Better to be Frustrated than Bored

Jan 23, 2017 by

For all of you who have taught students, you know that one of the rewards is seeing the “Aha moments” that students experience. One of the downsides (to instructors) of teaching online is that it is hard to “see” the reward of the “aha” in the same fulfilling way.

The reason we should care about the aha moments that students experience is that this kind of moment is tied closely to an emotional feeling. And memories with emotional attachments tend to be stronger (more memorable) than ones with no emotional attachment.

But have you ever stopped to think about what is going on right before the aha moment? Does the aha moment come after a well-organized lecture, a step-by-step example, a period of boredom, or a period of confusion or frustration?

An aha moment typically comes after a period of confusion or frustration. This means that you have to put students into that space where they are actually at the edge of what they know (the confusion/frustration space) to nudge them over to insights.

Anyways, I digress. I want to share findings from this paper: Better to Be Frustrated than Bored: The Incidence, Persistence, and Impact of Learners’ Cognitive-Affective States during Interactions with Three Different Computer-Based Learning Environments (Baker, et al, 2010).

The researchers set out to focus on cognitive-affective states that were hypothesized to influence cognition and deep learning: boredom, confusion, delight, engaged concentration, frustration, and surprise. The researchers use Russell’s Core Affect framework (2003) to map these states in two dimensions: valence (pleasure to displeasure) and arousal (activation to deactivation).

In this study, the researchers examined:

  • the cognitive-affective states the students experienced during the learning process
  • how those states persist over time (e.g. do students move from boredom to frustration more often than frustration to boredom?)
  • how the state affects the students choices on how to interact with the system (e.g. what causes students to game the system?)

While I will leave you to read the whole paper if you want all the details (the methodology involves three different interactive learning systems and three different methodologies), I think the nuance of definitions between a few of these terms is important. As defined in the paper:

  • frustration is dissatisfaction or annoyance
  • confusion is a noticeable lack of understanding
  • engaged concentration is a state of engagement with a task such that concentration is intense, attention is focused, and involvement is complete

Now let’s jump ahead to (what I consider to be) some of the interesting results. Engaged concentration was the most common state during the observation periods (60%) followed by confusion (13%). While boredom was only observed about 4-6% of the time, it was also the most persistent state (once bored, the student stays bored) across all three learning systems.

Within two of the systems where “gaming the system” was observed, a more in-depth analysis was performed. Boredom was significantly more likely to lead to gaming the system. Guess what wasn’t likely to lead to gaming the system … confusion, frustration, and surprise. Better to be confused than bored, huh?

There is quite a bit of new research being performed on the role of confusion in learning, but my gut feeling here is that confusion leads to self-insight, and learning gained through self-insight (because this is the aha where emotions are attached) should be stickier than learning delivered through other states.

Challenge: Vigilantly watch for states of boredom in your classes, and when you find them, intervene. Do something different. Put students into a space where they are challenged and maybe even a little confused. Give the learners a chance to grapple with the concepts and have those moments of self-insight.

Reference:

Baker, R. S., D’Mello, S. K., Rodrigo, M. M. T., & Graesser, A. C. (2010). Better to be frustrated than bored: The incidence, persistence, and impact of learners’ cognitive–affective states during interactions with three different computer-based learning environments. International Journal of Human-Computer Studies, 68(4), 223-241.

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Celebrate the Errors in Math Practice

Jan 11, 2017 by

Dear math students,

As you work through your mathematics practice, I’m going to challenge you to embrace making errors in an entirely new way. 

Many students believe that every problem in math homework should be perfectly constructed with no errors. It might look something like this:

A nicely ordered problem solution with no mistakes.

 

But when it’s time to study after the initial problem run-through, what does this perfectly constructed problem say? Does it coach you on remembering how you struggled? Does it remind you where you made an error? No.

When you make an error as you’re working a problem, please don’t erase it from the face of the earth. Certainly you should learn from the struggle and complete a correct solution, but record your deviations from the straightforward solution path in another color. Leave yourself notes (also in a different color) to remind you what you should have paid more attention to the first time around. Maybe that would look something like this:

Worked problem with highlights and notes to self

 

 

Sometimes you’re going to recognize but you don’t have the right answer but you’re not going to be sure what’s gone wrong. You should always try first to figure it out yourself first. This process of error analysis in a variety of different situations is key to developing problem solving skills in mathematics. Without exploration of the problem space (which happens with error analysis), your brain is just recording rote procedures without the ability to transfer those procedures to new kinds of problems. It will, essentially, stunt your mathematical growth.

