DataLiteracy

Do Kids Need to Learn to Graph by Hand?

Middle School Science Team Upends Expectations

Knowing how to create graphs by hand is an essential skill.

That may have been unexpected, coming as it does from the blog of a digital graphing tool. However, it’s important to clarify that using a graphing tool, like Tuva, and manually graphing are not at odds with each other; nor does one necessarily serve as a prerequisite. In fact, as the middle school science team at Northwest Middle School discovered, the two approaches are synergistic.

Northwest MS teachers Judith Neugebauer, Victoria Mauro, Anne Salisbury, and John Pikus.

“[Our students’] ability to see the numerical data in a graphical form is really transitioning from one realm to the other,” explained teacher Judith Neugebauer.

The team, which also includes teachers Victoria Mauro, Anne Salisbury, and John Pikus, is based out of a school in Salt Lake City. They began augmenting their manual graphing practices with Tuva’s digital graphing tools about a year ago.

The Most Persistent Problems for Novice Graph Creators

Adding digital graphing tools to the mix for novice graph makers is a step some are reticent to take. (Psst… I used to be amongst them.) Because digital graphing tools automatically do some of the steps for students, teachers wonder if students should know how to graph manually before they begin utilizing digital tools.

Before we address that concern, let’s take a step back to consider the most common skills with which novice graph makers struggle:

Placing variables on the correct axes
Setting up equal intervals and scaling them appropriately
Choosing an appropriate graph type
Accurately plotting data points
Including descriptive titles

The question is, then, will using digital graphing tools before students have mastered manual graphing prevent students from developing these important skills?

Better Together

Data literacy education expert, Molly Schauffler said that 15 years ago she would have said yes, but the development of drag-and-drop graphing tools, like Tuva, shifted her perspective.

“My sense now is that playing with the data and visualizing it on a digital platform gives students a visual sense of purpose, direction, possibility, and choice without getting mired in drawing and mechanics,”Schauffler said. “That said, I am still an advocate of hand drawing graphs alongside digital exploration.”

Schauffler is a founding member of a group called Partners in Data Literacy, a paleoecologist, an assistant research professor emerita for the University of Maine, and a former Tuva consultant.

“We still have them graph in their notebooks too, but this year it’s going way faster.”

The benefits of using both methods simultaneously are evident at Northwest, where teachers say making graphs on Tuva has hastened the development of manual graphing skills for their 7th- and 8th-grade students.

“We still have them graph in their notebooks too,” Neugebauer explained, “but this year it’s going way faster.”

The teachers there credit the uptick in pace to repeated exposure to and practice with variable placement and graph types in Tuva.

Our Suggestions for Achieving Synergy

Digital graphing tools exist on a spectrum from fully automated to completely open and incremental. When combining manual and digital graphing practices, consider how the features of the digital tool may impact skill development.

For Tuva users helping graphing novices master the five skills listed above, we suggest pairing manual graphing and Tuva in the following way:

Practice Manually	Practice With Tuva
Setting up equal intervals and scaling them appropriately	Placing variables on the correct axes
Accurately plotting points	Choosing an appropriate graph type
	Adding descriptive titles

In most instances, Tuva sets up intervals and plots data automatically once students have chosen which attributes (variables) to drag to which axes. Doing these things manually helps students understand a block on the graph represents a specific numerical increase.

That said, it is not necessary for students to practice establishing equal intervals and plotting data points every time they graph. In fact, sometimes it gets in the way of the other skills students are trying to master. Making graphs manually is so time-consuming that it is hard to achieve rapid repetition of a skill. Repetition is incredibly helpful for achieving mastery when it comes to placing variables, choosing graph types, and writing titles. Tuva enables targeted practice in these aspects of graphing. Students can also quickly and easily fix errors instead of needing to start all over, avoiding frustration and shutdown.

Swapped axes are a common woe of novice graphers.

Repeated practice can help.

Are We Graphing for Graphing’s Sake?

Perhaps, however, this entire discussion misses the point. Why is it important for our students to be able to create graphs? Is it simply so that they can create graphs? Of course not. The ultimate goal is to empower students to uncover insights about data through their graphs. Scientific literacy and data literacy are, after all, inextricable.

