Understanding 'Understanding'

The Framework for Understanding 'Understanding'

In a previous post "Learning in the brain" I discussed how information is processed in Working Memory and stored in Long-Term Memory.  A four-level model of memory representations was suggested to describe the processes every "piece of knowledge" (ideally) progresses through: Know, Understand, Use, and Master.  Here we dive into the relations between the first two: what is needed to progress from knowing something to understanding it. 

To briefly summarize, when a learner knows a concept, it is represented in the mind and may be recognized shortly after learning. 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.

Here I try to dive deeper into the 'making meaning' process that leads to the desired, yet elusive, state of 'Understanding'.  By combining the simplified model of learning in the brain (introduced here) with the behavioral inputs and outputs, I explore the essential components and the processes that underlie 'Understanding'. The goal is to clarify the pedagogical discussion about the actions we can take to support learners in the process of making sense.

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 interactions in the environment, in turn, reshape 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 biological process of creating new associations (or connections) is known as Consolidation. It is when 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. 

The elements of 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 so we should consider three main components:

• The new concept

• The  existing knowledge to be associated with the new concept 

• Meaningful associations between them (2)

All 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 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 and its consequences. If the brain is responsible for the following chain of processes: perceive stimulus --> process stimulus --> generate a response --> receive feedback --> process feedback in relation to response, then a new concept becomes meaningful when it is effectively integrated into 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 now be used to successfully 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 n “equality” or “equity”.

Thus, higher or more abstract levels of meaning critically depend on familiarity and experience with lower more concrete levels.

Memorizing and Understanding

What are the implications of these explanations to what is commonly referred to as two distinct modes of learning: memorization (as in rote memorization) and understanding?

Memorization usually means the ability to recite certain facts like “four times three equals twelve” – a student that is able to do that is not considered to demonstrate an understanding of multiplication. However,  according to the formulation above, the student does understand “four times three” at a basic level that allows effective communication in a 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 to demonstrate the meaning of the concept we can establish a higher level of meaning for “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 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. For a brilliant concrete example of these ideas,  read the short story  "Meaningful", by  Scott Alexander (3).

These levels have different consequences for long-term retention: additional, higher levels of meaning make the information more useful in an 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).  At the same time, a lower level of understanding should not be dismissed but rather considered and treated as an important step on the way to reaching 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 collection 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.

Importantly, this means that teaching broad and deep knowledge in meaningful ways is a crucial goal of education, especially in the age of technology and readily available information. The wealth of information cannot benefit learners unless it is effectively learned and practiced 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 will not last.  

What can we do when learners "do not understand"?

It may be helpful to approach the situation by breaking the process of understanding to its components and to consider potential problems in each. What is described here is naturally a theoretical, domain-general approach, which every teacher may apply to specific teaching materials, approaches and students. Some of the components described here are "straightforward" and unsurprisingly in line with the 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 key components:  new information, prior knowledge, and meaningful connections.  Below are some key points to consider about each of them, with some examples.

Considering new information, 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 new concepts without in-depth explanations.

• Including no-stakes predictions questions about upcoming new concepts (may help frame the learning, familiarize learners with the new terms).

• 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 (4)

• 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 than trying to teach the new without it (we cannot build the top of the pyramid without the basis) (5)

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. 

• A 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 (5,6)  some examples:

• The pyramids illustration above is a concrete example of the relations between the abstract concepts 'knowledge' and 'understanding'. 

• Real objects (e.g. fingers, blocks) are examples of number concepts.

•  Matrices of real objects are examples of 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 association with the concept and to prevent misattributions of other characteristics of the model. A demonstration may be attention-grabbing by nature,  but it is important to ensure explicit focus on the nature of the connection, on making the intended meaning (can be achieved by asking questions 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.‏ 

2. Levels of Processing By Saul McLeod, published 2007 , explained also in the previous page: Learning in the brain.

3. Meaningful, by Scott Alexander, a fiction story via Slate Star Codex blog - Thank you Adam Boxer for sharing!

4. Clark, R., Kirschner, P. A., & Sweller, J. (2012). Putting students on the path to learning: The case for fully guided instruction. 

5. 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.‏

• 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.

6. The Learning Scientists Podcast: Episode 10 - Concrete Examples

Further reading:

Willingham, D. T. (2007). Critical thinking. American Educator, 31(3), 8-19.‏ 

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

Hirsch, E. D. (2003). Reading comprehension requires knowledge—of words and the world. American Educator, 27(1), 10-13.‏ 

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. 

Understanding understanding – could an A.I. cook meth? by prof. Kevin Mitchell via Wiring the Brain blog.