Fighting Confirmation Bias Is Like Fighting Gravity (so let’s stop fighting it)

Photo by meriç tuna on Unsplash

When you learn about confirmation bias two things are usually explicitly stated. Confirmation bias is inescapable and that we should do everything we can to escape it. This is like saying it’s impossible to escape gravity but you should do everything you can to try to escape it. 

Is it possible to hack our bias to confirm our beliefs in such a way that we don’t  need to feel like we’re constantly fighting gravity? 

To answer that question we need to understand confirmation bias more fundamentally. 

As I scroll through my social media feeds I feel confirmation bias. More specifically, the posts that confirm my beliefs feel good. They bring me joy. I’m more likely to share them. Those that don’t confirm my beliefs make me feel uneasy, frustrated, or annoyed. I’m more likely to be skeptical of those posts and try to find holes in the logic, which will relieve my discomfort. It will make me feel like I needn’t change my beliefs to embrace this new information. I might even share my skepticism with my followers. 

Confirmation bias operates constantly in background as we go about our lives. If we believe women are bad drivers, we pay attention to examples of women driving poorly and put less weight on men driving poorly. If we want the Tigers to win a baseball game, we will notice when the umpires favor the other team and hurt our team.  If we think “the left” is a cancer on society, we find examples to confirm this and ignore counter examples. Likewise for “the right.” Confirmation bias is always there, telling us where we should direct our attention.

Confirmation bias rides on the rails of the beliefs we have in our mind. In fact, in some sense it’s not so much a bias as it is our brain’s primitive defense mechanism searching for beliefs counter to our own and “protecting” us from them. We perceive ideas that don’t map onto our current beliefs as threatening – hence the negative affect. The negative emotion signals our brain to heighten awareness and seek safety. We find “safety” (hits of dopamine), by poking holes in the ideas attempting to infiltrate our current beliefs. That brings us comfort, but decreases the likelihood we integrate new information that may be true. 

If we are biased to confirm our current beliefs because we instinctively view new ideas as threatening, it’s hypothetically possible to adopt and preserve beliefs that embrace new ideas. That is, we can believe that new ideas enhance our current beliefs. 

Here are a few specific beliefs we could embrace. 

Nobody’s cornered the whole truth on anything

We might start by downloading a belief in our brains that no one person, or group, has a monopoly on truth. This includes you. If we believe this then when we encounter a belief that we disagree with, we will seek out the parts of the belief that enhance our understanding. We’ll seek to integrate both viewpoints, yielding a richer understanding of the given concept. When we find the valid points within the opposing viewpoint, it will confirm our belief (which will literally feel good). 

Essentially, if conformation bias drives us to find information that confirms our belief, then we can set it about the business of finding information that disconfirms our currents beliefs so as to enhance our total understanding what is true. We believe that diverse viewpoints are necessary to a complete understanding, so we seek out those viewpoints, and when we find the truth contained in them, we get the dopamine hit and the reinforcement.  

Our ego isn’t interested in what’s true, only that we’re safe

I’ve read “Don’t Label Me” by Irshad Manji twice and I’m working to become a Moral Courage Mentor. (Moral Courage is Irshad’s approach to psychologically healthy diversity and inclusion training.) In her book and in the course I learned much about the ego, or “egobrain,” as Irshad calls it. This isn’t the “woo woo” ego from Freud – it describes our innate, primitive, threat-detecting system. It’s what’s driving confirmation bias as I’ve described it above. 

Let me pick a totally hypothetical and unrealistic but illustrative example of the ego brain at work (that definitely didn’t happen…). The other day I had a… difference of opinion with my wife. We were getting things ready for a garage sale, which we had discussed would be good to spread over two days, Thursday and Friday. On Wednesday afternoon it became clear to her that we were not going to be ready to have the sale on Thursday. This was not clear to me. As I was cooking dinner she brought up several things we still needed to do to prepare, to which I thought (and probably said) “I guess we’ll stay up late and do them.” She mentioned how she was getting pretty anxious about publicizing the sale without those things done, to which I thought (and probably said), “Well it will be fine, we can get it done.” Finally, she said, “Do we really need to have this sale tomorrow?” 

At this moment I felt my ego say “That’s what we planned and lets just stay up late and do it. Why do we have to change things last minute?!?” However, I’m getting better at noticing when my ego is talking and when my calm, rational mind is talking. This was definitely ego. I thought a bit longer before ejecting the first reaction that came to my mind and realized that it was not necessary to have the sale the next day. My ego wanted me to cling to my old beliefs, my wife presented an idea that was counter to them, and I took the extra second to put my ego to rest, consider the problem more carefully, and ultimately concede that she made a good point. My belief about the importance of sticking to the plan was incorrect and defending it was irrational. 

As I hope you can see, the ego is generating much of our confirmation bias. In fact, we could call our “bias to confirm” our tendency to “protect our current beliefs.” Herein lies another belief we can adopt that would be healthy to confirm: we must routinely speak truth to the power of our ego if we are to update our beliefs about the world. 

Every person is a “plural” 

We have biases towards other people based on the labels they either ascribe to themselves or that we ascribe to them. These labels help us build a caricature in our mind of that person. We reduce them to labels, extrapolate all of their other characteristics from the labels, and then judge them. We quickly categorize a person as someone worth listening to or worth ignoring. 

While this labeling, categorizing, and judging makes navigating our lives easier, it’s unfortunately a house of cards that only fuels confirmation bias. We see a person with a MAGA hat on and we believe we know nearly everything about that person. When he does something that confirms our mental model of a MAGA-hat-wearing person, our belief is confirmed. If he does something that runs counter to it, we either don’t notice or write it off as an anomaly, not to be taken seriously. Pick your favorite tribe to hate on – the same thought process applies. 

However, if we decide to look, we will find that below these labels every person conceals a richer personhood, revealing that they are dynamic and multifaceted. Manji calls a person that consistently bucks their labels a “plural,” and reminds us that if we look (and listen) hard enough we’ll find that every person is a plural. 

If we believe that each person is a plural, then confirming that belief means we pass on snap-judgements and assume there’s more to them than the caricature we’ve built in our mind. 

If we believe that each person is a plural, then we’ll seek the complexity of each person. When we find it, we’ll confirm our bias, thereby reinforcing the assumption that each person is a plural. 

“Wait, you can’t just choose what to believe!”

Sure you can. We do it all the time. Sometimes we don’t realize we’re doing it, but we do. Many times it feels like reasoning leads to concluding that a belief is true, but just as often, if not more, we want to believe something is true and seek out the justification later. 

