Your Brain on Maths: Educational Neurononsense Revisited

By Neuroskeptic | March 26, 2016 11:19 am

Earlier this week, I was asked on Twitter why I had never blogged about the “neuro-myths” of Jo Boaler. I confessed I’d never heard of her. So I looked her up and learned that Boaler is a professor at Stanford, and an expert on the teaching of mathematics. Her work in that field has been both influential and controversial.

Boaler argues that any child can become proficient at maths, given time, if they believe in themselves and in their ability to improve. Children should not be told that they have fixed traits such as ‘clever’ or ‘bad at math’, but rather they should be given a ‘growth mindset’. This is a mindset in which they see ability as learnable, and they see mistakes as chances to learn.

I’m no maths teacher, but Boaler’s ideas seem reasonable to me. We do learn from our mistakes, or at least we can do. On the other hand, I found some of Boaler’s claims about the brain to be problematic.

For instance, on her website,, “Brain Science” features prominently here, but not always accurately, in my opinion.

youcubedIn an article called ‘Mistakes Grow Your Brain‘, Boaler says that

Psychologist Jason Moser studied the neural mechanisms that operate in people’s brains when they make mistakes (Moser et al., 2011). Moser and his group found something fascinating. When we make a mistake, synapses fire. A synapse is an electrical signal that moves between parts of the brain when learning occurs… [this] is hugely important for math teachers and parents, as it tells us that making a mistake is a very good thing. Mistakes are not only opportunities for learning, as students consider the mistakes, but also times when our brains grow.

The study Boaler’s referring to here was published in 2011 in Psychological Science by Moser et al. of Michigan State University. Boaler refers to this paper in other places as well as this article. But as far as I can see, she is misunderstanding it.

Moser et al. used EEG to measure electrical activity in the brain of college students during performance of a simple button-pressing task (nothing to do with mathematics.) It’s known that after making an incorrect response, the brain responds with a negative voltage wave, the error-related negativity (ERN), followed by a positive wave, the error-related positivity (Pe). Together these are called the event-related potential (ERP). Moser et al. found that students with a ‘growth mindset’ showed a larger Pe compared to those with a ‘fixed mindset’.

Note that on these graphs, negative is up and positive is down:


Boaler’s right that ERPs are a product of coordinated synaptic activity. However, there’s no reason to assume that they reflect ‘brain growth’. Synapses are how neurons communicate with each other. They convey messages at very high speeds. An ERP could be said to reflect information processing. Learning however is a different, slower, process in which new synapses are formed, and existing ones are remodelled and strenghened. EEG can’t measure this process.

Meanwhile, on another youcubed page, Boaler says that Moser et al.’s data mean that

If you believe in yourself, and do not think that your ability is fixed, your brain is more likely to spark and grow when mistakes are made.

Moser et al. did find a larger Pe in those with a ‘growth mindset’, but this doesn’t establish that the mindset was the cause of the larger Pe. It might be, on the contrary, that people who tend to consciously note their own mistakes are more likely to adopt a growth mindset.

Another neuroscience case that Boaler discusses is Cameron Mott, who had a hemispherectomy (removal of the entire left hemisphere of the brain) at age 9, to treat epilepsy. As Boaler tells it,

Doctors expected her to be disabled for many years, as the left side of the brain controls physical movements. But as weeks and months passed, she stunned doctors by recovering function and movement that could mean only one thing – the right side of her brain was developing the connections it needed to perform the functions of the left side of the brain. Doctors attributed this to the incredible plasticity of the brain and could only conclude that the brain had, in effect, “regrown.”

The moral of Mott’s story being:

Such results should prompt educators to abandon the traditional fixed ideas of the brain and learning that currently fill schools—ideas that children are smart or dumb, quick or slow

It’s true that neuroplasticity is a remarkable phenomenon, especially in children. However, there are limits to neuroplasticity: there are plenty of cases in which children receive a brain injury early in life, or even in the womb, and never make a full recovery. These cases show that the brain is not entirely plastic.

I’m not criticizing Boaler’s educational ideas, and I certainly don’t take a side in the US ‘math wars‘ which apparently forms the context for the debate over Boaler and her work. But in my view her use of neuroscience is misguided. Neuroscience is nowhere near advanced enough to tell us that a certain teaching approach is better than another.

