“Science is built up of facts, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house.” – Henri Poincaré, mathematician and philosopher, 1905
The research on learning is clear. From mathematics to chess or even tennis – a distinguishing factor between beginners and experts in any field is that experts organize information in their brains. But we rarely plan our instruction to help reveal that organizational structure for our students.
Building expertise is quite complex. Nevertheless, we can use a relatively simple way to think about it to yield enormous results. If you’ve ever felt students struggle to grasp what you are teaching, try these steps below.
1. Teach organizing concepts differently from vocabulary words.
Concepts are the building blocks used to form patterns of thought in the brain. They are simply age-appropriate words we use to organize and categorize our world. Concepts include rhyme, imagery, word play, array, equivalency, product, scarcity, power, natural resources, physical properties, energy, force, and motion.
Vocabulary words are often taught by sharing the definition with students right away. But concepts — or organizing ideas — are better shaped by examining the common features among key examples, sometimes compared with non-examples. That way, students come to see concepts for what they are: words we use to organize our world. And even our youngest learners can see that these categories help us to make sense of the complexity of life.
Check out the spontaneous drawing from a five-year old in Figure 1. On the left, he explained, is a list of “animals” and on the right (the first word is supposed to be ‘garbage’) is “not animals.” Jaw dropping. This is what young people do naturally, but somewhere along their learning journey, we stop helping them to clearly see the ways in which our world is organized.
Figure 1: Five-year old drawing of “animals” and “not animals”
Depending on where students are in the learning journey, we need to help them determine the critical attributes that define certain organizing ideas, usually by examining key examples and comparing them to non-examples. Have students view images or tactile examples of key concepts you are teaching and ask them to come up with the critical attributes that objects in each group share.
For instance, science teachers can set up a table with plants that have seeds and another table with plants that do not have seeds. Ask students to explore each set to determine the critical differences between them. Or English language arts teachers give students examples of strong reasoning alongside examples of weak reasoning. Ask students what common characteristics make one set stronger than the others. Then, teachers can provide the clear, precise definition of the concepts. We want students to first turn on their brains; and investigate the common features of examples to clearly see how concepts organize our world.
2. Focus on connecting a couple of concepts at a time in a particular context or situation.
Once students understand the critical attributes of at least two concepts, we can ask them about the relationship between those concepts, as shown in a particular contexts or situation – such as a text, science lab, piece of art, or mathematical problem. Our guiding questions in this stage should be purposefully vague so that students figure out the specifics of the relationship between two concepts. My favorite question is simply: How are these concepts connected? Students must use evidence from the context to answer the question, thereby forcing their brains to grasp the structure of how the topic or subject is organized.
- How does the setting influence the plot of a story?
- What is the role of scarcity in international relations?
- What’s the relationship between multiplication and arrays?
- How does the structure of plants impact reproduction?
3. Transfer to a novel situation where those concepts are present.
Expertise requires that students make dozens of neurological connections in the brain, so we can’t stop with connecting just a few concepts only once. We need to present a novel situation where these original concepts play a role, preferably a relatively similar situation at first – a similar text, science lab, piece of art, or mathematical problem of some sort. Students should be prompted to reexamine, refine, and expand their understanding of the conceptual relationship based on this new situation.
See Figure 2 below as a way to think about how we can intentionally build that organizational structure in the brain by connecting concepts in relationship through specific situations or contexts. And then repeat the process in a new context to strengthen those connections. Asking students to apply their learning to new contexts should not be reserved for the end of a unit of study. Rather, transfer should be deliberately built-in throughout the unit.
4. Highlight additional concepts that play a role in both situations.
At this point, you should have explored at least two contexts or situations – the original one in step 2 and the one that you’ve transferred to in step 3. These contexts often contain additional concepts beyond the first two you’ve focused on. During this step, draw attention to a few additional concepts. Then prepare to transfer to yet another situation, this time bringing the original concepts along with the new ones.
Examples continued from the questions in step 2:
- How do setting, characters, conflict and plot interact in a story?
- What is the role of scarcity, power and sovereignty in international relations?
- What’s the relationship between multiplication, repeated addition, product, and arrays?
- How do the structure of plants, animals, and environment impact reproduction?
We can think of learning transfer – students applying their learning to a new and novel situation – along a continuum. We want to transfer to similar contexts while gradually moving students toward increasingly dissimilar or complex situations. See Figure 3 for the Learning Transfer Spectrum. Each time we transfer and layer on more concepts, we are helping to reveal the organizing structure that builds expertise.
Figure 3: The Learning Transfer Spectrum
Importantly, we are not “telling” students the organizational structure of our subject areas. Nearly all impactful learning requires effort and stretching. We are intentionally and gradually revealing the structure through fact-rich situations, guided by questions of conceptual relationship.
We can overlay the Learning Transfer Cycle – asking and answering conceptual relationship questions through the study of specific contexts – over the Learning Transfer Spectrum, to build units of study that look something like Figure 4 below. We want to begin with transfer to highly similar, academic tasks, and then increase the level of complexity and real-world application through each new context or situation.
Figure 4: Overlay of The Learning Transfer Cycle over the Spectrum
Many teachers have experienced success in asking students to use their desks as white boards or using sticky notes to help students arrange concepts in relationship, thereby visually revealing an overarching structure of the subject or topic. Importantly, students should explain how the concepts are related in sentences or a short paragraph after visually depicting the connections. See the photos in Figure 5 below, one from an elementary math classroom and another from a high school English classroom. Imagine if we included this step in our classrooms at least every couple of weeks?
Figure 5: Connecting concepts in elementary mathematics and secondary English language arts
When we design our units of study with this organizational structure in mind, not only will students forget significantly less than they would without this process, but they begin to transfer their learning on their own. Countless teachers who’ve used these steps – from Kindergarten to Grade 12 classrooms – have been blown away by what their students have shared about the ways in which each subject is organized. The connections students make to their lives are even more spectacular as we transfer to highly dissimilar, real-world scenarios. Try it out and join the growing group of teachers who intentionally build toward expertise in their classrooms.
Bransford, J. (2000). How people learn: Brain, mind, experience, and school. Washington, DC: The National Academies Press.
Didau, D. & Rose, N. (2016). What every teacher needs to know about psychology. Woodbridge, UK: John Catt Educational Limited.
Perkins, D.N. & Salomon, G. (1988). Teaching for transfer. Educational Leadership, 22-32.
Sousa, D. (2017). How the brain learns, 5th ed. Thousand Oaks, CA: Corwin Press.
Stern, J. Ferraro, K. & Mohnkern, J. (2017). Tools for teaching conceptual understanding, secondary. Thousand Oaks, CA: Corwin Press.