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I’ve always been a self-driven learner, but I’m starting to understand that there are limits to what I can learn on my own. As a teacher, I found myself working hard to establish a “community of learners” in my classroom. Now I’m finding myself at a crossroads where I could really benefit from a learning community of my own. Perhaps by laying out my ideas of interest here some potential mentor or peer group might find me.

My primary area of interest is in the application of technology to improve educational outcomes. I’ve taken a multi-disciplinary approach to building this expertise in both breadth and depth, building on my dual undergraduate degrees in Mathematics and Psychology. My graduate work in Learning and Technology focused on the use of online discussion boards in mathematics and helped prepare me for the emergency learning transition of early 2020. Since then, I’ve developed an interest in the applications of machine learning to help induce positive structural changes in education.

Artificial Intelligence (AI) is rapidly advancing and the field of education stands to be dramatically changed as a result. The question is not if AI will be used in school, but rather when and how. The existence of applications like PhotoMath have already shifted the focus dialog in my math classes from “the result” to “the process”. Large Language Models such as ChatGPT will revolutionize the way we think about student writing the same way. Rather than such tools being banned from classes, schools should instead focus their efforts on making sure students are equipped to collaborate responsibly with AI models.

The field of education presents some unique challenges for AI. The haphazard implementation of AI could cause immense harm, so the first order of business is to develop systems of safeguards against misuse. While AI grows in power with massive data sets, schools have competing legal obligations to be met regarding data privacy, transparency and ethics. Schools will need to have traditional engineering methods in place to detect algorithmic biases with regard to legally protected statuses such as race or gender before they can reliably depend upon consumer AI solutions. Equity needs to be built into AI from the ground up.

One of the challenges posed by AI produced content is our inability to distinguish it from human produced content. Our best tool for detecting AI produced content is to train another AI to do the job for us. These adversarial agents complement each other when trained in parallel. As the AI classifier that detects whether or not an artifact is human produced gets better, it forces the content producing agent to behave more human-like. These two AIs are designed to compete with each other, but the feedback loop created when they interact together allows them both to learn more efficiently.

Applying AI in education is going to require a whole ecosystem of agents who compete or cooperate to provide checks and balances on the values we which to instill. The first step towards this is to looking at education through a lens of game theory that critically examines the reward structure of the school. The challenge is creating a set of macro-level rules for interactions between AI and human agents that promotes collaborative behavior across the system. We need to shift the discussion from “how do we prevent students using AI to cheat?” to “how do we align our assessment methods with actual student growth?”.

One of our highest priorities with AI should be the development of an AI learner advocate. Ideally, the system would allow students and parents to articulate their long-term personal learning goals through natural language in an Individualized Education Program (IEP) and the AI would automatically configure itself as needed to monitor and advance those objectives. For example, an algorithm might be programmed to automatically alert teachers if they accidentally forget to include alt text in an assignment with visually impaired students in the class. It’s also important that students maintain a voice in the learning process, and AI may provide a powerful tool for students who have yet to learn how to self-advocate.

In the long term, AI could also provide considerable time savings to teachers by producing “just-in-time” lesson plans based on the available data. Writing lesson plans is a task that is often more tedious than it is difficult — assuming it’s not a direct copy of one from last semester. We’re reaching a point where AI can potentially automate the process of aligning experiences with instructional objectives, measuring progress relative to the course calendar, recommending accommodations based on IEPs, and formatting this data in a standardized template for administrators. This would free up more time for the teacher to spend customizing the learning experiences for their specific classes.

From a mathematical perspective, algorithmic lesson generation bears some key structural similarities to the “Many-Armed Bandit Problem” in probability theory. Consider the teacher like a gambler in a casino and the slot machines as various potential lessons that can be assigned to a student. The teacher wants to select the experience with the highest odds of paying-out for that student, but not every student will respond to that particular experience in same way. For a teacher to maximize the learning potential for all students, they must strike a balance between exploiting lessons that tended to work in the past with exploring new methods they have yet to try. The more information a teacher has about the student, the more reliably they’re able to predict what might work.

The fact that confidential health information about a student is often directly linked to academic accommodations presents a unique privacy problem for AI. In much the same way that Security needs to be applied across Development and Operations, so too must Accessibility be asserted across educational organizations. A substitute teacher doesn’t need to know every student’s complete medical history, but a classroom AI might be able provide them with the information that “students need a break” without revealing the fact that Johnny has ADD. There is a delicate balance to be made between controlling access to sensitive data on a need-to-know basis and using that data to provide teachers with actionable insights.