I think Apple makes better phones than Android makes and better computers than PCs. I’ve got, I think, good reasons to believe this but at no point in my life did I take a year and do an objective analysis on the features of each brand of technology. I had a couple good experiences with Apple products in high school and I’ve been happily feeding that belief ever since. 

More seriously, if we dig into our beliefs deeply enough I think we all get down to a priori assumptions that either consciously or subconsciously adopt. (Books have been written on that topic and I don’t have the space to explore that here. But if you think my argument falls apart because that claim is false, please let me know in the comments!) And, since humans are dynamic, we sometimes change those foundational beliefs. For example, I might go much of my life and assume that people are generally good people. I might then have an experience where I see the dark side of humanity and conclude that people are, in fact, generally bad. 

Is either true in a fundamental sense? 

How would we begin to answer such a question even remotely objectively? 

We can say that adopting either of those beliefs will impact the course of an individual’s life in meaningful ways, right down to daily interactions with other people. I think we can also conclude that a critical mass of individuals adopting either belief will have society-wide ramifications. Finally, in some sense one can choose to adopt either belief – and suffer the consequences. 

Now, not all beliefs are are equally true or pragmatic or will result individual or group-level flourishing. Not all are equally Good. Another book-length exploration would be required to explore what we mean by a Good belief, but for the narrow purpose of this essay let’s assume that it means developing a form of confirmation bias that doesn’t require us to constantly fight ourselves. 

I’m arguing that, given the malleability of our beliefs, we should adopt the the following: 

  1. None of us knows all of the truth which means the other people we interact with must know something important that we don’t – we should listen accordingly.
  2. Our ego often blinds us from the truth in an effort to maintain our current beliefs. This means we need to constantly be mindful of when it’s at work and keep it in check. 
  3. Every person is a plural. This means that we will be slow to put people in boxes and we’ll seek out the characteristics that demonstrate the individuality in their character. 

I’ve adopted these beliefs and I can tell you that my mind is in a healthier place. Remembering that people are plurals keeps me looking for the nuance in their personality. It motivates me to keep looking beyond the caricature I’ve built in my mind. Keeping my ego in check helps me avoid arguments for the sake of being right, as I explained in the story about my wife. I’m not perfect, but more often I find myself taking a breath to respond thoughtfully as opposed to reacting quickly. Remembering that I don’t know everything about anything motivates me to engage with those I disagree with to figure out what I’m missing. Finally, I find myself gravitating towards people who seem to believe the same things. 

In short, in feeding my confirmation bias I gain a richer understanding of nearly everything. 

It’s time to make school closures due to Covid an absolute last resort

Photo by Sharon McCutcheon on Unsplash

I’ve been working on this post for the better part of a week, trying to decide if it was worth posting. Then yesterday a New York Times headline came across my phone and it nudged me to hit “Publish.”

“India’s Lost Generation: Lengthy pandemic shutdowns have led to young people leaving school altogether, dimming the prospects for the country’s economic future”

As some epidemiologists, who I’ll come back to later, warned us about in fall of 2020, lockdown policies have have had a devastating impact on young people and it’s time to take that policy decision, school closures due to Covid, off the table.

I should start by saying that I’m not on any of the popular teams. I’m not on team Blue or team Red. I wasn’t on team Lockdown or team Open Everything. I’m not on team This Isn’t Even As Bad As The Flu or team It’s Gonna Kill Everyone. I’m not on team The Vaccine Will Fix Everything or team The Vaccines Are Worse Than The Disease.

I’m just trying to figure out what is true, regardless of who said it or what I’m supposed to think. Given the current situation with Covid and what we’ve learned over the last two years, I think we should be done with much of the health theater in our schools, including mask mandates, disinfecting surfaces constantly, and especially school closures with remote learning.

Let’s start with the policy that probably creates and has created the most harm to our kids – closing schools and subsequently switching to remote learning. I suspect the vast majority of schools in the 20-21 school year closed at some point and switched to remote learning. Some schools never opened for in-person learning last year. Policymakers and school leaders had a wide range of considerations to balance when making the decision to got to remote learning, among them the health of the students, the students’ families, the teachers, and the community at large. At the time there was no vaccine and the consensus was that schools could be places where the virus would proliferate, driving community spread. (I say “consensus”, because there were health experts pointing out that this did not seem to be the case. Even recent research found schools being open either didn’t drive hospitalizations or, in counties where there was already substantial spread, it was inconclusive.) This combination of factors and fear of the virus drove schools to err on the side of preventing Covid transmission at all costs.

The lack of a vaccine or other treatment meant that the fear many felt was understandable. Nobody wanted to see a teacher get severely ill or die because a student brought it into their classroom. Nobody wanted to see a student pass it to another student and have the latter student’s parents get severely ill. Nobody wanted to see a kid get sick and die. The probability of these things happening was probably low, but again, I can understand concerns and the decisions that followed. I’m not saying that I would’ve chose differently had I been given the power to make those decisions.

However, the decision was not without real costs. Switching to remote learning or hybrid learning put huge amounts of pressure on the teachers to radically change their approach to instruction. Many teachers did this poorly. (I don’t mean to demean the teachers that did it poorly. It would be like yelling a kid for not being able to read well when you’ve only taught him half of the alphabet. It’s not their fault.) Many administrators left the profession. Many teachers left the profession. A profession that already had a high burnout rate had gasoline poured onto the fire. It wreaked havoc with the mental health of educators and put strain on their families. Ask any teacher and you’ll find near universal agreement that last year was hell.

But we did it. We did it because we were told that it was required for our safety and the safety of our communities, even if it might be hard on our students (and their parents, and us, and so on). What I saw teachers go through last year was nothing short of heroic.

And the costs obvious don’t stop with the impact on teachers.

Most importantly the switch to remote learning hurt all kids and it hurt the most disadvantaged kids the most. The kids who only eat meals at school. The kids without access to internet. The kids with broken families. The kids with many siblings who had to provide childcare for the younger siblings. The kids with parents who were essential workers and couldn’t work from their laptops (not that working from your laptop and helping your kids get through school was that easy either). The kids that got addicted to video games or pornography or Tik Tok. The kids that were abused and it was never reported because a teacher never saw any signs to report. The kids that didn’t have access to after school programs or or other services that helped keep them out of trouble. The kids that missed out on extracurricular activities like sports, clubs, homecoming, prom, graduation ceremonies, etc. I could go on, but you can see how at some level every kid was harmed by these policies.

Oh! And many didn’t learn that much.

