The Struggle Is Real: Productive Struggle

Learning By Doing

Let's get this party started with a fun little puzzle. You may have seen this on your favorite social media platform [1]. 

See if you can solve it.

Struggling Productively

That was a difficult problem, right? Would you say you "struggled" while attempting to solve it? I know I did! This experience raises a couple of questions:

1. What, exactly, causes us to struggle?

2. When does struggling assist learning, and when does it harm learning? 

3. Under what conditions does struggling lead to long-term learning and transfer? 

Before we attempt to answer these questions, let's acknowledge the emotional components of struggling. I can only speak for myself, but phenomenologically, it doesn't always feel great. I get hot. I feel dumb. Intrusive thoughts distract me from the task-at-hand. Of course, if your working memory is loaded with these intrusive thoughts, then you have fewer resources to dedicate to the current task...which will ultimately cause you to fail!

Sources of Struggle

What causes us to struggle? 

Prior Knowledge: First, we may not have all of the prerequisite knowledge to solve the problem. Once we recognize this fact (hopefully earlier rather than later!), then we can treat it as a quest to find the missing information. 

Incorrect Assumptions: Another reason why we might struggle is because we've made an incorrect assumption. If you assume that a fox and wolf weigh the same, then you will eventually run into a road-block when solving the above problem. 

Unnecessary Problem Constraints: We might struggle because we imposed an unnecessary constraint on the problem. This often happens while solving an insight problem. For example, in the classic nine-dot problem, problem solvers unnecessarily add the constraint that they are not allowed to go beyond the edge of the box. 

Flawed Representation: Finally, we may have chosen a flawed or limited representation. We've seen time and again how important representations are for solving problems. For example, students fail to calculate the area of a parallelogram when presented outside of the canonical orientation (i.e., laying flat along the long side).

What makes struggling "productive?"

According to James Hiebert and Douglas Grouws's book chapter [2], productive struggle happens when a student is working on a problem just outside of their current ability level. This is related to Lev Vygotsky's idea of the "zone of proximal development" (see Fig. 1). 

There are things that you can do autonomously. These are well-practiced skills or declarative knowledge that you've mastered previously. There is also a bunch of things you can't do (at least not yet!). But in between those two spheres are things that you can do with some assistance.

Struggle is most productive when done under the watchful eye of a more knowledgeable partner. They are there to step in and nudge the novice in the right direction. 

Figure 1. Vygotsky's three zones, with the middle as the "zone of proximal development."

Struggle, then, is maximally helpful for several reasons. 

It allows students to appreciate the context of the lesson. If you just give a lecture on solving systems of equations, then the student may not have any appreciation for why systems of equations is a powerful problem-solving technique. However, if you first let them try to figure out how to calculate the weight of the chicken, fox, and wolf, then they might see the utility of systems of equations.

If a student is lacking a key piece of information, then struggling to solve a problem may expose a gap in their knowledge. An impasse in problem solving might force a student to confront the possibility that there is something wrong with their understanding [3]. 

There may be some small amount of discovery involved. For example, there are are (at least) three key insights when solving this animal weight problem: using variables (x, y, & z) instead of animals, isolating a variable for each of the three known weights, and finally substituting the isolated variables into the other equations. Having a key insight or making a discovery is highly motivating.

That brings us to the final reason. Struggle is useful because it necessarily engages a student's conceptual understanding. For any of the three key insights, there is a rich conversation that can connect back to knowledge that a student already possesses (e.g., the concept of a "variable," isolating a variable, variable substitution, and mathematical equivalence). 

The Classroom Connection

Struggling doesn't have to be fraught with negative emotions. In some contexts, struggling is actually kind of fun. Think about the last video game you played. Games are specifically designed to cause you to struggle. In fact, there is some research to suggest that players actually enjoy dying (the ultimate failure!) in first-person shooter games more than shooting other players [4]. Another example is a well-written mystery. You may struggle to figure out "who dun it," but it is an entirely enjoyable experience. It would be beneficial to everyone if academic tasks that cause us to struggle to be structured in a way that is more like a game, puzzle, or mystery. 

