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

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.