The Math Teacher Metaphor

July 25, 2019
The math teacher metaphor is an MBCT exercise used to show how our tendency to come to conclusions without getting all the information can have some terrible consequences.

There are many cases where your thoughts work more against you than for you. The problem isn’t so much what the thoughts are about, as is the way you come about them. They’re often cognitive errors that stem from poor frameworks embedded in your mind. This can cause problems in daily life. But the math teacher metaphor can help with this.

One example of these problematic cognitive frameworks is something called arbitrary inference. It basically means that you reach a conclusion without actually having evidence to support it. In some cases, there might even be evidence to the contrary.

Although it can be useful by pulling from your own experiences, this process can also lead you to draw some very off-base conclusions about the world around you. Let’s take a deeper look at that.

How drawing conclusions can be useful

To be fair, drawing conclusions based on one characteristic or concrete fact can save you time and effort. If someone tells Alejandra that Guillermo likes to do home chores and things like that, it’s no surprise she’d think he loves to cook. Thus, the next time they see each other, she might suggest a dinner where they both bring a dish.

But Will might not actually have any idea how to cook. You might want to say this mix-up is perfectly understandable, but that’s part of the problem. That “normal” experience you think you have in various situations could actually lead you to have an improper view of things.

A woman sitting on the couch with her knees in her chest, looking thoughtful, or concerned.

MBCT: Mindfulness-based cognitive therapy

MBCT is a model that combines two separate practices: cognitive therapy and Jon Kabat-Zinn’s mindfulness-based stress reduction program. The original goal of merging these two practices was to help prevent frequent relapses after a patient had finished therapy for depression. 

There were many studies about residual symptoms and relapses in depression patients after they’d finished a therapy cycle. The numbers were alarming. Approximately 70% of people showed cognitive symptoms of depression after therapy was over. Even the 75% of people who responded well to therapy had five or more residual symptoms.

In general, those symptoms were things such as an inability to concentrate, a lack of focus, trouble finding words, mental sluggishness, and trouble making decisions.

That’s what makes MBCT, developed by Segal, Williams, and Teasdale in 2002, so necessary right now. They created this form of therapy as something to do in group sessions. In these sessions, you’ll work on meditation, feelings, and emotions as a way to prevent a relapse.

MBCT helps you learn to redirect your attention towards ways of thinking that will help you get out of the web of depression if you find yourself there again.

MBCT and metaphors

Metaphors are a common tool in MBCT. The goal with this is to help people change their cognitive processes, and show them how to spot an irrational thoughtFrom there, they can learn to deal with that thought the right way.

One of the metaphors used in MBCT is the math teacher metaphor. This one involves closing your eyes so you can be fully aware of the thoughts, sensations, and emotions brought up by the story. Here’s how it works.

Awareness-building: The math teacher metaphor

Here’s the basic structure for the story:

“Clara is on her way to school. She’s worried about her math class. She doesn’t know if she’ll be able to handle this sixth grade class. This isn’t even a responsibility for her as a secretary.”

Once you’ve told the story, you should leave some time for people to think about it. Then, you can ask the group what happened in the story. In most cases, you’ll see them make mistakes because they’ve drawn quick conclusions.

Most likely, they’ll start out thinking that Clara, the character in the story, is a student. Then, they’ll think she’s a teacher, only to finally find out she’s a secretary.

The danger of drawing quick conclusions

What this exercise shows is that we tend to draw conclusions and alter them as we get more information. In this story, the truth came out after you got more information, but that’s not always the case in real life. Nothing and nobody has any reason to clear up any mistaken conclusions you’ve drawn. 

At the end of the day, it’s your responsibility to change the way you see things and the way you think. It shouldn’t be something someone else has to do for you.

Obviously, thinking that Clara is a teacher and not a secretary isn’t a dangerous mistake. But you can apply this story to many different aspects of life. For example, if Clara is really Belén, a lifelong friend, and you see her walking in the distance but she doesn’t wave, you might start to draw some conclusions.

For example: Belén is rude, Belén is really spacey, Belén is angry, Belén doesn’t like you anymore, or anything else like that. Those conclusions could end up having a major impact on your mood, even though none of those things is the case about Belén. She’s just nearsighted and couldn’t see you.

Along the same lines, imagine that Beatriz tells you the day of that she’s not going to be able to pitch in for Claudia’s present, even though she committed, and you already bought it. The rest of your friends might think she’s shameless, selfish, or careless, and that she must not like Claudia.

But these are conclusions they’re reaching without actually having much information. In other words, they could be wrong. Beatriz might be having money problems, or have just gotten into a fight with her girlfriend and acted impulsively. Or she might just be in conflict with Claudia without them knowing it.

A man looking out the window with his hand on his chin.

Is impacting other people your responsibility?

This way of thinking isn’t just dangerous in the sense that it can affect your mood. Remember: your thoughts influence your behavior. So, the conclusions you make could also lead you to act a certain way. But they aren’t necessarily right, and you might end up acting a certain way based on something that isn’t even true.

If you stop talking to Belén because she “snubbed you” or if the group of friends argues and gets angry with Beatriz for “being selfish”, even though it’s not true, you’re basically doing something you don’t actually want to. On top of that, none of it has any basis in reality, it’s all just in your head.

This is why it’s so important to really assimilate the math teacher metaphor and remember it any time you feel like you’ve reached too convenient a conclusion. Not only will it improve your rational thinking abilities but you’ll also end up taking the wrong side of things less often.

  • Cebolla, A. y Miró, M. (2008). Efectos de la Terapia Cognitiva basada en la Atención Plena: una aproximación cualitativa. Apuntes de Psicología, 26(2), 257-268.