Now, I don’t want you to get to the point of tears or breaking your keyboard out of anger. If you get near that stage please just ask a question (email, discussions, chat-a-friend, etc), leave a sticky note on the page as a reminder to go back, and move on to the next problem or section of problems. Just switching to a slightly different problem can not only get you unstuck, but sometimes give you insights into the “stuck” problem. 

When you figure out how to do the problem you were stuck on, make sure to go find that flagged problem (remember the sticky note?) and annotate your corrections.

Worked math problem with cross-outs and restarts and notes to self.

 

Now you might be thinking “why do all these error corrections and problem annotating in another color?” When it comes time to study for your major assessments, you will be able to see the places where you stumbled the first time you tried the problem. These “notes to self” are the places where you’re most likely to make the same mistake again. They benchmark places to remember to be careful and show you problem types to repeat practice before an exam.

Celebrate your errors.

Embrace the messiness.

Learn from your mistakes.

Study from your struggle points.

And be great at mathematics!

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Learning Math is Not a Spectator Sport

Dec 4, 2016 by

In November, I gave the keynote at the American Mathematical Association of Two-Year Colleges (AMATYC) Conference in Denver.

I have given versions of this talk that are not specific for mathematics, but I don’t have recordings of those. I promise that the math in this talk is not inaccessible and is used more for examples than a framework for the talk. In other words, don’t let the word “math” scare you away. The alternate version of the talk is “Learning is Not a Spectator Sport.”

Three triangles surrounding a central triangle with the letters C, I, and D
The first half of the video is the awards ceremony, so I’ve directed the embed link below to begin when the keynote actually begins at 45:48 (direct link to video on YouTube beginning at the keynote is here).


The talk emphasizes the importance of interaction, and as such, this talk has a lot of audience interaction in it near the beginning, so you may want to jump through some of that interaction as you watch (between 51:30 and 1:02:00).

At the end of the keynote, audience members are invited to participate in a Weekly Teaching Challenge to continue exploring the ideas and research in the talk. You’re invited too. Just sign up!

 

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Failure is a NORMAL Part of Learning

Sep 24, 2011 by

“Dr. Tae is a skateboarder, videographer, scientist, and teacher. Contrasting his observations of his own learning while skateboarding with the reality that is the current education system, Dr. Tae provides some insight as to how we might better educate in the future.” (from the YouTube description of this great TEDxEastsidePrep video called Can Skateboarding Save Our Schools?)

Some observations.  As Dr. Tae says, “Failure is Normal.” Period. You might try to solve a proof or a mathematics problems many times before you succeed at doing it correctly.  You will only learn the correct process by making mistakes.  I’d venture that more is learned from making the mistakes than by doing the problem correctly.  Every mistake branch tells you valuable information – this is something that didn’t work.  Huh.

This week I told my Calculus students that “division by zero” no longer means the problem can’t be done.  It just means “try another way.”  This is an incredibly hard lesson to learn.  Many learners are too quick to just give up when they encounter something that doesn’t work.

“Nobody knows ahead of time how long it takes anyone to learn anything.” – Dr. Tae

I agree. And yet, here we have the so-called modern education system, where 1 credit hour equals 15 weeks of one hour in class time and 2 hours of out-of-class time.  We predict, several times a year, that it will take 3 credits or 4 credits for every student to learn the topics that are covered in a course.  On top of that, we are starting to be held accountable if students aren’t successful enough.  If we don’t know ahead of time how long it takes any student to learn a body of knowledge, then why do we keep pretending we do?

Some time last year, I wrote down this quote in my Moleskein notebook, and I’ve been running back across it ever since:

“Grades are simply a measure of the speed at which a student learns.”  – Unknown source

If a learner manages to become competent at an average level during the period of learning (semester or quarter), they get a C.  If they manage to become expert, then they get an A.   I think there’s an argument to be made that learning math should be more about mastery, like skateboarding.  Either you “land the trick” (problem, concept, proof) or you don’t.  Any assigned grade in between just leads to problems down the road.  For example, “average” understanding of algebra and trigonometry leads to a pretty poor understanding of Calculus.

Another point from the video, “Learning is not fun.”  I would revise that slightly. The process of learning is not fun.  The process of learning is work.  The moment when you finally master a technique or synthesize an idea is fun, and it continues to be fun up until the point where it just becomes boring.

[Thanks to David Wiggins for pointing me to this great video.]

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