Page 22).”

You can think of these content connections as the vehicle through which students are applying their understanding of the standards. So, for example, if a sixth-grade student is learning about fraction relationships, one of the ways they may apply their knowledge is by reasoning with data.

At Tuva, this is already how we approach the development of math content. We see data as a way for students to both learn and apply their mathematical knowledge, while hopefully engaging with a context that is fun and relatable.

For example, in our 6th-grade activity Analyzing Dinosaurs with Fractions and Percentages, students use their understanding of part-to-whole relationships to analyze an interesting dataset on 28 commonly known dinosaurs, and ultimately make claims about the types of dinosaurs that existed across geological periods.

Moving From Clusters to Big Ideas

While the framework didn’t change the actual language of the standards (California continues to use the California Common Core State Standards for Mathematics), it did outline a reorganization of the standards around “Big Ideas” rather than the previously used “Clusters”.

Like most states that use the Common Core, California previously identified major grade-level clusters, which served as a way for educators and curriculum providers to identify the most important standards within a course. Those same priority standards are still identified via the size of each concept bubble in the course’s big ideas map (shown below).

While the big ideas maps for each grade level may at first look intimidating, they serve a pedagogical purpose: to help both learners and teachers of mathematics come to view math as a series of interconnected concepts that spiral across grade levels.

“Standards and textbooks tend to divide the subject into smaller topics, but it is important for teachers and students at each grade level to think about the big mathematical ideas and the connections between them .” (Chapter 2, Page 12)

Here at Tuva, we recently reorganized our math content library to focus on the big ideas of each grade level – specifically those which have strong potential for data applications.

The design of our new math library is intended to help teachers see the connections between content standards in their course and find rigorous data investigations that can support students’ conceptual understanding of the topic. Our content library buckets are intended to encompass multiple standards and will naturally have some conceptual overlap. Learn more about our reorganization in our recent blog post.

Student Engagement is Coequal With Content Mastery

The California framework makes it clear that student engagement in math is just as important as student mastery of content standards:

“When students are engaged in meaningful, investigative experiences, they can come to view mathematics, and their own relationship to mathematics, far more positively. By contrast, when students sit in rows watching a teacher demonstrate methods before reproducing them in short exercise questions unconnected to real data or situations, the result can be mathematical disinterest or the perpetuation of the common perspective that mathematics is merely a sterile set of rules.” (Chapter 2, Page 9)

If you’re familiar with Tuva and our vision for math and science education, this sentiment will feel very similar to our vision statement:

“Tuva envisions a world where every student experiences the joy of learning math and science through real-world contexts. We imagine a future in which all students possess data literacy and use it to contribute positively to society.”

And this isn’t just an empty vision statement; our teachers are already exemplifying the possibilities of teaching mathematics in this way. Read our previous posts about math teachers like Chad Boger and Annie Pettit who are making the learning personal and relevant for their students using Tuva tools and datasets.

Get Started Using Data in Your Math Instruction

If you’re looking for a place to get started integrating data into your math instruction, we have a few suggestions. This free middle school lesson on choosing the correct measure of center hooks students through an exploration of popular breakfast cereals and their nutritional content. For high school applications, try out this free lesson exploring the exponential growth of the cost of Super Bowl commercials over the years.