LaTeX for digital literacy

TLDR: If you are a secondary school math teacher and don’t use LaTeX to write math currently, you should consider it. If you know a bit of LaTeX, you may not have realized how well-supported it is on the web: you can use it easily in many environments. As more and more students participate in online learning, knowing a bit of LaTeX will help empower students to communicate mathematical ideas in digital environments.

You may not of heard of LaTeX, a digital typesetting system used extensively by mathematicians when they create mathematical documents: it’s how they get those equations looking so nicely formatted with all the strange symbols and subscripts. LaTeX is used for more than just for formatting tough algebraic expressions, however. LaTeX can be used to create the layout for entire papers, books, and presentations, and can be used to create professional looking documents for any kind of content.

An example of math formatting in LaTeX: the
quadratic formula

The odds that you have encountered LaTeX, or will very soon, are increasing. LaTeX, or portions of it, are becoming the standard way that math is written for the web: it is how it is written on Wikipedia, for example, and many platforms, including Wordpress, Geogebra, and Brightspace support its use. In fact, with the Javascript library MathJax, LaTeX can be used on any HTML page, and is used across the web and in many applications (like Desmos, for example).

The growing LaTeX ecosystem

When we need to write mathematics in an electronic document most of us hunt through the toolbar to find some kind of equation editor. There are many problems with equation editors: they are limiting, and they often produce results that are not quite right and either not portable or editable. When we write for the web, we generally are writing plain text, HTML, or Markdown documents for which there is no equation editor available: we need a standard, open, portable way to write mathematics. This is what LaTeX is.

LaTeX, and TeX the system it is based on, are computer languages, not applications or plugins. Although software is required to render anything written in these languages into nice mathematics (just like your browser is required to render HTML), you don’t need any special software to write LaTeX (Notepad, Sublime, vi, or any text editor will do).

LaTeX resembles HTML or Markdown in how it allows a plain text document to be enhanced with formatting instructions. Although you can format an entire document using LaTeX, it is often used only where needed within a document to provide the mathematics - with many platforms allowing you to insert LaTeX commands where required.

Not so long ago, to use LaTeX you would have had to download and install the software that processes your plain-text LaTeX instructions and churns out .pdf or .ps files; today this is no longer necessary. Externally hosted JavaScript libraries allow you to directly render LaTeX code in your browser, cloud-based LaTeX systems allow you to create LaTeX based documents online, and many platforms like Geogebra, Brightspace and others have LaTeX support built in (even Google Docs equation support uses a subset of LaTeX-style commands).

Part of being digitally literate means being able to communicate effectively using digital media, and being able to share your work within online environments. When you master a digital literacy, you are empowered and more effective: you are using the tools available to you, but you are less tied to specific platform - you can quickly adapt to new platforms and share your work in new ways. If you write and share mathematics using electronic documents or on online platforms, LaTeX is a digital literacy that you should consider developing.

What is required as a digital literacy for some is not required for all - writing mathematics for the web is, admittedly, somewhat of a niche activity. But those who need to do it really need to, and would like to do it well. Secondary math teachers once used hand-drawn overheads, handouts, and chalk-on-blackboards when presenting written mathematics to their students. We now post on wikis, blogs, and virtual learning environments, and create shareable electronic documents. LaTeX is, increasingly, the best way to write mathematics for all these mediums. Moreover, there is an empowerment in creating mathematics that looks like the cleanly laid out mathematics that is presented in modern textbooks and professionally published websites.

The ability to create digital content is seen as an essential part of digital literacy (Spires, 2012). In a mathematics classroom, particularly in online environments, the difficulty of producing digital mathematics content in written form can be a barrier to students’ effective communication. In addition to using other means of representing mathematics (using Desmos, Geogebra, and other applications, for example), students often need to present written mathematics - learning a bit of LaTeX may allow them to do this in powerful ways.

References

LaTeX. (2019, February 11). Wikibooks, The Free Textbook Project. Retrieved 16:19, February 27, 2019 from https://en.wikibooks.org/w/index.php?title=LaTeX&oldid=3515745.

