I recently heard a podcast episode (though I can’t remember which it was) where a woman shared an analogy that helped me sort out my own understandings around learning from mistakes. In the episode, the woman explained how it’s a common belief that practicing and making mistakes will help you learn and improve. But she had a slightly different take.

She applied the belief to typing. Many people spend over 50 hours per month typing yet they don’t seem to be getting much faster or more accurate. So even after years of practicing and making mistakes, many people still type at about the same speed they were typing when they graduated from college.

So, what’s going on here? Why aren’t they improving? After all, they are practicing and making mistakes. Why aren’t they getting better?

She goes on to explain that improving is more than just making mistakes. You must reflect on what happened and adjust your practice to avoid making them again. It’s intentional and reflective practice, not all practice. It seems intuitive to me.

Connections to Growth Mindset
When I first heard the typing analogy, it seemed to run counter to what Dr. Jo Boaler wrote in her book Mathematical Mindsets:

When I have told teachers that mistakes cause your brain to spark and grow, they have said, “Surely this only happens if students correct their mistake and go on to solve the problem correctly.” But this is not the case. In fact, Moser’s study shows us that we don’t even have to be aware we have made a mistake for brain sparks to occur.

In reading this, I realize that Dr. Boaler does not actually say that you learn from mistakes you are unaware of but rather that “brain sparks” occur. I wonder what exactly a “brain spark” is. Is it the same as brain activity? Is it the same as brain growth? Is brain activity or growth the same as learning?

Her findings come from this research done by Jason S. Moser. Admittedly, I am very, very far from being an expert in understanding all of the data, so I relied more heavily on his interpretation of the data. Here are two quotes that stand out from his conclusions along with my thoughts about what he said.

Growth mind-set was associated with enhanced attention to corrective feedback following errors and subsequent error correction.

I interpret this to mean that having a growth mindset makes you more open to and aware of errors you make. This leads to being more receptive to information that will help you improve and avoid future mistakes.

Together with past findings, the current results suggest that one reason why a growth mind-set leads to an increased likelihood of learning from mistakes is enhanced on-line error awareness.

This seems to extend what he previously said, and he explicitly connects “an increased likelihood of learning from mistakes” to being extra aware from having a growth mindset.


I am a huge fan of Dr. Boaler as well as her research and messaging around growth mindset. My only goal for this blog post is to have a conversation about whether you learn when you don’t realize you’ve made a mistake. This may seem like a trivial point, but I believe that we need clarity on this issue.

If we don’t actually learn from mistakes we are unaware of, then we need to do a better job of helping students reflect on and learn from their mistakes. For example, that is the purpose behind the Open Middle Worksheet. It isn’t enough to just have students try a problem six times. Students need to take a brief moment to reflect on what they learned from the previous attempt and how it will help them next time. Skipping that reflection doesn’t result in the same kind of improvement.

I’d love some push back to challenge my conclusions and better understand this idea. What do you think? What am I wrong about? Please let me know in the comments below.


  1. Not trivial at all. You’ve started the conversation and I’ll dig a little deeper over the summer and see what I find. Can’t wait to hear other opinions!

  2. My understanding of learning is that it involves reflection followed by an accommodation or an adaptation to a current understanding. I base this on my reading of von Glasersfeld’s research.

    • Thanks Tiffany. So then that would make me wonder if learning != brain spark or if there is new research or something else…

      • I’m curious about this too. After reading Jo’s book, a few of us at work were pondering this. I followed her references but still don’t “get it.” I’m keeping watch here to see if anyone poses a new idea or explanation. I understand from von Glasersfeld’s work that that there are attentional “pulses” in our brain but I can’t figure why they would be different for a mistake.