Some people don’t like the term “lost learning”. They bristle at the suggestion that we just fill brains like buckets and what – we didn’t put as much in the buckets last year? Fine. Call skipping over a year of education and whatever is typically gained from that year whatever you want to call it. The irony is that many of the teachers that quibble over the term “lost learning” are the ones that will make arguments like “it’s not what or how much students learn, it’s all the other things that students get from school that are important.” Well, students lost out on that stuff too. Regardless of what we name it, we will be reckoning with the consequences as a society for years to come.

As I mentioned, it’s not as if the “well-off kids” got out of this unscathed. Depression and anxiety were on the rise before the pandemic. I remember having many conversations with counselors about it in the years leading up to March of 2020. The school closures accelerated anxiety and depression for many students and initiated it for many others who had not previously struggled with their mental health. (Which, remember, is physical health. Sometimes in the conversations around policy we forget that. As if Covid is a real health problem and depression isn’t. As if Covid is the only thing that kills people or causes suffering.) For example, Kooper Davis was a high school senior from New Mexico, with no history of depression, and committed suicide in late 2020 in large part do to the downward spiral caused by the disruption to school and football. In the summer of 2020 the mental health of young people became so bad that one in four people aged 18-24 had seriously considered suicide. In December of 2020 in Massachusetts, emergency departments saw four times more children in psychiatric crisis. The data demonstrate a massive uptick in young people struggling with mental health, but that’s only the slice of suffering that can be turned into a data point. For example, it doesn’t account for the parents’ suffering as they watch their child suffer.

The decision is not weighing “public health” versus “students’ lost learning.”

It’s “public health” versus “students’ health + lost learning.”

The most frustrating thing is that we knew this in the summer of 2020. However, anyone that thought that schools should stay open because of all the benefits schools provide were written off as people who weren’t taking the virus seriously and didn’t care if people died. And it wasn’t just your MAGA-hat-wearing-election-was-a-fraud-and-Obama-wasn’t-born-in-the-US uncle who thought schools should stay open. In October 2020 epidemiologists from Harvard, Oxford, and Stanford wrote the Great Barrington Declaration, which argued against locking down society and for a model called “focused protection”. In this model schools would generally not close. They were immediately labeled as fringe epidemiologists and accused of wanting the virus to “rip” through society. None of this was true. In fact, a recent email leak revealed that the head of the NIH said as much in an email to Dr. Fauci. He called the authors “fringe epidemiologists” and called for a “quick and devastating public take down of its premises.”

I digress. But my point is that throughout this pandemic one approach has been sanctioned and adopted as if there were no other alternatives worth considering because all “serious” people supported the sanctioned approach. This simply isn’t true. And hindsight shows us that we did real damage with these policies.

But we can change our approach going forward. Nearly anyone that wants to be vaccinated, including kids, can be vaccinated. We are much closer to herd immunity. Kids, thank god, continue to be unlikely to suffer severe illness. While we educators are not doctors, we still might consider adopting the principle of “First, do no harm.” If we do that then I think shutting down schools and remote learning should be a thing of the past.

The arguments for continuing with the policy of shut downs based on community transmission are exceedingly far-fetched. Given that the vaccines are very effective at preventing severe disease and death we are left with wild hypotheticals as justification for closing schools. For example, maybe a student will catch Covid at school, bring it home to their parents, they might be unable to get vaccinated because they’re immunosuppressed, and they’ll get a severe case of Covid. Or maybe a student will pass the virus to another student, he or she will visit a grandparent in a nursing home, the vaccinated grandparent might still be at high risk because of their age, they’ll get sick, and then spread it through the nursing home. Or maybe leaving schools open will be the thing that nudges hospital capacity over the edge.

I will grant that things like this might happen. Actually, if the numbers are large enough, they will happen. But we must remember the following:

By shutting down schools we are imparting certain harm on our students in exchange for prevention of an exceedingly unlikely possible harm on others.

There is one exception to this. If the number of staff absent reaches a critical level then schools may need to temporarily close. Likewise, if the number of students in attendance drops to a threshold that the day no longer “counts” then closing may be the only option. This would be similar to situations in the past in which flu has spread through a school or district, forcing a closure. These two situations are distinctly different from using a metric like community spread. The former situation could also be alleviated to an extent if state health departments adopted the five-day quarantine guideline instead of a ten-day quarantine, given the CDC’s updated guidance, or even allowing teachers back when they have a negative antigen test. And they don’t require a switch to remote learning. We must keep in mind that for many kids there’s no difference between remote learning and a day off – except that one has academic consequences.

I recognize that leaders have difficult, often impossible, decisions in which there is no good answer. I don’t mean to criticize them. I just hope that they have the humility to consider what I’ve laid out above and change course if they find it compelling. We need to have grace with each other, but that doesn’t mean we shouldn’t critique the decisions of decision makers and implore to make different ones. We can do this without being rude, ungrateful, or antagonistic. In fact, if we truly hope to change anyone’s mind, we must.

Jo Boaler, Tracking, Education Research, and Honesty

Image credit: https://dilbert.com/strip/2012-06-22

A few years ago I read Jo Boaler’s book, “Mathematical Mindsets” and I thought it contained some good ideas. There were a few things that I thought were not realistic or would be difficult to scale, but overall I found the book useful. Our department read it together, and I remember a colleague pointing out that Boaler often cited her own research. That revelation made me more skeptical of her work, especially when she provided citations.

Was she only seeking out data that confirmed what she already believed?

Despite this I would have considered myself a “fan” of her work. In subsequent years I used some of her resources from Youcubed and subscribed to her email newsletter. The content was a mixed-bag of resources and opinions, but she was clear in her book and in her work that “tracking,” the education model in which students are separated into courses based on their ability, needed to be eliminated. It was unfair, meant weaker math students weren’t exposed to “rich” mathematics, perpetuated inequities, and the research showed de-tracking was better for all students. If we wanted to fix mathematics education in the United States, according to Boaler, we would need to de-track mathematics, helping teachers to incorporate “low floor, high ceiling” tasks that are accessible to all students at a particular grade level.

My intuition about de-tracking is skepticism for reasons I might explore in another post. For now I want to focus on what’s happening in California surrounding their proposed mathematics curriculum, the de-tracking program San Francisco Unified School District implemented in 2014, and how advocates, Jo Boaler chief among them, are using misleading (or missing) data to push for policy that has little to no evidence to support its adoption.

This NY Times article gives context regarding the curriculum and the debate around it. From the article:

The California guidelines, which are not binding, could overhaul the way many school districts approach math instruction. The draft rejected the idea of naturally gifted children, recommended against shifting certain students into accelerated courses in middle school and tried to promote high-level math courses that could serve as alternatives to calculus, like data science or statistics.

