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.

A High-Pitched Cavitation: Feedback

Learning By Doing

Let's play a game called, Concept Identification. No wait. That sounds really boring. How about Counter Spies, Like Us? That sounds more like a game people would actually play! Here's the backstory: 

You are a counter-intelligence officer, and you just intercepted a code from an enemy spy. Your goal is to classify their coding patterns into two types. The first is called "DAX" codes and the other is "MED" codes [1]. Based on your previous training, you were given the following examples. 

DAX Codes: 

 

MED Codes:

 

Now it's your turn to classify two new codes as either DAX or MED. There is one of each. The answer can be found at the end of this post [2].

(A)

(B)

How did you do? If you got them both right, then you lead your team to victory and earn a promotion! If you got one right and one wrong, then you get out of the war zone in time, but leave your mission incomplete. If you got them both wrong, then you might want to rethink your career in counter-intelligence.

"Thanks for the Feedback." –Nobody, ever.

In some situations, you want feedback. In fact, you can't survive without it. For example, it's difficult to improve your job-related skills if your manager doesn't give you explicit feedback. In other circumstances, however, feedback—especially negative feedback—is neither wanted nor appreciated. Tell a coworker they look "tired" and don't be surprised if they throw you some shade.

So what's the deal with feedback? When should we give it? When should we withhold it? When is it effective, and when does it backfire spectacularly? The obvious answer is, "It depends." Let's dig in and talk about what it depends on. 

"Right up to your face and diss'd you." –The Sounds of Science, Beastie Boys

Kluger and DeNisi conducted a meta-analysis of empirical studies on feedback [3], and they concluded there is a moderate effect size of feedback on performance (d = 0.41). However, the authors go on to explain that in a third of the studies, feedback actually decreased performance. The obvious question is why?

According to their theory, the effects of feedback can be categorized into three hierarchical categories: task learning, task motivation, and meta-tasks (which includes feedback about your self). Their theory states that feedback is effective when it is directly targeted to the task. But if you move up the chain, then feedback begins to lose its effectiveness. It can even backfire (i.e., make people worse) when the person feels it is targeted at them personally.

Figure 1: A hierarchical arrangement of control processes.

Let's look at some examples. Suppose we played an interactive version of Counter-Spies, Like Us, and I give you a 3-by-3 grid. I then ask you to give me a MED code. My job as the trainer is to tell you if you're right or wrong. That feedback is targeted toward the task learning and should move your attention to applying more effort to finding which features of the grid correspond to its label. Negative feedback often results in the person increasing their effort, so long as the feedback is clear, non-arbitrary, and the learner feels like there is hope in detecting the pattern. 

Suppose the feedback wasn't about the task. Instead, the feedback caused you to move your attention up the hierarchy where you focus attention on your self. You might have doubts about your ability to detect patterns, and that you lack the intelligence to do anything difficult. 

What might that feedback look like? If the feedback was something like, "No, that's not right. Most people get this eventually." Which causes you to think, "Oh great. So if I'm not getting this, then what does that say about me??" The goal, of course, is to keep the learner's attention on the task and on the specifics of what can be done to improve.

The S.T.E.M. Connection

There are many other factors that contribute to one's ability to learn from feedback, including personality factors, learning goals, prior knowledge, and task complexity. Each of these factors can interact in complex ways. 

Fortunately, Dr. Valerie Shute has compiled an extremely clear set recommendations for maximizing the positive effects of feedback and minimizing the negative effects. Starting on page 177 her paper, Focus on formative feedback, Dr. Shute outlines 31 perscriptive guidelines for offering formative feedback. The guidelines include what you should do when giving feedback, what to avoid, and when to give feedback. I highly recommend taking a look at this valuable resource. Here's just one example:

#	Prescription	Description and references
2	Provide elaborated feedback to enhance learning.	Feedback should describe the what, how, and/or why of a given problem. This type of cognitive feedback is typically more effective than verification of results (e.g., Bangert-Drowns et al., 1991; Gilman, 1969; Mason & Bruning, 2001; Narciss & Huth, 2004; Shute, 2006).

Both giving and receiving feedback is a difficult process. But, as we have seen, there are ways that we can maximize our benefit from formative feedback. Just keep it task-focused...and stop dissing people! 😉

Share and Enjoy!

Dr. Bob

Going Beyond the Information Given

[1] Tweney, R. D., Doherty, M. E., Worner, W. J., Pliske, D. B., Mynatt, C. R., Gross, K. A., & Arkkelin, D. L. (1980). Strategies of rule discovery in an inference task. Quarterly Journal of Experimental Psychology, 32(1), 109-123. 

[2] Code (A) is MED, and Code (B) is DAX. The rule that generates MED codes is there must be a yellow square in the bottom row. DAX codes are the opposite. They must not have any yellow squares in the bottom row.

[3] Kluger, A. N., & DeNisi, A. (1996). The effects of feedback interventions on perfor-
mance: A historical review, a meta-analysis, and a preliminary feedback interven-
tion theory. Psychological Bulletin, 119(2), 254–284.

[4] Shute, V. J. (2008). Focus on formative feedback. Review of Educational Research, 78(1), 153-189.

