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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.

HS Junior Melds Stats With Civics to Gain Insights into Infant Mortality

Data Crosses Disciplines, Yields Powerful Learning

Up until the mid-1800s, children had a 50% chance of dying before age 15. By 1950 the childhood mortality rate was closer to 25%. Today, it sits at 4.3% globally. Childhood mortality rates have experienced a steep, steady decline across the world.

So, when Kate Harrison, a high school junior in Charlotte, North Carolina, was sifting through data about infant mortality rates in different countries, Syria’s data gave her pause.

“Syria in particular has these two spikes, and I got really interested, thinking, what was happening at the time?” she said.

Thus was born a semester-long investigation.

Data Transcends Disciplinary Boundaries, Deepens Learning

Harrison was enrolled in an honors statistics class at Fusion Academy where she’d been charged with undertaking an interdisciplinary project. She’d decided to apply statistics to explore history, but identifying a focus took time.

Her original idea was a bit nebulous, but it centered around trends in warfare over time. To clarify her question, she began exploring data. In the process, she stumbled upon the Syrian infant mortality data. That’s when nuanced and intriguing questions pushed their way to the forefront.

Harrison immediately noted an association between the timing of armed conflicts in Syria and the spikes in infant deaths. She noticed that after the start of the Islamist uprising in Syria in 1981, infant mortality increased by 4.24%. The nation suffered an even more drastic 52.7% increase in the infant mortality rate from 2010-2014 at the beginning of the Syrian Civil War.

Harrison discovered that in both instances there had been a concurrent rise in overall mortality. However, she knew that infants didn’t fight in the wars, so what were the underlying connections? Harris worked with her faculty advisors, social studies teacher Rick Fera and statistics teacher Chad Boger, to brainstorm variables that may have influenced infant mortality.

Variables she explored included birth rates, governmental regimes, international aid, gross domestic product, basic sanitation, basic healthcare access, and vaccination rates. She compiled data about these factors from Our World in Data and the World Health Organization and imported it into Tuva for analysis. Harrison said identifying changes and interpreting patterns was easier for her when she used Tuva.

“You really just can’t tell using a table because there’s so many numbers and so many different data points,” she said. “And so getting to put that all into one tool and really visualize it without having to go through the hassle of actually plotting out each point, and probably doing something wrong, was very helpful.”

Surprises in the Data

In some cases, Harrison was surprised at the lack of correlation between variables. She had assumed, for example, that GDP would have a large impact on infant mortality rates, but the data did not show a correlation. In fact, Syria experienced a financial crisis a few years before the civil war, but the infant death rate did not experience a resultant increase.

What did show a correlation with infant mortality – vaccination rates. In the early 1980s, Syria engaged in a national immunization campaign, and infant mortality rates showed a steep decline. However, when immunization rates faltered during the civil war and uprising, infant mortality spiked again.

Using Data to Inform Priorities in War-Torn Nations

“This data suggests that immunization programs and keeping healthcare systems intact should be a high priority in war-torn nations,” Harrison concluded. “Several relief programs are focusing on integrated management of childhood illnesses, which includes improving case management strategies of healthcare providers, healthcare systems, and families.”

Boger, Harrison’s teacher, applauded her work, saying she’d exceeded his high expectations. This spring, Harrison will have another chance to explore her passions with a civics math class she’s enrolled in.

“I personally see data as the backbone of any social change.”

She is also beginning to think about life after high school. She’s begun exploring four-year colleges and aspires to pursue degrees in political and environmental sciences.

“I personally see data as the backbone of any social change,” said Harrison. “Being able to visualize and look at data clearly is essential to taking meaningful action and maximizing your impact. I see this, especially with environmental justice and climate change. Data will help determine which areas are most in need of relief and which areas will face the most impact. I hope to be able to focus on data-driven environmental policy work in the future.”

Inspired? Explore Data You’re Passionate About

Find data that sparks your curiosity.
Click “Upload Dataset” from your Tuva dashboard or type tuvalabs.com/upload in your web browser’s URL bar.

3. You may now import a dataset from your computer, Google Drive, or One Drive, or by dragging and dropping your CSV, XLS, or XLSX file into the gray rectangle.

4. You’ll be prompted to review your data. Afterward, you’ll be taken to a visualization screen where you can begin analyzing your data.

For more detailed information and instructions, visit our Support Page: Uploading Data into Tuva. Also, we’d love to see the data visualizations you create! Share it with us at jocelyn@tuvalabs.com.

Tuva Redoubles Commitment to Integrating Data Literacy Across the Math Curriculum

Math Content Library Revamp First Step in a Larger Effort to Support Teachers

Calls to incorporate data literacy in K-12 education are gaining momentum across the country. States like Virginia, Utah, Oregon, and California are taking major steps to create updated state standards or dedicated high school pathways.

Some of the states who’ve recently incorporated data literacy into their standards.

As a company dedicated to building a future in which all students possess data literacy and use it to contribute positively to society, Tuva applauds these changes. We also recognize implementing change takes work. Teachers, schools, and districts deserve support as they work to integrate data literacy across their math curriculum. To help maintain the momentum, Tuva is placing renewed energy on its resources for mathematics teachers.

As part of this effort, we recently revamped our math content library to make it easier for math teachers to locate lessons that will help them weave more data into their curriculum. The library has been reorganized to better reflect what teachers are teaching, with separate pages for each course.

“We’re hoping these changes will enable our math teachers to spend less time searching and more time teaching,” explained Tuva Math Educational Specialist Colleen McEnearney.

The content in the library has not changed; the navigation system has. Teachers are prompted to select a course: 6th-grade math, 7th-grade math, 8th-grade math, algebra 1, algebra 2, or statistics/AP statistics.

Each course page is divided into the big ideas of that course. These big idea buckets represent areas within each course where real-world data can greatly enhance students’ understanding of the content. For example, the 8th-grade math page includes the big ideas: interpreting scatter plots and associations; informal linear models; two-way tables; and formal linear models.

All lessons connected to a big idea are clustered on the page, so teachers can scroll through them all at once.

Previously, teachers had the option to sort lessons by course or concept, but this posed challenges. When filtering by course, they would see all lessons related to the course’s standards, requiring manual searching for specific concepts. Searching by concept, while possible, often resulted in diverse grade-level materials, necessitating manual sifting for grade-appropriate content within the old organizational system.

Tuva’s math content library revamp eliminates these time-consuming issues and makes finding the just-right lesson much more efficient. Explore our newly remodeled math content library.

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.”