Why you don’t see me hyping AI

There’s no ignoring the recent wave of advancement in artificial intelligence or AI. From the near photo-realistic outputs of Stable Diffusion to the pseudo-coherent text produced by ChatGPT, generative machine learning algorithms have taken the world by storm. As someone with a background in mathematics and statistics, these are without doubt fascinating advancements that I’m interested in from a technical perspective. At the same time, I have numerous concerns about these algorithms from an ethical perspective that I don’t think I’m alone in holding. That cheesy line from Spiderman about power and responsibility rings truer now than ever. To assume that we can reap the rewards of AI without accepting any risk would be a fallacy of apocalyptic proportions.

If you’re looking for a review of the literature on the hidden risks of AI, there are more intelligent people than myself that you should probably be looking for in a peer-reviewed journal. There is very little I can say about ChatGPT that hasn’t already been better articulated in Stochastic Parrots. Instead, what I’d like to offer you today is a story of a stupid teenager and his chat bot. I don’t expect it to alter the course of history or anything, but maybe it’ll provide some insights into why you should care how these technologies are being used.

I started programming in my early teens and AI was always something of a holy grail. I was especially partial to the Turing Test as an indicator of consciousness. In this test, a computer program is tasked with deceiving a human into false believing that they are engaged in a text-only conversation with another human. Turing argued that if human experimenters couldn’t distinguish between programs and people then we’d have to consider the hypothesis that machines could effectively “think”. There are arguments to be made about whether or not the Turing Test measures what it intended to, but advances in Large-Language Models have made it clear that this standard is now just a matter of time.  In fact, I’d argue that the Turing Test was “effectively passed” in the early 1980’s by a program called ELIZA developed by Joseph Weizenbaum. 

ELIZA was designed to be a sort of “virtual therapist”. A human user could talk to the computer about things that were on their mind, and ELIZA would turn their statements around to form new questions. For example, if you told ELIZA “I had a rough day at work” it might acknowledge that you’re feeling upset and inquire about it: “I’m sorry to hear that. What about your day made it rough?”. ELIZA didn’t actually know very much about the world, but it could engage a human in a fluid and convincing conversation that led the user towards self-reflection. Some users walked away from ELIZA feeling like they were engaged in dialog with a real therapist. A recent preprint from UCSD researchers indicates that ELIZA’s performance on the Turing Test is between that of GPT-3.5 and GPT-4.0.  Not too bad for a program from the 80s. 

Of course, any deep interaction would reveal the lack of “intelligence” on the other side. ELIZA couldn’t answer questions about the world. All it could do is to classify different sentences into schema and then transform them into canned responses using key tokens from the input text. Simple rules like “I feel <sad>” would get matched and transformed into “Why do you feel <sad>?”, which gave ELIZA the illusion of being a good active listener. This might sound kind of sad, but ELIZA was probably better at active listening than I am – and I knew it all too well.

As a teenager in the late 90s, we didn’t have the pervasive social media outlets we have today. There was no Facebook or Twitter for you to doom-scroll. Maybe you had a public facing Geocities or MySpace page, but that was only if you were a nerd like myself. The de facto standard for internet communication was AOL Instant Messenger (or AIM) .  Even if you weren’t subscribed to AOL’s internet access, you probably still used the stand-alone AIM application for direct messages because it was literally the only service with enough members using it to be useful. You can’t have real-time communication without a shared protocol shared by people.

The application wasn’t even that great by today’s standards. It was full of what would now be considered negligent security vulnerabilities. In early versions, you could easily kick someone offline by sending them an instant message with some malformed HTML. If someone saved their password for easy login, it was literally stored in a file as plain text and could be subsequently looked up by anyone who knew where to check. It was the wild west era of the internet.

Around the same time, I discovered a project called ALICE.  Richard Wallace had taken ELIZA’s token handling foundation and generalized it into an Artificial Intelligence Mark-up Language (or AIML).  This separated out the “code” and “persona” of the chatbot into two separate data sources.  The HTML-like syntax made it easy to customize the bot’s responses into whatever you wanted.  The application would read these source templates in and use them to craft a response to any message you gave it. 

While I’m reading article after article online trying to figure out how this stuff works, I keep getting instant messages from people. These messages are not malicious in any way, but receiving them has a tendency to “pull me out” of whatever I’m doing at the time. Sometimes I’m pulled into fun stuff through these messages, but often than not they were just an annoyance. As a teenage boy in the 90s, the vast majority of these interactions went down like this:  

sup?

WHASSSUP?

not much, u?

just chillin’

cool deal. me too.

anyways.. I got some homework to do. I’ll catch ya later!

aight. peace out!

That’s when I got the brilliant idea to fake my own AIM account.

While exploring the flaws in the AIM application, I discovered I could hijack the message queue that distributed incoming messages to the appropriate chat window.  This allowed me to parse the incoming message text and send fake keystrokes back to that window to produce a response. All I really needed to do was to invoke the chatbot as an external process to generate something to say.

I took an open source implementation of ALICE and started modifying the AIML code.  I removed any instance where the bot acknowledges itself as an artificial intelligence and instead taught it to lie that it was me. I added custom responses for the greeting I customarily used and gave it some basic knowledge about my areas of interest.  The only difficult part of this was getting the bot to handle multiple conversations at the same time, which I managed to accomplish by running separate instances of the bot for each person to message me.

I think I let the bot run for most of the week without anyone really noticing, until this one day where I got an instant message– from a girl.  Not just any girl either, but one I totally had a crush on at the time. My heart sank as I read the messages interspersed between the AI dribble.

Ryan, are you okay?

This isn’t like you.

No really, I’m worried about you.

If there’s something wrong, we can talk about it.

Please tell me what’s going on. I’m really concerned about you.

I felt sick. I immediately killed the process running the bot and seized control of AIM again. I don’t even remember what kind of bullshit excuse I made before abruptly going offline, but I’m pretty sure I didn’t have the courage to own up to the truth.  I had been “seen” through the eyes of another person in a way I hadn’t experienced before, and the worst part about it was that I didn’t like what I saw. I saw a person who lied to their closest friends in the name of science. 

I know this won’t make up for what I did, but I’m sorry.

I’ve since then learned a lot about research ethics in psychological studies.  Sometimes having deception is a necessary component to studying phenomena you’re interested in, but that is not sufficient reason to forgo the acquisition of “informed consent” from the people involved in the study.  

I think this is the reason why I’m frustrated with the current zeitgeist regarding AI. It seems like we’re rapidly falling into the trap outlined by Ian Malcom in Jurassic Park.  Some people are so preoccupied with what they could do with AI that they don’t stop to think about whether or not they should.  As a result, we’ve all become unknowing participants in an unethical research study.  While this behavior might be excusable coming from a punk teen who doesn’t know any better, this should be considered completely unacceptable coming from multi-billion dollar companies claiming to be advancing the forefront of intelligence. It’s not that “I’m scared of AI”, it’s that “I’m scared of what people will do with AI” when they acquire that power without putting in the effort to truly understand it. 

The wave of AI images coming from DALL-E and Midjourney on all my social media don’t self-identify themselves as being artificially produced. The burden of identifying them has been left to unwitting viewers and it will only become more difficult over time. While this makes for entertaining stories on Last Week Tonight, there’s a big difference between using AI to make funny pictures to share with your friends and using it to develop sophisticated social engineering methods to separate users from their passwords.  

The reality of our time is that many AI offerings are being falsely advertised as a solution for intractable problems. No image generator could possibly produce pictures of John Oliver marrying a cabbage without first being trained on a set of labeled images including the likeness of John Oliver.  Any AI image generator trained solely on ethically produced data sets, like the one from Getty, will inherently lack the capacity to reproduce the likeness of pop-culture celebrities. Either the generative AI will fail to produce the likeness of John Oliver or it was trained on a data set including his likeness without seeking prior permission.  You can’t have it both ways.  

In much the same vein, it would be impossible to ask ChatGPT to produce writing “in the style of Ryan Ruff” without it first being trained on a data set that includes extensive samples of my writing. Obviously, such samples exist because you’re reading one right now. However, the act of you reading it doesn’t change my rights as the “copyright holder”. The “Creative Commons” licenses I typically release my work under (either CC-BY or CC-BY-NC-SA depending on context) require that derivative works provide “attribution”.  Either AI will fail to reproduce my writing style or it illegally scraped my work without adhering to the preconditions.  In the event my work is stolen, I’m in no financial position to take a megacorp to court for compensation.

