Learning and Teaching-Cognitive Load Theory Part 1

When I started to teach engineering classes after many years away from teaching at a college level, I was looking for ways to buttress my teaching and I was looking for a solid reference to give me confidence to overcome my own fear of failure in the classroom.

My first instinct was to research the latest teaching literature for help. Most of what I was reading was focused on the techniques and tools that were available to the teacher or coach, not exactly a how-to approach.

As I broadened my investigation, the literature eventually steered me towards the cognitive sciences: how learning and retention works neurologically, a different direction than what I had expected. Instead of focusing on strategies and tactics for the teacher/coach to be more effective, this approach focuses on how the instructor should adjust their teaching philosophy to conform to how students/players can best learn.

Cognitive Load Theory (CLT) shows up continually on my radar, I first learned about it from the books that I had read upon the recommendation of Coach Vern Gambetta. (Brown, 2014) (Lemov, Teach Like a Champion: 49 Techniques that Put Students On The Path to College, 2010) (Lemov, The Coaches Guide to Teaching, 2020) (Lemov, Woolway, & Yezzi, Practice Perfect: 42 Rules for Getting Better at Getting Better, 2012). Even as I was intrigued by those books, I still felt lacking in background on CLT, so I read a couple of papers, both by the originator of the concept, John Sweller. His original paper was published in 1998. (John Sweller, Cognitive Architecture and Instructional Design, 1998). He also wrote another paper celebrating   the 20^th  anniversary of the original paper, discussing the developments that had augmented and evolved from the original theory after its initial introduction (John Sweller, Cognitive Architecture and Instructional Design: 20 Years Later, 2019).

Somewhere along the line, a monograph Cognitive Load Theory in Action by Oliver Lovell  (Lovell, 2020) came onto my radar, which focused on not only the theory but has neatly summarized teaching strategies which turns CLT from concept into effective and tangible practice. Lovell had worked in close consultation with Sweller to organize and summarize the CLT ideas that were in the original paper while also broadening the original idea with  additional work that was done in the intervening years.

What follows is a discussion structured along Lovell’s monograph, after I added some thoughts on the topic that are specific to my situation: teaching college engineering classes, coaching junior volleyball, and applying the method to my own learning practice. I do this s a means to help me understand topics that I felt were important. It aligns with the following quote from Joan Didion: “I write entirely to find out what I’m thinking, what I’m looking at, what I see and what it means.”

What is CLT?

Cognitive Load Theory is primarily based on what we know of the structure of the human memory and how that structure affects how humans learn and more importantly, recall all the information, knowledge and experience which makes up our learning arsenal.

There are five main principles which underlie CLT.

1.     Memory has Architecture.

2.     Knowledge is Categorized as Biologically Primary or Secondary

3.     Working Memory can be Categorized as either Intrinsic or Extrinsic

4.     The Knowledge Can be Either Domain-General or Domain-Specific

5.     Element Interactivity is the Source of Cognitive Load

Memory has Architecture.

The first essential principle of CLT states that humans’ memories have an architecture which consists of three major resources: environment, working memory and long-term memory.

The environment is everything that exists outside of our brain, all the external resources that we can consult for information: anything and everything that surrounds us which can be used to augment our working and long-term memory. Both Barbara Tversky’s (Tversky, 2019) and Annie Murphy Paul’s  (Paul, 2021) books have chapters devoted to how humans use the space surrounding us in extending our memories to that space.

The second architecture is the working memory:

·       It has limited capacity, able to keep 3-7 elements of information at one time.

·       It is where all the thinking takes place.

·       It is the domain of conscious thought: that is, we are actively managing the memory consciously.

·       It is the limiting factor of human thinking, the bottleneck to our ability to learn effectively.

·       It is where the unfamiliar and unknown at that instant takes up more of the working memory capacity than the familiar and known.

·       It uses chunking and automating the information to reduce the cognitive load on the working memory.

The last architecture is the long-term memory:

·       It is unlimited in capacity although the information that is most often recalled is those that are most easily recalled, i.e., those that are most often recalled or had been recalled most recently.

·       It is divided into three key form of knowledge:

o   Episodic: refers to life events,

o   Semantic: refers to factual information

o   Procedural: refers to process memories.