It’s easy to lose sight of that goal, however, in the day-to-day slog of asking kids over and over and over, “If you count up by ones, will you have enough space on your graph paper?” or, “Where does the independent variable go again?” And if we’ve lost sight of our goal, chances are our students never even knew a larger purpose existed in the first place. Of course, student motivation suffers when there is a lack of purpose.

Northwest teacher Anne Salisbury said Tuva has helped boost student engagement in the graphing process.

“I think using Tuva has convinced them that graphing has a purpose,” she said. “The point is not just to make a graph; it’s to use a graph. In the past we spent so much time getting them to physically graph on paper, that we did not have time to analyze data that is already graphed and figure out what it means.”

Former Scientist Centers Data in Her HS Biology Instruction

Maria Lee, High School Bio Teacher

Before Maria Lee became a science teacher, she was an environmental scientist. Her experiences working on salmon restoration in Washington State influence her approach to instruction.

“Primarily, I understand the importance of data,” Lee explained. “Data is not perfunctory; it is really an essential part of understanding science.”

As such, Lee dedicates a substantial portion of her high school biology course at East High School in Salt Lake City to the mathematical aspects of scientific understanding. In the past when working with data, Lee has had students use premade graphs or make their own using spreadsheets. This year, she opted to use Tuva. Now Lee calls out Tuva as one of her three favorite curriculum supplements, alongside leading EdTech platforms Newsela and Nearpod.

Lee was introduced to Tuva last year, but was hesitant to use it, fearing the learning curve would be steep. When she finally dove in this year, she discovered her worries were unfounded. Lee noted she did not spend time learning the Tuva tools in advance, but learned them in tandem with her students.

“ After just one day of playing around with Tuva with my students, I felt so comfortable- nearly expert level.”

“Suddenly, They Could See It”

The reasons for Lee’s enthusiasm are multiple. First and foremost, incorporating Tuva has accelerated her students’ learning.

Her first unit, a riff off of OpenSciEd’s Ecosystem Interactions and Dynamics, leaned into analyzing and interpreting line graphs and scatter plots. Lee described a class in which students were identifying whether or not there was a relationship between rainfall and wildebeest behavior in the Serengeti.

An example of student work from Lee’s class. Lee pulled data from OpenSciEd into Tuva.

Up to this point in their OpenSciEd unit, they’d primarily used line graphs to observe change over time. Now, they were struggling with the transition to scatter plots, getting confused about time versus relationship.

Lee uploaded the data onto Tuva and projected a scatter plot of rainfall vs. wildebeest occupancy on her interactive whiteboard. Then she had students come up and trace the dots from left to right and try to describe what their hand was doing- going up, going down, staying steady, or moving erratically. Some students were getting it, but many were not. Lee had them activate the least squares line.

Then, she said, “suddenly they could see it!” The line helped them ignore the background noise and identify the trend.

Another student work sample, this time with a scatter plot.

Student Ownership

Lee also said she appreciates the level of ownership Tuva gives students in the process of data exploration.

“Tuva puts students first in their interaction with data, so that they are driving their interaction and learning with the data and not getting it secondhand through a teacher filtering it for them.”

This level of independence is possible, she said, because Tuva leaves room for making mistakes and fixing them. With other tools, she’s needed to be more prescriptive because mistakes are harder to recover from.

Academic Communication: Scaffolding Up

Finally, Lee credits Tuva with creating more opportunities for extended learning. For example, when working with a class of multilingual learners, she found that Tuva’s interactive graphing tools accelerated the learning process enough that some students had time to deepen their interpretation.

Her class was working on the Tuva activity Dynamic Wildlife. (You can interact with the Wolf and Elk in Yellowston dataset the activity uses below!) She asked all students in the section to use the Identify and Interpret ( I²) method to discuss the wolf and elk population data. For example, a student might identify, “I see the line goes up at the start of the graph,” and interpret, “This means the number of wolves was increasing.”

Try dragging and dropping Elk Count (observed) onto the Y2 axis.

Many students completed this task quicker than they would have with print resources or spreadsheets. Lee capitalized on the newly-freed time to teach them to add quantitative measures, such as year and population count, to their evidence.

Lee noted that her class’s work with Tuva fits perfectly into the larger district goals, such as strengthening academic discourse and writing. Referring to Tuva as a “writing-science interface”, she said, “It’s the only tool I know that is really actively improving reading and writing skills for science. ”

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 November.

“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.