LaTeX/Installation. (2019, February 15). Wikibooks, The Free Textbook Project. Retrieved 17:14, February 27, 2019 from https://en.wikibooks.org/w/index.php?title=LaTeX/Installation&oldid=3516765.

LaTeX Project. (2019) An introduction to LaTeX. Retrieved February 27, 2019, from https://www.latex-project.org/about/

Spires, H.A., Bartlett, M.E. (2012). Digital Literacies and Learning: A Path Forward. North Carolina State University College of Education. Retrieved February 26, 2019, from: https://www.researchgate.net/publication/267380552_With_Contributions_From_Digital_Literacies_and_Learning_Designing_a_Path_Forward

Wikipedia contributors. (2019, February 17). Help:Displaying a formula. In Wikipedia, The Free Encyclopedia. Retrieved February 26, 2019, from https://en.wikipedia.org/wiki/Help:Displaying_a_formula

Wilkins, D.R. (1995). Getting Started with LaTeX. Retrieved February 26, 2019, from https://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/

twitter filter bubbles

Many educators use Twitter to build their personal learning network and participate in an online community of fellow educators. If we build our networks too narrowly, however, we may be co-creating an over-personalized environment that actually closes us off from new ideas. Our personal learning networks may become "filter bubbles" - and part of the reason for this is the nature of social networks and how platforms for them are built. Some of the filtering that leads to this potential narrowing of perspective is self-inflicted, but some of it is built into the platform itself, which tends to reflect our own interests back to us and also emphasize those things which resonate on social platforms.

Filtering is the whole idea
The whole idea of the Twitter timeline is that it presents a filtered selection of what people are saying on Twitter based on whom you have selected to follow. This filter is one that you, as a Twitter user have explicitly chosen - or have you?

Where do your follows come from?
You've chosen to follow a few people (well, more accurately you follow twitter handles) by making an authentic choice - these are usually people you've met or heard about, or institutions you are interested in. But a fair number of the people, institutions, or bots that you follow may come from other sources

• Twitter recommends some twitter handles to follow explicitly. These appear in the "Who to Follow" pane. How are these selected? They may be followed by handles you follow, have many followers, post many tweets... Twitter has some algorithm that determines, based on a set of signals, who they will recommend to you. So if you take Twitter's recommendations, perhaps part of your network was built with the help of this algorithmic filter.

• You may also choose to follow handles based on re-tweets from your existing network, or maybe by looking at whom handles in your network follow. Here the mechanisms of retweeting and following contribute to your network - these mechanisms amplify certain types of tweets and promote certain types of handles, ones that are more "shareable," which generally are more personal, controversial, or otherwise trigger immediate emotional responses. Retweeting and following (and choosing to display follower lists) are examples of social network mechanisms, designed to increase engagement, but also potentially adding to the coherence (or narrowness) of the your networks and its tendency to amplify socially heightened content.
  
• You may get some followers yourself, some which you might recognise, but most of which you likely don't. There is a temptation to follow-back when you get a follower, so you and someone (or something) else may be mutually re-enforcing your filters by reflecting similar values and interests back to each other. This is a general feature of social networks, a filter that arises from social networks' tendency towards network reciprocity.

Your timeline is not your timeline
Imperfect as your network is, the timeline is an accurate view of what is happening in it, right?

In The Filter Bubble, Eli Pariser describes how Facebook's EdgeRank algorithm selects what appears in your NewsFeed (p 37). He suggests later (p 225) that Twitter is more transparent than Facebook since its timeline is not filtered, but includes "everything everyone you're following says."

That was back in 2011, but in 2015 Twitter started applying filters to the home timeline by default (you can opt out). Twitter documentation suggests that this is largely a quality filter, used to filter out duplicate tweets and bots, but Twitter also sometimes use EdgeRank-like signal evaluation to insert or elevate tweets in the timeline, as they say:

Additionally, when we identify a Tweet, an account to follow, or other content that's popular or relevant, we may add it to your timeline. This means you will sometimes see Tweets from accounts you don't follow. We select each Tweet using a variety of signals, including how popular it is and how people in your network are interacting with it.

And depending on the device you are on, you may get a summarized view of top tweets, again "top" being chosen based on signals which derive mainly from the popularity of the tweeter and the sharing potential of the tweet.