Perhaps our struggle as educators and instructional designers, is to figure out how to make struggling an enjoyable educational experience! 🧩


Share and Enjoy!

Dr. Bob

Going Beyond the Information Given

[1] I adapted this problem from Sara Van Der Werf's blog, and you can follow her on twitter @saravdwerf. This might also be a good time to link back to our prior conversation about problem isomorphs.

[2] Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. Second handbook of research on mathematics teaching and learning, 371-404.

[3] VanLehn, K. (1988). Toward a theory of impasse-driven learning. In Learning issues for intelligent tutoring systems (pp. 19-41). Springer, New York, NY.

[4] Ravaja, N., Turpeinen, M., Saari, T., Puttonen, S., & Keltikangas-Järvinen, L. (2008). The psychophysiology of James Bond: Phasic emotional responses to violent video game events. Emotion, 8(1), 114-120. https://doi.org/10.1037/1528-3542.8.1.114

The Mind’s CEO: Executive Function

Learning By Doing

Let's play a game. It's super fun...I promise! Download and print this file. Your goal is to cross out all of the lower case d's with two dots above it. Try to be as fast and accurate as possible. Don't forget to time yourself. Ready? Go! [1]

Back to the Front

Stop me if you've heard this one. The left hemisphere of your brain is responsible for logical processing; the right hemisphere is designed for creative and wholistic thinking. While there may be a tiny grain of truth to these over-generalizations, there is a much less talked about difference in brain functioning. As you go from the back of the brain to the front, thinking goes from extremely concrete to highly abstract. 

That's right! The very back of your brain is reserved for visual processing and low-level muscle control. But as you move forward, toward your forehead and eyes, thinking becomes much more complex. This is the location of higher-order thinking skills such as planning, organizing, and problem solving. This area of the brain called the pre-frontal cortex. This is where you will find executive functioning.

Executive function includes several different cognitive processes. They include, but are not limited to, working memory, response suppression, and attentional focus. 

Working Memory

Baddeley's model of working memory features three components (see Fig. 1). There are two slave systems — the visuospatial sketchpad and the articulatory loop — and a central executive. The central executive controls the operation of the slaves systems. It can store and retrieve information from each slave system, and it can also re-represent the same piece of information in different forms (e.g., translating a piece of an image into a word, or vice versa). 

In other words, the central executive must make decisions about the relevance of information and how best to represent it. It must also decide which information needs to be refreshed and maintained in working memory and which information can be safely discarded.

Figure 1. Baddeley's model of working memory.

Response Suppression

We all know how difficult it is for some people to suppress the urge to respond in certain situations. Below are several examples of response suppression, categorized by the domains in which they were found:

Popular Culture: Response suppression failure has made its way into movies (e.g., Roger Rabbit cannot contain himself when faced with the old "shave and a haircut trick") and games. In a previous post on Ironic Processing, we talked about the frustration inherit in the game of Taboo!.

Psychology: We also see examples of response suppression in the materials used in cognitive psychology. The Stroop task is a classic example because, in one variant of the task (i.e., when the color of ink and word conflict), you must suppress the urge to read the word and name the color of ink. 

Neuroscience: The frontal lobe (i.e., the seat of executive functioning), is responsible for response suppression. There is a really interesting example from neuroscience where Phineas Gage had his fontal lobe damaged. After his accident, he became something of a jerk. His behavior strongly suggested that he could not suppress his urges.

Classroom: Response suppression in the classroom is very real, and it can take on many different forms. Behaviorally, little kids (eventually) learn that they must raise their hand before blurting out the answer to the teacher's question. 

A more cognitive example can be found in the world's shortest IQ test: 

1. A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost? _____ cents

When confronted with a question like this, you may feel the need to suppress your intuitive answer (10 cents) and apply your knowledge of algebra to determine the answer ((b+100) + b = 110). In this case, the fast answer isn't the right answer [2].