An analogy can be drawn comparing the human memory definition to computer system configuration. Working memory is analogous to Random Access Memory (RAM), long term memory is analogous to the hardware memory: HDD’s or SSD’s. Whereas the CPU is the brain itself, serving as the central traffic control for the knowledge that is being passed around. Even though this analogy can only carry us so far, as the human brain and nervous system are not as clearly defined as a computer system because the computer system is essentially a Von Neumann machine designed to be a simple imitation of what we think human cognition functions. Another place where the analogy falls apart is the transfer of knowledge from the working memory to the long-term memory. Human memory is such that it takes many iterations of transferring the knowledge from working to long-term memory before it is made permanent, whereas the computer has a specific storage function to more the data from the working memory to the long-term memory.

The analogy holds true for our purposes. The working memory actively using the brain to consciously process all the new and unknown information, knowledge, and experiences; while recalling the familiar and known information, knowledge, and experiences without using the brain because the information has been chinked and automated so that the recall is done subconsciously, without adding to the cognitive load.

This architecture is the foundational model for CLT, the arguments for implementing the strategy and tactics suggested by CLT are built upon the bedrock assumption that the three-resource model is correct.

Knowledge is Categorized as Biologically Primary or Secondary

The second essential principle states that knowledge can be categorized as either biologically primary or secondary.

Biologically primary knowledge refers to knowledge that:

·       Are unconscious, fast, frugal, and implicit.

·       Are acquired by humans through evolution.

·       Are Knowledge that cannot be taught.

Biologically secondary knowledge refers to knowledge that:

·       Are slow, effortful, deliberate, and conscious.

·       Have evolved through the last 1000 years.

·       Needs to be taught.

Working Memory Load can be Categorized as either Intrinsic or Extrinsic

The third essential principle states that our working memory can be categorized as either intrinsic or extrinsic cognitive loads.

Intrinsic cognitive loads are those that are critical to learning whatever it is that we need to learn. They are:

·       Part of the nature of the information that we are learning.

·       Core learning.

·       Information that we WANT the learner to have in their working memory.

Whereas the extrinsic cognitive loads are:

·       A part of  the manner and structure of how the information is conveyed to the learners.

·       Disruptive to the learning task because it distracts the learner from learning by occupying valuable working memory space.

The crux of the problem is that the working memory capacity is finite; that is, the intrinsic and the extrinsic loads are vying for the same finite resource: the working memory. Ideally, the learner needs to optimize the use of the working memory for intrinsic loads and minimize the use of the working memory for extrinsic loads. Note that it is desirable to optimize the intrinsic load rather than also minimizing the intrinsic load as we want to minimize the extrinsic load. The reason for the difference in goals is that we wish to devote as much of the working memory to the intrinsic (productive) learning mode, what is variable is whether an appropriate amount of intrinsic load is placed on the working memory for optimal learning, or whether too much, or too little intrinsic load is placed on the working memory.

The Knowledge Can be Either Domain-General or Domain-Specific

A fourth essential principle states that the knowledge that the learner is being exposed to can be  divided into domain-general versus domain-specific.

Domain-general skills are:

·       Biologically primary

·       General capabilities

·       Generally applicable

·       Transferable

·       Examples are:

o   Problem solving

o   Creativity

o   Communication

o   Teamwork

o   Critical thinking

Domain-general skills are assumed to exist, can be taught, learned and transferred.

Domain -specific skills are:

·       Biologically secondary

·       Applicable to only specific domains.

The difference between novices and experts in each domain is that experts have more relevant domain-specific knowledge. Which means that the novice uses more thinking in performing tasks while experts use more knowledge. The novices use up more of the working memory to think (conscious) rather than recall and the experts use up more of the working memory to recall knowledge rather than to think (subconscious).

An expert:

·       Has a larger collection of situations and associated actions stored in their long-term memory.

·       Can explain why these situations imply taking the specific actions,

·       Can derive the solutions from foundational principles,

·       Can explain the mechanism behind them,

·       Can recognize the situations and execute an appropriate action,

The payoff is that the expert can recognize a larger cache of problems and situations and the necessary actions to deal with each problem and situation, whereas the novice has a much smaller cache of memory.

If the biologically secondary domain-specific knowledge is not transferable, how does the learner go about improving their performance in a specific domain? The answer, according to Lovell and Sweller, is to increase domain specific knowledge in the long-term memory to expand the number of potential solutions available from the long term memory which can be recalled into the working memory.