Children doing well in maths is a behaviour, and if we want to find the best way to modify a behaviour, neuroscience is no substitute for studying that behaviour. In this case, we could try randomized controlled trials of different approaches to teaching. This will tell us more than any amount of EEG data.

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  • Rolf Degen

    One recent research review even concluded that educational neuroscience has nothing useful to offer to learning and instruction:

    • RationalCenter

      I have read this review, and I find it rather ridiculous, frankly. Let’s take them in order:

      “Trivial, in the sense that the recommendations are self-evident.” When is it considered a bad thing to confirm common sense through research? We have a long history of finding out that practices we considered “common sense” where, in fact, ineffective or worse. It is not trivial to provide evidence of recommendations that had no previous research basis.

      “Misleading, in the sense that the recommendations are already well established (based on behavioral studies.)” Ignaz Semmelweis discovered that washing hands between patients prevented the spread of disease. He couldn’t explain why. Based on this, using this researcher’s logic the discovery of bacteria was “misleading,” because the recommendations were already well established. When research can describe the underlying mechanisms for successful practices, it can further inform how to improve and modify those practices.

      “Unwarranted, in that the recommendations are based on misrepresentations of neuroscience or the conclusions do not follow from neuroscience.” – This is just poppycock. All areas of research suffer from misapplication of their results by uninformed practitioners. This is not unique to neuroscience, and it does not have any bearing on the larger question of whether neuroscience can inform instructional practice.

      Neuroscience is in a period of tremendous growth, and to quote one researcher, we’ve learned more in the last 25 years than in the previous 2,500. To state unequivocally that understanding the physical changes in the brain is not relevant or informative to evaluating instructional practice is simply foolish. Instructional practice does not take place in a vacuum – everything that has happened in a child’s life before they sat in that classroom and what happens after impacts the structure of their brain, and impacts the effectiveness of the learning activity. The exact same instructional practice delivered with total fidelity will have different impacts on students, because they aren’t all the same. Understanding the underlying differences gives us guidance in adapting to make learning more effective. We are seeing explosive growth in our understanding of the brain, and the idea that somehow this knowledge of how we learn won’t be of value in the process of learning is incredible. I would challenge the researcher to find any other area of study where basic research in the mechanics of a system (engineering, medicine, geology, astronomy, etc.) did not lead to better practices. Why is this any different?

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  • OWilson

    This is typical of the current state of the teaching profession. It’s a “feel good” alternative way to excuse poor educational outcomes. “Mistakes are not really bad, if you (survive long enough to ) learn from them”, but they won’t enhance a productive and satisfying journey through life.

    On a par with its sister theory, “Slow Learning”, it seeks to explain and justify the status quo, which is dismally failing education in the U.S. We are just trying to “rush the students through” the system to the point they cannot retain anything they are being taught, is how this one goes.

    They can cite correlation to stimuli until the cows come home, but there is no empirical way to prove their theories. There are huge difference in student IQ and cognitive ability (the schools themselves have a litany of all these “learning disabilities”, which they seem to conveniently ignore here :)

    (Actually most politically inspired doctrinaire theories are designed to be not easily falsified)

    They require you to “believe”.

    • Uncle Al

      growth mindset” Orange County Mensa just got an 11-year old member, maybe 5 feet of skinny. Accompanied by her mother, she wandered around an Open House, then talked about non-Euclidean geometries. Growth that, Boaler.
      How to Learn Math is a free self-paced class for learners of all levels of mathematics. It combines really important information on the brain and learning with new evidence on the best ways to approach and learn math effectively.” Crush your enemy, drive it before you, hear the lamentation of the diverse.

      • RationalCenter

        There is no conflict between the concept of growth mindset and the idea that some people have a natural aptitude. The conflict is with the idea that only people with a natural aptitude can be successful or outstanding, and that’s simply a myth that research has consistently shown to be false. Focused effort and a desire to constantly improve is far more predictive of success than any innate talent.

        • Uncle Al

          September 1969, more than 1200 students were enrolled in majors organic at Michigan State. June 1973, 14 graduated BS/Chem. I stood high upon the corpses of others who “tried.”

          “1,5-Migrations of Silicon Between Oxygen Centers in Silyl Beta-Diketones J. Organomet. Chem. 188 129 (1980) Even my undergrad slop was not too sloppy.