Attentional Focus 

In a previous post, we talked about the "myth of multitasking." Most people think they can do multiple things at once, but there are severe limitations. You might be able to walk, talk, and chew gum, but you won't be able to listen to a lecture, deeply process the contents, and simultaneously take notes. People are serial processors (as opposed to "parallel processors"). A useful metaphor for attention is that it is a spotlight, and it can only shine on one thing at at time. 

As serial processors, we need to make decisions about which stimuli to pay attention to. This is where executive functioning comes into play. When an alert goes off on our phone, we have to decide to pay attention to it (or not). Unfortunately, that "decision" isn't really a decision anymore. Over time, we become conditioned to immediately abandon what we were thinking about and look at our phone. In other words, we have trained our attentional system to give our phone primary status. Ideally, we would structure our learning environment so that it removes unnecessary distractions. Keeping cellphones on "Do not disturb" mode and out of view is the best way to prevent our attention from being captured.

Attentional distraction can also be internally generated. For example, if you are a minority, and you are reminded of your minority status, perhaps because of an off-hand comment or some other feature in the environment (i.e., you are the only one of your group), then those distracting thoughts can pull attention away from the task at hand. This phenomenon is called stereotype threat, and it has pernicious effects on performance [1].

The final example of attentional focus is on information within a task. Suppose you are asked to solve the following problem: 

Derek has 4 action-adventure video games and 9 board games. Desi has 3 role-playing video games and 2 lawn games. If they combine their games, how many video games do Derek and Desi have? 

Notice that this problem has some very tempting, but completely irrelevant, information. One skill that students need to learn is to ignore the distracting information as they solve the problem. Some teachers might recommend highlighting the relevant information (or crossing out the irrelevant information). The goal is to help the attentional system stay focused on the relevant bits.

The Classroom Connection

How can we structure the classroom environment to support the development of executive functioning? Here are a few recommendations:  

1. We should strive to limit the number of distractions in the classroom. Put smartphones away and out of sight. 
2. If the mode of instruction is primarily a lecture, then tell your students not to take notes during the lecture [2]. Instead, ask that they listen to what you are saying. After class is over, students should then be given a chance to write down everything they remember. I assume this is a controversial recommendation, so expect students to push back.
3. Response suppression and attentional focus are both skills that can be learned. One way to develop these skills is mindfulness training, which is starting to gain some empirical support [4]. 

In summary, executive function is a critical component to higher-order thinking and reasoning. In other words, it definitely deserves the corner office! 

Share and Enjoy!

Dr. Bob

Going Beyond the Information Given

[1] This "game" is a test of executive function because you have to hold in working memory the symbol-to-match. The stimuli were created to be highly confusable; therefore, you must suppress certain responses (e.g., the "d" with only a single dot above it, or a "d" with two dots below it). I heavily borrowed the design from the "d2" test of executive function: Lyons, E. M., Simms, N., Begolli, K. N., & Richland, L. E. (2018). Stereotype threat effects on learning from a cognitively demanding mathematics lesson. Cognitive science, 42(2), 678-690.

[2] The "intuitive" versus "algebraic" answer is a good example of the distinction Daniel Kahneman makes in his book Thinking, Fast and Slow. 

[3] I was fortunate enough to take a course from Herbert A. Simon. He didn't let us take notes during his lectures precisely because we are serial processors. In other words, he applied the findings from cognitive science (a field he helped start!) to his own class. 

[4] Bellinger, D. B., DeCaro, M. S., & Ralston, P. A. (2015). Mindfulness, anxiety, and high-stakes mathematics performance in the laboratory and classroom. Consciousness and cognition, 37, 123-132.

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.

How to Build an Atom: Analogical Reasoning

Learning By Doing

You are leading a siege on the most fortified castle in the land. Your army is ready to attack, but just at the last minute you notice that sending all of your soldiers across the wooden bridge will collapse it. How will you attack the castle, without your army being eaten by the mote-dwelling alligators?

