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! 

Criss Cross: Aptitude by Treatment Interaction

Learning By Doing

 Let's play a fun game called Guess Which One. The answers are provided in the next section. No cheating! 

1. Guess which list of word-pairs has more accurate recall:
     A. A list provided by an experimenter.
     B. A list that you personally generated.

2. Guess which study method leads to deeper learning:
     A. Re-reading the material
     B. Testing yourself on the material you just read.

3. Guess which instructional method is better: 
     A. One-on-one human tutoring
     B. An intelligent tutoring system (i.e., a computer tutor)

4. Guess which study strategy is more effective: 
     A. Paraphrasing an expository text
     B. Self-explaining an expository text

5. Guess which type of text leads to a better understanding of the subject matter: 
     A. A minimally coherent text
     B. A globally coherent text

"Criss cross" –Owen, Throw Momma From the Train

If you've been reading this blog for a while now, you may have noticed that some answers have been discussed in previous posts.

1. The generation effect would predict that personally generated items are more memorable than those provided by someone else; therefore, the answer is A. 

2. The research on desirable difficulties predicts that students are better off quizzing themselves than re-reading the material. The best answer is A. 

3. This is a tough one. If you believe the early research on Intelligent Tutoring Systems, humans were the gold standard. But then Kurt VanLehn called that conclusion into question. The answer is A (but I'll accept B if you cite VanLehn, 2011). 

4. The research on self-explaining pretty clearly indicates that students learn more when they self-explain because they are using their background knowledge and reasoning to repair their flawed mental models. The answer is unequivocally B.

5. The answer is A or B. Wait, what? That's right! The answer to #5 is "it depends." This post is about the conditions upon which learning outcomes depend. Read on.

The Aptitude x Treatment Interaction

To better understand what's going on with the fifth question, let's take a step back and talk a little bit about research methodology. One of the most common experimental studies is to contrast the outcome of an experimental group with a control group. But instead of just comparing the outcomes of an experimental condition with a control condition, you have two levels of each independent variable. 

To make this more concrete, suppose you hypothesize that listening to music hurts learning performance. However, you don't think that all music hurts. Instead, you hypothesize that lyrically complex music hurts learning lists of words; whereas, instrumental music doesn't have any impact at all. 

To test your hypothesis, you design a study where there are two types of music and two types of lists to memorize. For the musical manipulation, you play a lyrically complex song versus techno music without any words. For the item manipulation, the first is a list of only words, and the second list only contains numbers. When you run this experiment, you plot the results with a line graph (see Figure 1). 

Figure 1: A cross-over interaction between music type and item type. 

Notice that the impact of music depends on the interaction between the type of music and the item type. If you listen to techno music, then there isn't any improvement or cost to recall. If you listen to lyrically complex music, then you get a little boost when memorizing lists of numbers. But if you listen to a song with lyrics, then it completely wipes out a participant's ability to memorize words. 

Said another way, there is a music-by-item interaction. When we talk about learning manipulations, we need to be sensitive to potential interactions between a student's aptitude and the learning situation they are in. Why? Because their learning outcomes might depend on it! 

Going back to our rousing game of Guess Which One, the answer to question #5 is "it depends" because students who have lots of background knowledge learn better from a minimally coherent text while students who do not have the same background knowledge learn better from a globally coherent text [1]. In other words, there is an aptitude (i.e., high vs. low background knowledge) by treatment (i.e., high vs. low textual coherence) interaction.

Students with a large amount of background knowledge are better served by minimally coherent texts because they must supply the missing information. They need to do more generative work while reading the text. As we have seen in other contexts, being generative during learning is beneficial for deep learning. The low-prior knowledge students, however, require a maximally coherent text because they lack the background knowledge to generate the connections. Therefore, they need more support and scaffolding when learning a new topic. 

The S.T.E.M. Connection

The above finding underscores how important both formative assessments and personalized learning environments are. In theory, if a teacher had enough data to diagnose how well each student understood a topic, then they could assign each student a different text. A knowledgeable student would get a minimally coherent text, while a low-knowledge student would get a maximally coherent text. 

Unfortunately, in practice, things are much more tricky. It would be a lot to ask a teacher to come up with two (or more) versions of a textbook. However, some labs are applying latent semantic analysis (LSA) to help match a given student to a particular version of a text [2]. The goal is to select a text that maximizes the reading comprehension for a particular student. This is an exciting area of research and one to keep an eye on as more textbooks are distributed digitally.

Someday, perhaps we can synthesize all of the (right) answers to Guess Which One and develop a learning platform that can handle the multitude of interactions between all of the variables that influence learning. That would be extremely powerful (and wouldn't require anyone to be thrown from a train!).


Share and Enjoy!