As a former teacher, the idea of a computer listening and watching everything I do in the classroom is terrifying. We cannot permit AI to become an electronic police force is schools. At the same time, I also know that the amount of data produced in a live class is more than any single person could analyze on their own. The subtle timing of a student’s confused facial expression can often speak volumes about that student’s understanding. I would not the least be surprised if an AI could even out perform me on this task, but also know there will always be an unavoidable risk that this AI might be wrong and cause irreparable harm. The tech industry mantra of “move fast and break things” is an inappropriate philosophy for schools.

Instead, education must adopt AI slowly and with confidence. Educational data must be treated with the same level of careful stewardship as healthcare data. Researchers need to gradually integrate AI through a series clinical trials and monitor the system as a whole for changes. Much like a teacher, AI needs to build a relationship of trust with all of the stakeholders in the environment. Students and parents need to know the AI is working for them and not against them. Teachers and administrators need to have the power to overrule AI assessments where appropriate.

I realize that these scenarios might seem like widely disconnected fields, but I’m finding that they have some common mathematical threads. I accepted a long time ago that I might spend a lifetime working on Millennial Problems I’ll probably never solve and instead try to focus on making progress in small steps. I’m working to further my knowledge of Category Theory because I’m finding the language of maps and objects to be extremely valuable in modeling complex systems. I feel there’s a deep connection between Complex Analysis, Linear Algebra, and Topology that I’m just shy of understanding. I’m also starting to realize a need for better Statistical tools, particularly in the properties of different Probability Distributions used for modeling risks.

I’m very much open to graduate level research opportunities in Mathematics or Computer Science that would advance my understanding of the topics described above. If you’re in a department working towards these high level goals and have an opening for a research assistant, please feel free to reach out to me through any of my social media profiles.

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It’s only recently that I’ve starting embracing Satanism, but it’s precisely for that reason that I feel the need to write this. Satanic Ritual is traditionally a very private process unique to the individual practicing it. My Sol Invictus may not be representative of others, but that does not make it any less valid. At the same time, I can’t expect others to understand the impact of celebrating a holiday that I quite literally designed on my own. I hope that maybe by describing what Sol Invictus means to me that I can help others to be more inclusive of people like me during the holiday season.

To understand the role of Sol Invictus, it might be be helpful to first define “Satanic Ritual”. It’s most certainly not like what you see in the movies. In fact, much of Satanism is actually built around the symbolic opposite of these depictions. One of the defining characteristics of Satanists as a group is that we are fundamentally opposed to the idea of “blood sacrifice”. It’s why we’re drawn to the symbol of “the rebel” over “the lamb” in the first place. The purpose of a Satanic Ritual is consciously align the symbolism of one’s surroundings with ones that are needed to empower oneself toward self-actualization.

I hate Christmas.

As a result, I’ve intentionally constructed my Sol Invictus celebration to make it as emotional distant from Christmas as possible. The two holidays are inherently incompatible by design. I will never find joy in Christmas, only pain. Sol Invictus is about accepting that I feel this way for legitimate reasons and providing myself with the tools I need to overcome that adversity.

My first Sol Invictus as a Satanist was really about the act of setting aside time for myself to reflect on why I hated Christmas so badly. I tried to objectively describe which holiday symbols I hated “with a whole heart” and why. Once I had established a list of my intellectual enemies, I scoured the great depths of Wikipedia for symbols with which to destroy them. In the process, I somehow wound up with a page full of notes on the laws of thermodynamics.

Now that I’m coming full circle with the Satanic calendar, Sol Invictus has symbolically solidified it’s role as my Fire holiday. At first I was hesitant to use such a cliché, but the first step towards understanding Fire is that temperature is Transitive so I thought my symbols should be as well. The four elements align close enough with the four states of matter that I allowed myself to just roll with it. It’s hard to associate an emotion with Plasma, but Fire is alive and will consume anything in its path to stay that way. I can feel its Heat.

Perhaps it might help to place these holidays in Order with common symbolic associations:

  1. For the Spring Equinox, I celebrate “Hexennacht” which I associate with Earth and Hunger.
  2. For the Summer Solstice, I celebrate “Litha” which I associate with Water and Love.
  3. For the Fall Equinox, I celebrate “Halloween” which I associate with Wind and Fear.
  4. For the Winter Solstice, I celebrate “Sol Invictus” which I associate with Fire and Anger.