  3. This is an interesting conversation, for sure. I don’t understand what would cause a “brain spark” unless it’s recognition of a mistake, whether sub-conscious or fully conscious. In Moser’s study, he was asking native English speaking college students to identify letters that appeared in a specific place in a string of characters. I think we can safely assume that the participants all knew how to identify letters and could have been said to have mastered the task. When these students made a mistake in this task, their brains likely knew it right away because they were being asked to use a skill they’d already mastered (and built upon) in a new and complex way. In this way, if I’m teaching my 6th graders how to multiply decimals and they make a computation mistake, I expect that brain “spark” because multiplying is a skill they already have and I’m just teaching them to use that skill in a new and complex way. However, I don’t expect that “spark” if my students make an error while I’m teaching them a completely new skill or idea. How does their brain recognize the error if it doesn’t have anything to compare it to?

    I think you’re on the right track that we, as teachers, need to provide students with feedback about their mistakes and errors. (Yes, I distinguish between the two. See this post from Sarah Carter: https://mathequalslove.blogspot.com/2015/07/analyzing-errors-free-poster.html) While students are learning a new skill or idea, we need to point out the errors, classify them (see the linked post), and help students identify what led to the errors. As students develop mastery, that has to include a transfer of responsibility for identifying mistakes. As students become more proficient with the skill or idea, they can learn to recognize the brain “spark” as a cue to review what’s been done.

    This metacognition is important, and I think it’s overlooked as a teaching tool in math. We explicitly teach students to reread what doesn’t make sense to them, to make use of tools and structures to construct understanding, but too many students just blindly perform procedures in math with little to no understanding of what they’re doing. Emphasizing the MPs is a good start, but I believe we have to get students identifying their own mistakes and misunderstandings for true learning and growth to occur.

    So, do I think that it is possible to learn without realizing you’ve made a mistake? No, because I think we have to distinguish between mistakes (doing something you knew was incorrect) and errors (doing something wrong when you didn’t know any better). Without feedback following an error, I don’t think the brain would recognize it as being wrong. If we can train ourselves and our students to recognize that “spark,” to be aware of the feeling that goes along with making mistakes, and to be open to admitting the mistakes and seeking to improve, then that’s where the power of a growth mindset lies.

    • Wow. So much for me to think about. I also did not think about the difference between error and mistake. I had used them interchangeably. I also haven’t thought deeply about the categories of mistakes and errors. Also something I want to think about more.

      I also hadn’t thought much about the specifics of the task. I see what you mean though. They had such little time to make a response that I could see that they would make a decision and then process it a bit later as they had more time to think about it. That might be the source of the brain spark.

      Thanks for pushing the conversation along Kate.

  4. I am similarly skeptical of the notion that mistakes in and of themselves are somehow beneficial. I share your assertion that it is through feedback and reflection that real growth can occur.

    • My intuition agrees with you Laura, but I am trying to figure out if I am missing something in this discussion or maybe misinterpreting Moser’s study.

  5. I have just started reading Jo’s book and I also had a problem with that section. I teach 3rd grade math. Here is the scenario that popped into my mind. A student is given the problem 8×3 and writes the answer 11. Was there a spark? They accidentally did addition instead of multiplication. When I see the mistake I usually prompt them with some sort of open ended question and they (still convinced that they did the calculation correctly) say, “Yes. See.. 8… 9,10,11.” They recognize their error when they look at the problem again but to follow the logic Jo is sharing, that would be the second spark where they are aware of the mistake. How can there be a spark when the student is confident they have done the problem correctly? This really confuses me and I am eager to see what you find out. Thanks for posting!

    • Thanks Dawn. I do realize that sometimes there are counterintuitive findings in science and that just because it doesn’t make sense to me, doesn’t mean it isn’t true. I’m just trying to more clearly understand the research. I actually emailed Moser but he never replied.

    • I took it as your brain is sort of “priming” to learn. When that initial mistake is made, because of the wiring in our brain (perhaps parts we don’t yet understand) recognizes the mistake and a “spark” is created. Once this happens, there needs to be reflection/guidance/reteaching to assist in correcting the mistake, which in turn causes there to be a second spark. THAT 2nd spark is when the learning occurs. That’s how I made sense of it. I’m looking forward to continuing to read others’ ideas here.