          “Undergraduate Awards in Analytical Chemistry”Analyt. Chem. 43(12) 70A (1971). Compete against me on a level playing field.

          • RationalCenter

            Congratulations on your success, which you probably attained that through hard work and effort. Perhaps you did have an innate talent that made it easier, and that colors your view of this topic. But as a scientist, you should recognize that your personal experience is anecdotal evidence, and neither confirms or contradicts the point under discussion.

            The research on this is very consistent (I recommend you look at Dr. Angela Duckworth’s work as a starting point), and you and the 13 successful graduates almost certainly did not represent the highest IQs of the original 1,200 students, as IQ has been repeatedly proven not to be predictive of success. There are more important traits than native intelligence.

            This may conflict with your personal experience and your beliefs, but the research evidence is quite clear. Schools that are applying these concepts are using the best, most current science, and should be commended, rather than condemned for adopting strategies that are contrary to long-held cultural myths about talent.

          • Tol
          • RationalCenter

            My statement on IQ and academic success is indeed incorrect. I was thinking about the research on IQ and professional success, post-school. However, the article you shared also points that that while there is some correlation between IQ and academic success (it’s not perfect), “conscientiousness” is equally predictive. A large metastudy referenced in the article concludes “This research has demonstrated that the optimism of earlier researchers on academic performance–personality relationships was justified; personality is definitely associated with academic performance.” IQ is just part of the picture, and not as important as it is traditionally made out to be.

    • RationalCenter

      No, they don’t require you to “believe.” I just attended a national conference of researchers studying mindset and related topics, and their studies are consistent and robust.

      More importantly, your description of what they mean bears no relation to the topic. Issues of mindset are absolutely *not* about excusing poor educational outcomes, but how to instead achieve excellent outcomes and have a productive and satisfying journey through life. It is the opposite of what you described.

      None of the researchers involved in this work would argue with the point that their are differences in IQ and cognitive ability. What they will show you, however, is there is scant correlation between IQ and personal success (, and that other factors such as persistence and mindset are far more important, and that these are skills that can be taught and learned.

      The core concept of the work of Dweck, Duckworth, and others is that regardless of your current skill set, with the appropriate work and support you can improve. The brain is plastic, and separate major disease or physical abnormality, can increase in efficiency over the function it has today.

      As to “Slow Learning,” we know (this has been imaged in live rat brains) that learning is a process of building and reinforcing synaptic connections between neurons. We know that the strength of these connections is developed through repeated activation of the connections, and that this repetition works best if it is spread over time intervals of days and weeks. Slow learning is applying the best research available, and it’s certainly not an attempt to “justify the status quo.” It’s a pushback against the status quo, which has students rushing through material in a way that we know is ineffective for the majority of learners. Countries that beat us in international test scores figured this out a long time ago, and they cover significantly less content spread over a longer time than in U.S. schools. The results speak for themselves

      • OWilson

        Thanks for your comments.

        Obviously you are well informed on the subject.

        My limited experience as a member of the UK Grammar school system, both as a teacher and a governor, saw excellence in teaching, with relatively limited budgets. Budget meetings were regular and demanding.

        I also spent time doing research on teaching assistants in the public secondary school system, spending time in classrooms and observing the efficacy of the teaching system. Their budgets were relatively of little concern to the staff.

        It was all about the “culture” and the “ethos” of each system, In my case virtually across the street from each other.

        Much different philosophy and much different outcomes, unfortunately. Much different absentee rates among teachers, too.

        The usual whine of the teachers unions and their favorite politicians, is more money, more teachers, not effective change in standards. I used to joke teachers would not be happy until there were no more standard exams and one teacher for each pupil.

        As you probably surmised, I’m not a fan of unions in the teaching system.

        I was involved in 2 OFSTED Inspections, which seemed to back up my take on the situations.

        Your experience may be different.