Fight the Power!: Retrieval Practice

Learning By Doing

Let's start with a handful of questions. Without looking back at any of the previous posts, try to answer the following questions:

1. What are the three processes involved in memory? 
2. What is the shape of the forgetting curve? 
3. How many items can be held in working memory at the same time? 
4. What is the capacity of long-term memory? 
5. Are there memories that we never forget?

The answers can be found at at the end of this post [1]. 

Wait...what was I going to say? 

Do you remember sliding down the memory curve? If not, it's okay. It’s been a while. Forgetting is a normal (and adaptive!) part of memory. Forgetting is non-linear, meaning it decays quickly and eventually slows down. If you plot it on a graph, then it might look something like this (see Fig. 1). The y-axis is the probability of successfully recalling a memory, and the x-axis is the amount of time that has elapsed since the last time you tried to recall that same memory. 

Figure 1. An idealized forgetting graph.

Notice the shape of the graph. It resembles a power function. In fact, most mathematical models of forgetting follow a power function, P = at^−b , where P is the probability of accurately recalling an item, t represents time, and b is the forgetting rate [2]. 

In another past post, we tried to address the question of why the forgetting curve looks like this. John Anderson and his colleague Lael Schooler put forth the argument that memory is adapted to our informational environment. We forget because the environment does not demand that we remember. Put another way, memory, and therefore forgetting, is a reflection of the environment. That's an interesting argument because it means we can structure the environment in such a way that guards against forgetting.

Inoculating Against Forgetting

If Anderson and Schooler's argument is accurate, what can we do to improve our memory? Burr Settles, Research Director at Duolingo, has an excellent suggestion. In his blog post, he suggests that we treat forgetting by administering little booster shots over time [3]. If you remember a vocabulary word accurately, then the system waits a longer time span than if you forget. If you forget, then the system asks you to recall that word more frequently. It's pretty ingenious, and it's an excellent example of using technology to solve a tricky educational problem.

The concept behind the recommendation is called retrieval practice. In other words, you give your students an opportunity to retrieve a word, concept, or fact from long-term memory. Merely attempting to recall an item ends up helping to boost that item's strength in memory. The critical component is that you try. If you fail, however, then you are going to need feedback (i.e., you need to see the item you were trying to recall). Retrieval practice has been shown to be more effective than rereading or reviewing the same material [4].

It seems weird, but that's how memory works. By the fact that you are trying to recall something signals to the memory system that this item is important, and that I need to remember it for next time.

The S.T.E.M. Connection

How do we harness Dr. Settle's suggestion in a classroom environment, where specific items (such as words) are not being tracked by a computer for each individual student? Is there a way to help teachers administer those memory booster shots to their students? 💉

The traditional method of teaching is to introduce a topic, solve a few illustrative problems that relate to that topic in class, assign some homework problems, and then give a test a few days or weeks later to see if the students retained the material. For highly important topics, the same items might make a reappearance on the final exam. Wouldn't the unit test and final exam count as a booster? 

Depending on the time series, probably not. There are two potential problems. First, if a topic hasn't been discussed in several weeks, then it is likely the memory system is going to treat that memory as unimportant, and it will find itself on the fast side of the forgetting curve. Second, if too much time elapses between the presentation and evaluation, then the probability of successful recall is going to be very low.

There are a couple of ways to combat this situation. First, if you are an educator, and you are in complete control over the homework items assigned to your students, then you can "sneak" an old item into the current problem set. The problem, of course, is that if you do this too often, then your inoculation graph might look like this:

Figure 2. Spaced practice for multiple items with different decay rates.

As you can see, this can get really messy, really fast. One way to deal with that complexity is to schedule homework assignments where all of the problems are review items.

Second, if your domain has facts or skills that build on older ideas, then students will automatically receive practice on the foundational material. Math is a great example. Learning about ratios can help students understand slope, which then leads into solving linear equations. By exercising the more complex skills, such as solving linear equations, student receive practice on ratio reasoning.

I understand that implementing these suggestions is difficult because there are a lot of factors at play in the classroom, but I hope it is helpful to think about forgetting in terms of multiple, overlapping power functions. With that image in mind, we can keep giving doses of anti-forgetting shots [5].

Share and Enjoy!

Dr. Bob

Going Beyond the Information Given

[1] Answers are: 1) encoding, storage, and retrieval; 2) it's a decelerating power curve; 3) between five and nine items; 4) extremely large; 5) there is evidence that we have permanent memories for some items.

[2] Of course, there is some debate about that. Two of undergraduate professors argue that the empirically observable power law might be an artifact of averaging over multiple exponential functions. I know. Your mind is blown, right? Mine was too when I first heard their argument. All of the gory details can be found in: Anderson, R. B. & Tweney, R. D. (1997). Artifactual power curves in forgetting. Memory & Cognition, 25, 724–730.

[3] Burr Settles, B. (2016, December 14) How we learn how you learn. Retrieved from https://making.duolingo.com/how-we-learn-how-you-learn.

[4] Roediger III, H. L., & Butler, A. C. (2011). The critical role of retrieval practice in long-term retention. Trends in cognitive sciences, 15(1), 20-27.

[5] If you've been following this blog, you might notice that booster shots show up every so often. This post is at attempt to boost your memory of the forgetting curve and the environmental factors that influence memory!