Somewhere in this mess of pagan mythology and pop culture references I recognized a pattern that had faced many times before. This was my “grief cycle”. It’s a never ending War that engages me in battle out of nowhere and demands emotional labor that I’m ill equipped to provide. To love someone is to fear losing them.

Sol Invictus is about leveraging my anger to fight my way out of negative feeling of guilt, shame, and self-doubt. It’s about providing myself space to meditate on the obstacles to my happiness and how best to destroy them through Knowledge. It’s a process of reflection to learn how I can leverage my survival instincts towards rational self-interests.

Maybe part of the miscommunication here is my anger gets perceived as unhappiness. Please don’t assume that’s the case. If anything, I’ve come to accept that I enjoy being angry sometimes. It helps me get Work done. I even find myself chasing the thrill of the fight for that “in the zone” feeling that accompanies it. Think of me like a big puppy with a lot of Energy. I’m happy to play with you, but “play” and “fight” are innately intertwined and I sometimes forget how sharp my fangs are.

How does one buy a gift for a puppy? Pursue the aisle for something cute and fluffy that fills your heart with joy? What kind of reaction do you expect to receive in response to this present? Very soon, that stuffed animal’s entrails will become its extrails. Will you scold the puppy for this? Or will you accept that it is in the puppy’s nature to rip out that squeaker as swiftly as possible?

In reality, my opposition to gifts probably is a minority opinion amongst Satanists. Arguably the LaVeyan philosophy is to test the sincerity of the giver’s altruism by accepting the gift without reciprocation. For me, this feels dishonest so I typically ask those around me to “not get me anything”. If I ask this of you, it’s because I care about you enough to tell you the truth. I’m the type of puppy that finds myself moping atop a pile of cotton balls and shredded cloth with eyes full of shame.

I literally have boxes full of Christmas presents I’ve been given in the past that have gone untouched for years. I should honestly just throw them away at this point but I don’t because of some irrational sense of guilt. Quite honestly, I’m tired of feeling that way and trying to learn how to say goodbye to things. Sol Invictus has become part of that process. I understand that some people take pleasure in gift giving at this time of year but it’s hard being asked for a list of things that I want while I’m simultaneously struggling to understand my own needs.

When you need something it doesn’t carry quite the same meaning as a gift. This is why you’re likely buy the puppy a toy rather than kibble in the first place, because the puppy needs to be fed anyway. In reality though, the toy is just filling a different kind of need. That puppy was going to destroy something one way or another, it was only a matter of “what” and “how”. You can’t take the Chaos out of the puppy, so you just do your best to redirect it with the toy. At that point, is the gift really a gift or is it an act of manipulation?

Is this how other people view Halloween candy? Let’s flip the script for a second and imagine an extreme version of Trick-or-Treating. Every year, the neighborhood bullies systematically test each house on the block for candy quality. If you fail to provide everyone with a suitable offering, then they TP your house every night until you move out. Since the demand for full-size chocolate bars has skyrocketed, so have the prices. Some of your neighbors are living off instant noodles all year round just to ensure they can afford enough Snickers to keep the peace.

If this were my only experience with Halloween, I’d probably hate it too. Instead, my version of Halloween is closer to a secular version of “Dia de los Muertos”. The candy is tool for symbolically externalizing my grieving process. It’s about remembering what brought joy to the people who are important to me. It’s about allowing myself space to hope that the werewolf knocking at the door might secretly be someone I love. I know that my dead grandmother is never coming to get these Werther’s, but maybe she might still manage to bring a moment of happiness to some random kid by proxy. The gift has already provided me with some small emotional fulfillment independently of the act of giving it away.

It’s not impossible for me to imagine a world where I’d be okay with “Sol Invictus Gifts”, but my experiences with “Christmas Gifts” are too similar to the extreme Trick-or-Treating described above. As a teenager, I wasn’t as open with my beliefs as I am now. Revealing myself as an atheist was often instant exile from a social clique. Every day from Thanksgiving to Christmas, I feel a needed to armor myself up for situations in which I might be “outed”. I lived in fear that I’d be put on the spot by receiving a gift from someone I’m not particularly close with. Do I lie to them with smile or tell them my honest beliefs? I feel more like I’m being tested for compliance than the beneficiary of an altruistic act. This is especially true when it happens at school or work.

One of my worst experiences was to being invited to a “Christmas Potluck” by a supervisor. When I tried to say I couldn’t make it, it got upgraded to a meeting and became mandatory. After forcing me to concede that I’d stay for the meeting but leave immediately after, they proceeded to ask me how I’d be contributing to the potluck. When you don’t give me the option to say “no”, that’s when it becomes oppressive. I’m not usually one to bite the hand that feeds me, but there are limits to what I’m willing to tolerate when cornered.