In discussions about AI we often neglect the fact that deception is an inherent component of how they are constructed. How effective we measure AI to be is directly linked to how effectively it deceives us. As poor of an intelligence measure as the Turing Test is, it’s still the best metric we have to evaluate these programs. When the measure of “intelligence quotient” (IQ) in humans is a well-established “pseudoscientific swindle”, how could we possibly measure intelligence in machines? If you want a computer program that separates true statements from false ones, you don’t want an “artificial intelligence” but rather an “automated theorem prover” like Lean 4. The math doesn’t lie.

I think one of the big lessons here is that the Turing Test wasn’t originally designed with machines in mind.  I still remember discovering this when I looked up the original paper in Doheny Library. The “imitation game” as originally described by Turing was primarily about gender.  It wasn’t about a machine pretending to be a human, but rather a man pretending to be a woman.  

Personally, my present hypothesis is that Turing was actively trying to appeal to “the straights” with how he described the imitation game. My incident with my AIM chatbot had taught me that there were large differences between how I interacted with “boy” and “girls”.  Conversations with “boys” were shallow and unfeeling – easily replicated by my script. Conversations with “girls”, however, were more about getting to know the other person’s perspective to determine if we’re a potentially compatible couple.  Casual conversation and romantic courtship require two entirely different strategies. Maybe the Turing Test was less about determining if machines could think and more about determining if machines could love.

Every now and then I feel overwhelmed by the flood of interaction that is constantly and perpetually produced by social media. Sometimes I wonder if my presence could be automated so that I never miss a “Happy Birthday!” or “Congratulations!” message ever again, but then I remember this story and remember that’s not really what I want.  I don’t care about “likes”. I care about building “friendships” and there’s no possible way a bot can do that on my behalf.  

Maybe I could be a better friend if I collected data on my social interactions.  At the same time, I don’t need any sophisticated statistics to tell me that I’m kind of an asshole. I’d like to think that the people I call my friends are the same people that would call bullshit on me when necessary, so I trust in them to do so. This is the difference between real human relationships and fleeting conversations with a chatbot. 

There’s nothing inherently wrong with the class of algorithms that have fallen under the “AI” umbrella, but how we use these tools matters.  Presently these bots are being marketed as a substitute for human labor but the reality of our legal system dictates that there still needs to be a human accountable for their actions.  The only viable path to survival for AI focused companies is to become “too big to fail” before they get caught for using pirated data.

I’m not going to sit here and pretend that AI won’t have its uses. Maybe AI will come up with solutions to important problems that humans would never have thought up. If every other technique for solving a problem is unreliable, there’s less harm to be caused by attempting to solve that problem through massive amounts of data. It makes sense that such statistical tools might come in handy in fields like marketing or cybersecurity where the rules of the system are ambiguously defined.  

What is clear to me is that there exist problems for which AI will never be a viable solution. GitHub’s Copilot won’t ever magically solve Turing’s Halting Problem. It’s called “undecidable” for a reason. Using ChatGPT won’t make me a better writer, nor will using DALL-E make me a better artist. There is no substitute for the process of turning my thoughts into a concrete form, and the only way to get better at those skills is to engage in them myself. Learning the internals of how AI works may have helped make me a better mathematician, but I wouldn’t expect it to solve P = NP anytime soon. 

Given my background in teaching, I was recently asked what I thought about applications of AI in education and I think it’s incredibly important that we take an abundance of precaution with its integration. This is something I’ve written about before, but I think it merits repeating that “AI needs to build a relationship of trust with all of the stakeholders in the environment”.  In our society, we depend on teachers to be “mandated reporters” for child abuse and I don’t think AI can responsibly fill this role. Without having the lived experiences of a human being, how could such an AI possibly know what symptoms are out of the ordinary?  What if it’s wrong?

Our very notion of “intelligence” is arguably shaped by the common human experience of schooling.  In my time teaching, I learned that the profession depended as much on “empathy” as it did “knowledge”.  Most of the people I’ve met who “hate math” developed this mindset in response to abusive teaching practices.  In order for AI to ever succeed in replicating good teaching, it needs to learn “how to love” in addition to “how to think” and I don’t think it ever can.  

Even my use of the word “learn” here seems inappropriate. AI doesn’t technically “learn” anything in a conventional sense, it just “statistically minimizes an objective cost function”.  Seeing as “love” doesn’t have an objectively quantified function, it therefore it’s impossible to replicate using the existing methods of machine learning.  Even if a machine were capable of expressing love, the act of replacing a human being’s job with such an AI would go against the very definition of what it means to love.

As with any new technology, AI can be used to make our lives better or worse depending on how it’s used. Let’s not lose sight of “why” we’re constructed these systems in the first place: to improve the quality of human life. Building these programs comes with a very real energy cost in a world where humans are already consuming natural resources at an unsustainable rate. If the expected pay-off for these AI systems is less than the expected environmental costs then the only responsible course of action is to not build it.  Anyone who fails to mention these costs when it comes to their AI product should be treated as nothing short of a charlatan.

I can’t shake the feeling that we’re in the midst of an “AI hype bubble” and it’s only a matter of time before it bursts. I can’t tell you not to use AI, especially if your job depends on it, but as your friend, I feel it’s important for me to speak up about the risks associated with it. 

True friends know when to call bullshit.

Teaching Statement

I didn’t become a teacher with the intention of doing it forever.  My original goal was to design educational video games, but I felt it would be presumptuous of me to build such technology without ever having set foot in a classroom.  Becoming a math teacher seemed like the fastest way for me to find out what kinds of tools schools actually needed. Now I’m not even sure I’m the same person.  

I made countless mistakes during the twelve years I spent teaching, but the one thing I think I got right was approaching it with a “here-to-learn attitude”.  Learning can only take place with the learner’s consent.  Opening one’s self up to learning a new skill means allowing oneself to be vulnerable to mistakes.  Teaching is about creating an environment where multiple learners feel comfortable with the risks of engaging in that process together. The first step is to establish a relationship of trust.

In all honesty, relationship building has never been one of my strengths so I had to make an active effort to improve on it as a teacher.  I found that the most powerful method for facilitating a student’s learning is to simply ask what they need and listen to what they say.  Really listen and trust them.  It’s incredibly difficult to learn when you’re tired, hungry, or stressed. Sometimes “taking a break” is a necessary stage in the learning process. Treating people with kindness is a prerequisite for any meaningful learning to take place.   

One of the most difficult challenges for me as a teacher was learning how to navigate spaces of trauma.  For me, mathematics is something that evokes feelings of joy but my experiences are both highly abnormal and shaped by privilege.  More often a student’s experiences with mathematics are shaped by structural forms of oppression including racism, sexism, and ableism.  Learning how to openly reflect on how I was complicit in these systems was a key factor in my growth as a teacher.  I believe students should be able to see themselves in mathematics, so I tried to actively seek out and integrate the stories of mathematicians from diverse backgrounds into the curriculum.  The self-work continues to be an ongoing process.

My goal as a teacher was to construct an environment where my students could freely “play” with mathematics.  I feel learners are entitled to the opportunity of exploring mathematics and discovering new knowledge on their own.  Often the play comes with a set of constraints that help direct it towards a specific objective, but the important qualities are that the task has a low skill floor and high skill ceiling.  There should be both an easy way for everyone to engage and the depth to encourage further exploration.  Too often we fall into a trap of erroneously thinking there’s “one right answer” in mathematics, so I make it a point to include questions with “no wrong answer”.  I found this helped to foster a culture of collaboration in the classroom because everyone’s input is of equal value in the discussion.

Exploration has limited effectiveness when you’re obligated to address very specific learning objectives, so I usually follow up with some form of direct instruction to fill in the gaps. It’s not quite as engaging, but sometimes students need a concrete example of the behavior they’re expected to model. Our brains are very efficient at mirroring actions.  I’ve found that “worked examples” can also provide a valuable resource afterwards when the student is attempting to replicate the process on their own.  As the number of examples grows, the metacognitive process of learning how to organize this information can reveal insights into its structure.

The next phase of the learning process is to engage in a cycle of formative assessment and feedback known as “practice”.  Any new skill must be practiced to be maintained.  This is one area where I think educational technology excels, because it can enable nearly instantaneous feedback to learners.  While my students often enjoyed the “gamification” of practice, it’s important to select such products carefully.  I’ve learned it’s important for developers to remember that “accuracy is more important than speed” and “some skills cannot be assessed through multiple-choice”.  As our technology improves, so will our automated feedback.  I’m particularly excited about the potential applications of “Large Language Models” in this area, but the application of Artificial Intelligence will also require a great deal of testing before it meets the ethical criteria necessary for use in the classroom.