The draft also suggested that math should not be colorblind and that teachers could use lessons to explore social justice — for example, by looking out for gender stereotypes in word problems, or applying math concepts to topics like immigration or inequality.

Evaluating the Success of SFUSD’s Framework

The evidence that advocates are using to promote this curriculum is largely from San Francisco Unified School District’s de-tracking program which they implemented in 2014. (“It also promoted something called de-tracking, which keeps students together longer instead of separating high achievers into advanced classes before high school. The San Francisco Unified School District already does something similar.”) They claim that they reached all of their goals with the program and show progress along many metrics . But a group of data scientists, teachers, lawyers, parents, and students put together a report outlining how SFUSD is either actively hiding data (as some California Public Records Act requests, California’s version of FOIA, have been ignored), intentionally misleading the public, or is simply incompetent.

The group, Families for San Francisco, put together a report (cited in the NY Times) explaining the problems with SFUSD’s nationwide campaign espousing the success of its new framework. They share evidence that de-tracking was an overwhelming positive decision for the students in SFUSD. Here are a few revelations from the report worth noting. They begin by going through each of the three goals outlined by SFUSD, the claims made by SFUSD about progress on those goals, and their analysis.

The first goal was to “Reduce the number of students forced to retake Algebra 1, Geometry, or Algebra 2 by 50% from numbers recorded for 6/2013.” SFUSD claims a “dramatic increase in student comprehension” and a drop in Algebra 1 repeaters from 40% to 7% in a press release from 2017. Here is the analysis of this claim from Families for San Francisco.

Facts: The grade distribution we received from SFUSD showed no improvement at all in Algebra 1 grades. The repeat rate did come down, but only because in 2015 SFUSD eliminated the requirement to pass the Algebra 1 California Standards Test (CST) exit exam as a condition of progressing. The effect of this change was later partially acknowledged by the Math department in the speaker’s notes in one of their presentation slides in 2020: “The drop from 40% of students repeating Algebra 1 to 8% of students repeating Algebra 1, we saw as a one-time major drop due to both the change in course sequence and the change in placement policy.” Finally, in conducting our review of SFUSD’s claims, we were unable to obtain any such “longitudinal data” they refer to nor could we replicate the repeat rate numbers quoted by SFUSD using data obtained via a CPRA request. We have deep concerns that SFUSD is claiming credit for student achievement that is either untrue or unsubstantiated by the data or both.

The second goal was to “Increase the number of students who take and pass 4th year math courses (post- Algebra 2 courses) with a C or better by 10% by 6/2018.” SFUSD claims that “456 more students, or 10.4% more students are taking courses beyond Algebra 2 in 2018-2019 than were in 2017-2018.” Unfortunately, this claim is misleading. Here is the analysis from Families for San Francisco.

Facts: Enrollment in advanced math classes at SFUSD has gone down, not up, and SFUSD has produced no data about pass rates.Advanced math is commonly understood to mean courses beyond Algebra 2, including Precalculus, Statistics, and Calculus; however, SFUSD’s claim that its enrollment in “Advanced Math” enrollment has increased depends entirely on counting students enrolled in its “compression course” — a third-year course combining Algebra 2 with Precalculus. The problem with this framing is that the University of California (UC) rejected SFUSD’s classification of its compression class as an advanced math course due to its failure to meet UC standards for Precalculus content. Once we exclude the enrollment data for the compression course, the enrollment number for advanced math shows a net decrease (emphasis mine) from 2017-2018 (the final cohort prior to the implementation of the new math course sequence).

The third goal was to “Increase AP Math enrollment & pass rate for Latino & African American students by 20% by 6/2018.” SFUSD claimed that “(a) ‘AP Math enrollment has also increased over a two-year period from 2016-17 to 2018-19’; (b) that ‘AP Statistics enrollment has increased 48.4%’; and (c) that Latinx AP Math enrollment increased 27% over the same period.” Families for San Francisco’s investigation found these claims inconclusive because they were unable to get all the data necessary to verify them. Here’s what they write.

Facts:Whether SFUSD met its original goal to increase Latinx and African American AP Math enrollment by 20% from June 2014 to June 2018 is unknown because in spite of our requests, SFUSD has not produced complete data for this period. For the two-year period from 2016–2017 to 2018–2019, African Americans are not listed among “subgroups who met or exceeded the 10% growth target” and SFUSD has not disclosed any performance outcomes. The five-year data for school years 2016-2017 through 2020-2021 shows that enrollment by African American students has fluctuated from year to year while enrollment by Latinx students has been more or less on the rise. And because SFUSD does not release data on the pass rate for AP Math exams, its success rate is unknowable.

Not only are the pass rates unknown, the enrollment data available shows that the claim of increased AP math enrollment is misleading.

Meanwhile, the claim of increased AP Math enrollment overall is misleading. The number of SFUSD students overall taking AP Calculus is down. The number taking AP Statistics is up but it is concentrated at three specific school sites (Lowell, Ruth Asawa SOTA and Balboa). The other schools showed no significant increase.

It seems clear that SFSUD did not meet their goals and is intentionally spreading misinformation with data “showing” they’ve reached their goals. This is frustrating enough as it demonstrates a clear effort by supporters to confirm their own bias and manipulate the data to mislead the public. But Families for San Francisco also points out that new inequities were introduced since the overhaul of their math program (which, keep in mind, is a model for the new California math sequence). For example, by the end of tenth grade “Algebra 2 enrollments of Black and brown students have declined because most students cannot afford the costly work-arounds afforded by their white and Asian counterparts.” Read their report for a more detailed explanation of why, but essentially it comes down to parents that can afford a workaround will do so, and those that can’t likely won’t.

None of this has stopped advocates from pushing the narrative that de-tracking, at least in the approach that SFUSD took, is good for students. Jo Boaler, a researcher in math education, should be able to take a dispassionate look at the evidence and conclude that the experiment failed. But she seems unable or unwilling to do this.

Here’s a tweet from Boaler in 2018 pointing to SFUSD data.

Here’s another one.

For a more detailed argument from Boaler and other math education experts, here’s a piece entitled “Opinion: How one city got math right,” which concludes with the statement, “We congratulate San Francisco Unified on its wisdom in building math sequences that serve all students increasingly well.”

