What's the Big Deal with Big Ideas?

TEACHING MATH AS A COHERENT STORY

When students begin their mathematics journey, we carefully frame what they are learning in ways that allow them to engage in concrete or pictorial representations of the math. In the early grades, they don’t look at an abstract math sentence. Instead, we guide them to see that math sentence (equation) as a story.

As students progress through elementary school, math too often becomes a series of lessons without any clear connections across the concepts, causing students to lose the thread of the math story we so carefully tell in the earliest years of instruction. Fortunately, Big Ideas are designed to help students see math as a continuous and interconnected story, from TK through high school, allowing the storytelling from the earliest years to meaningfully persist.

Big Ideas represent a shift in thinking in how educators and publishers should approach math teaching. In the past, teaching was often organized around the content standards. A curriculum would typically align to both major and minor standards throughout the year, and the emphasis was on the alignment and coverage rather than thinking about how the learning takes place from a student’s perspective. As a result, students often perceived math instruction to be a series of disconnected procedures to solve problems algorithmically rather than understanding how their current learning built upon previous understanding and prepared them for future learning.

BIG IDEAS MAKE  LEARNING STICKY

Research tells us that new knowledge sticks best to existing knowledge. When students can build on a developing integrated body of knowledge, learning is simpler, less susceptible to errors, and less likely to be forgotten.

The Mathematics Framework for California Public Schools takes this idea that knowledge is sticky and transforms the focus of math education to ensure that everything sticks. It sets the stage for students to build a conceptual understanding of math and see how interconnected the core concepts of math are—across a single grade level and across the entirety of their math learning journey. In focusing on Big Ideas, content is organized for students around the coherent flow of math, not around the standards. Because we know that learning is sticky, high-quality math programs sequence the learning in a way that allows students to see the connections from one piece of learning to the next, creating a schema that supports the development of conceptual understanding. 

WHAT IS THE ROLE OF THE  CONTENT CONNECTIONS?

Big Ideas connect to other Big Ideas at the same grade level. While each Big Idea doesn’t necessarily connect to every other one, you can see through the example that they are linked to many other grade-level Big Ideas, creating a web of coherence across the math for that level. The Content Connections serve as threads that tie Big Ideas together across grade levels.

Figure 6.52. Grade Three Big Ideas

Figure 6.52 Source: California State Board of Education, Mathematics Framework: Chapter 6 – Mathematics: Investigating and Connecting, Transitional Kindergarten through Grade Five (California Department of Education, July 12, 2023), 117, fig. 6.52, https://www.cde.ca.gov/CI/ma/cf/index.asp.

For example, in grade three there is a Big Idea focus on fractions as relationships. When students get to grade four, the related Big Idea focuses on visual fraction models before they get to grade five, where the related Big Idea is about seeing division. You can see how these Big Ideas start to build over time, and that’s because they are tied together by the Content Connection of Taking Wholes Apart, Putting Parts Together. At each grade level, students build a layer of knowledge that they add more understanding to over time to get a more complete picture of parts and wholes. 

While Big Ideas advance by grade level, the Content Connections remain the same for all grades TK through high school. The way they are applied builds in complexity as the grade levels advance. This ensures that there’s continuity to what students are learning, adding to the stickiness of the new knowledge they build in each grade.

THE BOTTOM LINE

With the Content Connections and Big Ideas threading together a coherent progression of learning from year to year, students can truly begin to see math as a story. Over time, they will make connections from previous learning to new learning, and they will build a deep and lasting conceptual understanding of math. That means that by the time students arrive at a topic like division, they will have the background knowledge from their fractions learning to see that division is not a discrete math concept. There is a logical learning progression from fractions to division.

By developing this conceptual understanding, students move beyond memorizing complicated procedures for math and are able to solve complex problems because they understand the why behind the math, not just the how.

To see how Big Ideas help drive a coherent story of math in Eureka Math^2® California, visit https://greatminds.org/math/eurekamathsquared/california.