        • RationalCenter

          Thanks for your thoughtful reply. It is an unfortunate reality that even if the work on mindsets and related strategies are based in good research, the application of those strategies can be a total failure if done inappropriately. Dr. Carol Dweck, the researcher who literally wrote the book on mindsets, was a keynoter at the conference I attended. One of the core themes of her talk was her frustration that after twenty years many people who think they are applying her strategies are doing it incorrectly, and with a poor understanding of the concepts. There’s an old saying that “Culture eats strategy for breakfast,” so trying to implement any instructional approach will fail if it is not supported by a strong and healthy staff culture. I have been fortunate enough to work with schools that have that kind of powerful culture, but have also encountered the opposite. How to improve those that struggle is one of the great challenges of education.

          • OWilson

            Absolutely, and the oft given answer is “better training for our teachers”.

            I believe that politics rears its head everywhere it has been given influence or control of budgets.

            It was hard to believe that while our grammar school was graduating polite candidates to both Oxford and Cambridge from our Lincolnshire school, the public secondary school down the street was graduating car thieves and thugs.

            The difference was so noticable (it was a small town) that the County School Board intervened and tried to actually merge the schools, because they couldn’t stand to see success achieved outside their dictates. The Head who basically gave her life to her pupils, and had a record of success nationally, was under constant fire from the beurocrats, while the other Head down the street was basically left alone.

            This inspired me, when asked, to become the Science Link Governor, to support this beautiful woman who was being targeted for being too successful, and for a couple of years, we managed to keep them at bay.

  • Uncle Al

    any child can become proficient at maths, given time, if they believe in themselves and in their ability to improve” Khan Academy online. Underperformers will never understand ∇ × (∇Φ) (that being nothing in the grand scheme of things). The 700,000 Los Angeles Unified School District California Academic Performance Index tests average IQ 83-86. They cannot read, write, or make change of a dollar in their heads.

    Children doing well in maths is a behaviour” So is one rep bench pressing your body weight. Almost all women and many men do not behave. Exercise builds muscle in men. Stupidity is forever.

    • CarolAST

      I’m female, and I bench pressed my body weight the first (and only) time I was ever on such a bench. Did it without big muscles, too.

      • Uncle Al

        No charitable affirmation required. Those who can, do. Those who can’t, teach. Those who can’t teach, teach teachers. Those who can’t teach teachers manage teachers. Those who can’t manage teachers manage programs. Those who can’t manage programs dictate policy. Those who cannot dictate policy carry guns.

  • RCraigen

    I wish the author had taken a stand on Boaler’s educational positions in the Math war which are entirely propped up by pseudo-neuroscience assertions (and a couple of unreplicable studies whose data she treats as top secret). Like most Education gurus she spouts platitudes and so … as noted at the beginning of the article … at the top level of what Boaler says there’s not much to quibble with. Just some fine-sounding platitudes.

    Underneath are prescriptions for teaching that are problematic. She’s one of the biggest proponents of minimal-guidance instruction, for EG. She’s also a strong opponent of memorization, and claims to have never memorized her times tables and asserts that it has never done her harm (her broader argument makes it clear that she believes NOT having those in her memory makes her better at math — and prescribes that teachers strive for the same with their students).

    So while I’m happy for the careful and factual exposition of the research behind the claims, I would personally prefer not to have had the equivocation. Because she’s got such high level exposure these unsubstantiated ideas are misinforming a lot of classroom teachers.

    • Neuroskeptic

      I’m not qualified to speak out about the ‘math wars’, not least because I’m British so my own childhood was not a battlefield in these wars. And I’ve not had time to look into the different arguments.

      • RCraigen

        Boaler is British too, and the “math wars” is found there too, although not by that name as much, and it is more often rolled into the larger question of progressive educational methodology. One needn’t dig into philosophical arguments as many of the claims on the side of Boalar et al amount to “Cognitive science has shown” … Learning styles, brain buttons, brain gym, mantle of the expert and so on. For the remainder, there is plenty of empirical evidence for where wisdom lies. For their use of pseudoscience in Britain I’d recommend Tom Bennett’s “Teacher Proof” and for the history of empirical failures of progressive education methods in your nation it would be hard to beat Robert Peal’s “Progressively Worse”.

        • Jo Boaler

          I am happy to read the article and always glad to discuss ideas to improve knowledge. This commentator though, as well as “justbabywhy” cross a line into disrespectful and defamatory comments that I always send to my lawyer, as defamation is illegal. Neuroskeptic, you will like the new article I am writing with a Stanford neuroscientist, I will let you know when we release it.