That piece is from 2018, but she doesn’t seem to have revised her opinion, at least not publicly. I’m subscribed to her newsletter and in one she sent out in August entitled “New Evidence Supports De-Tracking” she links to a recent paper by her and David Foster. Throughout this paper she cites her own work to justify claims. It doesn’t appear to be peer-reviewed and is not published in a journal but hosted on her Youcubed website. The research in that paper looks promising, but given everything I’ve laid out above it’s difficult for the average educator to tell if this is real evidence or if the goal posts have been moved. Would a 23-page report by an interested organization yield all the same problems as discovered by Families for San Francisco in their extended report analyzing the data from SFUSD?

I don’t know the answer to that. I do know, however, that this case study represents a problem endemic in education research. I’ve yet to go to a serious professional development session in which research couldn’t be found to support whatever intervention the organizer was promoting. When educators seek out research on different topics in education it is very difficult to find a consensus. Given that, as of 2014, less than 1% of education articles were replication studies and that “replications were significantly less likely to be successful when there was no overlap in authorship between the original and replicating articles,” educators, in my experience, are understandably skeptical of education research. Boaler and other researchers that agree with her on this give us a reason to maintain that skepticism.

Honesty

No one is immune to confirmation bias. The longer you’ve maintained a viewpoint, I suspect, the harder it is to let go of that viewpoint. However, one of the antidotes to confirmation bias is surrounding yourself with honest people who hold a diversity of viewpoints. Surrounding yourself with people who agree with you, or who disagree but won’t point out the errors in your thinking, means you will remain in error. If you are a person with the ear of a great number of educators, that means those educators who listen to you uncritically will also remain in error. If you are rewriting a curriculum for a state whose standards have an outsized impact on standards adopted throughout the country, then your errors will have an outsized impact on math education in general.

Jonathon Haidt explains how easy it is for humans, and social scientists, to fall into the trap of motivated reasoning in this piece, “Why Universities Must Choose One Telos: Truth or Social Justice.”

A consistent finding about human reasoning: If we WANT to believe X, we ask ourselves: Can-I-Believe-It?”But when we DON’T want to believe a proposition, we ask: Must-I-Believe-It?”This holds for scholars too, with these results:

Scholarship undertaken to support a political agenda almost always “succeeds.”

A scholar rarely believes she was biased

Motivated scholarship often propagates pleasing falsehoods that cannot be removed from circulation, even after they are debunked.

Damage is contained if we can count on “institutionalized disconfirmation” – the certainty that other scholars, who do not share our motives, will do us the favor of trying to disconfirm our claims.

I’m not claiming that everything Boaler says is incorrect and I’m sure her intentions are good. As I mentioned above, she is indicative of a much wider problem. I’m saying that someone who either knowingly manipulates data or can’t see the error in her analysis of the data shouldn’t go on perpetuating those ideas without criticism from educators who care about math education. In most situations educators don’t have the time or expertise to truly evaluate the claims made by education researchers. In this case Families for San Francisco did the legwork and revealed that the emperor has no clothes.

I encourage math educators that read this to share their report widely, counter claims and proposed changes that are based on SFUSD data, and promote an environment in which leaders in education are concerned about truth and pursue it through viewpoint diversity. Since Boaler is a leader in progressive math education, it’s up to people who support her work to point out how her analysis is flawed. We must call on her to stop pushing for policies that don’t help, and may actually harm, students in the name of falsely vindicating her ideas. It may be easy to dismiss critique’s from the “other side” as they will always have critiques. It’s much harder to dismiss a careful critique from within one’s tribe.

If this ordeal shows us anything it’s that we must be careful who we valorize – and that we must keep our eyes open and be ready to criticize their ideas when appropriate.

Antiracism in your school: 9 ways to keep the conversation rational and unifying

A few years ago, I noticed that the words diversity, equity, and inclusion were steadily gaining in popularity, especially in K-12 education. At first, I couldn’t see a problem with the concepts. But as I dug deeper I discovered that much of the movement behind these words, although advanced by people with the best of intentions, was contradictory, illogical, and somewhat unethical. Take the defining of every action as either “racist” or “anti-racist, for example. It’s easy to find examples that seem to be neither, but more importantly this framing necessarily divides the staff of a school and narrows the set of ideas discussed, rather than diversifying it. A search for structural barriers to the learning of minority subgroups of students should be taken up by every district, but I’m deeply skeptical that the captivating ideas of the current moment give us the tools to identify and remove those barriers.

Although diversity, equity, and inclusion initiatives have been issues of focus in higher education for a while, the suite of ideas, which I term “the social justice suite of ideas”, such as antiracism and white fragility, skyrocketed in popularity in K-12 schooling shortly after the killing of George Floyd by the police. As the ideas began to gain traction in K-12 schools and school districts—beyond just living on Twitter—I decided to create guidance for K-12 administrators and school leaders, like has been done for university leadership and administrators, to ensure they can avoid the nearly inevitable pitfalls that come along with the social justice suite of ideas. 

I want to be clear about something at the outset—if there are structures in schools that create a disparity in outcomes between different groups of students then we should make an honest effort to understand them and to have a clear-headed discussion about altering that structure. But I reject the assertion that disparity is only caused by racism and the conclusion that the social justice suit of ideas is the only remedy for the disparity. 

Notably, there is no lite version of diversity, equity, and inclusion. It’s not as if you can do training for a year and be done with it. Because, according to the social justice suite of ideas, all inequities are structurally caused, the remedy is diversity, equity, and inclusion training, and if inequities persist, then you need to do more of the “work”. But the social justice suite of ideas asserts that inequities will always remain—advocates of these ideas proclaim that the work is never done, which points to one contradiction in these ideas. As Robin DiAngelo, a prominent figure advancing the social justice suite of ideas stated, “I will never be completely free of racism or finished with my learning”.  

There are ways for administrators and school leaders to ensure that this movement brings about positive change. First, understanding the language of this movement is important because many of the words and phrases used seem inherently good. (Who wouldn’t want to be “anti-racist”?) New Discourses has an encyclopedia of the terms used in the social justice suite of ideas. Then, when teachers, staff, and community members propose implementing the suite of social justice ideas in your school, I suggest following these nine steps:

