What a Load: Cognitive Load

 

Learning By Doing

Before we dive in, let's do a couple of math problems. Take a moment to compute the sum of the following number sentence: 

34 + 66 = ?

Ok, not too bad, right? I intentionally picked some numbers that are fairly "nice." Let's try another one: 

34 * 66 = ?

Same numbers, different operator. Also, much harder, right? Why is the second problem more difficult than the first? If you were an instructional designer, what would you do to help support a student who is learning multicolumn addition and multiplication for the first time?

"I'm carrying quite a load here." —Marge Gunderson, Fargo (1996)

The obvious answer to the question, Why is the second problem more difficult than the first?, is because the cognitive load is higher for the multiplication problem. Let's take a moment to model the cognitive operations as they are applied to each digit. In addition, we will also track the numbers as they enter (or leave) working memory. 

For the addition problem, the first thing we should ask ourselves is, Is this the right representation? The problem is stated as a linear number sentence: 34 + 66 = ?. But is that the easiest way to represent the problem? Perhaps it is easier to mentally transpose the numbers so they are stacked, with the place values aligned, like this: 

    66

+  34

    ??

Now I can mentally run the addition algorithm.

1. To start, I have two items in working memory (WM: 66, 34). 
2. I focus my attention on the ones place and recall the sum of 6+4. Now I have to add a new item to working memory, which is "10." Unfortunately, I can't think of it as a single item because I need to put zero in the ones place value and carry the "1" to the tens column. That brings our working memory total to 4 items (WM: 66, 34, 0, 1). 
3. Now I focus my attention on the tens column. I need to compute the sum of 1+6+3, which is "10." Now I have a new item, which brings my total up to five items (WM: 66, 34, 0, 1, 10). 
4. I can probably drop the "1" from working memory because I already processed it; however, I do need to assemble the sum by putting 10 in front of my zero in the ones column (WM: 66, 34, 0, 10). 
5. Now I have my answer, 100. All of the items can now be expunged from working memory. 

Suppose instead, I decompose the digits so they are "60+6" and "30+4." The tradeoff is that I now I have 4 items in working memory to start; however, maybe the trade-off is worth it. 

1. I start by decomposing the digits (WM: 60, 6, 30, 4).
2. If I add from left to right: 60 + 30 is 90 (WM: 60, 6, 30, 4, 90). 
3. Since I computed the sum, I can drop 60 and 30 from working memory (WM: 6, 4, 90). 
4. Once I add 6 + 4, and get 10, I can drop 6 and 4  (WM: 90, 10). 
5. Now I am down to two items. I add 90 + 10 and get my final answer. 

I modeled the addition problem twice to demonstrate that cognitive load depends on how you represent the problem. Both methods hit a peak of 5 items. However, the second method dropped down to 3 and 2 items very quickly; whereas, the first method had to carry 4 or more items for a longer duration.

If we conduct the same cognitive task analysis for the multiplication problem, we will find that the number of digits in working memory spikes at 14 or 15 items (depending on how you solve it). Since the limit of working memory is only 7±2 items, we are well beyond what most of us can carry around in our heads. 

You can almost feel the weight of the extra digits as you try to track all of the partial products. That extra weight you feel is the very essence of cognitive load.

Trading Cognition for Perception

This might be difficult, but imagine the point in your life when you did not know how to add. Your teacher had to help you at first, and then slowly withdrew their support as you progressed. It's likely your first experience with addition involved working with objects and/or your fingers. An adult might ask, "What is 2 plus 3?" To answer that, you hold up two fingers, and then start counting up to three. Once you've counted out three fingers, then you start and count up the total number of fingers. This is a very early strategy that kids use.

Over the course of your childhood, you may encounter the problem "2 + 3" hundreds, maybe even thousands, of times. With that much practice, you soon discard your counting strategy and commit the chunk "2 + 3 = 5" to long-term memory. Now, when you encounter the stimulus "2 + 3," you don't need to compute anything. Instead, it becomes a recognition task. 

In other words, you trade cognition (i.e., computation) for perception (i.e., recognition). Repeatedly solving the same problem, until it becomes routine, also goes by the name automaticity.

The S.T.E.M. Connection

What does this mean for education? We want our students to convert extremely basic symbols into larger and more complex chunks of information. For example, we want our geometry students to see the formula A = 2πr, not as an equation with five separate symbols. Instead, we want them to see that whole formula as a single chunk. 

Why is that important? It's important because larger, more complex chunks means that working memory has more space for processing and computation. When various symbols, such as "2+3," are encoded as a single item, then working memory load decreases. If your student sees "5" instead of taking the time to work out the sum, then that student has the mental space to process more complex ideas. 

Cognitive load is not relegated to instructional materials. For instance, if students are thinking about their Instagram feeds, or are worried that they are going to fail an exam, then all of these intrusive thoughts are part of working memory. Those thoughts add to the students' cognitive load. The space in working memory is limited, which means intrusive thoughts are in competition with the space needed to actually solve problems, follow a logical progression of ideas, or recall items from long-term memory [1].

Our goal, as educators, is threefold. We want to: 

1) supply our students with representations that are conducive to the task at hand; 

2) help our students create higher-order chunks that are stored in long-term memory; 

3) and, reduce unwanted, negative, or intrusive thoughts that compete for space in working memory. 

We each carry a different load. Let's ensure it is a manageable cognitive load!

Share and Enjoy!

Dr. Bob

Going Beyond the Information Given

[1] Spencer, S. J., Steele, C. M., & Quinn, D. M. (1999). Stereotype threat and women's math performance. Journal of experimental social psychology, 35(1), 4-28.