Fast forward a few hundred years. You are now a world-class oncologist, and you are working with a new technology to treat cancer. It's called a "gamma knife" because it uses gamma rays to kill cancerous cells. At high energy levels, a gamma ray will destroy healthy tissue. At low energy levels, it can't knock out the cancer. How can you use the gamma knife to destroy the cancerous cells, without harming the surrounding tissue? 

Did you solve each of the problems? If so, how did you solve them? (Note: the image for this blog was meant to serve as a hint.) Did you notice a similarity between the two scenarios? Did the second scenario help with the first (or vice versa)? This famous analogical problem was originally stated by Mary Gick and Keith Holyoak in 1980 [1].

Nucleus : Sun :: Electrons : Planets

Much of our problem solving is done analogically. We see a problem, and when we're lucky, it might remind us of a similar problem we've solved in the past. If a true relationship exists, then we can extrapolate from the past to the current problem. The history of science contains several illuminating examples of this process.

Take, for instance, Ernest Rutherford's model of the atom that he proposed in 1911 [2]. Knowing that the atom was made up of protons, neutrons, and electrons, he took what he knew about the solar system (i.e., the base), and applied the same logic to the structure of the atom (i.e., the target). The proton and neutron were found at the center of the atom, much like the sun sits at the center of the solar system. The electrons revolved around the nucleus in a manner similar to the planets revolving around the sun. In other words, Rutherford saw a mapping between the atomic nucleus and the sun and the electrons and planets (see Figure 1).

Figure 1: The analogical mapping between the solar system and the atom

Notice, however, that there are some properties of the solar system that he did not map onto the atomic structure. For instance, the sun gives off an intense amount of heat and might be considered "yellow." Nowhere in this theorizing did Rutherford claim that the nucleus gave off heat or is "yellow." That means Rutherford was sensitive to the properties and relationships between the two systems. He knew that some of the properties of the base domain (i.e., the solar system) should not map onto the target domain (i.e., the atom).

"Hey! That thing gotta hemi?"

To better understand the psychological processes used during analogical reasoning, Dedre Genter and her colleagues built a computational model called The Stucture Mapping Engine (SME) [3]. One of the key features of the SME is the emphasis that it places on relations instead of features. 

Let's take electricity for example. In the early days, when scientists were trying to make sense of the concept of electricity, they likened it to something they understood quite well: the flow of water. The analogy is that electrons are like water and they move from one location to another. A battery is like a reservoir, and gravity is like the difference in electrical potential. The SME looks for alignments between the relations in the base and target domains. For example, it sees a commonality between two different types of FORCES (i.e., gravity vs. electrical potential) and two different types of ENTITIES (i.e., water vs. electrons).

It necessarily throws out the surface-level features that are irrelevant to understanding how electricity works. For example, one feature of water is that it is blue. Since this is a feature and not a relation, the SME does not transfer the features water is blue or water is wet onto electrons.

The S.T.E.M. Connection

There are several learning studies that explicitly instruct students to do their own analogical comparisons between two sources of information. For example, my friend and collaborator, Tim Nokes-Malach and Dan Belenky, explicitly trained students in a physics class to compare worked-out examples of rotational kinematics problems. The students had to answer questions such as: 

• What is similar and what is different across the two problems?
• Are there differences in what the two problems ask for in terms of acceleration? If so, what are they?

The goal was to motivate the students to compare and contrast the two examples, with the hope that the students could then see the mappings between the relations of the two examples. In their study, the authors demonstrated doing this analogical comparison led to better performance on far transfer problems. 

This kind of intervention could be done for many topics. The goal, of course, is to show how relations in the base domain map onto the target domain. It's also relevant to talk about how the features of the base and target domains don't necessarily have to align. 

Analogical reasoning is extremely powerful because it can extend the knowledge that we have into the unknown. It can help us draw upon the knowledge we have from previous problems we've solved and apply that knowledge to problems we've never seen before. That's pretty cool (analogically speaking, of course). 


