Understanding 'Understanding'

What is understanding from the "learning brain" point of view?

Exploring the components of 'understanding' (with some visual examples)

What can be applied in the classroom? and how can we help students when they don't understand?

The Framework for Understanding 'Understanding'

The previous page discussed how information is processed in Working Memory and stored in Long-Term Memory. A Four-levels model of memory representations was suggested: Know, Understand, Use and Master. Here we dive into the relations between the first two, the next page discusses retrieval practice that is generally more relevant to the later stages.

To briefly summarize, when a learner just knows a concept, it is represented in the mind and may be recognized shortly after learning, but not much more. When it is explained in terms of already familiar concepts and their relationships, the concept is potentially understood. It is argued and demonstrated that any incoming information should be processed meaningfully in Working Memory, in order to become knowledge that is stored in Long-Term Memory.

In this page we try to delve deeper into the 'deep processing' or 'making meaning' that hopefully lead to the elusive state of 'understanding'. We all have an intuitive sense regarding the theoretical and practical implications of 'understanding' - here we use the mechanistic point of view of the learning brain in order to explore the components and the processes that underlie 'understanding', and hopefully gain some tools to better help learners when they don't understand.

How memories are created and represented?

The framework of the discussion assumes, on the basis of current scientific understanding(1), that groups of synchronously active neurons in the brain underlie (among other processes) memory and behavior. Behavior and interaction in the environment, in turn, reshapes these neuronal representations, which potentially influence future memory and behavior.

When we experience something new, information enters the brain through processes of sensation and perception giving rise to certain patterns of neuronal activity. At the same time, already existing patterns are activated as one attempts to decipher the new experience in terms of the things that are already stored in the brain.

Potentially, following the learning experience a new representation of a new concept will be formed, as well as new connections to existing information.

For example, in the (probably long) process of learning a new concept like "Multiplication":

The process of creating new association (or connections) is termed Consolidation. It's a biological process in which new synapses are formed and others get stronger, following their activation in real-time' Consolidation is the essence of "neuro-plasticity": our life-long ability to create new memories and new connections following every experience. In this processes connections are formed between neurons to form new representations or retrieval pathways, others get stronger (and sometimes also weaker) changing the potential future behavioral output.

What drives Consolidation?

Using these terms it is possible to say that when teaching, the goal is to support deep or meaningful processing of the information that would potentially promote the consolidation of new information into the network of existing information. To do that we should consider 3 main components:

  • The new concept
  • The existing knowledge that we want to connect to the new knowledge
  • Meaningful connections between them

All the three components should be ACTIVE at the time of learning in the brain of every learner. The process of consolidation is known to be dependent on activation: only active neurons or representations are candidates for consolidation and stabilization. (This idea goes back to the the theory by Donald Hebb from 1949 that brings together behavior and the brain and is summarized by the known phrase "Neurons that fire together wire together").

We can think of the new and existing knowledge as representations, or unique neuronal patterns (as depicted above), and of meaningful connections as the connections that are formed between them, and will drive future associations. An important question would be - What drives the creation of connections? Why one connection is effective and another is not? Why do some connections last while others do not? What do we mean by :understanding" or by "making meaning" ?

What is Meaning?

The answer suggested here is that a new concept becomes meaningful once it enables the brain (and hence the learner) to respond effectively. In other words, once the new concept was integrated within the existing network in a way that supports a potential action or a decision. If the brain is responsible for the following chain of processes: receive stimulus --> process stimulus --> generate a relevant response, then a new concept becomes meaningful when it is effectively embedded in such a chain.

For example, when a child first learns the word ‘Ball’ – it becomes useful once an effective association was made with the already familiar object. Only then she can understand the sentence “Kick the ball”, and respond to it. The new concept can be now used to successfully to execute an action.

At the basic level of learning concrete meaning is attached to a meaningless concept (e.g. a word) – like the name of a person (Jess), an action (Play) or an object (Ball). The meaning relies on the ability to use the new concept to communicate or act effectively, which is usually accompanied by positive feedback (received from another person, or from the mere accomplishment ). A recurrent successful use reinforces the associations within the network, and the concept becomes more robust.

We can conclude that low-level meaning relies on concrete experiences.