In the reality of schooling, there’s likely to be a summative assessment stage in the learning process as well, but I tend to think this distinction is artificial.  As far as my class policies were concerned, all assessments are treated as formative where possible.  I tried to allow my students the opportunity to retake assessments as often as needed to the extent I was able. This is another aspect of teaching I found heavily supported by technology.  The combination of algorithmic question generation with automated feedback made it possible for me to focus on the broader picture provided by the data over time.  

If anything, I tend to look at summative assessment data as a tool for self-reflection.  As a student, summative assessments provide me with a form of external validation that I have in fact learned what I set out to learn.  As a teacher, the relation between assessment data and my own performance was always a little bit fuzzy but the process of looking back at that data and asking questions about what I could do differently was an essential part of my personal self-improvement.  I think it’s important to not put too much stock in any one assessment and instead use multiple data sources like observations and interviews to help triangulate areas for growth.  

The final stage in the learning process is to teach what you have learned to someone else.  I think we sometimes overlook this stage because it starts a new cycle of learning, but there are subtle differences between having a skill and being able to teach that skill to others.  Through attempting to teach math, I often found myself seeing old concepts in a new light.  My knowledge of geometry and data analysis grew deeper each time a student asked me “why?”.   Sometimes the most powerful phrase in the classroom is “I don’t know. How can we find out?”.  Likewise, I’m thankful that I had co-workers that were more knowledgeable about teaching than myself and capable of sharing that expertise.  I’m hopeful that I’ll be able to use what I’ve learned about teaching to help others as well.

I’m not necessarily looking for another “teaching job” but the act of teaching has become inseparable from how I learn.   Even if no one reads what I write, the act of putting my thoughts into words has power in it.  No matter where I go or what I do, I will learn new things and attempt to teach them to others.  We face a critical moment in society where we need to recognize the true value of the skills that teachers can bring to an organization. Every organization must learn to grow and teachers are experts on learning how to learn.

a dream of hybrid

[The following is a work of fiction, but it doesn’t have to be.]

8:07 AM: I pull into the high school parking lot. As part of Group E, my badge won’t even allow me into the building until 8:15 because everyone has staggered start times to prevent overcrowding the hallways. I do some light stretching and practice Tai Chi in the parking lot while I wait. It helps me focus up for the day.

8:20 AM: I breathe in the aroma from my fresh cup of coffee before setting it down on my desk, putting on my mask, and picking up my tablet. My desk is right near the door, as I’m always the last person in and first person out. I still have a couple minutes before students arrive, so I catch up the school’s internal social media network while I wait. The Science Teacher on my team has recently started blogging, so I read her latest post and leave some supportive words in the comments.

8:25 AM: My class of 8 students are starting to line up outside the classroom, in an order now habit based on seating, and I greet each of them at the door. On the first day I told them that I’m not exactly comfortable with handshakes yet, so they have their choice of a Young Frankenstein elbow bump or an eastern bow. They all know I’m a total weeb so the bow is surprisingly popular. As I take attendance on my tablet, it gives me a reminder that it’s Tim’s birthday. I wish him a happy birthday and let him know that all his teachers signed a card for him which he’ll find on his desk.

8:32 AM: The students watch a pre-recorded video from the principal on the large monitor at the front of the classroom containing the days announcements. Meanwhile, I sit down at my desktop PC and start checking in students from the Zoom waiting room. As I say hello and log their attendance, one my of two monitors provides me with “just in time data” on the student I’m talking to. I congratulate Sue on her team’s Rocket League victory and give Kay some encouragement for their upcoming Debate.

8:45 AM: Class has officially started, but it’s not really “mine”. The English Teacher’s lesson is broadcast live into my classroom from the one down the hall. My class is actually one of 8 classrooms that constitute a single cohort. All 8 teachers and 64 in-person students in the cohort share a common start time, common classes, common lunch time, and common departure time. These groups were established through data clustering algorithms designed to group students with common needs while also promoting classroom diversity. While the English Teacher’s lesson is running, I monitor backchannels like the chat room and answer homework questions on the discussion board. We have another 64 students in the course who are still fully virtual, but only about half of the online students sign in for synchronous activities and the rest are self-paced do to various circumstances.

9:10 AM: The English lesson is wrapping up and the Teacher outlines the details of the group activity to come next. We try to include have a five minute stretch break every half hour where students can stand up and break from the monotony of extended computer time. The kids also appreciate time to socialize freely amongst themselves.

9:15 AM: A deep “a-hem” grabs the attention of my students, and I begin facilitating the small group activity. We’re reading Concrete Rose as a class (and by “we” that includes myself) so we have some heavy conversations about systemic racism and its relation to gang violence ahead of us. Fortunately, I’ve been well prepared for these through substantial planning with my team. It’s still a strange feeling to be a “Math Teacher” in this kind of situation, but it gives me a chance to see students how develop students develop their arguments in a way I wouldn’t ordinarily see in my content area. I’m learning as much from the experience as they are and scribble down notes on how I can build deeper connections into my next stats lesson.

9:40 AM: Following the small group session, we take some time for each class to “share in” to the rest of the cohort. It’s always surprising to see how each “class” approaches the topic from a slightly different angle. After the English Teacher summarizes some key themes from these discussion, the Social Studies Teacher chimes in with a follow-up question relating our reading to the Black Lives Matter movement. This clues in the students to what learning experiences await them after their break. Their Social Studies time follows a similar pattern as the English class, with about half an hour of teacher-to-cohort livestream followed by a half hour of small group activities.

10:45 AM: Our cohort’s “lunch hour” begins — or at least that’s what we’ve taken to calling it. It really more of a combined lunch and study hall period which makes it easier to follow social distancing guidelines by staggering our trips to the cafeteria. My class won’t actually “go to lunch” for a while still, so I spend the time helping students catch up on missing assignments or help out with upcoming projects. Our class DJ throws on some hip-hop instrumentals which helps lighten the mood. Some of students can’t really restrain from singing along but the masks muffle out most of the sound so you can’t make out the words unless you know the jam in the first place.

11:03 AM: The persistent cranking sound of the automatic hand sanitizer dispenser fills the hallway as my students and I prepare to make our way to the cafeteria. We pick up our meal and immediately return to class to eat. Our actual lunch time is strangely peaceful. It’s one of the only times in the day where we’re not wearing masks but no one is really talking because we’re too hungry. A soft burp and whispered “excuse me” break the silence and gives way to laughter.

11:31 AM: Most students have finished eating by now but our lunch hour isn’t quite over. We still have some time in the schedule for students to wash their hands, use the restroom, and wrap up what they were doing during study hall. Meanwhile I take some time to prep the browser tabs I’ll want to have open for my upcoming presentation.

11:45 AM: I take a deep breath. Even after a year of teaching online in Zoom the camera still makes me a little anxious, but once I start talking about math I soon find my groove again. My lesson is simulcast from my desktop to the monitor at the front of my class, the seven other classrooms on the hall, and to about 40 students who are learning remotely. All 100+ students have joined me in a Desmos Activity, so as I’m talking to them about means and standard deviations they can manipulate the graphs in real-time. Continuing with the themes established by the English and Social Studies lessons earlier, we’re examining crime data before and after the implementation of three strikes policies. While I’m providing whole-cohort instruction, some of my co-teachers are providing live feedback through Desmos while others are direct messaging me with observations or student questions.

12:15 PM: We come back from another stretch break into small group instruction. Each of the teachers in my cohort has chosen a data set from a pool based on their interests. We’ve found that when we’re more engaged in the data as teachers that students get more into it as well. There’s a distinct math component of the task students requiring students to find the mean and standard deviation, but not all the data sets are normally distributed. Each class has to put analysis in context and decide whether or not this is the right tool for a job and what external factors might be influencing those numbers. I play the role of moderator as each teacher’s class reports back in.

12:45 PM: The final lesson of the day is led by our cohort’s Art Teacher. The theme of today’s lesson is “juxtaposition” and we review several examples from a variety of media. I can feel the excitement growing in the room as students start brainstorming what kind of symbols to use in their upcoming assignment.

1:45 PM: The students finish up their artistic compositions a while ago, and they’re now busy sharing their creations on the school’s social network. This time is technically a 15 minute break period for the students, who are presently taking turns using the restroom and refilling their water bottles. I take advantage of the opportunity to send my wife a text and see how her day is going.