Conversely, how does one leverage the biologically primary, domain-general, and transferrable  knowledge to improve the biologically secondary, domain specific, and non-transferable knowledge? The answer is to apply transferable knowledge within the context and the constraints of the specific domain. It is an indirect way of leveraging what is already resident within us when we are born to acquire new knowledge that is new to us?

Element Interactivity, the Source of Cognitive Load

The final principle is that the number of elements in a given problem and situation and the amount of interactivity each element has with the other elements determine the amount of cognitive load being placed on the working memory. Element interactivity depends on the nature of the activity as well as the background knowledge stored in the long-term memory inherent in the learner: novice learners will have minimal knowledge base to draw upon, while the expert will have an extensive knowledge base. In addition, the expert also is experienced, so that they can effectively “chunk”, i.e. consolidate and automate the knowledge to effectively bypass thinking and allow their knowledgeable self to react automatically.

Perniciously, the amount of interactivity rises geometrically as the number of elements increases linearly, this kind of growth in interactivity will overwhelm the working memory in short order.  The elements and the interactivity of the elements can also be divided into intrinsic and extrinsic loads following the second principle stated.

Indeed, this is the main idea that saves our working memory from constantly being overwhelmed: we can separate the intrinsic and the extrinsic; optimizing the learning from the former and minimizing the chatter from the latter.

According to Lovell, intrinsic load is optimized through well-crafted curriculum sequencing and the extrinsic load is minimized through good instructional design. All of which is also covered Lovell’s book, digging deeper into the granularity of

·       Strategies and tools to optimize the intrinsic load.

·       Strategies and tools to minimize the intrinsic load.

Which will be covered in a separate article, CLT Part 2, because this first part has optimized my intrinsic memory, and I need a break.

Part 2 is on how teachers can minimize extrinsic load on the learner through honing their  presentation. (https://polymathtobe.blogspot.com/2023/04/learning-and-teaching-cognitive-load.html)

Part 3 is on how teachers can minimize the extrinsic load on the learner through structuring their practices and lessons. (https://polymathtobe.blogspot.com/2023/05/learning-and-teaching-cognitive-load.html) 

Part 4 is on how teachers can optimize intrinsic loads on the student. (https://polymathtobe.blogspot.com/2023/08/learning-and-teaching-cognitive-load.html)

References

Abrahams, D. (2022). Retrieved from Daniel Abrahams: Helping People Perform: https://danabrahams.com/blog/

Brown, P. C. (2014). Make It Stick: The Science of Successful Learning. Canbridge MA: Belknap Press.

John Sweller, J. J. (1998). Cognitive Architecture and Instructional Design. Educational Psychology Review, 251-296.

John Sweller, J. J. (2019). Cognitive Architecture and Instructional Design: 20 Years Later. Educational Psychology Review, 261-292.

Lemov, D. (2010). Teach Like a Champion: 49 Techniques that Put Students On The Path to College. San Francisco: Jossy-Bass Teacher.

Lemov, D. (2020). The Coaches Guide to Teaching. Clearwater, FL: John Catt Educational Ltd.

Lemov, D., Woolway, E., & Yezzi, K. (2012). Practice Perfect: 42 Rules for Getting Better at Getting Better. San Francisco CA: Jossey-Bass.

Lovell, O. (2020). Sweller's Cognitive Load Theory In Action. Melton, Woodtidge UK: JohnCatt Educational Ltd.

Paul, A. M. (2021). The Extended Mind-The Power of Thinking Outside the Brain. New York: Houghton Mifflin Harcourt.

Tversky, B. (2019). Mind In Motion-How Action Shapes Thought. New York: Hachette Book Group.

 

 

 

Book Review-A Mathematician's Lament By Paul Lockhart

In the forward to this monograph. Kevin Devlin of Stanford University, a well renowned mathematician, tells the story of how Paul Lockhart, someone who had given up his career as a research mathematician to devote himself to the mission of improving K-12 mathematical education, turned an earnest but obscure essay into a resounding statement.

The first genesis of this book is as a 25-page document that was passed around in the mathematical education circles. It became a sensation because many felt that Paul Lockhart had hit the nail on the head with his observations; observations and beliefs that resonated with mathematics educators; indeed, he struck a very sensitive nerve. As this document was passed around, it became a clarion call to mathematicians, mathematics teachers, and anyone who has a passion for how mathematics is taught.