Share and Enjoy!

Dr. Bob

Going Beyond the Information Given

[1]  Gick, M. L., & Holyoak, K. J. (1980). Analogical problem solving. Cognitive psychology, 12(3), 306-355.

[2] Allain, R. (Sept. 9, 2009) The development of the atomic model. Retrieved from https://www.wired.com/2009/09/the-development-of-the-atomic-model.

[3] No, the structure mapping engine doesn't gotta hemi, but it does a pretty good job modeling the analogical processes that humans use! Check out their original paper: Falkenhainer, B., Forbus, K. D., & Gentner, D. (1989). The structure-mapping engine: Algorithm and examples. Artificial intelligence, 41(1), 1-63.

[4] Nokes-Malach, T. J., VanLehn, K., Belenky, D. M., Lichtenstein, M., & Cox, G. (2013). Coordinating principles and examples through analogy and self-explanation. European Journal of Psychology of Education, 28(4), 1237-1263.

Stuck In a Rut: Einstellung and Mental Set

Practicing the Water Jar Problem...With a Vengeance!

If you are into puzzles, this one might sound familiar because it's been around for about 70 years [1]. It is so famous that it was actually used in the movie Die Hard: With a Vengeance [2]. In the movie, the two main characters are attempting to save a school full of children from being blown up while the bad guy has them solving some seriously challenging problems all over the city. To make sure you are prepared if you ever find yourself in this situation, you can get some practice by working through the problems below.

Your goal is to measure out a precise amount of water, given three empty jars. The first problem is a warm-up with only two jars. Jar A holds 29 units of water, and Jar B holds 3 units. Your goal is to measure out 20 units of water exactly. How do you do that? First, you fill Jar A completely. Then you use Jar A to fill Jar B three times (i.e., 3 units x 3 refills = 9 total units). After you fill Jar B three times, you are left with 20 units of water (29 units - 9 units = 20 units).

Now it's your turn [3]. Use the interactive widget to solve problems 2 through 11. (Hint: be sure to empty a Jar before attempting to refill it.)

A: 21

B: 127

C: 3

Target: 100

0

0

0

Einstellung: The Mechanization of Thought

While solving the problems, did you notice a general pattern that started to emerge? They all followed a standard solution template, namely: Fill B, then use B to fill A, and then use B to fill C twice. Stated symbolically, it might look like this: B-A-2C. That seems to work really well until you hit Problem 9, but it works for all the other problems (e.g., Problems 2-8, 10-11).

If you have been reading this blog for a while, then you probably guessed there must be a twist. Indeed there is. The twist is that, even though the B-A-2C pattern works for all but Problem 9, there is a more efficient solution for Problems 7-11. Go back and see if you can figure out it [4]. 

If you used the B-A-2C algorithm for any of the problems past 6, then you fell prey to Einstellung, or the "mechanization of thought." How does this happen? When you approach a new problem for the first time, and you don't know what to do, you start applying general problem-solving heuristics. Once you have some success with a solution strategy, you try it again. Lo and behold, it works! You are rewarded by applying the same algorithm over and over. This sets up a mental bias against trying new solution strategies. It is almost like a set of mental blinders.

Mental Set

Einstellung occurs when you create a solution strategy where none existed previously, and you keep using it as you try to solve new problems. In this case, the knowledge that is hindering you from trying new problem-solving tactics is currently held in working memory. Can our prior knowledge, stored in long-term memory, have similar effects? Consider the following brain teasers [5]:

1. The 22nd and 24th presidents of the United States had the same mother and the same father, but were not brothers. How could this be?
2. Picture two plastic jugs filled with water. How could you put all of this water into a barrel, without adding the jugs or any divider to the barrel, and still tell which water came from which jug?
3. As I was going to St. Ives, / I met a man with seven wives. / Every wife had seven sacks, / Every sack had seven cats, / Every cat had seven kittens. / Kittens, cats, sacks, wives, / How many were going to St. Ives?