2:00 PM: A line of school buses forms outside the main entrance, but my cohort won’t be actually dismissed for another hour since we were one of the later groups to arrive. The students use this time to complete their “homework”, which now seems like a misnomer since it all gets done at school. They have short reading assignments, reflection prompts from their English, Social Studies and Art Teachers, and couple math problems from myself. Each teacher keeps an open breakout room in Zoom during this time, so students can hop in and out as needed for additional help.

2:55 PM: The students have officially been dismissed for the day and I take a few minutes to collect myself before meeting with my fellow cohort teachers to plan tomorrow’s lesson. Most of the planning has already taken place asynchronously throughout the day by the Civics, Biology, Spanish and Computer Science Teachers, so they present the tentative plan over Zoom and solicit input from the rest of the team. In addition to the 8 “Core Teachers”, our team is supplemented by a group of 4 “Specialists” who help ensure that we’re meeting the needs of all our students. These specialists include a Behavioral Psychologist, a Social Worker, an Instructional Designer, and a Data Analyst, but all of them have been through considerable training on how to meet the needs of students with disabilities. They also help manage our students that are still fully virtual throughout the day and double as substitutes in the event any of the Core Teachers are absent. The system is designed this way to keep contract tracing as simple as possible.

3:47 PM: Our planning meeting wraps up a little early, so I take some time to catch up on the school’s social network again. I post a brief reflection from this morning’s discussion on my school blog and grade a few assignments in my queue.

4:06 PM: My work day was technically over at 4:00, but I got a little carried away responding to feedback on my blog post and lost track of time. I start packing my things to leave for the day. Per school policy, my cohort needs to leave by 4:15 PM so that the disinfecting team can be brought in to deep clean the classrooms. All of my work supplies stay at work and I walk out the door with a clear conscience regarding tomorrow’s instructional plan. I won’t have to even think about work until the following day.

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Categorized as Education

metablogpost

Our school’s new LMS has a blog feature, so I figured it was time for me to write a blog post about blogging. An act of “metablogging”, as it were, to introduce the technology to some newly formed online learning communities.

Let’s start with the basics.

The word “blog” is short for “web-log” — which is itself a technojargon smash-up of “World Wide Web” and “Log File”. I think most of my readers are familiar enough with the Internet to know what it means to be on the “web”, but perhaps the “log” needs a bit of explaining. A “log file” is a incrementally written record of “events” over “time”. Programmers often use logs to track down bugs in our code. Perhaps that’s why blogging evokes such strong feelings for me.

As a blogger, I publish an incremental record of my ideas at specific points in time publicly on the Internet in order to track down the errors in my understanding of the world through collaboration with my Personal Learning Network.

It’s kind of like an open journal and I would be lying to you if I didn’t describe that process as “scary as fuck”.

And yes, I’m capable of “code-switching” as needed, but I’m also a person who believes that sometimes an expletive is necessary in order to communicate an idea. The very notion that “you can’t say that” is precisely why blogging is so scary in the first place! I’ve written numerous posts where I got to the end and just never clicked “Publish” because the thought of it going out was absolutely petrifying.

Blogging is the art of failing in public.

That vulnerability is why it’s so important to establish a Personal Learning Network (or PLN) — a group of people that share a common interest in collectively furthering their knowledge about a topic. Blogging only works when you have an audience that’s receptive to where you are in your own development and will support you on your quest to get to the next stage. You need a PLN that’s empathetic to what you’re going through, but will also call you out on your “bullshit” (I’m pretty sure that’s the technical term) when you inevitably spew it. You need people you trust to hold you accountable for your personal growth.

It’s strange to think that my personal blog has been around for over a decade now — back to when I was a “new online student”. I can see certain themes emerge through my writing (i.e. self-reference!). I like to write when I’m angry; it’s hardest when I’m sad. There are some key changes in my thinking due to major events in my personal life and other changes that occurred as my PLN evolved over time. Looking back, I feel an immense sense of gratitude to all the people I learned together with online. Day after day, they inspire me to fight to become a better version of myself.

My hope is that this blog post might inspire you to start a blog of your own and begin the search for your own PLN. I know from personal experience that joining the “blogosphere” can help make online learning a lot less lonely and a lot more productive. Writing a blog takes work, but it can also be an extremely rewarding creative outlet if you keep at it. I encourage you to give it a try!

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Categorized as Education

Logarithms and Ethnocentrism

(Note: I also created an interactive version of this post in the Desmos Activity Builder. Try it here.)

Hey y’all!

I want to tell you a story today about racism and mathematics.

Well, to be more specific, I’m going to make the argument that trends in mathematical notation can have culturally biased consequences that conferred systematic advantages to white people. I’m going to make this argument through a sequence of math problems, so I hope you’ll follow along and attempt them.

I don’t know if I’ll be able to “prove” this argument to you in the course of this activity, but hope this activity at least instills a sense of “doubt” in the idea that math is objectively neutral.

Without further ado, let’s get started.

Place a mark on the number line where you think “1 Thousand” should go.

Got it?

Okay, I’m going to make a guess as to where you placed it.

Ready?

Did you place it at point P below?

Sorry, I hate to be the one to break it to you, but according to the ‘math powers that be’, this is technically incorrect. However, I want you to hold onto this idea because I’d argue that you’re not as wrong about this as they say you are.

Here’s where you “should” have placed it.

When mathematicians present you with a graph, we implicitly assume that the graph is on a “linear scale”. That means that each unit is equally spaced along the line.

One billion divided by one thousand is one million, which means that “1 thousand” should be placed “1 millionth” of the way between 0 and 1 billion.

At the scale of this graph, this number is so close to the 0 that they’re visually indistinct.

So what about that other point?

That’s actually placed at the value 1/3*10^9 or “one third of a billion”.

However, I don’t want you to think you’re wrong if you placed it here. In fact, this is the correct placement of 1000 on another type of scale.

Check out the following scale instead:

So what would you call a scale like this?

Take a second and write it down.

Go ahead. I’ll wait.

According to the “mathematical community”, this is called a “logarithmic scale”.

Under a logarithmic scale, each successive “unit” gets multiplied by a common factor, such as 10, rather than adding. This results in a scale like in the diagram, only the “0” is actually 10^0 = 1.

There’s even research suggesting that human may actually be predisposed to think of numbers this way, and that the linear scale is a learned behavior. We see it in Indigenous cultures, in children, and even other species. Thinking “linearly” is a social norm that is distributed through cultural indoctrination. It’s like mathematical colonialism.

Here’s my problem with that diagram. If I hadn’t been taught to call this a “logarithmic scale”, I would have called it a “power scale” or an “exponential scale”. Doesn’t that name intuitively make more sense when you see this sequence of labels?

Before we go any further, let’s talk about mathematical notation.

What do you think makes for “good mathematical notation”?

What sort of patterns do you see in the ways that mathematicians name things the way they do?

Here’s what I perceive as the primary patterns in mathematical notation.

Mathematicians sometimes name things “descriptively”: the name tells you what the thing is. For example, the “triangle sum theorem” tells you implicitly that you’re going to add up three angles.

Mathematicians sometimes name things “attributively”: the name tells you who came up with the idea. For example, “Boolean Algebra” is named after “George Boole”.

Mathematicians sometimes name things “analogously”: using symbols with visual similarities to convey structural similarities. For example, “∧ is to ∨ as ∩ is to ∪”.

Mathematicians sometimes name things completely “arbitrarily” for historical reasons. Don’t even get me started on the “Pythagorean Theorem”

Where would you classify “logarithm” in this scheme?

Personally, I think it depends on who you ask.

If you know a little Greek (which is a cultural bias in itself), you might argue that this label is “descriptive”. The word “logarithm” basically translates to “ratio-number”. The numbers in this sequence are arguably in “ratios” of 10, but does that actually convey enough information for you to know what logarithms really are?

I’d argue that this label is in fact “arbitrary” and actually refers to “how logarithms were used” rather than “what logarithms are”.

So what is a logarithm?

Generally speaking, we define a “logarithm” as the “inverse power function” or “inverse exponential function”.

Just as subtraction undoes addition, and division undoes multiplication, a logarithm undoes a power.

For example, 10^5 = 10000 so log10(10000) = 5.

Though a little clumsy, maybe this will make way more sense if we just used the following notation:

log10(10000) = power?10(10000) = 5

The natural inverse of “raising something to a power” would be “lowering it” it right? The mathematical statement, log10(10000) says this:

“What power of 10 will give you the number 10000?”