The algorithmic filter (similar to the one that recommends you follow others) that injects and prioritizes tweets in your timeline, and the related filter that curates the "In case you missed" notifications may also contribute to the handles that you choose to include in your follow list, further building your network in specific ways.

So what?
As a platform for educators to share ideas, Twitter sometimes seems as close as we are likely to come to the convivial ideal of a free exchange of ideas from around the world.

However, on Twitter both your network itself (your follows and your followers), and your view of it (your timeline and notifications) are shaped by social tendencies, algorithms, platform mechanics, and emotional responses, along with your own interests, biases, and habits.

Perhaps not an ideal way to get information, ideas, and inspiration, but perhaps still the best available?

References
Pariser, E. (2011). The Filter Bubble: How the New Personalized Web is Changing What We Read and How We Think. New York: Penguin

triple e and a Desmos activity

As a math enrichment activity with a group of ESL students from grades 9 to 11 (ages 14-17), I ran a computer lab activity where the students used desmos.com to explore how periodic functions can create circles, spirals, and other curves.

In a brief pre-lab session, we talked about sine and cosine as periodic functions - we reviewed concepts like  amplitude and period, but did not discuss the how these functions are related to trigonometry. The activity was presented as a printed page of instructions without much additional background information.

The goals of the lab activity were:

• have the students explore and better understand how changes in the algebraic representations of the sine and cosine functions affected their graphs;
• understand that simple periodic functions can be combined to create more complex periodic functions;
• observe that periodic functions can be combined to create circles, spirals and other interesting curves;
• experience how mathematical ideas can be explored in a playful way.

Using desmos.com following the provided instructions, the students would create graphs of sine and cosine, and adjust parameters to change the amplitude and period.

These waves were combined into a new more complicated wave:

Combining in a different way allows the sine and cosine to form a circle:

And, with some small changes, the circle can be made into a spiral that can be wound up by adjusting parameters:

Some students went on to additional instructions that allowed them to create other spiral patterns, like this:

Four classes of fifteen students at a time participated in the lab activity, it was hosted in a small computer lab with about ten workstations. Students had various levels of English language proficiency, were in various grades (grade 9 - grade 11), and had previously completed one other Desmos-based activity.

The triple e framework helps us think through what worked in this activity and what could be improved.

Engagement Questions

Does the technology tool help students focus on the learning goals (content) with less distraction(s)?

The students were mostly focused on working through the instructions, rather than on exploring and experimenting. Because the groups of students were small, I was able to help the students focus on experimenting by going around the lab and asking questions about how the changes in the parameters affected the graphs. Once further prompted, the  responsiveness of the technology (moving the sliders allowed graphs to be easily altered) helped engage the students in the learning goals.

Does the technology tool help to motivate students to begin the learning processes?

Desmos has an interesting design - unlike many similar tools, construction does not proceed by navigating through layers of menus searching for the right button to click - there are almost no menu items at all. Desmos also does not use a specialized or proprietary set of commands to carry out actions - instead it uses standard mathematics conventions: to create something, you simply begin describing what you want to create using standard mathematics. This design is similar to how Geomter's Sketchpad approached geometric constructions. This can be a little intimidating at first, but once students know how to start, there is a very low barrier to beginning to create meaningful mathematics.

Does the technology cause a shift in the behavior of the students, where they move from passive to active social learners (co-use)?

In requiring students to provide the descriptions of what they want to make, and to actually add in the "sliders" and parameters required to modify their constructions, Desmos is an active learning environment. It provides the opportunity for social interaction through sharing of graphs - this was a feature that we did not explicitly use - better use of the platform would take advantage of this social dimension.

Enhancement Questions

Does the technology tool aid students in developing or demonstrating a more sophisticated understanding of the content? (creates opportunities for creation/production over consumption)

The desmos.com graphing tool definitely creates opportunities for creation/production. Once engaged, some students were experimenting and creating their own variations on the curves and graphs outlined in the handout.

In this particular activity, it can be argued whether or not the students were achieving a more sophisticated understanding: using the technology, students were able to go beyond where they could have in exploring the combinations of functions, but we intentionally skipped over much content (the detailed behavior of the functions, the trigonometric foundations, etc.). Ultimately, explorations like this one provide a far and high level view of where we can go with periodic functions, other activities can be used to help solidify the foundations for students so that they can gain confidence in their understandings.