At higher levels of learning, well-established concrete concepts are used as examples for more abstract or more general concepts. For example, if we wish to teach what “equal” means we can say “If Jess has one ball and Danny has one ball, then they have an equal number of balls”. We establish the meaning of the new concept “equal” on the basis of already known concepts (“Ball”, “Jess”, “has”, "one" etc.) and the already known interactions between them (having one ball). Later, we can go further up the pyramid and give “equal” more abstract meaning as in “equality” or “equity”.

Memorizing and Understanding

what are the implication of these explanation on what is commonly referred as two distinct modes of learning: memorization (as in rote memorization) and understanding ?

Memorization usually means the ability to recite a certain fact like “four times three equals twelve” – a student that is able to do that is not considered to demonstrate understanding of multiplication. However, according to the formulation above, the student does understand “four times three” in a basic level that would allow effective communication at a low level and in a very specific context (i.e. answering a question in a math quiz). To create a higher level of understanding additional concrete examples are required (e.g. “Jess has three baskets, four balls in each”) as well as explicit connection to the new concept (“so we can say Jess has four balls multiplied by three ”). By adding more familiar (concrete) examples that demonstrate the meaning of the concept we can establish a higher level of meaning for the concept “Multiplication”. As a higher-level concept, it will be useful in an increasing number of contexts and situations (and as educators we should supply these opportunities during the practice stage and beyond). Every time it is used effectively it is rewarded and hence strengthened.

The common terms “memorizing” and “understanding” may be mapped into lower and higher levels of understanding respectively. Understanding (at each level) is demonstrated by the possible actions that are achieved on the basis of the available background knowledge and on the meaningful connections that were explicitly learned and practiced.

These levels have different consequences for long term retention: additional levels of meaning make the information more useful in increasing number of situations, and every time it is used it is also practiced and reinforced. Hence, striving to achieve higher levels of meaning-making is unequivocally an important teaching goal, creating various opportunities for practice is another (see next page). In the same time, lower level of understanding should not be dismissed but rather considered and treated as a step on the way to reach the next level.

Constructing the Knowledge Base

Hopefully it becomes clear that knowledge and understanding can be viewed as components of the same thing: knowledge is the collections of concepts represented in the brain, and understanding is the connections that they form between them. Knowledge and understanding are interrelated and dependent on each other. This view highlights two important features of our learning system: New knowledge is built on the basis of the previous knowledge and they must be related by meaningful connections.

Concrete Example

The process of constructing knowledge can be described as building a pyramid: a new piece of knowledge (Orange triangle) is placed on top of the existing structure of knowledge (Grey triangles), in a meaningful way (correctly aligned). The final structure is dependent on the existing layers and on the correct placement of the new one (or on all the three components of understanding).

Extending the Analogy

As more and more information is acquired meaningfully, more pyramids and larger pyramids are created with increasing number of opportunities for higher-order learning (where a whole pyramid becomes just a brick in a new one), and interdisciplinary learning (that is supported by several other pyramids; top panel.). These types of higher-order learning are impossible to attain meaningfully without the supporting lower-level structures of knowledge (bottom panel).

This strongly suggests that higher-order thinking abilities, like critical thinking and creativity, are attained only on the basis of a solid body of domain-specific knowledge. They cannot be acquired as general skills, as explained here. We should teach the relevant body of knowledge and then support a deliberate practice of the way of thinking we wish to develop among learners.

Check out the "Building Pyramids" Project page, for more illustrations and explanations

Importantly, this also means that the previous knowledge should be effortfully structured in the brain of every learner individually. Hence teaching wide and deep knowledge in meaningful ways is a crucial goal of education, and especially in the age of technology and readily available information. This wealth of information cannot benefit learners unless it is effectively learnt and becomes their own knowledge. Using, the pyramids analogy: whole pyramids cannot be "imported" into the brain, but rather gradually and effortfully built on the existing base.

To the Classroom

Anyone who teaches may often feel discrepancy when aiming at a certain level of complexity, while some of the learners “still do not understand”. They may attain a lower level of understanding, but this is not enough, as this kind of knowledge will not be useful enough and won't last long.

What can be done when learners do not understand?

It may be helpful to approach the situation by breaking the process of understanding to its components and to considering whether the problem lays in any of them. What is described here is naturally a theoretical, domain-general approach, which every teacher may compare against a specific teaching materials, approaches ,and even specific learning processes of individual students . Some of the components described here are "straight forward" and unsurprisingly in line with most existing lesson and topic plans. However, some of the processes are more subtle than others and are more often taken for granted, it might be fruitful to explicitly consider them in order to locate and target gaps in students' learning:

The route to understanding includes these three basic components: new knowledge, prior knowledge and making meaningful connections. Below are the key points to consider about each of them, with some examples.