While we’re at it, can we stop the act of pretending to have a “Holiday Party” when it’s really a “Christmas Party”? You don’t get you use the general term when there’s only one being represented. Do people really think we won’t notice the lack of Hanukkah or Kwanza decorations at the event? I do. If you feel left out too, know that you have my sympathy and solidarity. One of the frustrating experiences for me a young atheist was that I never even had a symbol to be represented with around the holidays. I’m lucky that my real friends recognize this and point me towards “the Bah-Humbug Room”. Sol Invictus is all about empowering myself to reclaim the space that belongs to me. Every puppy deserves a play pen.

In summary, here’s what you should know about this hip new (old?) Satanic holiday called “Sol Invictus”:

  • My Sol Invictus is December 25th. Reclaiming this specific day is important to me personally, but other Satanists may have entirely different customs.
  • Rituals vary widely among Satanists, but we generally enjoy good food, good drink, and good company like anybody else. Acknowledging human nature is a common entry point to Satanism.
  • Understand that sometimes Satanists will need time alone to engage in self-reflection. It may be helpful to provide a quiet place for contemplation as needed.
  • Be conscious of power dynamics at school or work. Context can make a big difference in how holiday symbols are interpreted.
  • Provide a way to “opt out” of activities with minimal effort. The Satanist doesn’t owe you an explanation of their personal trauma.

As a bonus for reading this far, here’s a photo of me and my friend Dougal:

Selfie of the author and a Scottish terrier

Dougal understands that he might need to be separated from the mini-humans for safety’s sake but wants you to remember that puppies need attention too.

If you’re a Satanist here looking for advise on how to build your own holiday ritual, here are some of the resources I found helpful:

  • Anton LaVey, The Satanic Bible. Whether you find yourself leaning towards The Church of Satan or The Satanic Temple, this feels like required reading. It’s important to understand the role this work played relative to the “Satanic Panic” of the 80s. Decide for yourself which ideas to keep and which to destroy.
  • bell hooks, All About Love. In order to look at LaVey objectively, I found myself routinely comparing him with hooks. They present dramatically different perspectives on life but share a common philosophy of self-love.
  • Shiva Honey, The Devil’s Tome. This was a convenient resource for designing my own rituals. Having a basic framework in place for the holiday allowed me to focus on how to make it work for me.
  • Ernestine Hayes, The Tao of Raven. In my quest to celebrate the sun, it would be remiss of me not to mention the inspiration I found in Raven. Here I learned how I could be devious and practical at the same time.
  • Shannon Lee, Be Water, My Friend. It’s impossible to understand Fire without also understanding its relation to Water. Lee provides many practical examples of using self-affirmations to reach one’s objectives.
  • Pull from whatever sources you enjoy! My holidays would up being influenced by Donnie Darko, Wandavision and Final Fantasy. The benefit to having your own symbols is that you get to decide what they mean.

Ave Sol Invictus! And Happy Holidays to all!

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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.

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Student: “Hey Mr. Ruff, do you know a _______ Ruff?”
Me: “Uhh… Yeah…”
Student: “Hehehehe… That’s his brother.”
(10 minutes later)
Student: “Hey Mr. Ruff, do you still live on __________ Drive?”
Me: “Can we please get back to work on our geometry?”

Look kids, I get it. You’re growing up in an era where you have a massive amount of information at your finger tips.

I decided to leave the title and text above exactly intact as I had originally written on April 27, 2018. I’ve had some difficulty coming back to this because my little brother passed away four days later due to sudden heart failure. It’s now four years later and I’m still trying to reassemble the pieces of my broken heart. My therapist warned me that I couldn’t write my way out of depression, but it feels important for me to finish what I started here.

I’m not even sure where I was going with this in the first place. I think I just wanted to vent about the incident but couldn’t figure out how to do so without doxxing anyone. It’s not like I didn’t know this information was out there. I couldn’t be angry at this student for looking me up in publicly available records, but I also couldn’t help feeling vulnerable either.

The reality is that my digital footprint is massive. I’ve had a presence on the Internet since I was a teenager and you can still find some of that content if you know where to look. Some of that content is downright awesome! You’ll find teenage me engaging in philosophical discussions on artificial intelligence and building interactive websites. At the same time, there’s little doubt in my mind that you’ll also find me saying naïve or prejudiced things that I’m most certainly NOT proud of. This is the double-edged sword of participating in open forums.

