Have you ever noticed that experts sometimes have a hard time being understood by others? Sometimes it seems that shortly after they begin, people are lost and don’t understand what they’re saying. Perhaps the reason this happens is because the expert is so familiar with her topic that she talks in a way that makes sense to her… because she can’t remember a time when she didn’t understand what she was saying.

To illustrate what I mean, check out this image I first saw shared by Sara VanDerWerf. I’ll come back to this image later in the blog post, but all I’m going to say at this point is, “Do you see it?” Take 20 seconds to examine the image and then continue reading.

Often, the reason experts have trouble communicating is because of a cognitive bias called the Curse of Knowledge. The short version is that when you know a lot about something and are trying to explain it to someone else, it’s hard to figure out how much detail you should share. It may feel like you have to make a choice between talking about it using the proper terminology and details (which makes many people feel lost) or changing the way you communicate (and feeling like you are “dumbing it down”).

In math education this happens when you don’t know how much background to give students. Do you just give them a formula / algorithm to use or do you help them understand why it works and where it comes from? There isn’t a perfect answer to this question, but the challenge of figuring out how much information is just right is part of this cognitive bias.

What’s especially important to understand is how we might think we know how much is just enough information to give but might actually be very wrong. To show you what I mean, let’s come back to that image I showed you earlier. So, did you see it?


Before I reveal what “it” is, I want you to try and take a mental image of whatever you think you see right now and hold onto it. If you’ve never seen this image before, then there’s a good chance that once I show you what “it” is, you’re going to have a very hard time remembering how you didn’t always see “it”.

Once you’re ready for the reveal, click on this link to see what “it” is. As to not spoil this, I’m going to continue talking about “it” in vague terms.

When Sara first showed us the initial picture, I had no idea what the big deal was and wondered what she was talking about. Once Sara pointed “it” out as shown in the picture in the link, it blew my mind. It seemed like everyone else in the room felt the same way.

Here are three things I realized:

  • At first, I had absolutely no idea what “it” was.
  • Once I saw “it”, I had trouble understanding how I didn’t always see “it”.
  • Once I saw “it”, I felt embarrassed for not always seeing “it”.

I felt certain that if I showed this picture to others, they would immediately see “it” since it was now so obvious to me. In reality, what I have found over and over again when trying this with large groups of educators is that more than 95% of people experience it much like I did. The only exception so far has been my wife who immediately saw it, thought it was obvious, and left me questioning my choices in life.


Implications for Education
It’s important that we consider what this could mean for education. Consider that the Curse of Knowledge might explain why teachers and students may not understand each other. Pretend that instead of the image we just used, “it” was finding the area of a circle.

From our teacher perspective, we’d be so confused as to how students can’t see “it”. I mean, it’s so obvious, how can they not? It would have been so long since we weren’t able to see “it” that we’d forget what it was like and be frustrated with students for not figuring it out.

From the students’ perspective, they would not see “it”. All they’d see is a wall and wonder what their teacher was talking about. They would feel bad because it would seem like it should be obvious, but it wasn’t. It would seem like they were missing something, but were not sure what it was.

This hypothetical interaction could very well be happening in our classrooms right now. Is it possible that we have our own “it” that is so obvious to us as teachers that we can’t understand how it’s not obvious to our students?

For example, I’ve noticed that people who deeply understand fractions feel so comfortable that they have a hard time comprehending how others don’t understand them. It can make it challenging to know what to say. “Do I just teach students the procedures or do I talk about how and why they work?” What may seem obvious to us may not seem that way to the person we’re talking to.


More Examples
The Curse of Knowledge certainly was a factor when the Common Core’s Standards for Mathematical Practice were written. I’m sure that the authors did not think “How can I write these so that very few people understand them?” Yet, as I have written, they are really tough to make sense of. I’m sure that when someone knows as much about mathematics as these authors, it would probably be really hard to dial in the right level of information. The crazy thing is that they probably thought these standards were understandable. For comparison, here’s my “readable” version of the Standards for Mathematical Practice.

I also see this happening when people write descriptions for their sessions at math conferences. Writing a description for your session seems like a situation where you should use proper terminology so you sound like you know what you’re talking about. However, it often results in writing descriptions that few people understand. Sometimes it seems like the only people who will really understand your description are the people who already know what you’re talking about and therefore won’t come. The people who might benefit from what you share will often feel so lost after reading your description that they’ll be too confused or embarrassed to attend. So, defeating the Curse of Knowledge and finding that balance is essential.


I hope that this blog post has given you some additional perspective. The Curse of Knowledge is something to keep in the back of your mind when communicating with others. If you’re not careful, you’ll be arguing with someone because you both see “it” differently. If you’ve dealt with situations like this or have other examples to share, please let me know in the comments below.


  1. Excellent blog, Robert. I didn’t see “it”, either. Great teachers make the “it”, whatever “it” is, clear and understandable for their students in whatever way it takes (lecture, activity, other) which makes sense for them (the students), not necessarily him/her (the teacher). Thanks for sharing about the “Curse of Knowledge”.

  2. This reminds of a quote from Diana Sinton, a professor I had in a Spatial Literacy course. I keep the quote hanging in my office to remind me each day. It goes like this, “Empathetic Teaching…the key to successful teaching is remembering what it’s like to not know (and being able to act on that).”

  3. I like the picture. I always enjoy that kind of thing (like the famous “Trick Donkeys” puzzle).

    I take issue with the headline though. I don’t think the problem is being too smart. To be honest, I find the idea upsetting, and not only because being an expert in something is very different to being “smart”. It seems to suggest that teachers having subject knowledge is bad. But then, it sounds like the problem is more lack of patience or empathy. I think teachers should aim for a certain flexibility of thought and be able to shift between seeing things in different ways. But knowing more stuff is not the problem.

    Also, I think there is a next level to knowledge as well. Suppose a word BLOOP has several meanings. You may have:
    A) people who don’t know the word BLOOP at all.
    B) people who know BLOOP and only know of one meaning.
    C) people who know the word BLOOP can mean different things to different people.

    A group C person might say to a person in group B: “What do you mean by BLOOP?”, and the person in group B might impatiently reply, “how can you not know what BLOOP means?”, and refuse to explain. To them it is “obvious”. I find the more I learn, the more I see nothing as obvious.

    • The “too smart” part refers to the curse of knowledge reference, where having too much knowledge about a topic warps your ability to accurately judge how much explanation is needed. I’m not saying that having lots of content knowledge is bad.

      • I appreciate your replying! I came here from Twitter and it did seem like people interpreted it that way a little bit, so I was maybe responding more to that.

        (And it hit a nerve, because I’m a new teacher and maybe I’m just not cut out for it. I thought loving mathematics and knowing a lot about it would be a plus, but it’s actually viewed negatively by a lot of people, and maybe with good reason…)

        Anyway, I’m glad I commented because now I’ve been receiving your emails and they are very interesting. Thanks very much. 🙂

  4. So love this!! Going to share with my math team as well as my grade level teams. It really made me think about how our teaching needs to be conceptually based before we move onto to math that is so abstract that we lose our students!!
    Thank you!!!

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