A Mathematicians Lament is short and compact. Paul Lockhart had a lot to say, and he says it with urgency and alarm. Part I of  the book is the lamentation, he goes into everything that he feels is wrong with mathematical education. He makes his argument progressively starting with a discussion on mathematics and culture,  then a discussion on mathematics in the school, a dive into the national mathematics curriculum — a chapter in which he was unsparing in his criticism. In the last chapter in Part I, Lockhart zeroes in on a well-known and well reviled target: high school geometry.  Lockhart gave it a subtitle: Instrument of the Devil. This is his coup de grâce, his pronouncement on the abysmal state of mathematics education in the United States.

He expounds on the insidious practice of limiting mathematics education to just computation, while emphasizing the mechanical and uninspiring practice of training skills without giving the students a vision of what true mathematics is. We don’t give the students enough credit for being perspicacious enough to sense the immutable and deep beauty of mathematics. We don’t give the allure of the mathematical abstraction enough credit for being able to inspire and elicit  passion from the students; we think that the average student could not fathom the depths of meaning of mathematics; and that the student can only appreciate mathematics in its most utilitarian and unimaginative incarnation. It is an insult to the students and to mathematics.

As an engineer by training, I managed to survive my formal mathematics training with my love of mathematics intact, even though I knew my talent for theoretical math is limited.  I recognize all the stated pitfalls and shortcomings of how mathematics is taught because I had experienced it firsthand.

Although I  appreciate the beauty of mathematics, as I had aspired to be an applied mathematician; unfortunately, I had made a mess of the higher math that I took as a grad student in engineering, I didn’t have the patience nor the curiosity to sustain my interest because I was studying to gain a degree rather than studying for the love of a discipline. I was resigned to take enough applied math to help me become an engineer even though I was always curious about doing pure mathematics. Even as I have  resigned myself to the fact that I won't ever be a pure mathematician nor  even be a good applied mathematician, I have come to appreciate and love the subject.

In the second part of A Mathematician’s Lament — titled Exultation — Paul Lockhart made his elevator speech  to  anyone and everyone reading about the beauty of mathematics. He assiduously avoided the equations, a smart decision in my estimate. He dealt with mathematics as a holistic entity. He is much more eloquent in stating his case than I will ever be, so I will let the reader  read the book rather than dilute his passion and his narrative.

He discusses the common sensical instinctive aspect of  mathematics. There are crude but effective sketches about the points that he wanted to make, adding to the intuitive charm of the narrative.  He refrains from delving into the dreaded and unwelcoming geometry that he wrote about in Part I;  he uses simple sketches to ease the reader into mathematical thinking.

When he hit his stride talking about mathematics, it is a beauteous expression of passion he speaks of the raw beauty of mathematics that makes it so attractive, intoxicating,  and habit forming for so many. It is as if  mathematics is some kind of addiction. And to mathematicians that I know, and to a much lesser degree to me, that addiction is very real.

The second part of the monograph reminds me of the passion exuded by another book written by a mathematician. Francis Su wrote Mathematics for Human Flourishing, (Su 2020). I reviewed it in 2020. (https://polymathtobe.blogspot.com/2020/02/book-review-mathematics-for-human.html) Prof Su had the advantage of having a book to make his point about the allure of mathematics. It is perhaps a good companion book to buttress the second part of the argument.

The monograph is an extended essay identifying the problems with the way we have taught mathematics, how the math that is taught is contrary to what the mathematics lovers love about mathematics; what mathematics is in the eyes of those that are knowledgeable in the art; while  proposing in broad strokes what need to be done to change that paradigm. It is a timely and necessary clarion call to our society and our educators that we are irresponsibly squandering our opportunity to educate our society in the art of thinking, questioning, and creating. It is an attempt to reverse the trend, and more broadly, it is a valiant attempt to convince a math deficient public that they are missing the boat, and our society will suffer.

I hope that this is not just preaching to the choir, but the obstacles to universal understanding of the importance of the subject is quite high. I hope that Paul Lockhart is not too late.

Works Cited

Su, Francis. Mathematics for Human Flourishing. Yale: Yale University Press, 2020.