There was much less risk of exposure when I was young and anonymous. Now that my digital footprints can be traced back to my real identity, there’s a strong sense of fear and anxiety that looms behind every word. Who is going to see this? How will they judge me for it?

Having quit my teaching job at the end of the 2020-2021 school year, my concerns about this have somewhat shifted towards “employability”. When I read this tweet from The National Cybersecurity Alliance saying that “70% of job recruiters rejected candidates based on information they found online”, I can’t help but wonder if that’s actively happening to me. If so, how would I even know?

I’m not the type of person to put up a façade. I will speak my mind to a fault. I call bullshit when I see it and try to own up to my mistakes. I’m proud of who I am. I fight fiercely for what I think is right.

The truth is that these very same qualities that I view as my strengths could be easily be flagged as “risks” by potential employers. I’ve made my peace with the fact that I’m a threat to any organization that’s not conducting its business ethically. There’s solace in knowing that those aren’t the types of the company I’d work for anyway, but I only have this choice because I come from a position of privilege to start with.

We’re entering a “damned if you do, damned if you don’t” era in social media. Having no online presence at all looks suspicious, but oversharing is also a considerable liability. People need to be held accountable for what they say online, but a moment of being human captured on the Internet shouldn’t permanently disqualify one from earning a living wage.

It’s not unreasonable for an employer to conduct research on prospective employees, but there is a strong need for for transparency in how that data is collected and used. The United States is in desperate need of privacy regulations in human resources. If something in my digital footprint is used against me in the hiring process, I should have the right to know what and how.

Lately I’ve been paralyzed by fear whenever I post something online. When you’re uncertain how your words will be interpreted, it’s quite easy to file it away under drafts but the silence is not sustainable. I need that sense of community now more than ever.

I’m going to try to start writing again and more frequently. Even if it scares me. Even if it feels forced. I can’t help if a potential employer stumbles across my digital footsteps, but I can assert control over the direction those steps are taking. Blogging can only work as a tool for self-growth if I accept the risks of making a mistake in public and write anyway.

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[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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When I joined Twitter back in 2009, I settled in on the following profile for myself: “I’m a video game developer turned educator, and hope to combine the two to make learning math FUN for people of all ages.”

At the time this seemed an appropriate description of myself, but I’ve been teaching for over a decade now and it seemed like time to update it. Many of the notions I had about teaching coming into the profession have since changed, as well as my very my sense of self-identity. I wanted a new Twitter bio to make a statement that would capture as much about my present day self as I could possibly fit in the 160 character limit. Here’s what I’ve settled on (for now):

“Professionally: mathematician, psychologist, programmer, & educator. Personally: atheist, socialist, musician, & gamer. Expect uncensored combo of both. He/Him.”

I think this is the first time I’ve publicly called myself a “mathematician”. I’ve always been too nervous to do so when I only have B.S. and not a Ph.D., but years of teaching has changed how I thought about this label. I want my students to feel comfortable calling themselves mathematicians. How could I possibly hope to communicate this when I was hesitant to do so myself?

I came to the conclusion that having a degree doesn’t make one a mathematician. Having mathematical thinking permeate every aspect of one’s being makes one a mathematician. Under that definition, this is most certainly is a label I would use to describe who I am. If unilaterally calling myself a mathematician helps to remove this stigma of not having a Ph.D. for others, than it’s about time I start doing so.

I started thinking about what other terms I wanted to normalize using and the rest of the bio just sort of fell into place. It’s kind of a liberating feeling to simultaneously challenge certain labels by expressing myself. If this is what it means to play “identity politics”, then not only am I going to play — but I’m going to play to win.

This one goes out to all the future mathematicians.

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Back in March, I wrote an article entitled Choosing whiteness in which I reflected on ways in which a family myth of Native American ancestry influenced my early conceptions of race. Since then, I started doing research into this myth through Ancestry.com, including a DNA test. I can now say that have substantial evidence indicating that I am not, in fact, Native American. I sincerely apologize for any harm I may have caused by falsely identifying as such.

It turns out that my darker skinned ancestor likely had a hereditary condition called “hemochromatosis” — a genetic marker I share with them. A build up of iron caused by this condition causes the skin to take a bronze/gray color which would explain why this particular ancestor looks so different from the rest of the family in old photos. Photographic technology has a well established bias towards lighter skin. This is probably how the family myth came into being.

