Tag: Math

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.

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. 

Rural Math Teacher Uses Real-World Data to Promote Equity

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

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

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

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

Surfacing Social Justice Issues with Data

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

Boosting Inclusion by Helping Student Connect Personally to Data

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

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

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

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

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

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

Inspired? Surface social justice with these resources.
Tuva Lessons and Datasets About Current Social Issues

Introducing the Model Shop – Enabling Students to Learn Modeling

From the CCSS Standards of Mathematical Practice – Modeling with Mathematics practice:

“Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another.” 

From the High School Common Core Standards on Modeling:

“Modeling links classroom mathematics and statistics to everyday life, work, and decision-making. Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions.”

From Science and Engineering Practice in the NGSS – Developing and Using Models practice: 

“Models include diagrams, physical replicas, mathematical representations, analogies, and computer
simulations. Although models do not correspond exactly to the real world, they bring certain features into
focus while obscuring others. All models contain approximations and assumptions that limit the range of
validity and predictive power, so it is important for students to recognize their limitations.” 

Building on our Signs of Change content initiative that brings history and mathematics together for students, we are excited to announce the Model Shop, our next math and science content initiative dedicated to an incredibly important concept – Modeling.

The Model Shop contains Tuva datasets and activities that enable your students to build a strong foundation about Modeling. Students get an opportunity to use elementary, linear functions to make mathematical models of real data. 

Through our activities and lessons, students will get an opportunity to answer the following questions – What is a mathematical model? How is a mathematical model developed? How does the mathematical model represent our reality, and what is the meaning behind the curve and the parameters? 

We are starting the Model Shop initiative with linear models, giving students an opportunity to create a model for data related to a pencil sharpener, book pages and thickness, Chinese trains, Hooke’s law, and others. Over time, we will continue to add datasets and activities beyond just linear models, including logarithmic, quadratic, exponential, and others. 

All the Tuva Datasets and Activities in the Model Shop are fully accessible only to Tuva Premium customers. Learn more about Tuva Premium here or get in touch with us directly.