The answer to that question is 5. This is the essence of a logarithm.

So why don’t we just call logarithms “inverse exponents”?

Well, we call them “logarithms” because this was the term popularized by a guy named John Napier in the early 1600s.

Normally I’d be okay with the guy who created something getting to name it. However, I don’t think that honor should necessarily go to Napier. This idea of “inverse powers” had shown up in the early 800s thanks to an Indian mathematician named Virasena, and the way Napier employed logarithms was similar to an ancient Babylonian method devised even earlier than that.

What Napier did, in my opinion, was convince other white folx of the power inherent in logarithms.

Please, allow me to demonstrate with some “simple” arithmetic. Try to do these two problems without a calculator.

Problem A: 25.2 * 32.7

Problem B: 1.401+1.515

Go head, take as much time as you need.

Which problem was harder?

Problem A, right?

Here’s the mathematical brilliance of the logarithm. It turns out that this “inverse power function” can be used to take a very difficult multiplication problem and turn it into a much simpler addition problem. Problems B can be used to provide a very reasonable approximation to Problem A in a fraction of the time if you look at it through the use of logarithms. They didn’t have computers back then, so they used tables of precalculated logarithms to drastically speed up the computation of large products.

Here’s how it works.

Start by looking up the logarithms of the numbers you want to multiply:

log(25.2) ≈ 1.401

log(32.7) ≈ 1.515

Once you’ve taken the logs, add them together.

1.401+1.515 = 2.916

Finally, do a reverse look up to find the number that would produce this logarithm.

log( ? ) = 2.916 = log( 824.1 )

This reverse look-up is really the power function: 10^2.916 ≈ 824.1.

Pretty neat?

The result 824.1 is pretty darn close to the actual value of 824.04. It’s not perfect because we rounded, but it’s reasonable enough for many applications.

This idea of using logarithms to speed up calculation resulted in the invention of the “slide rule”, a device which revolutionized the world of mathematics. Well, more accurately, it revolutionized European mathematics at approximately the same time that the British Empire just happened to start colonizing the globe.

Let’s spell that timeline out a little more explicitly:

~800 CE: Indian mathematician Virasena works on this idea of “inverse powers”.

~1600 CE: John Napier rebrands this idea as a ‘logarithm’.

~1700 CE: Invention of “slide rule” using logarithms to speed up calculations helps turn Europe into an economic powerhouse.

~1800 CE: The British Empire begins colonizing India.

Do you think this is a coincidence?

I don’t.

I think European mathematicians were quite aware of the power this tool provided them. Naming this tool a “logarithm” was a way of intentionally segregating mathematical literature to prevent other cultures from understanding what logarithms really are.

When a tool provides this much computational power, the people using that tool have a strong motivation to keep that power to themselves.

It’s like the recent linguistic shift in the usage of “literally” and “figuratively”. People have used the word “literally” to describe things “figuratively” in such large numbers that they have literally changed the meaning of the word.

Logarithms have been used to describe exponential behaviors for so long that the relationship between “powers” and “inverse powers” has become blurred by mathematical convention.

This has far reaching consequences for mathematics education where we need students to understand the implications of exponential growth. This is even more important considering the recent COVID-19 pandemic.

Consider the following example from the New York Times:

If I accidentally referred to the second graph as an “exponential scale” instead of “logarithmic scale”, would you still know what I was talking about?

What’s the point of calling it that?

I think we need to acknowledge that there exist “self-reinforcing power structures” in mathematics. These mathematical tools provide power to people, so those people fight to keep that power to themselves. This is an act of “segregation”.

After time, these tools become unavoidably common place. Now we’re in a situation where mathematicians argue that these norms should be “assimilated” because their use has become so widespread.

As a result, these cultural biases have resulted in a sort of mathematical colonialism that masquerades as objectivity. I believe that this ethnocentrism systematically disenfranchises BIPOC by hiding the true history of these mathematical ideas. This, in turn, results in systematic biases in test scores between whites and BIPOC, which then reinforce the original stereotypes.

It’s a vicious cycle of racism.

Wouldn’t you agree?

It might be too late to stop the use of the word “logarithm” in mathematics. It’s now something of a necessity to understand a wealth of other mathematical advances that have been built on top of this concept. However, that doesn’t mean we should pretend that this term is completely neutral either.

I hope you’ll leave here today with a better understanding of why it’s important to look critically at our mathematical conventions and acknowledge that math is not exempt from cultural biases.

Thanks for reading!

Geometry is racist.

I have a confession I need to get off my chest. I think Geometry is racist. Well, not geometry (the discipline of mathematics), but specifically Geometry (the course commonly taught in American High Schools). I realize that in presenting this argument I’m going to have to make some rather sweeping generalizations about human history, but I that it’s important for me to put this hypothesis into words because I don’t think there’s enough evidence to disprove it.

Fair warning: this may be a lengthy read.

I believe that the reason the curriculum of Geometry specifically references Pythagoras, Euclid, and Descartes is because this emphasis provided Whites another means by which to rationalize slavery. Greek society was a prototype for White society because it used mathematics and philosophy to moralize slavery, and Descartes provided Whites a method of reconciling this position with Christianity.

To understand this, we first need to acknowledge that the entire human history of mathematics is intertwined with human slavery. Both mathematics and slavery emerged in early civilizations after the transition from hunter/gatherer to agricultural society lead to social stratification and the development of written language. In fact, I think mathematics is a necessary precondition for slavery. The very concept of slavery depends on a life being assigned a quantifiable value. Slave labor provided the ruling class with the time and resources to work on furthering mathematical knowledge, and then advances in mathematics were used to increase the efficiency of the slave trade. This vicious cycle quickly elevated the slavers to a god-king status which they then exploited to moralize their slavery.

Our oldest mathematical texts are from Egypt and Babylon, approximately 4000 years ago. Surviving records such as Plimpton 322, the Moscow Mathematical Papyrus, and the Rhind Mathematical Papyrus show that teachers have been giving math worksheets of roughly high school level difficulty since at least 1900 BC. What’s interesting about these three texts is that all three of them show evidence of the Pythagorean Theorem — over a thousand years before Pythagoras was even born! There’s also a strange lack of evidence attributing the theorem to Pythagoras, along with indications that proofs of it may have been circulating in Mesopotamia and India several hundred years prior. The very fact that this theorem bears the name of Pythagoras despite this questionable lack of evidence should alone be sufficient evidence of Geometry’s racism, but Pythagoras is only the first of three dominoes.

When Pythagoras supposedly lived around 500 BC, the Greeks (and Romans) had lively slave trades. However, unlike the god-king theocracies of Babylons and Egypt, the Greeks fashioned themselves as a “Democracy”. The Greeks needed an alternative means of moralizing slavery and whether he intended it or not, Pythagoras’ merger of mathematics and philosophy provided them with all the justification they needed. The Greeks used philosophy and mathematics to separate themselves from the people they enslaved, which served as a prototype for White society. Those that didn’t measure up to Greece’s intellectual standards were labeled as “barbarians” and treated as less than human. To paraphrase Plato, these barbarians were in the dark and needed to be shown the light. Incidentally, the “barbarian tribes” of Northern Europe enslaved by Greeks and Romans were likely a source of genetic markers for light skin, light hair and light eyes that would later be associated with “Whiteness”.

Meanwhile, mathematics probably continued to develop in the Middle East with influence from early civilizations in India and China. However, we don’t know by exactly how much. There’s another strange lack of mathematical records from Babylonian society under the Persian Empire. What we do know is that when Alexander the Great conquered the region in 331 BC, the Greeks assimilated a wealth of astronomical data. It’s quite likely that the Greeks stole whatever mathematical data they could through military conquests and these materials ended up in the Library of Alexandria where Euclid would have had access to them. Euclid’s work is based on a set of stolen mathematical literature that Euclid was privileged to have access to. While it’s impossible to discount the probability that Euclid might have added some original ideas, I do think this fact merits taking a closer look at his work and evaluating whether or not it belongs in our school’s curriculum.

My problem with the presentation of Euclid in Geometry (the course) is the parallel postulate. To be fair, presenting Euclid’s axioms as fundamental truths about the universe made sense in mathematics education up until as recently as 1905. We now know that space is not “flat” as Euclid assumed, but that gravitational forces can bend space around a mass. My understanding is that we teach Euclidean geometry because (a) it’s a useful approximation of reality and (b) it provides an introduction to axiomatic systems. The main issue with Euclid as presented in Geometry is that its axioms are presented without proof and we have solid scientific evidence that one is not always true. How can we ever expect students to think critically about information when we don’t question the assumptions made in mathematics?