I can’t undo the harm I’ve caused by perpetuating this myth, but what I can do is share the truth as I now know it. I’ve cross-referenced my genealogy research with Native Land. What follows is the history of the lands stolen by my ancestors (to the best of my knowledge):

My earliest white ancestors mostly immigrated from England in the late 1700s. They usurped the lands of the St. Lawrence Iroquoians , Ho-de-no-sau-nee-ga (Haudenosaunee), Mohawk, and Omàmìwininìwag (Algonquin). Through the early 1800s, many of them migrated west through the lands of the Ho-de-no-sau-nee-ga (Haudenosaunee), Anishinabewaki ᐊᓂᔑᓈᐯᐗᑭ, Attiwonderonk (Neutral), Mississaugas of the Credit First Nation, and Mississauga, then eventually south through the lands of the Shoshone-Bannock. Others took a more south-western path, through lands of Mohican, 𐓏𐒰𐓓𐒰𐓓𐒷 𐒼𐓂𐓊𐒻 𐓆𐒻𐒿𐒷 𐓀𐒰^𐓓𐒰^(Osage), Chikashsha Yaki (Chickasaw), Cheyenne, and Núu-agha-tʉvʉ-pʉ̱ (Ute). These two paths of white ancestors eventually converge, forcibly displacing the Eastern Shoshone and Goshute.

From here, my ancestors start to migrate to the southwest. They likely travelled south through lands of the Hopi, Pueblos, Western Apache, and Hohokam on their way towards the west coast. Eventually, they settle on land stolen from the Chumash, Tongva, and Kizh.

My parents are married on Wašišiw Ɂítdeh (Washoe) land and I’m eventually born on Fernandeño Tataviam land. I was raised on the land of the Cahuilla and now reside on Chesapeake land.

I don’t know what words to offer that would ever make up for the atrocities my ancestors were complicit in, but I hope that acknowledging these tribes and the lands that were taken from them is a step in the right direction.

This whole experience has challenged a lot of my preconceptions about the relationship between my DNA and “who I am”. I’m going to do what I can to continue unpacking my own baggage in the future.

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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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[This blog-post was originally written as a sequence of Tweets, so please forgive me if comes off as awkwardly chunked.]

Last week, Stephen Colbert asked Bernie Sanders what could be done for Joe Biden to win over “Bernie Bros”. I can’t speak for anyone but myself, but the thought of a Biden candidacy scares the hell out of me. I hope you’ll listen to why & consider that it’s “Not Me Us”.

I believe that the 2020 Election is going to be all-out “Information Cyber-Warfare”. Trump is a Compulsive Liar whose only hope of winning reelection rests in convincing the public that Biden is even less trustworthy than he is. Don’t underestimate his ability to do so.

Biden’s whole campaign rests on the premise that “Trump is worse”, but the greatest threat to the Biden campaign is going to be old video footage of Biden himself arguing against the positions he now claims to support. Biden has a “primary source” problem.

Consider this example. On Sunday, The New York Times runs a story about Tara Reade. There’s a bit that’s a little… contradictory. Well, maybe it’s best to just read it yourself.

Given that this sounds a little extreme, I try do the responsible thing and go looking for additional sources. I find over a dozen different videos of Biden touching little girls in ways that I could only characterize as sexual assault.

How am I supposed to argue that Trump’s “grab them by the pussy” comment is inappropriate while Biden stands accused of doing precisely that? Maybe Joe should start listening to himself. I believe Tara.

https://twitter.com/DavidAgStone/status/1243109935140835328?s=20

So when this Compulsive Liar starts accusing “Fake News” New York Time of covering up allegations of Biden sexually assaulting women, how am I supposed to argue otherwise against all this video evidence? The only weapon that works against liars is the truth.

If the Biden campaign really wants to beat Trump in November, the first result on a Google search for “Biden touching little girls” had damn well better be a formal apology, a personal commitment to engage in sexual misconduct awareness training, and a plan for accountability.

Instead of anything remotely resembling corrective action, the strategy appears to be an attempt to frame Tara Reade as Russian asset. I guess blaming Russia is the default response when Democrats have nothing else to go on.

I can’t talk about the DNC framing people as Russian assets without disclosing that I actively helped the Virginia Green Party get Dr. Jill Stein on the ballot in 2016. I ultimately voted for HRC (by a die roll) but can’t help notice the similarities in discourse.

I have no doubt that there are Russian bots that are attempting to interfere in our election. The question is if the intention is “dividing us up” or enabling a candidate that Trump thinks is “easier to beat”. Perhaps they succeeded at both.