          • justbabywhy

            Hi Jo, I apologize for the disrespect in my previous comment. Please do forward also my edited comment to the lawyer, along with the original. Cheers.

          • Jo Boaler

            I appreciate the apology, I won’t be sending the comments along, so don’t worry.

          • RCraigen

            Do send my regards to your lawyer Jo, and Happy Easter to you! She must have quite a file on me by now. I won’t be editing as I don’t feel anything I’ve said here is inappropriate. Is “education guru” considered derogatory nowadays? Or is the “top secret” comment regarded as beyond the pale? As far as my reading of the existential literature by you, our friends Bishop, Milgram and EducationRealist informs it seems to me to be a fair assessment. If there are any factual errors in what I’ve said I’m happy to correct them. In the meantime I’m still looking forward to your promised response to the points raised in Bishop and Milgram’s original critique of the Railside Study.

          • daqu

            “When we make a mistake, synapses fire.”

            Wasn’t something utterly essential omitted from this sentence? How can anything special happen when we make a mistake *unless* we know about it?

      • justbabywhy

        Yes, quite shockingly, she was actually the Marie Curie Chair of Mathematics Education in England from 2006 to 2010.

  • Aileen

    Are any of you teachers? Have you tried, or talked to a teacher who has tried teaching the “growth mind-set” to students who struggle in math? I am a special ed teacher, and have seen more growth from my students this year than the past 4 years I’ve been teaching.
    I don’t know, or care if the science is correct. The message is what the students need to be taught. So often, any student who struggles in math, feels unsuccessful so often, that when they make a mistake, they can’t intake information. It’s as if they go to fight or flight over one wrong answer.

    Convincing my 3rd graders that if they make a mistake, and find the correct answer on their own, or with a little guidance, they get smarter, has made them look at mistakes differently. A student will make a mistake and stay calm. A peer will give them reassurance that they have the opportunity to become smarter. The student will work through the problem, and get high fives from class mates.

    This author is most likely correct that the growth comes from the student paying better attention to their mistakes. I don’t care really. Jo Boaler’s suggestions allowed my students to learn from their mistakes, rather than be embarrassed by them. It has taught my students to be supportive to their peers as they struggle, rather than taking the opportunity to blurt out the answer to show how smart they are.

    It is unfortunate that Ms. Boaler’s conclusions are incorrect, but she is a math teacher, not a brain scientist. I think her teaching suggestions are pretty solid, and because she has a “growth mind-set,” I’m sure she would be open to someone better explaining the studies to her.

    • Neuroskeptic

      As I said in the post “I’m no maths teacher”. I’ve got nothing to say for or against her approach to teaching. I’m just saying that neuroscience is not able to help us decide which approach is best.

    • OWilson

      The primary purpose of teaching is to prepare the pupil to enter the adult world with an understanding of how it, and the people who populate it, actually works.

      The problem arises if teachers themselves are not in touch with the real world.

      If a certain political view becomes dominant in the field, then teaching tends to reflect that viewpoint, even if it is at odds withe the values of the world outside.

      The world is a competition for resources, and even in the so-called humanitarian fields, religion, charity, medicine, politics, and yes, teaching, there are those who have secured for themselves, power, influence, privelege and wealth.

      In that Global world, students will not be “high fived” by peers after mistakes, they will not get “reassurance that they have the opportunity to become smarter” by “supportive peers as they struggle” with their mistakes.

      In the real world those mistakes can do serious damage to others.

      (And yes, I was once a teacher)

      • CarolAST

        A classroom is a “real world,” too. It is as entitled to its own rules as the “real world” to which you refer. Or perhaps you think that your harsh “real world” rules should be extended to the nursery as well?

        • OWilson

          That’s why many stay in the classroom :)

          They remain sheltered from reality, for a while.

      • RationalCenter

        In the real world, failure is a regular and predictable experience. Learning how to deal with it is a critical skill. Read about entrepreneurs – they fail repeatedly, even the successful ones, and they know failure is part of the learning process. Microsoft is an example of a business that has been very successful, even though most of the products they have released have been failures.