  1. Define all the terms at the outset so everyone is clear as to what is being discussed, and then agree upon the terms. 
  2. Demand specificity in regards to the problem being addressed. If the charge is racism, continue to demand specificity. Do not accept the charge that we are all racist to some degree and the gap can be fixed by all of us interrogating our own racism. 
  3. Demand to see data that demonstrates there’s a problem. Make sure that the data presented is data that everyone agrees is meaningful. For example, someone might claim standardized tests are racist. A reasonable question might be, “if they’re racist then why should we care about disparities in their results?”
  4. Look for proxies that might get at the root of the problem or help more students. For example, if racial or ethnic disparities exist, are there other factors that correlate with the racial disparities, like poverty or childhood trauma? 
  5. When activities or professional development are suggested, demand to see research supporting the efficacy of the activity or training. Be careful here—there is a lot of pseudoscience masquerading as research. Make sure the research actually supports the professional development and is relevant to the data used to demonstrate the problem. Simply because the author has a Ph.D. does not mean the preceding text is high-quality research. 
  6. Do not let the advocates define you. The social justice suite of ideas has created a binary— you are either a racist or you are anti-racist; there is no place to stand in between. This relies on a redefinition of the word that makes the bar for “racism” so low that anyone can and will trip over it. If you resist  suggestions from the social justice suite of ideas in the ways that I mentioned above, you risk being called racist. Do not cede this linguistic territory. Begin compiling a list of all the ways you’ve reached out and supported minority students and communities. This almost certainly won’t be good enough―if there’s any kind of achievement gap across any metric then there must be racism causing it, according to the social justice suite of ideas. But it can be used to demonstrate to the broader community (within and outside of the school) that you are in fact working on supporting students from different backgrounds. 
  7. As a follow-up to number six, you might want to consider beating the advocates to the punch. What disparities might the group be aware of or will find? Point them out to the group and propose research-based ideas for how they might be remedied or how you are attempting to address them currently. 
  8. Be very careful with appeasement. Resist the thought, “well if I give them this then they should be happy”. Staunch advocates for these ideas won’t be happy until all subgroups are achieving at the same levels. As I mentioned above, the solution, in the minds of advocates, is to advance the social justice suite of ideas, even if those same ideas have so far failed to fix the problem. They will contend, there must be more racism amongst the staff and the staff must not be working hard enough to eradicate it—the staff must not be doing enough antiracist work.
  9. Draw lines. As you learn more about what advocates want, make sure that you draw lines that you won’t cross. A reasonable line might be that you won’t approve mandatory implicit bias training. As one of the early researchers on implicit bias stated, “mandatory (implicit bias) training has the potential for backlash”. The Implicit Association Test, on which the training’s justification rests, has plenty of staunch critics. They cite the low test-retest reliability, weak evidence that implicit bias leads to actual discrimination, and questionable methodology in early meta-analyses. When drawing lines, be sure to engage with a diverse set of perspectives. 

If structures in your district hold back certain groups of students then you should work to remedy or eliminate those structures. But you should do this in a rigorous, scientific, and careful way. Book studies of “How to be an Antiracist” or “White Fragility”, diversity training, or implicit bias training will not provide solutions to the problems. 

While listening to Mike Strambler, professor of psychiatry at the Yale School of Medicine, in a roundtable discussion put on by Heterodox Academy’s HxK-12Education Community, he made a point that resonated with me. While discussing the problems with the social justice suite of ideas as they relate to K-12 education, he pointed out that no one in education wants there to be massive disparities between different groups of students, and that rich discussion can come from trying to eliminate structures that lead to those disparities. But the way that happens most effectively, he suggests, is by doing the following: defining the goals at the outset, identifying the metrics that will be used to evaluate those goals, and settling on methods that arise from bringing in a diverse set of viewpoints into the discussion. An effective solution is more likely with this approach (and division amongst staff less likely), than one grounded exclusively in the social justice suite of ideas. (You can see the beginning of that discussion here).

Further Reading:

You’ve been mandated to do ineffective training. Now what?

Diversity, Equity, and Inclusion in K-12 Professional Development: The Mission Versus the Reality

Responding Constructively to Mandated Diversity Trainings

We’re Teaching Slope Fields at the Wrong Time

In our textbook slope fields come during the differential equations unit, which for the last 8 years made sense to me. But every year there were groans from students and comments about how “pointless” they are.

Well, here’s why students think they’re pointless.

They already know antiderivatives. So they can take many differential equations and find the family of functions whose derivative is given. Many of the basic slope field problems can be somewhat easily antiderived, especially once students know about separation of variables.

“But, wait. Not all differential equations can be antiderived!”

This is true. And I point this out to students. They don’t really seem to care when they have to plot 25 line segments on a sheet of paper. For one problem. Especially once I show them how easily a computer can plot slope fields. I also think it’s in part because they don’t connect to very much. We just do the section and move on.

So I’ve been thinking about this for a few weeks, on and off, trying to figure out how to motivate the lesson. Here’s what I’ve come up with.

When I teach a derivative rule (the power rule for example), the next day I teach the antiderivative. It’s fairly easy for students to follow and then remember, because they just learned the derivative the previous day. Antiderivatives are just the process of undoing a derivative. This is as opposed to how my textbook does it, which is save all antiderivatives for the integration chapter. Anyway, instead of doing that, I think I’m going to show slope fields in between. In other words, I’ll teach a derivative, then use a related differential equation to get students to think about what a “slope equation” means and plot it, and THEN teach the antiderivative rule.

It would go something like this:

  1. Teach the power rule.
  2. The next day give students something like dy/dx=x – 1 and ask them to think of it as a “slope” equation. Inputs are whatever you want, outputs are slopes. Ask, “What will this look like?” Help students work out a sketch of the slope field.
  3. Then teach the antiderivative rule.

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There will certainly be some students that figure out the antiderivative rule prior to or during work on the slope field(s). But at least this provides more of a motivated use for a slope field:

“What does the function whose derivative is ______________ look like? Well, we have this slope equation and it gives us the slopes of tangent lines at whatever point we want. Let’s use that to build a graph that gives us an idea of what that function (or family of functions) looks like.”

You could use this throughout the units on derivatives, including things like implicit differentiation. For instance, “We know how to derive x^2+y^2=9. But what if you’re given something like dy/dx=2x/y? What would that family of curves look like?” And then you can use a slope field.

It’s possible that this isn’t a great idea. Maybe it’s better to just leave slope fields as their own thing, drag the students through them, and move on. But I do think it would help students understand that a differential equation is a “slope equation”, and that it’s useful. I also think it might help students better understand what a “solution” to a differential equation is and how we might visualize it. Last I can imagine students would come to the “differential equations” unit already fairly comfortable with a lot of the concepts in it.

Any thoughts on this? Drop them in the comments!

Update: The first activity inspired by this post is located here.

Another update: The second activity, involving trig functions, is here.

I have a couple of questions about “Social Justice Math”

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I have a couple concerns regarding “Social Justice Math” that I don’t think I’ve seen addressed. (If they have been, please let me know.)

From what I’ve read SJM is billed as a way to bring real world problems into the classroom with a “justice” lens. Problems related to climate change, economic inequality, racial equity, etc., would be used in class as frameworks for learning different math concepts. (Read more on that here.) In fact, it sounds a lot like Project Based Learning but with a more refined list of suggested issues to study.