Dr. Bob

Going Beyond the Information Given

[1]  McNamara, D. S., Kintsch, E., Songer, N. B., & Kintsch, W. (1996). Are good texts always better? Interactions of text coherence, background knowledge, and levels of understanding in learning from text. Cognition and Instruction, 14(1), 1-43.

[2] Wolfe, M. B., Schreiner, M. E., Rehder, B., Laham, D., Foltz, P. W., Kintsch, W., & Landauer, T. K. (1998). Learning from text: Matching readers and texts by latent semantic analysis. Discourse Processes, 25(2-3), 309-336.

Why Do I Need to Know This?: The Classic Student Lament

Learning By Doing

Read the following passage, and do your best to remember all the essential information. And before you ask...yes, there will be a quiz at the end. Good luck!

The procedure is really quite simple. First you arrange things into different groups depending on their makeup. Of course, one pile may be sufficient depending on how much there is to do. If you have to go somewhere else due to lack of facilities that is the next step, otherwise you are pretty well set. It is important not to overdo any particular endeavor. That is, it is better to do too few things at once than to do many. In the short run this may not seem important, but complications from doing too many can easily arise. A mistake can be expensive as well. The manipulation of the appropriate mechamism should be self-explanatory, and we need not dwell on it here. At first the whole procedure will seem complicated. Soon, however, it will become just another facet of life. It is difficult to foresee any end to the necessity for this task in the immediate future, but then one never can tell.

Pop Quiz:

1. What is the first step?
2. What is the second step?
3. What might happen if you do too many things at once?
4. How will you know when you are done? 

Once you have taken a shot at answering the questions, feel free to look back at the passage to check your answers. If you had a difficult time with the quiz, why did you struggle? What was it about the passage that was hard to comprehend? What would have made it easier? When you were reading, did you stop and wonder, "What is the point of this?"

If you are an educator, then you have probably been asked, "Why do I need to know this?" or some variation therein [1]. How did you respond? Is there a reasonable answer to this question, and one that makes sense to a novice? In the post that follows, we will look at two possible responses.

Response #1: Remember there are no stupid questions, just stupid people. – Mr. Garrison, South Park

An easy, knee-jerk reaction to declare it a stupid question. Or, you could respond by saying: 

• You need to know this because any bright, upstanding student in a modern world should know these things. 
• As a voting citizen, you need to be informed of certain facts and have the ability to critically evaluate politicians' claims. 
• You don't want to be tricked as a consumer, and you should want to be able to make informed decisions.
• Or, perhaps the worst response of all: Because I said so!

Honestly, it might be impossible for you to answer the question because, as an educator, you might not know what the future holds for your students. 

For example, there is currently a huge demand for Data Scientists. As of this writing, there were 31,913 results when I searched for "data scientist" in the Jobs section of LinkedIn [2]. Every major corporation is interested in hiring someone who can apply Machine Learning to help solve their business problems. In fact, the concept of Deep Learning wasn't possible until about 10 years ago, and the advances since then have continued to accelerated. Therefore, it would be especially difficult to explain to a student that they need to know something when the technology that draws upon that body of knowledge hasn't been invented yet. Who knows what the hot job title is going to be in 10 years from now?

One way to address the Student Lament is to appeal to the unknown future and explain that knowledge is cumulative, and that there exists a prerequisite structure wherein higher-order concepts build upon foundational knowledge. For example, to understand Machine Learning it helps to know linear regression. If you want to tackle linear regression, then you might want to learn how to solve linear equations. To solve linear equations, it might help to understand ratios...and so on until you get to the most basic principles of counting.

Response #2: Always the beautiful answer who asks a more beautiful question. –E. E. Cummings

A second response to the Student Lament is that it is exactly the right question to ask, and students should never cease asking why they need to know something. Let's look back at the passage that opened this post. When you read it, did you feel like something was missing? What got in your way of comprehending the text?

In the original study that used this passage, the authors had three experimental conditions [3]. In the baseline condition, the authors had participants listen to the passage, and then they answered some recall and comprehension questions. As you might imagine, they did terribly. The second condition gave them a title to the passage, which was "Doing Laundry," only after they heard the passage. This group didn't fare any better than the baseline condition. However, the third condition was given the title before they heard the passage. That group did the best. Why? Because they had some context about what the passage was about. Providing the context allowed the participants to better comprehend what was being said.


The same is true for our students. They will most certainly do better if they understand how the current lesson fits in with the overall content of the course. It also helps to provide context because then they can draw upon their prior knowledge to better comprehend the current lesson. The passage about laundry is purposefully written so that the listener has to fill in the gaps with their prior knowledge.