Considering new knowledge, prior knowledge and meaningful connections:

1. The new concept is explicit, distinct, and clear.

It is helpful to present the new concept before learning - to establish familiarity, if possible even more than once. For example:

  • As a preview for the lesson - presenting just the concepts without explanations.
  • No stakes questionnaire or quiz about upcoming new concepts (may help frame the learning, familiarize learners with the new terms).
  • A light homework assignments, targeted at establishing familiarity, not deep understanding.

Present the new concept explicitly, clearly and distinctly to ensure processing

  • Explain the concept explicitly and directly, repeat several times.
  • Give a straightforward explanation, rather than let students explore and discover. Making meaning by itself may be a demanding mental task.
  • Present a minimal possible number of new concepts in one session, if there is more than one , they should be clearly distinct (temporally and conceptually).

2. Relevant prior knowledge is available and active.

If prior knowledge is not available there is no other way but to teach it.

Time is better spent at teaching the basics then trying to teach the new without it ( we cannot build the top of the pyramid without the basis)

The relevant prior information should be ACTIVE at the time of learning

  • Teacher reviewing relevant material is often creating an illusion of active prior knowledge., the same is true when one or two students volunteer to review. It is tempting to assume that students intuitively relate to their prior knowledge, but it is better not to, especially when they are novices.
  • Short questionnaire on the required knowledge would serve as effective retrieval practice, and as preparation for the new learning,

3. Creating explicit and meaningful connections between prior knowledge and new concept

Connections are understood on the basis of already familiar connections: use familiar and well-grounded concrete examples that represent well the type of connection we are teaching. some examples:

  • The pyramids illustration above is a concrete example for the relations between the abstract concepts 'knowledge' and 'understanding'.
  • Real objects (e.g. fingers, blocks) are examples for number concepts.
  • Matrices of real objects are examples for the multiplication concept.
  • Visual or physical models help explain scientific concepts like DNA, chemical bonds, forces, currents etc..

The nature of the connections in the example is discussed explicitly and distinctly to ensure making the appropriate connection to the concept and to prevent misattribution of other characteristics of the model. Demonstration may be attention-grabbing by nature, but it is important to ensure explicit focus on the nature of connection, on making the intended meaning (can be achieved by asking question after the demonstration).

References and Additional Reading

1 Tonegawa, S., Liu, X., Ramirez, S., & Redondo, R. (2015). Memory engram cells have come of age. Neuron, 87(5), 918-931.‏

Willingham, D. T. (2009). Why don't students like school?: A cognitive scientist answers questions about how the mind works and what it means for the classroom. John Wiley & Sons.‏

This book is based on research and written especially for teachers, includes clear explanation, compelling examples and demonstrations, and classroom applications. Specifically relevant are the following chapters:

  • Chapter 2: “Factual knowledge must precede skill” on the importance of knowledge as building blocks.
  • Chapter 4: “We understand new things in the context of things we already know, and most of what we know is concrete”. On the importance of familiar concrete examples, deep knowledge and transfer.

McLeod, S. A. (2007). Levels of processing. Retrieved from www.simplypsychology.org/levelsofprocessing.html

Willingham, D. T. (2007). Critical thinking. American Educator, 31(3), 8-19.‏ https://www.aft.org/sites/default/files/periodicals/Crit_Thinking.pdf

Willingham, D. T. (2006). How knowledge helps: It speeds and strengthens reading comprehension, learning-and thinking. American Educator, 30(1), 30.‏

https://www.aft.org/periodical/american-educator/spring-2006/how-knowledge-helps

The Learning Scientists Podcast: Episode 10 - Concrete Examples

http://www.learningscientists.org/learning-scientists-podcast/2018/1/3/episode-10-concrete-examples?rq=concrete%20examples

Hirsch, E. D. (2003). Reading comprehension requires knowledge—of words and the world. American Educator, 27(1), 10-13.‏ https://www.aft.org/sites/default/files/periodicals/Hirsch.pdf

No “far transfer” – chess, memory training and music just make you better at chess, memory training and music. By Alex Fradera via The British Psychology Society, Research Digest. https://goo.gl/y9ZijH