  6. I had always assumed that the ‘brain spark’ was an instant internal recognition of an error, but unless you do something about it, that what it stays. You don’t learn from your mistakes until you start thinking about them. This is similar, in my opinion, to the difference between immediate memory and working memory. Pieces of information flood the brain and unless meaning and relevance are attached to the information within the first 30 seconds, it has gone. The same would apply to an error. Feedback, both internal and external are what turns an error into a learning experience.

  7. No you don’t learn from brain sparks and pseudo-neuroscience does more harm than good. If you look at the research referenced by Jo Boaler, it deals with with something the participants already know, not the new content. I stopped referring teachers and parents to youcubed after Dr. Boaler did not acknowledge there might be an issue with her statement.

    • I can tell that you’re frustrated but I’m not quite where you’re at. I do wish someone would acknowledge this point and clarify it. I even emailed Dr. Moser but got no reply.

  8. I think it is important to note that the term “Brain Spark,” is a colloquialism and not scientifically descriptive. The neuroscience of learning is based in fMRI studies that attempt to correlate oxygenation levels in the brain with neural activity. Higher oxygenation being associated with the resultant activity. There is, as far as I have seen in the literature, no actual “spark,” that occurs.
    I believe Dr. Boaler, who was writing for a more or less popular audience, was taking needed and warranted liberties in the language she chose. The most critical piece of her work being the idea that we as educators embrace failures, mistakes, errors, and plain-old-“derrrr”s as opportunities to grow rather states to fix in time and label a student as. Her message, in my opinion, is that fixing a student’s grade based upon the mistakes or errors they make creates a fixed mindset which is detrimental to their ultimate learning.

    The application of neuroscience as learning research is in its infancy still and as such care must be taken when attempting to generalize much. Language is fluid, and as such let’s give everyone some grace when critiquing.

    • Thanks Chris. It wasn’t my intention to critique Dr. Boaler’s work. What I was trying to do is get clarity because educators frequently interpret what she’s said as that you learn from any mistake regardless of whether you reflect on what happened or not.

      As I said in the conclusion, “If we don’t actually learn from mistakes we are unaware of, then we need to do a better job of helping students reflect on and learn from their mistakes.”

  9. I am actually very very fortunate in that I work for a district that honors mathematics learning beyond curriculum. In fact, I teach a class titled Mathematical Mindset. How fun is this? It is unreal and a dream to teach like this. I get to help kids learn that every one of them is good at math, and I don’t use worksheets. Of any sort.
    So, to respond to the original prompt, I have always had trouble understanding how we learn if we are unaware of our mistakes. My thought has always been that we learn very deeply by understanding that we indeed have made that mistake, and then make corrections. I’m still not convinced either way. Open to all thinking around this idea.

    • Would o be able to send you a message? I very interested in what you do and trying to go that direction myself.

  10. If you don’t know you made a mistake there
    Is no connection being made. Metacognition means I know when I made a mistake and I react to
    It. I change my thinking.

  11. Intuitively I believe that I will not learn if I make a mistake but don’t know I’ve made one. However, the way that I am corrected makes the biggest difference to my understanding. E.g. If I am prompted to think about if my answer is a sensible size and can make my own correction, then more learning occurs compared to me being told tha answer directly.

    • I agree and I absolutely get that my intuition can be wrong. I just want clarification on this research. I’ve written to Dr. Moser multiple times and even contacted his graduate assistants. Can’t get a response from anyone.

  12. I think that perhaps when we struggle with a problem then our ‘brain sparks’. Struggle is perhaps more likely to lea to a mistake so perhaps the ‘brain spark’ should be attributed to the struggle and not just to the mistake that might follow. There are so many things in life that I constantly get wrong because I never invest the effort/ planning/ thinking to change. When I do, then I learn to do things right next time. Can learning math be different to this?