The S.T.E.M. Connection

The goal of this exercise is to simulate being a clueless student, which should (hopefully) increase our empathy towards their plight of learning something new. How might that change our instruction? One simple method is to use a warm-up task. You can ask your students to work on a task that is a prerequisite to the upcoming Lesson. You could also show a curriculum map, and indicate where they currently are, and show where they are going. With the right visualization, this could be extremely empowering to the student because they can chart their progress through the sequence. It might also help them see connections between (seemingly) disparate concepts and ideas. 

As the passage that opened this post stated, "It is difficult to foresee any end to the necessity for this task in the immediate future." While certainly true for laundry, it might also be true for lesson planning!


Share and Enjoy!

Dr. Bob

Going Beyond the Information Given

[1] Another personal favorite is, "Is this going to be on the test?" Apparently, knowledge is only worthwhile unless one is tested on it!

[2] https://www.linkedin.com/jobs/search/?keywords=data%20scientist 

[3] Bransford, J. D., & Johnson, M. K. (1972). Contextual prerequisites for understanding: Some investigations of comprehension and recall. Journal of Verbal Learning and Verbal Behavior, 11(6), 717-726.

Reading Room Material: Misbehaving

Your Tank is Empty

You glance down at your gas gauge. You're coasting on fumes. Time to fill 'er up! There are two gas stations across the street from each other. Which gas station would you choose? 

Gas Station A: The price for gas is $2.45 if you pay with cash, and a $0.05 surcharge for using a credit card.

Gas Station B: The price for gas is $2.50 for using a credit card, and a $0.05 discount for paying with cash. 

What is "Behavioral Economics?"

I'm not sure if this is apocryphal or not, but I believe Hitler famously asked, "Guns or butter?" [1] At first glance, his statement seems like a false dichotomy. But if you dig a little deeper, you find that the common denominator is nitrogen. You can either turn nitrates into gun powder or you can convert them into fertilizer [2].

What does "guns and butter" have to do with Economics? Simply put, Economics is the scientific examination of making decisions when resources are scarce. In a world of finite resources, you have to pick. Do you want guns and tanks, or do you want plows and tractors? You can't have both, so you have to choose.

Where, then, does the "behavioral" aspect of behavioral economics come into play? I'm glad you asked because Dr. Richard Thaler, author of the book Misbehaving, has a terrific answer [3].

What's the Big Idea? 

Before delving into Dr. Thaler's big idea, a little context is necessary. Every scientific theory is based on a few core assumptions. Economics is no different. Neoclassical Economics assumes that people are rational and are able to make optimal decisions to further their own agenda. In other words, I know what makes my life worth living. It might be different from yours, but we both are able to decide what's best for ourselves. In economic jargon, we are experts at maximizing our own utility (read: "happiness"). For simplicity, Thaler refers to these rational types of people as Econs.

Assuming people are rational, various factors are deemed irrelevant when making decisions. In the scenario that opened this post, both options should be equally appealing to an Econ. If we observed Econs filling up their cars, about half of them would choose Station A and the other half would choose Station B. 

But what do we observe when we watch Humans purchase gas? Which gas station would you purchase gas from? Gas stations that offered a surcharge on credit cards quickly learn that humans overwhelmingly prefer discounts.

Thaler's book is chocked full of big ideas. Probably the biggest among them is the idea that economic theory is based on the faulty assumption that we are Econs instead of Humans. Unfortunately for Neoclassical Economics, humans are swayed by supposedly irrelevant factors, or "SIFs" for short.

The Big SIF: The Sunk Cost Fallacy

What's an example of a SIF? Personally, one of the hardest lessons for me to learn was to ignore "sunk costs." I bet this has happened to you, so I'm sure you can sympathize. A couple of years ago, I bought a ticket to a brew festival. The lineup of craft brewers was incredible, and I was excited to try some new libations. But on the day of the beer fest, I came down with fever. I tried to coax myself to go. I couldn't let all that money go to waste! But then a lesson from college came back to haunt me. That money is gone. I can't jeopardize my health because that would be considered, "throwing good money after bad." In the end, I had to stay home (and ignore the sunk cost of my ticket!). 

The sunk cost fallacy is just one example of many SIFs that Dr. Thaler describes and had a hand in discovering. By the end of the book, you are left wondering how Economist can continue to believe in a rational individual. More importantly, How must economic theory change to accommodate these SIFs? I guess it's up to us misbehaving Humans to figure it out. 


Share and Enjoy!

Dr. Bob

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[1] According to the all-knowing wikipedia, it looks like Hitler didn't coin the term, but the Nazis did use the concept of "guns or butter" in their propaganda. 

[2] Making decisions on a stingy planet also calls to mind our discussion on Opportunity Costs.

[3] Thaler, R. H. (2015). Misbehaving: The making of behavioral economics. WW Norton & Company.