Euclid’s mathematics is not irreplaceable within the mathematics curriculum. We could just as easily teach students about axiomatic systems using first-order logic. Instead of teaching compass and straightedge constructions, we could teach origami. In fact, teaching these alternatives could not only increase the diversity of the mathematics but simultaneously increase the rigor. There is some really great math showing that we can solve problems with paper folding that are impossible to do with a compass and straightedge only. Learning origami would help prepare students for high level physics and computer science. We owe it to our students to do better than Euclid.

Approximately 300 years after Euclid, the Roman Empire was nearing its peak and Christ was born. The death of Christ coincides with the start of two centuries of peace. It’s no wonder that early people considered this a miracle. Early Christians were originally persecuted in the Roman Empire, but by 380 AD it would become the state religion. If you think about it, Christianity offered the Romans a pretty sweet deal considering their involvement in the religion’s origin. The Romans killed Jesus, and through Jesus’ death were forgiven all their sins. And that meant all their sins: slavery included. To suggest that otherwise would be heresy. Before long, Christianity had accumulated so much Power that they rewrote the entire calendar around their own beliefs.

The spread of Christianity throughout Europe is relevant to our discussion because the next major event in mathematical history happens to coincide closely with the birth of Islam. Around 800 AD, Muhammad ibn Musa al-Khwarizmi developed the branch of mathematics we now call “Algebra” and started a new mathematical revolution in the Middle East. This presented Christianity with a threat because geometry was always considered sacred and the followers of Islam were creating new mathematics for another god. The bible says “Thou shalt have no other gods before me“. By 1100 AD, Christianity had come to the conclusion that since they couldn’t disprove the Muslims mathematically, the only other option was through force. The Christians took to war against the Muslims and with each mosque they burned they destroyed part of that mathematical progress. Remnants of this “Holy War” persist through the present day.

It’s because of this religious tension between Muslims and Christians that our story leads to Rene Descartes. Another essential component of the Geometry curriculum is the idea of Cartesian geometry which is an merger of algebraic principles with Euclidean geometry. The very name would have you believe that Descartes invented it, but that honor should probably be attributed to Fermat. No, I think there’s another reason we attribute it to Descartes, and that is because of his work in ontology. Most people are familiar with “I think, therefore I am“, but that statement is really the first axiom in a system that Descartes constructed in order to develop a mathematical argument proving the existence of God. Descartes is one of a few mathematicians that attracts cross-curricular study because of this. We don’t even provide his argument a fair critique. Like his Greek counterparts, we treat Descartes’ work as gospel when in reality he was just repackaging the ideas of others. In this case, Descartes had taken the Muslim-sounding “algebra” and re-packaged it in form that would be more acceptable for Christians.

The philosophical assertion “I think, therefore I am” takes on another meaning when we put it in context of mid-1600s White society. By associating “thinking” with “existing”, Whites were able deny Blacks basic human rights by labeling them as “unthinking savages”. It’s the very same strategy employed by the Greeks to justify slavery, only the vocabulary had shifted. The same idea would later manifest itself through literacy tests, and persists today through standardized testing practices. Whites retain Power by defining a culturally biased set of standards.

A few weeks ago I listened to a podcast from Freakonomics that described America’s Math Curriculum as a “Geometry Sandwich”. Ever since I taught it I’ve been asking myself the same kinds of questions:

  • Why “sandwich” Geometry in the middle of two years of Algebra?
  • Why are Euclid, Pythagoras and Descartes the only three names that students explicitly learn in Geometry?
  • Why is the name al-Khwarizmi not given the same level of treatment in Algebra?

The most probable explanation I can come up with to answer all three of these questions is that the American Math Curriculum is racist. It is probably not the intent of the Curriculum developers to be racist, but racism is not about the intent — it’s about the consequences of the behavior. There is a non-zero probability that cultural biases exist within our Math Curriculum and they produce racist consequences. Mathematics is a just tool, but people decide how that tool is used. We can either continue to use that tool to enable racism, or we can use that tool identify and dismantle it.

For me, I’ve decided that the probability of the Math Curriculum being racist is too high for me to ignore. I’ve decided on the following course of action:

  • I plan to start substituting “Right Triangle Theorem” in place of “Pythagorean Theorem”.
  • I plan to start substituting “Rectangular Coordinate System” in place of “Cartesian Coordinate System”.
  • I plan to pay closer attention to situations where Euclidean geometry is implicitly assumed and question whether or not this assumption is warranted.
  • I plan to make a consistent effort to present a diverse range of mathematicians in my classrooms.
  • I plan to actively look for other artifacts of racism in the curriculum and address them accordingly.

I realize that my argument here needs work and that I’m personally having difficulty disentangling race and religion. Even if I haven’t yet convinced you that “Geometry is racist”, I think there’s sufficient evidence here to conclude that it’s definitely not anti-racist. That fact alone is reason enough for me to act. If you’re also a teacher of mathematics, I hope I’ve convinced you enough to join me in these actions.

I used to identify my race as “Decline to state”

Recently I’ve read a couple of books (namely, White Fragility and How to be an Antiracist) that have made me reexamine certain aspects of myself through a lens of racial privilege.

For a significant period of my life, I refused to identify my race as “White” on any survey I completed. I’ve since realized that my doing so was an act of racism and I apologize. While I can’t change the past, I hope that sharing my story will serve as a token of my promise to make amends in the future.

The new information which led me to this conclusion was this idea that the white race begins with slavery. I had previously defined “White” as a ~2000 year old construct when in reality it began ~400 years ago. This redefinition caused all sorts of cognitive dissonance until I learned about a defensive mechanism that white people often have called channel-switching, where we redirect discussions about racism to other factors. I discovered I had been subconsciously conflating the “White Race” with “Christianity” because I identified them both with the same structure of “White Power”. I had falsely assumed that since “White Power” was inherently “Christian” that the “White Race” through which “White Power” manifested was also “Christian”.

What bothers me most was that I knew that race and religion were not the same, and was careful not to invoke my atheism as a minority defense. I’d even openly identify as “Caucasian”, but the term “White” triggered in me a storm of rage and “Decline to state” was the calm. I thought that distancing myself from that label made me “not racist”, but I was wrong. The only way to engage in antiracism is through accurate statistical measurements of racial disparities. I wasn’t thinking about the potential harm that mislabeling myself could do, placing my own individuality over the welfare of others, and I’m sorry.

I’m going to try to continue down this path of antiracism, but I need help. I’m trying to look at this as a data analysis problem and realized that I don’t have enough information to properly disaggregate race from religion. I don’t know how to authentically engage in antiracism without also being antireligious. This presents a problem because I’m “in the closet” at work. I carefully avoid revealing my thoughts on religion because I fear that doing so could get me fired. In order to learn how to navigate this space, I need more information about this intersection of race-religion.

The first step I can take on my own. Quite frankly, I need to learn about how and why so many blacks adopted the religion of their oppressor. I believe that the best way for me to acquire this knowledge is through the narratives of black thinkers who are critical of the role religion plays in the white power structure. I plan to seek out black atheists, listen to their stories, and lend whatever weight I can to their voices. I’ve known for a long time that black atheists were underrepresented in the atheist community and it’s time I did something about it.

The second step is going to require feedback. I accept the premise that there is a non-zero probability with which I will commit acts of racism in the future. I need friends of color to call me out when this happens and engage me in an honest discussion about why. If you do this publicly, I will make my best effort to model antiracist behavior in response, but do so with the understanding that my response will likely be influenced by my antireligious views.

If you are reading this and are someone I work with, I hope you can understand the thin line I’m attempting to walk. I propose we establish a hidden signal: invoke each others’ first names when calling out acts of privilege (in whatever form that may take). This will serve as a reminder that what follows is being said as a friend and that we’re both together in this fight for equality as human beings.

Engineering a 21st Century Education

As a game developer turned teacher, the one most difficult part of the transition was paper. I’m not even talking about the thousands of copies of handouts and worksheets for students. I’m talking about the paper that compromises the layers and layers of bureaucratic processes that any sufficiently large organization develops over time. The forms. The reports. The mundane paperwork that must be done to uphold the laws that govern the operation of a school.

I get it.

It’s stuff that must be done.