The NLP and AI tech to do this is readily available, it’s just a matter of finding enough appropriate training data. What’s more likely? A huge data set of rational political discourse? Or a huge data set of aggressive Internet trolling? My guess would be the latter. Ya nyet Bot.

This real life Turing Test gets even more difficult when the Biden campaign is putting out troll bait campaign ads like this one. How do they expect to win over Sanders supports, many of whom identify as “socialists”, by lumping them in the same category as “plutocrats”?

Furthermore, this demonstrates a clear misunderstanding of what the word “socialist” even means. Without “socialist” institutions like the UNITED STATES POSTAL SERVICE, we can’t even have a “democratic” election during this pandemic. “Vote By Mail” is necessary to beat Trump.

Personally, I think the anti-Russia & anti-Socialist rhetoric is actually a disguise for anti-Atheism. It’s a relic of Cold War propaganda, just like how the phase “under God” was added to the Pledge. It explains why older and more religious voters leaned toward Biden.

Make no mistake, this idea that the DNC rigged the primary against younger voters is going to be a cornerstone of the Trump campaign. It would be unwise for the Biden campaign to blame the victims of this oppression rather than the policies that disenfranchise them.

This rigging arguement can potentially be dismantled by Biden campaign thru policy. By coming out in favor of approval voting, making election day a national holiday, and abolishing the electoral college, Biden could demonstrate solidarity with 3rd-party and independent voters.

Biden also demonstrates ageism with his proposal to lower the Medicare eligibility age to 60 and his continued support for ACA-like policies. Obamacare is essentially a tax on the youth that enables the healthcare system to continue profiting off the deaths of the old.

In response to COVID-19, Biden said he would “listen to the scientists” & “listen to the doctors”. Well Joe, I think the science is in and it says “Medicare for All” is NECESSARY to curb the devastation caused by pandemics like the one we’re presently facing.

If Bernie Sanders had been the nominee, we could point to his long history of supporting policies that would have minimized harm caused by the pandemic. The DNC sacrificed that argument by making Joe Biden the presumptive nominee on the basis of votes cast during the crisis.

There is ample evidence suggesting that our health care system is systematically disadvantaging Blacks, Indigenous and People of Color, who are literally dying of COVID-19 at disproportional rates due to man-made causes. Allowing this system to perpetuate itself is enabling systematic racism.

Biden’s campaign has an opportunity here to use “new evidence” from the outbreak as a justification for adding Medicare for All to his platform. In fact, he NEEDS TO if he wants to earn the trust of progressives. It’s a matter of life or death for some voters. Medicare for All Or Bust.

Likewise, I think it’s contradictory for Biden to say he’ll “listen to scientists” & not support an aggressive Green New Deal. The scientists are all saying that we need aggressive action NOW to preserve the continued habitability of our planet. There is No Planet B.

If I’m correct about the role disinformation will play in the 2020 election, this Compulsive Liar is going to double-down on every lie he’s ever told while simultaneously pointing out every inconsistency that Biden has ever engaged in. Complete with video evidence.

I’m not going to be able to argue that Biden didn’t do the things that he did. Instead, the only course of action left open to Biden is to openly acknowledge his own mistakes & run a campaign that depicts his ability to adapt to new information as a boon rather than a bane.

Come November, I plan to vote in such a way that I believe minimizes harm. However, it would be dangerous to presume that this necessarily dictates a vote for Joe Biden. I won’t say “Never Biden”, but there ARE reasons why I’m not a Democrat & it would be foolish to ignore them.

Don’t dare try to equate my involvement with the Green Party with support for Trump. You can’t use the “excluded middle” argument against a Compulsive Liar while Biden also has a tenuous relationship with the truth. His inconsistency makes me distrust him.

I’m not saying all this to help Trump & I don’t think anyone who read the whole thread could come to that conclusion. On the contrary, I’m saying all this precisely so that Joe Biden can understand what he’s up against & how to win the support of “socialists” like myself.

As one last point, I’d suggest that Joe Biden convincing Alexandria Ocasio-Cortez to be his VP would assuage many of my fears about a potential Biden administration as a former Bernie Sanders supporter. AOC4VP!

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IBM Data Science Professional Certificate Capstone

Introduction

When I first connected to the Foursquare API, I did a test search around my current location (Portsmouth, VA) and found only a dismal selection of venues to look at. For my capstone project, I thought it might be interesting to see if I could use the Foursquare API to locate other Virginia cities with a similar Foursquare venue profile to found out what characteristics these cities share in common.

