**Today’s guest post is written by ****Julie Stern****, an author and consultant who focuses on conceptual understanding.**

Have you ever been frustrated by how quickly students seem to forget what you’ve taught them? Or by their struggles to use what they’ve learned in one context in a new, but related context? When we intentionally help students build schema, we can solve both problems.

Schema is a mental structure to help us understand how things work. It has to do with how we organize knowledge. As we take in new information, we connect it to other things we know, believe, or have experienced. And those connections form a sort of structure in the brain.

*Consider the following quotes from education researchers:** *

“The reason experts remember more is that what novices see as separate pieces of information, experts see as organized sets of ideas.” Donovan & Bransford, 2005

“It turns out that people who do well in math are those that make connections and see math as a connected subject.” Jo Boaler, 2014

“Cognitive scientists think of deep learning—or what you might call ‘learning for understanding'—as the ability to organize discrete pieces of knowledge into a larger schema of understanding.” Meta & Fine, 2019

If a hallmark of expertise is organized thinking, how do we help students to see the *structure *of the subject we are teaching?

Enter the noble index card. This low-tech tool has the power to revolutionize your teaching practice. Post-it notes work, too. They allow students to physically build and manipulate schema as they learn. Let me show you.

First, we start with individual concepts, which are the building blocks of schema. Concepts are words we use to organize and categorize our world. When we look at our curriculum standards or learning outcomes, the nouns are usually the concepts. Examples include: story patterns, character, fraction, whole number, living things, organelle, leadership, and sovereignty.

We can start with examples of concepts that students already know. For instance, we can use ocean, desert, and rain forest as examples of the concept of habitat. Or we can put groups of different concepts in front of students and ask them to try to determine the features that differ between the groups. One middle school science teacher put a few simple circuits on one table and a few parallel circuits on another table. Students tinkered with the circuits on each table and discussed what differences they noticed between the two groups.

Once students acquire initial understanding of a concept, it’s time to consolidate their understanding (Fisher, Frey & Hattie, 2017). They can do this using index cards, collecting these cards as visual representations of the building blocks of expertise. Many teachers use the SEE-IT model. See the steps in Figure 1 below.

**Figure 1: SEE-IT Model for Consolidating Understanding of Single Concepts **

Source: Adapted from Stern et. al, 2017; originally adapted from Paul & Elder, 2013.

Social studies teacher Jeff Phillips asked his students to complete this activity to consolidate their understanding of the concept of “services.” And English/language arts teacher Trevor Aleo asked his students to complete the steps with the concept of “symbol.” See both student examples in Figure 2 below.

**Figure 2: SEE-IT Card Examples for Social Studies and Language Arts **

When students elaborate on their understanding of concepts, it presents an opportunity to correct any lingering misunderstandings. See the student example in Figure 3 below. Notice that the student wrote that a leader has a “right” to change society’s perspective, demonstrating a common confusion in social studies. In a democratic society, governments have authority derived from the people, while people maintain rights, derived from birth. This is an important distinction that we can now correct.

**Figure 3: Example of Misconception of a Concept**

Now—on to the really good stuff. Once students have acquired, corrected, and consolidated their understanding of individual concepts, it’s time to connect the concepts in relationship. That’s where schema is built.

This next step comes during and after students have explored a fact-rich context such as a complex mathematical problem, science experiment, literary text, or social studies context. Students use their learning experiences to generalize into organizing principles about how the world works (Erickson & Lanning, 2014). They can now physically arrange the note cards or Post-it notes to demonstrate how concepts are related. Then, they should write a sentence or paragraph that explains the relationship.

Science teacher Julia Briggs asked her students to connect the concepts of matter, arrangements, subatomic particles, and properties. Then, Ms. Briggs asked students to write a couple of sentences about how the concepts are related. Notice how the note cards serve to make a structure among the science concepts in the example in Figure 4 below.

**Figure 4: Science Example of Sorting and Connecting Concepts to Build Schema **

Similarly, math teacher Courtney Paull asked her students to connect five concepts using Post-it notes: linear models, table, story, graph, and equation. Then, they wrote a paragraph about how the concepts are related.

The students wrote,

Because a story, equation, graph and/or table are part of a linear model, as long as you have one component you can find the rest by using the present numbers. The table is used to find patterns in the input and output, while the equation helps find the specific values for x and/or y. A graph gives us a visual representation of the pattern and the story helps us make connections to real world situations.

Wow. Imagine if we had all learned mathematics this way. See the picture in Figure 5 below.

**Figure 5: Mathematics Example of Sorting and Connecting Concepts to Build Schema **

The index cards and Post-it notes help students to physically build an organizational structure or schema directly on their desks. Importantly, schema is not built with just one pass at making connections. Schema is built through multiple experiences of making connections. This activity can and should be repeated throughout the unit, semester, and school year. Students can add more concepts and make more connections each time they transfer their understanding to a new situation, eventually writing several paragraphs about how the concepts are connected and related.

Regular readers of this blog are likely familiar with John Hattie’s research, called *Visible Learning*. His meta-analysis of factors that influence student learning shows that an effect size of .40 is the average of all influences. So, we can think of .40 roughly as a year’s worth of growth. Anything above .40 has the potential to accelerate student achievement (Visible Learning Plus, 2019).

Here’s how the strategies above measure up:

- Using examples of concepts from students’ prior knowledge = .93
- Clarifying misconceptions about concepts (conceptual change) = .99
- Asking students to elaborate and organize their understanding of concepts = .75
- Mapping concepts in connection to other concepts = .64
- Strategies to transfer learning = .86

Exciting, isn’t it? Intentionally teaching for schema is supported by both cognitive science and meta-analysis of student achievement. Grab some index cards or Post-it notes and help your students both retain information and transfer it to new situations.

**For more practical ways to apply this research in the classroom, see ***Tools for Teaching Conceptual Understanding, Secondary*** or ***Tools for Teaching Conceptual Understanding, Elementary***. **

**References:**

Boaler, J. (2014). Tour of Mathematical Connections. YouCubed, Stanford Graduate School of Education. Retrieved from: https://www.youcubed.org/resources/tour-mathematical-connections/

Donovan, S., & Bransford, J. (2005). *How students learn: History, mathematics, and science in the classroom. *Washington, DC: National Academies Press.

Erickson, H. L., & Lanning, L. A. (2014). *Transitioning to concept-based curriculum and instruction: How to bring content and process together*. Thousand Oaks, CA: Corwin Press.

Fisher, D., Frey, N., & Hattie, J. (2017). *Visible learning for literacy, grades K-12: Implementing the practices that work best to accelerate student learning*.

Meta, J. & Fine, S. (2019). *In search of deeper learning. *Harvard University Press: Cambridge, Massachusetts.

Paul, R. & Elder, L. (2013). *How to write a paragraph: The art of substantive writing (3rd ed.).* Tomales, CA: Foundation for Critical Thinking.

Stern, J., Ferraro, K., & Mohnkern, J. (2017). *Tools for teaching conceptual understanding, secondary.* Thousand Oaks, CA: Corwin, A SAGE Company.

Visible Learning Plus. (June, 2019). 250+ Influences on Student Achievement. Corwin Press: Thousand Oaks, CA. Retrieved from: https://us.corwin.com/sites/default/files/250_influences_chart_june_2019.pdf