The problem isn’t that it exists, it’s how schools deal with it. The school has limited resources available so it needs to get the most out of the resources it has. That makes sense, right? The school administration has ready access to a large number of highly trained, adaptable, resourceful, and intelligent individuals on hand with a wide range of skills covering every discipline imaginable. It has teachers.

I’m always more than happy to help when needed! I just get frustrated when I’m asked to perform work that could be reduced or eliminated by technology.

In my last post, I talked about school being a game and the need to meta-game it. One of the first issues that I think we need to talk about are “opportunity costs”. Every hour that teachers spend on administrative tasks is an hour that is not being spent on teaching. Furthermore, these costs are recurring. If schools could automate 10 minutes worth of administrative tasks each day from a teacher’s workload, they would save each teacher about 30 hours of work over the course of the year. That’s a lot of time that teachers could reallocate towards improving instruction.

Teacher time is a valuable resource and finite one. Education needs to be engineered to get the most out of that time. Based on my short time as a teacher so far, here are some of the systems that I think could be optimized:

We need a complete “Electronic Individualized Educational Plan Record” system overhaul. The current generation of “Student Information Systems” is grossly insufficient to deal with the complexity of our educational legislation. Schools need to keep documented records of adhering to a student’s legally entitled accommodations, and a significant amount this documentation is still being done on paper. We have the technology to design an educational record system that is secure, fault tolerant, and efficient. It would take an substantial initial effort, but imagine the time that it could save school staff in the long run.

We need a better “asset management system” for school property used by students. It’s very frustrating to me as a teacher when I need to fill out carbon copied checkout lists for textbooks by hand in the year 2016. When a student doesn’t return the textbook, I’m required to fill out another carbon copy form, manually address an envelop to the student’s home, and put it in the mail bin for processing. Why isn’t this process electronic yet? I should be able to snap a picture on my phone, press a button to assign it to a student or document its return, and everything else should be taken care of by a computer program. We clearly have the technology to do this.

We need a “behavioral intervention tracking and diagnostic system”. The school keeps paper records of certain student behaviors such as tardy slips and misconduct reports — which again are filled out by hand on carbon copy paper. There are also some cases where the teacher is expected to intervene in certain ways such as contacting the parent. The issue is that there are so many different rules that I need to keep track of and responses that I need to take to that data. We need a system that that can track behavior data from multiple sources and suggest interventions based on a statistical models of what has and has not worked for that student.

On top of moving from antiquated “pen and paper” systems, we also need to improve interoperability between the educational software we already use. There’s some good ideas happening with the Tin Can API, but the support from technology providers just isn’t there yet. I love to see new ideas in educational software! The problem is that some of these applications seem to neglect the teacher’s experience with the product. We need to set higher standards for educational software.

Whenever my students complete a learning activity on the computer, it should automatically go into my grade-book. The grade-book should automatically flag any items that need to be manually graded, and the process of providing feedback to the student should be as stream-lined as possible. More detailed information about the student’s performance should be stored into a database for later statistical analysis.

The other problem is the lack of standards regarding assessment items. For example, my students love Kahoot. I would totally use it way more if it were easier for me import multiple choice questions from an existing database. If I could program randomly generated questions in MyOpenMath, export them to a standardized format, and then import them into Kahoot, I would be one happy teacher.

I don’t think any of these technologies are unrealistic. It’s not like I’m asking for facial recognition software to replace hall passes or an artificially intelligent grader (although those would be kinda awesome too). If schools want to instill “21st Century Skills” in their students, they need to lead by example. In the “21st Century”, knowing what processes can be automated by technology is a crucial skill to have. To do otherwise is a disservice to both teachers and students.

I used to think schools needed more games

I love games! I love playing them. I love making them. I love theorizing about them. They’re an essential part of who I am as a person.

I used to think schools needed more games.

I was working as a video game developer and was fascinated by “tutorial levels”. You know, that part of the game that is designed to help you learn how to play the game. Some games neglect their tutorial level and it comes off feeling like a dry lecture. Go here. Push button. Repeat. However, I’ve also been completely awed by some games that take their tutorial levels to a completely different level. Games like The Elder Scrolls and Guild Wars for example. The experience is so seamlessly integrated with the “game” that you don’t even realize you’re playing a tutorial. You just play. By the time you’ve completed the tutorial, you were totally immersed in the game and knew exactly what you needed to.

I used to think schools needed more games.

There’s an certain authenticity to this learning that I never really experienced as a student. I thought if I could design the perfect “tutorial level” for math, then everything else would just fall into place. The students would have fun. They’d learn real mathematical concepts in a natural environment. They’d grow and develop as individuals and as a group. I’d be like a “math teacher” and “guild leader” all rolled into one (although I probably wouldn’t run IWAY).

I used to think schools needed more games…

…and then I started teaching.

The problem is not that school doesn’t have enough games, it’s that school has too many games. Now, I’m not talking about the latest web app: Kahoot, Quizizz, Manga High, etc.. Those are certainly a type of game that has a place in school, although perhaps the number of apps is getting overabundant as well, but I’m talking about the games that are school. School itself is like a “Live Action Role Playing Game”. Everyone invents their character, acts out their role, cooperates with some players, competes with others, and are rewarded or punished in accordance with the game master’s rules.

Now school being RPG isn’t a problem on its own. The problem is that there are a whole bunch of mini-RPGs being played simulatenously, and all of them have conflicting rules. Here is a short list of a few games that might be going on at a given time:

  • The students are playing a game with each other. They compete with each other for social status while cooperating against outside threats to their system.
  • The teachers are playing a game with their students. The teachers are trying to maximize student learning while the students are trying to minimize the work they have to do.
  • The administrators are playing a game with their teachers. The administrators are trying to maximize test scores while minimizing teacher burn-out.
  • The school board is playing a game with their administrators. The school board is trying to maximize community approval while minimizing school funding.
  • The parents are playing a game with their school board. The parents are trying to maximize the quality of education while minimizing the amount of attention paid to local elections.

Within these games, temporary alliances are made to accomplish mutual goals. Teachers and parents might cooperate to get students in for extra tutoring. Administrators and school boards might cooperate for better community awareness. Sometimes these alliances help the system as whole and sometimes they detract from it. It’s one of the most complex network systems I’ve ever seen.

I used to think schools needed more games…

…and now I think schools need to have a closer look at the games that are already being played there.

In most of these games, competition is the dominant strategy. Students that are competing for limited scholarship funds have little incentive to help one another. Schools that receive funding based on standardized test scores have a very strong incentive to focus on instructional strategies that produce short-term results over long-term retention. School boards are underappreciated as a position of political power and tend to just “fly under the radar”. Until we fix the reward systems so that they encourage cooperation, the games will continue to be frustratingly difficult for everyone involved.

We need to start meta-gaming school. We need to look at how the rules affect the relationships between players. We need to look how those rules can be changed to encourage more co-operation and less competition between the parties involved. Until we have these conversations, we’re never going to win.

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Categorized as Education

What I’ve discovered, learned or shared by using #mathchat

This was a #mathchat topic in July of 2012 that I really wanted to write about but didn’t quite get around to at the time.  This happened partly because I was busy juggling work and graduate school, but also because I felt a bit overwhelmed by the topic.   I’ve learned so many things through my involvement in #mathchat that the idea of collecting them all was daunting.   It also kind of bothered me that my first attempt at a response to this prompt turned into a lengthy list of tips, books, and links.  This type of content makes sense on Twitter.  It’s actually the perfect medium for it.  However, to turn this into a blog post I needed some coherency.  I felt like there was a pattern to all of these things that #mathchat has taught me but I just couldn’t quite put my finger on it.

A year and a half has passed since this topic came up.  It’s now been 6 months since the last official #mathchat.  Despite this, Tweeps from all over the world continue using the hashtag to share their lesson ideas and thoughts about math education.  It’s inspiring.  The weekly chats might have stopped, but the community continues to flourish.  Looking back on how things have changed on #mathchat helped put perspective on how #mathchat changed me.  I think I’m finally ready to answer this prompt.

What I learned by using #mathchat was that learning requires taking risks.

On the surface, it seems like this assertion might be obvious.  Whenever we attempt something new, we run the risk of making a mistake.  By making mistakes we have an opportunity to learn from them.  The issue is that we go through this routine so many times that it becomes habitual.   When learning becomes automatic, it’s easy to lose sight of the risks and how central they are to the learning process.