I think this information might be valuable to providers of APIs like Foursquare, because it would allow them to enact targeted plans to engage excluded communities and increase coverage of their app.

Data Sources

  • List of Virginia Cities from Wikipedia
  • Geolocation data scraped from Geonames.org
  • Foursquare API

Methodology

I started by web-scraping a table of Virginia cities from Wikipedia. Next, I used the list of Virginia cities to look up corresponding zipcodes and geographic coordinates from Geonames.org. Once I had compiled a list of cities and zipcodes, I used the Foursquare API to search for venues near each location. Next, I had to clean up the data to remove duplicates of venues that were within the search radius of more than one city.

I started with a high level analysis using only the “Foursquare venue density” of each city. I divided the density into quartiles to visualize the results. This revealed some obvious trends related to population density, so I decided to further break down the data using a k-means clustering algorithm using the venue categories.

Results

My initial cursory analysis looked only at the venue density near each city. Using a histogram of the venue density revealed that Portsmouth was actually had much higher venue density than I had originally thought (at 9.125 venues/zipcode). A significant number of Virginia cities had no Foursquare venues at all.

Number of cites by approximate Foursquare venue density

To get a rough idea of where these low and high density areas were, I color coded each city by quartile.

VA Cities by Foursquare Density Quartile

To get a better idea of what venues were present in each location, I used a kmeans clustering algorithm to identify cities with similar types of venues. These algorithm produced the following clusters:

Cluster #1 contained the cities of Chester Gap and Ferrum. This cluster scored high in venues identified by ‘Sandwich Place’ and ‘Trail’.

Cluster #2 contained the cities of Penhook, Greenway, Great Falls, West Mclean, and Culpeper. This cluster scored high in venues identified by ‘Garden Center’, ‘Home Service’, and ‘Park’.

Cluster #3 contained only the city of Fort Monroe and was identified based on ‘Beach’ venues.

Cluster #4 contained the majority of Virginia Cities. This includes: Marshall, Suffolk, Emporia, Elliston, Colonial Beach, Colonial Height, Martinsville, Vienna, Burke, Centreville, Hampton, Danville, Newport News, Virginia State University, Rocky Mount, Williamsburg, Reston, Poquoson, Mount Vernon, Vinton, Lorton, Lexington, Dunn Loring, Radford, Fairfax, Salem, Waynesboro, Norton, Buena Vista, Lynchburg, Staunton, Chesapeake, Annandale, Henrico, Winchester, Manassas, Fairfax Station, Virginia Beach, Roanoke, Covington, Portsmouth, Fredericksburg, Newington, Fort Eustis, Herndon, Chantilly, Hopewell, Springfield, Charlottesville, Bristol, Fort Belvoir, Falls Church, Richmond, Clifton, Norfolk, Alexandria, Harrisonburg, Mc Lean, and Merrifield. These cities were characterized by having a high diversity of Foursquare venue types.

Cluster #5 contained Virginia cities with no Foursquare venues at all. This includes: Wirtz, Warsaw, Franklin, Galax, Glade Hill, Haynesville, Henry, Village, Farnham, Oakton, Catawba, Callaway, Randolph, Redwood, Sharps, Boones Mill, Bent Mountain, Union Hall, Petersburg, and Waterford.

These clusters produced the following map:

Virginia Cities by Foursquare Venue Type Cluster

The source code used in this analysis can be found on GitHub:

https://github.com/rruff82/Coursera_Capstone/blob/master/Coursera%20Capstone.ipynb

Discussion

This map showed several similarities with the venue density map, implying that the number of venues was a very strong factor in the clustering. Foursquare seems to have a very limited venue selection outside of major cities and urban areas.

The rural cities primarily had venues related to natural attractions (parks, trails and beaches). This pattern suggests that Foursquare might be able to improve its coverage of Virginia cities through advertising targeted at outdoor activities. Partnering with companies like REI or Bass Pro for incentives to increase the Foursquare user-base could potentially draw in users from under represented Virginia cities.

Conclusion

Overall, the results of this analysis were very much in line with what one would expect based on population. Cities with high populations had higher rates of Foursquare usage, and thus more venues to work with. Foursquare would need to make a substantial effort to draw in users from rural areas to increase coverage in Virginia. A more detailed analysis should try to control for factors like population and demographic information to rule these out as intermediate factors before attempting to identify patterns in venue types.