The first concern I have is that, like it or not, “Social Justice” is associated with the political left.

Do those advocating for SJM openly say this is a political slant on mathematics and embrace it as such? (Let’s call this “motivation A”.)

Or do they argue they’re talking about social justice (fairness to people in general, without the political connotation) and not Social Justice? (Let’s call this “motivation B”.)

In the former case I’d have real concerns if I was conservative minded person and my child was in that class (or independently/liberal minded and concerned about one political viewpoint seeping into mathematics curriculum). In the latter case the perception will still almost certainly be taken as a leftward spin on math, again because “social justice” is attached to the political left.

The second concern I have is, what exactly is the “social justice” aspect of the math. Is it simply the selection of the topics chosen? Or is it in the conclusions that come from the students’ analysis? Will the teacher point out that social problems are complicated and that both the left and the right have something to say about their causes and solutions?

I can imagine a teacher trying to present these problems in an unbiased fashion and letting students arrive at a variety of remedies to the problems (motivation B folks). But I would bet money that many teachers implementing SJM will be pushing students to arrive at solutions from the political left (motivation A folks).

If they weren’t, then why call it “social justice” math? Why not call it “real world mathematics” or some other less politically charged title that still acknowledges you’ll be analyzing problems that humanity faces? (Again, this seems a lot like a political form of Project Based Learning.)

I fear “Social Justice Mathematics” is the title because they don’t want students to learn to take a dispassionate approach to the problems. They want students to take a certain, Social Justice approved, approach to analyzing the problems. If this is the case then I think we’d be right to push back against SJM, and if it isn’t the case then SJM will face a branding issue for the foreseeable future.

Are my concerns justified or am I way off base? I’d love to discuss it in the comments.

“Why do we need this?”

My students in precalculus class have asked a few different times over the last couple of weeks, “When will I need this?”. I encourage them to ask this question of their teachers, because the teacher should be able to answer it. But when it comes up in the middle of a lesson I don’t really have time to answer it fully, so here are my thoughts, in a thought out format.

  • The blunt answer is that this is an elective and no one is making you take this. And if someone is making you take it (your parents, for example) then I can’t help you. I wouldn’t be satisfied with this answer if I was you, but it is true.
  • We don’t know and you don’t know what you’ll end up doing, so it’s better to err on the side of a broad knowledge base in high school.
  • These are things you need to understand if you’re going to take more math. Why might you take more math?
    • You might want to study math
    • You might want to go into a math related field
    • You might want to go into a science related field where calculus, at a minimum, will likely be required
    • You might want to go into pre-med or pre-vet (or pre-law?), where you’ll likely have to pass a calculus class
    • That’s what this class is designed for. That’s it’s stated purpose. It’s to get you ready for calculus, regardless of the reason you might end up taking calculus.
  • I admit, math is also a gatekeeper. It’s a way to check your level of competence. I’m not making a statement about whether that is right or wrong, but it is true. See a great exploration of this idea in Bad Drawings here.
  • But more broadly, math is giving you a language to describe and understand that world. Sinusoidal behavior (which is what we’re studying now) is everywhere. Anything that works on circular motion or has periodic behavior can be described by sine or cosine waves.
  • It also helps you exercise your rational thinking and pattern finding muscles. We don’t always do a great job of helping you work the pattern finding muscles, but the reasoning muscles are exercised every day. When you solve a problem you are reasoning. You put together a chain of logical statements, either explicitly or implicitly, to arrive at a conclusion. And those statements aren’t the same for each person, which is a great thing. There’s often more than one logical way to arrive at the same conclusion. But this mindset, of taking on assumptions and arriving at logical conclusions based on those assumptions is a vital component of thinking critically. It’s how we persuade other people. It’s how we make progress. It’s how we call BS on people when they make claims or statements that don’t make sense.
  • Mathematics, and the different parts of mathematics, can be viewed as games of sorts. You are given some rules (axioms, theorems, etc.) and then you see what is true given those axioms. You see how far you can push the rules and how far you can get in the game. But they’re often better than an arbitrary game. Many times they have implications in reality (although this isn’t a necessary condition for interesting mathematics and is not necessarily where mathematicians spend all their time). And sometimes those implications aren’t seen at the time, but turn out to be useful later on in science. A mathematical truth is a truth about reality itself.

The fact that we attach grades to mathematics does minimize some of this. It’s not a fun game to play if there are real consequences (in terms of grades) for not understanding the rules quickly enough. And I get that. But I reject the notion that we should throw the whole project out the window because what you’re learning on a Tuesday in precalculus might not help you navigate your grocery shopping trip.

Thinking, Fast and Slow (Part 3)

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The first two parts of this series were created using Adobe Spark Page. I found while creating this third part that most of what was in it was text, and that a more stable place to host it was probably my blog. Hence, here it is. I’d encourage you to check out Part 1 and Part 2, if only briefly, before reading this part. 


We see in the last few chapters of Part I of the book that System 1 is a story teller. This system helps you make a coherent narrative of the world. This, like most things, has positive and negative aspects. I think the shortcomings of this tendency are important to understand.

The first problem with System one is that it’s relatively easy to manipulate it, especially since so much of it happens automatically. Take the following example from the book. Read the two words below.

Bananas

Vomit

In the second or two it took you to read those words and immediately following reading them you had a reaction. Some of it was physical, like the hair on your arms probably stood, your sweat glands were activated, your heart rate went up a bit. But you also likely sketched out a story that involved bananas causing the vomit (or in some other way being connected to the vomit). You did this automatically as system one is attempting to fit the input into a coherent story.

This, like most things, has positive and negative repercussions. It means that we are likely to seek out and find information that fits with the story system one is telling us. “Sally is lazy.” “James is smart.” “Maria is a hard worker.” Once we’ve put these narratives in our mind, system one tries to find information that fits the narrative. And while system two should be the hero here, always evaluating the assumptions of system one, it turns out that system two is a bit lazy. It’s much easier for system two to just go with the narrative. It takes cognitive work to constantly be evaluating everything system one is telling you, so often times that work is avoided by system two.

The key here is that we are aware of the narratives and stories we have in our minds. We need to be on the look out for information that both confirms our narrative (to be sure it does in fact confirm the narrative and that we aren’t overlooking something) and negates the narrative (so that we can change the narrative in our minds to better represent reality).