If these questions tripped you up, it's likely that your prior knowledge artificially created a constraint that did not exist in the problem itself. For example, the first question is tricky because the wording of the question caused you to activate your knowledge of your concept of brother. That concept requires two or more people. Once you recognize that you have made a faulty assumption, that the 22nd and 24th president were two different people, then you can easily solve the problem. 

When prior knowledge causes us to be blind to our own assumptions, we call that a mental set. We might blame a mental set for a problem that we encountered in a previous post where we were trying to arrange matchsticks to form four equilateral triangles.

The STEM Connection

How do you avoid getting stuck in a mental rut? How can you help your students avoid set effects? 

Fortunately, the recommendation for avoiding Einstellung is somewhat simple. In the original study, the experimenters noticed that the participants were surprised when they were shown the more efficient solutions. Their reactions included: "How stupid of me" and "How blind I was." The experimenters decided to re-run the experiment, but this time they reminded the second batch of participants: Don't be blind! This advice was effective because problem solvers adopted the more efficient solution at a much higher rate than the first batch of volunteers. Our advice should be the same to our students. Remind them that there may be a more efficient solution lurking out there, just waiting to be discovered. 

Another way to avoid Einstellung is to walk away from the problem and return after some time has passed. The goal is to let all of those items in working memory lose their activation so you come back to the problem with a fresh pair of eyes (and a clean working memory!). 

Avoiding mental set is a little more tricky because prior knowledge is almost always useful. We don't want to encourage our students to forget what they know because that would run completely counter to our educational mission! This is probably easier said than done, but I think the advice here is to be open to your prior knowledge, but just don't be constrained by it. In other words, we should be neither blind nor self-constrained!

Share and Enjoy!

Dr. Bob

For More Information

[1] Luchins, A. S. (1942). Mechanization in problem solving: the effect of Einstellung. Psychological Monographs, 54(No. 248).

[2] In the movie, the main characters had to measure out four gallons of water using a 5- and a 3-gallon jug. Here is the problem statement and its solution. 

[3] Another special thanks to Josh Fisher for creating the interactive version of the Luchins water jar problem. 

[4] It turns out that they can be solved by completely ignoring B and adding or subtracting A and C. Problems 7, 9, 11 all use A-C; and Problems 8 & 10 both use A+C. 

[5] I stole the first two brain teasers from a card game that we own called MindTrap. If you like these kind of puzzles, then you might enjoy this game. The third was stolen from Simon Gruber from Die Hard.

The Downside of Expertise: Part 1

Editorial Note: I am so excited about the next topic that I had to split it across two posts. For Part 1, I introduce the idea that, while expertise is great, there is a cost associated with it. In Part 2, I will talk about the origin of research on expertise and its educational implications. Let's jump in with a real mind scrambler!

The Backwards Brain Bicycle 

Grab a junky bike and pull the handlebars and stem out of the steerer tube. Next, weld one gear onto the steerer tube and another gear onto the stem (the stem is the piece connected to the handlebars). Once you're done, it should look like this:

Due to your modification, when you turn the handlebars to the right, the front wheel pivots to the left (and vice versa). Before you embark on your maiden voyage, what do you suppose will happen? If you're not sure, take a look at this fascinating video.

What happened to this poor engineer? Why did it take him eight months to learn how to ride his "backwards brain bicycle"? The answer to that question is related to why a softball pitcher can reliably strike out the best batters from Major League Baseball (MLB).

"Swing and a miss" --Harry Doyle

In MLB, there is a distance of exactly 60.5 feet between the pitcher's mound and home plate. When a pitcher throws a 95 mph fastball, the ball arrives in a little less than half a second (.43 seconds, to be precise). That means the batter needs to decide whether he should swing (or not) in about a quarter of a second. Otherwise, the ball will blow past him as he stands there and ponders whether he should swing. 