Consider the act of reading a book.  For many, like myself, this is the routine method of learning new information.   In fact, it’s so routine that the risks aren’t readily apparent.  That doesn’t mean they aren’t there.  Have you ever read a book and found yourself struggling to understand the vocabulary?  For me, Roger Penrose’s Road to Reality is still sitting on my bookshelf, taunting me, because I can’t go more than a couple pages without having to look things up elsewhere.   Attempting to read a book like this entails a risk of making myself feel inadequate.  It’s much easier to read a book that’s within one’s existing realm of knowledge.  By taking the risk out of reading, it becomes a recreational activity.  This isn’t necessarily a bad thing — we could all use some relaxation time now and then — but it’s not until we step out of that comfort zone that the real learning begins.  Have you ever read a book that made you question your own assumptions about the world?  It’s not often that this happens because we’re naturally drawn to books that reaffirm our own beliefs.  When it does happen, the impact can be quite profound.  The further a book is from your existing world model the greater the risk of that model being challenged by reading it, but the potential for learning scales in proportion.

I was rather fortunate to have discovered #mathchat when I did.  I had signed up for Twitter at approximately the same time I started teaching math.  Anyone that’s ever been a teacher knows that learning a subject and teaching that subject are two entirely different beasts.   I’d been doing math for so long that most of it was automatic.  It wasn’t until I started teaching that I realized I had forgotten what it was like to learn math.   As a result, I was struggling to see things from the perspective of my students.  I needed to step out of my own comfort zone and remember what it was like to learn something new.  It’s through complete coincidence that my wife stumbled upon Twitter at this time and said, “Hey, I found this new website that you might find interesting”.

I didn’t join Twitter looking for professional development.  In fact, for a while at the start I didn’t even know what “PD” stood for.  I joined Twitter purely out curiosity.  I was never really comfortable interacting socially with new people, and it seemed that this was an opportunity for me to work on this skill.  I called it “my experiment”.   I didn’t even use my full name on Twitter for the longest time because I was afraid of “my experiment” going wrong.    I started simply by looking for topics I was interested in, following people that sounded interesting, and speaking up when I felt I had something to say.  One of my saved searches was “#math” and I started trying to answer questions that people were asking on Twitter.  This lead to making some of my first friends on Twitter.   I noticed that some of those people that regularly tweeted on #math also frequently tweeted with the hashtag #edchat.  I started to observe these people would often post multiple #edchat Tweets within a short period of time and had inadvertently stumbled upon my first real time Twitter chat.  Once  I started participating in #edchat my network grew rapidly.  From there, it was only a matter of time before I discovered #mathchat.

My social anxiety was still quite strong at this time.  With each Tweet, I was afraid that I would say something stupid and wake up the next day to find that all my followers had vanished.  However, #mathchat provided a welcoming atmosphere and discussion topics that were relevant to my work environment.  This provided me with an opportunity to engage in discussion while mitigating  some of the risks.  I knew that each topic would be close to my area of expertise and the community was composed of people who were also there to learn.  There was a certain comfort in seeing how people interacted on #mathchat.  People would respond critically to the content of Tweets, but always treated each participant with dignity and respect.   I was experiencing first hand what a real learning community could be like.

A frequent motif in these #mathchat discussions was Lev Vygotski’s model of learning.  With my background in psychology, I was already familiar with the concepts and vocabulary.  However, #mathchat helped me link this theory with practice.   I became more and more comfortable with a social perspective on learning because I was learning through my social interactions.  While I had known the definition of terms like “zone of proximal development”, I wasn’t quite to the point where I could see the line separating what I could learn on my own and what I could learn with assistance.  I had always been a self-driven learner, but in order to be successful in learning I needed to limit myself to areas that were close to my existing skills and knowledge.  I needed to minimize the risks when learning on my own.  Learning in a social environment was different.  I needed to become comfortable taking larger risks with the reassurance that the people I was learning with would help me pick myself up when I fell.

The #mathchat discussions themselves were not without risks of their own.  Colin took a risk himself by creating #mathchat.  It was entirely possible that he could have set this chat up only to have no one show up to participate.  Indeed, many a #mathchat started with an awkward period of silence where people seemed hesitant to make the first move.  There’s much lower risk in joining a discussion in progress than starting one from scratch. The risk is lower still by simply “lurking” and only reading what others have said.  As time went on, there was a growing risk that #mathchat would run out of topics for discussion.  This risk has since manifested itself and #mathchat has entered a state of hiatus.

I’m aware of these risks only in hindsight.  At the time, I wasn’t really conscious of the shift occurring in my own model of learning.  What started to make me realize this change was the adoption of my two cats.  This provided my another opportunity to put learning theory into practice by training them (although it’s arguable that they’re the ones training me instead).  The smaller one, an orange tabby named Edward, responded quickly to classical and operant conditioning with cat treats.  The larger one, a brown tabby named Alphonse, didn’t seem to care about treats.  It quickly became obvious that I was using the wrong reinforcer for him.  With his larger body mass and regular feeding schedule, there was no motivation for him to consume any additional food.  It’s easy to forget that in the experiments that these concepts developed from, the animals involved were bordering on starvation.  The risk of not eating is a powerful motivator for these animals to learn in the experimental setting.  My cat Alphonse was under no such risk.  He was going to be fed whether he played along with my games or not.  I’ve since learned that Alphonse responds much better to training when there’s catnip involved.

The key to successful training is very much dependent on being able to  identify a suitable reinforcer.  What functions as a reinforcer varies widely from subject to subject.   With animal studies, survival makes for an universal reinforcer as the reward of living to procreate is (almost) always worth the risk.  However, humans follow a slightly different set of rules because our survival is seldom in question.  We’re also unique in the animal kingdom because we can communicate and learn from others’ experiences.   In a typical classroom situation, the ratio between the risk and reward takes on greater significance.  We’re faced with such an overabundance of information about the world that we can’t possibly learn it all.  Instead of maximizing performance on a test, the desired outcome, a common alternative is for students to minimize the risk of disappointment.   It’s often much easier for a student to declare “I’m bad at math” than to go through the effort of actually trying to learn a new skill.  Rather than taking the high-risk choice of studying for the test with only a moderate payoff (a grade), these students opt for a low-risk low-payoff option by simply choosing not to care about the exam.  When looked at from a risk/reward perspective, maybe these students are better at math than they’re willing to admit.

The solution, as I discovered through #mathchat, is to lower the risks and adjust the rewards.  I’ve started working on making my courses more forgiving to mistakes and acknowledging them as an integral part of the learning process.  I’ve started working on increasing the amount of social interaction I have with students and trying to be a better coach during the learning process.  There’s no denying that I still have much to learn as a teacher, but thanks to #mathchat I have a clearer idea of how to move forward.  For me to progress as a teacher, I need to more comfortable taking risks.  It’s far too easy to fall into habit teaching the same class the same way, over and over.  I need to do a better job of adapting to different audiences and trying new things in my classes.  Fortunately, there’s a never ending stream of new ideas on Twitter that I’m exposed to on a regular basis thanks to my “Personal Learning Network”.

I feel it’s a crucial time for me to be sharing this perspective on the role of risk in learning.  There seems to be a rapidly growing gap between teachers and politicians on the direction of educational policies.  There’s a political culture in the US that is obsessed with assessment. Policies like Race-to-the-Top and No Child Left Behind emphasize standardized testing and value-added measures over the quality of interpersonal relations.  The problem with these assessment methods is that they don’t take the inherent risks of learning into consideration.  Risk is notoriously difficult to measure and it doesn’t fit nicely into the kinds of equations being used to distribute funding to schools.

There was recently a backlash of (Badass) teachers on Twitter using the #EvaluateThat to post stories of how our assessment methods fail to capture the impact teachers make in the lives of their students.   Teachers are the ones that witness the risks faced by students up close.   It’s our job as teachers to identify those risks and take steps to manage them so that the student can learn in a safe environment.  As the stories on #EvaluateThat show, many teachers go above and beyond expectations to help at-risk students.

While teachers struggle to reduce risks, policy makers continue to increase them through more high-stakes exams.  At times it almost seems like politicians are deliberately trying to undermine teachers.  Maybe what we need in education policy is a shift in the vocabulary. Lets stop worrying so much about “increasing performance outcomes” and instead focus on “decreasing risk factors”.  Doing so would encourage a more comprehensive approach to empowering students.  For example, there’s strong statistical evidence that poverty severely hinders student success.  By addressing the risks outside of the classroom, we can enable students to take more risks inside the classroom.