One major theme of the associative machine is this: when there is some sort of external input to your brain you’re not consciously aware of what’s going on in your brain. When you see an object or hear a sound or experience a feeling, you’re flooded with ideas which in turn activates more ideas. Only a few will pop up in consciousness and this flood of ideas is largely out of your control.

What does this mean for teaching?

When we deal with students we have to remember that fact. Much of the time they (and we, whether we care to admit it or not) are at the mercy of system one. Actions that you take or that other students take in the classroom can set off chain reactions in a student’s brain. The result could be positive or negative. You can imagine starting a lesson with some sort of introduction that primes students for learning, giving them some ideas that ignite other ideas (you might call this engaging prior knowledge) or put them in a positive mood. The latter idea is from Eric Jensen and is also described in the book and that is that being in a good mood helps your brain be prepared to understanding new concepts. You could also imagine taking some action that results in an unwanted behavior. The key to dealing with these behaviors is figuring out what the underlying cause of the behavior is. What is triggering their associative machine to result in the behavior?

The last note I want to make here is that we need to help students understand what’s going on in their brain. Just as I encourage anyone reading this to try to keep a check on the automaticity of system one, we should find ways to help students do this as well. I think doing activities that encourage metacognition is a critical step in that direction, but that’s a topic for another day.


Image is “Thinking” by Lee Thatcher. The original work can be found here.

The Absurdity of One-to-One Initiatives

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As comes up every year, someone in our department suggested we go one-to-one. Of course, this sparked lively debate. So much so that do to the frequency of these debates and the cycle of outrage I invariably go through after each one, I’m motivated to write out the multitude of reasons that going one-to-one with textbooks is an absurd idea.

First, let’s talk about costs. A good textbook costs close to $100. Sometimes less, sometimes more, depending on how many you buy. If a kid has five classes, that means it’s going to cost roughly $500 dollars per student to go one-to-one textbooks. And it’s not just $500 one time. Of course not, because in a few years much of what’s inside the books will be dated. They will need to be updated and some of them will be so obsolete they’ll need to be replaced entirely. Do we want to go through the up front costs and then the future costs to update and replace them?

Second, let’s talk about letting teenagers carry around several hundred dollars in textbooks. Have you seen the average teenager’s bedroom? Of course not! There’s too much stuff on the horizontal surfaces (and maybe even the vertical surfaces) to actually see any substantial part of the room. Are we going to let kids, who can hardly get a dirty tissue to the trash can across the room, be responsible for hundreds of dollars worth of school property? I think this is a nightmare that no administrator or teacher wants to deal with.

Third, I’d ask you if the cost is worth the benefit. Sure, textbooks have lot’s of knowledge in them. Give students books corresponding to the subjects they’re learning allows them to easily and quickly look up information, helpful diagrams, maps, and other media, but don’t we have teachers for that? Teachers have much of this knowledge, and if they don’t, then they can look it up in their book and deliver it to the students. What’s the point of a teacher if all the information is easily available to the students? Sure, the best teachers might use the books in coordination with their teaching ability to create near sublime learning experiences, but this would surely only be the most motivated of teachers, not the norm.

Fourth, it would be a logistical nightmare. Suppose your high school has 1000 students. Then we are talking about THOUSANDS of textbooks to keep track of. Not just keep track of, but record those that go missing and those that are damaged. Then schools have to make determinations about how much the damages cost. Then who pays for it? The students? What if it’s an accident? What if the student can’t afford it? What if they get lost in a house fire? Who’s on the hook for the bill then? And who does this burden of tracking fall upon? The library? The administrators? The teachers? There’s no good options. And then, who fixes them? Do we offload this responsibility on the already short staffed library personnel? We’d probably have to hire somebody to spend part of their day repairing textbooks, so tack that on to the bottom line.

It seems clear that the costs of trying to put the these resources into the hands of each student almost certainly outweigh the benefits. But this fight will never die. Year after year we’ll continue to hear how we should “give students access to the tools they’ll be using when they leave us”. Given what I’ve outlined above, I can’t see the logic that results in this being a good idea.

Update: I should make something clear. This is purely satire. I am simply trying to make the argument that when it comes to discussions of 1 to 1 technology I think the problems that are brought up are often ones that we have solved in other contexts. This situation never came up in my department. And even if it had, I would never throw them under the bus like this publicly. Once again, this is purely satire.

We should always be learning something new

Last week I started auditing a class on Hapkido, which is a Korean martial art. A friend asked if I’d be interested in attending the once-a-week class with him and I said I would. Having never done any martial art at any time in my life (I don’t even think I’ve watched any of the Karate Kid movies in their entirety), I was nervous. However, partway through the class I realized that there is clear value in learning something completely new.

I want to list a few feelings I had, as I think they reminded me of what it’s like to be a learner, as an adult or a teenager.

  • I didn’t want to make any mistakes. When the instructor demonstrated something, I wanted to do it perfectly. This notion is ridiculous because, as the instructor also pointed out, it takes thousands of repetitions before something becomes muscle memory. For as much as I preach the importance of mistakes in learning, I was shocked at how somewhere in my guts I still didn’t want to make them.
  • I didn’t want the instructor to come by me. Or at least if he did I wanted to be working on my right side (which I thought I was better at). I was afraid he’d find something I was doing wrong. Which I consciously knew would not be bad as it would get corrected and then I’d improve.
  • I compared myself to the people around me, unconsciously ranking myself. Better than that person, worse than those two, etc.
  • Frustration. I’ve never been particularly coordinated and I was consistently frustrated at knowing in my mind what I wanted my body to do, but struggling to make my body do it.

I walked off the mat at the end of class and my mind was reeling.


“Now I know why students are apprehensive to ask questions.”

“Now I understand better why a student might get uncomfortable while I hover over them watching them work out a problem.”

“I have to constantly remind myself to embrace the difficulty. That’s where growth comes from, but it’s difficult to do in practice.”

“Having an instructor that recognized we were all learning was incredibly helpful. He created an atmosphere where mistakes were not viewed as setbacks, but part of the process.”


My main takeaway was that these are feelings I need to constantly grapple with. I need to try to put myself in situations in which I’m the learner, with relative frequency. It helps me better understand where my students are coming from and I think will ultimately help me become a better teacher.

Also, here’s one more thought that has popped in my head recently and probably doesn’t need an entire blog post, but fits with the theme in this one. I’m in my fifth year teaching precalculus, AP calculus, and algebra II and I can feel myself having less empathy with my students, with people learning the concepts for the first time. The first year I taught these courses I think I had a better understanding of their struggles as I was solidifying my understanding of the concepts prior to teaching them as well. I’m not entirely sure what this means for my teaching now, but I think awareness of it is important.