        Engineer and writer Fred Hapgood described the role of failure this way:

        “What humans do in these cases is: think up a completely wrong (but sincerely felt) approach to the problem, jump in, fail, and then do an autopsy. Each failure contains encrypted somewhere on its body directions for the next jump: ‘strengthen this part,’ ‘tie this down next time,’ ‘buy a better battery.’ Good engineering is not a matter of creativity or centering or grounding or inspiration or lateral thinking, as useful as those might be, but of decoding the clever, even witty, messages solution space carves on the corpses of the ideas in which you believed with all your heart, and then building the road to the next message.”

        It is the person who does not experience failure that is not living in the real world. The people who experience failure and have the capacity to learn and grow from those failures who are the successes in the real world.

        • OWilson

          I do agree with you for the most part.

          But I believe in accountability too.

          The problem is what do you do with the folks are failing their responsibilities in the school system, but want to protect the status quo with “more money” and “more teachers”.

          Jobs, tenure and pensions are quite important to all, especially the ineffective ones.

          Some people assume that all teachers are doing an excellent job, under extreme unfavorable conditions.

          I was in both systems long enough to see the union supported feather bedding that pervades the system. I have family still involved with it.

          It takes a lot of effort, confrontation and expense to weed out a failed teacher.

          It only take a minute to replace a dead battery.

          I want my kids to be taught to avoid failure, not to embrace it :)

          Check that battery and tires before you go on a long trip, even if you do have mommy’s credit card for a tow! :)

    • justbabywhy

      “I don’t know, or care if the science is correct.” Really? As a teacher, you don’t care about this?

    • Uncle Al

      Kids “struggling in math” have defectiver teachers (process repair by Khan Academy) or lack talent. The former is teacher union mandated. The latter is no bar to Liberal Arts, Fine Arts, trades; government employment, military, criminality (including politics), and counter-control; teaching. Do cops count rounds fired?

      A math teacher must count to the highest number achievable on its fingers as unique configurations. 10 is no math teacher (smaller is a shop teacher). 1023 is OK, 59,048 is a show-off (thumbs are limiting). 3,628,800 is discharge for cause – insubordination (or an organic chemist re bullvalene before degeneracy). Intelligence discriminates against the stupid, the majority deserving of Social Justice stolen from the able and productive.

      Hedy Lamarr’s frequency-hopping torpedoes had musician George Antheil doing the counting.

      • Doc Bear

        Or have, as I have, a learning disability in this area. Since I went on to earn a Doctorate in Oriental Medicine and my graduates led the field in passing the National Boards, it’s not the kiss of death. With a lot of support and hard work, I was later able to handle physics and organic chemistry very well. The idea that a child who struggles in one area either has a defective teacher or ‘lacks talent’ creates a totally false dichotomy – there are many potential reasons beyond those you stated.

        • Uncle Al

          There is no worthwhile investment in the congenitally inconsequential. Make-work compassions’ costs are stolen from productive people under threat of prosecution as “the proper thing to do.” Any group demanding survival of super-preemies, Mongoloid idiots, spina bifida, childhood cancer…must personally pay for their upkeep. I vote “dead.” Losing a billion losers barely dents Terran overpopulation. Empty compassionate hospitals, asylums, and hostels into graveyards unless their beneficiaries’ families’ wholly pay for it themselves. Repair potholes instead.

  • Mavan

    Great post!

    Slightly reluctant to point this out given your next post, but there’s a Moser/Mosel typo.

    • Neuroskeptic


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  • teknowh0re

    I agree she is misunderstanding the data AND making false claims probably in order to profit somehow. Synapses lighting up…when has that ever been associated with learning or brain growth? I have NEVER heard that anywhere. I thought this was just an indication of information (electrical impulse) moving from one neuron to another. Where did she get these crazy ideas?
    Perhaps she isn’t firing on all cylinders…

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  • Matthew Gudenius

    I have written a critique of the numerous fallacies in Boaler’s book, Mathematical Mindsets… including: misleading data representations (truncated graphs) to exaggerate data differences; incorrect summarization of research conclusions (and, in some cases, claims that are actually antithetical to the corpus of research); and a focus on manipulable (rather than standardized assessment) data in schools she showcases as exemplary:



No brain. No gain.

About Neuroskeptic

Neuroskeptic is a British neuroscientist who takes a skeptical look at his own field, and beyond. His blog offers a look at the latest developments in neuroscience, psychiatry and psychology through a critical lens.


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