Because it truly is a split-second decision, the batter must look for an edge. One place to find an edge is to move upwards in the stream of events and find a reliable cue for swinging. One of the cues that batters use is the pitcher's grip on the ball. If they hold it with two fingers over the top, then it is a fastball. If they put more distance between their forefinger and the thumb, then it will be a curve ball. The other cue that batters look for is the spin on the ball, which transmits itself as a certain "color" of pitch. 

MLB players log thousands of hours behind the plate trying to hone their batting ability. In effect, they become experts in watching, categorizing, and reacting to a variety of different pitches. So if they truly are expert batters, then why can softball pitcher Jennie Finch strike out batting legends Barry Bonds and Albert Pujols? [1]

The explanation is fairly simple. Expertise is highly narrow. When faced with a typical softball pitch, MLB batters are watching for something that will never come. They've essentially wired their brain to perceive and react (without much conscious intervention, mind you) to a highly narrow band of stimuli. Because overhand pitches used in MLB tend to fall, the batter watches for a ball that starts high and gets pulled to the ground. A softball pitcher throws underhand, so the ball starts low and has the possibility of rising. They also are watching for the aforementioned cues of the pitcher's grip and the spin on the ball, but the grip that a softball pitcher uses is completely different. By changing the narrow band of stimuli that a batter is trained to read, you can essentially reduce and expert batter to a novice, or possibly even worse.

But let's stop talking about muscular expertise. What about conceptual expertise? Are there any hidden costs there?

Looking in All the Wrong Places

Another way in which expertise can steer a person wrong is by biasing her to look for solutions within the prescribed content area of her specialty. Consider the following experiment [2] where baseball experts were given a creativity test called the Remote Associates Test (RAT). Their job was to look at a list of three words and figure out what single word binds them together. There were multiple experiments and conditions in the original study, but the one relevant to the current discussion was between lists of words where the domain knowledge was relevant and applicable and a different list of words where the domain knowledge was irrelevant and misleading. 

To make this concrete, suppose you are a baseball expert, and I give you the following three words: 

Baseball-Relevant:     WILD     DARK       FORK

What word connects these three? A baseball expert might answer PITCH (e.g., wild pitch, pitch dark, and pitch fork). The word "pitch" comes straight out of baseball, and it is therefore relevant to the solution to this RAT problem. When solving baseball-relevant problems, baseball experts had an accuracy rate of about 38%. This was roughly the same accuracy rate among baseball novices, who identified the connecting word 40% of the time.

But then the experimenters switched things up and gave baseball experts and novices a list of words that seemed like they might be connected to baseball, but ultimately they were not connected. Here is an example: 

Baseball-Irrelevant:     PLATE     BROKEN       SHOT 

What single word connects these three [3]? The first two words seem to hint at HOME (e.g., home plate and broken home), but then HOME doesn't really go with the last word (what is a home shot or a shot home?). How do you think the experts did? Their performance plummeted. Their accuracy rate dropped by over half, to 15%. Baseball novices didn't show the same drop in their performance; in fact, they showed the same accuracy rate of 40% on the baseball-relevant and irrelevant tasks. 

What's going on? Why can't baseball experts suppress their knowledge? Even when the experimenters warned them that baseball knowledge was irrelevant, they still couldn't turn it off. They seemed to be biased towards looking for solutions that are aligned with topics that they know a lot about, which actually interfered with performance when the solution was not aligned with their area of expertise. What may also be surprising is that the experts, at least for this task, did not out-perform their novice counterparts. In my next post I will explore situations in which being an expert can help, or hinder, performance, depending on the task at hand.

That concludes Part 1 of The Downside of Expertise. Check back next week for the conclusion and the connection to education!

Share and Enjoy!

Dr. Bob

For More Information

[1] Why MLB hitters can't hit Jennie Finch and science behind reaction time. Sports Illustrated, Volume 119, Issue 4. (July 29, 2014) [link] [video]

[2] Wiley, J. (1998). Expertise as mental set: The effects of domain knowledge in creative problem solving. Memory & Cognition, 26 (4) 716-730.

[3] The word that binds PLATE, BROKEN, SHOT together is GLASS.