Does the technology create scaffolds to make it easier to understand concepts or ideas?

The slider concept definitely provides a scaffold that allows students to understand how changes in parameters affect graphs of functions. Because Desmos uses standard mathematical conventions, the representations of the functions in desmos.com look exactly like the algebraic representations that students would use with pencil and paper. This isomorphism between the representation of the functions inside and outside the tool means that the learnings from the technology can be applied without the technology: the scaffolding can be removed and the structure of the learned concepts remains intact.

Does the technology create paths for students to demonstrate their understanding of the learning goals in a way that they could not do with traditional tools?

The dynamic nature of the graphing tools provides opportunities to demonstrate understanding that simply do not exist outside the tool. This is one of the great advantages of using dynamic graphing and dynamic geometry tools, like Desmos.

Extension Questions

Does the technology create opportunities for students to learn outside of their typical school day?

As a web-based and free tool, Desmos is available anytime inside and outside school. Students were encouraged to use the tool for other classes and assignments. Some created accounts on desmos.com and were experimenting after the activity and class were over.

Does the technology create a bridge between school learning and their everyday life experiences?

Desmos does have the potential to be used for more recreational and artistic uses. Within the realm of mathematics, students can use desmos.com in many of their classes (and beyond), primarily because (1) it has many powerful mathematical features, and (2) it uses standard mathematics - which is, as we like to say, a universal language.

Does the technology allow students to build skills, that they can use in their everyday lives?

One of the fears that stalk all mathematical tools is that, in using the technology, students will not develop the skills and understandings that they would develop in doing the calculations and graphing by hand.

Because it uses standard mathematical constructs and representations, students who want to go further in their Desmos explorations end up learning more mathematics and mathematical conventions in order to do more with Desmos. Graphs in desmos.com are very close visually to (high quality) hand drawn graphs, so working in Desmos can help inform students of best-practices in drawing their own graphs by hand. Part of a comprehensive approach to learning using Desmos would be to pair online graphing with pencil and paper activities. Students can go further and do more with the technology, and the use of technology can help improve their work without the technology.

Improvements

Reflecting on the triple e questions, raises the following possible areas for improving this activity, and the use of the desmos.com graphing calculator in general:

1. Be aware of how the desmos.com interface affects student engagement. New users can be intimidated by the "blank canvas" that Desmos presents. 

2. Be aware that engagement with the tool may be limited by the student's understandings of standard mathematical conventions. Use this as a learning opportunity to review/learn the standard conventions that are used in Desmos.

3. Ensure that any Desmos activity allows students to go beyond what they would be able to do without the tool, enhancing their understanding of the underling and/or associated concepts.

4. Enhance student learning by encouraging students to take the time to explore changes in their constructions by adding in sliders, and by combining constructions in various ways.

3. Take advantage of the accessibility of desmos.com to encourage students to explore mathematics outside of school and extend their learning.

4. Extend mathematics beyond the isolated experience of performing a calculation or drawing a graph by taking advantage of the sharing options on desmos.com to have students share the results of their explorations. 

References

Desmos Graphing Calculator. (2019). Desmos Graphing Calculator. [online] Available at: https://www.desmos.com/calculator, accessed on February 6, 2019

Kolb, E. (2013) Engage, enhance and extend learning: Find out what these terms really mean when you integrate technologies into your lessons. Learning & Leading with Technology, 40(7), 21-27. Retrieved from http://www.learningandleading-digital.com/learning_leading/201305?pg=22#pg22

framework perspective - TPCK, 3E, and SAMR

When thinking about the effective use of educational technology, you need perspective: theoretical perspective.

We need methods of evaluating learning activities that make use of technology, ways of making decisions about how to use technology in our own teaching practice, and guidance in how to help teachers use technology effectively.

Luckily bright folks have been thinking about these things, and have come up with theoretical frameworks to help us. Three of the most widely used frameworks for understanding the effective use of educational technology are TPCK, Triple E, and SAMR.

The TPCK framework takes a teacher knowledge perspective. You can learn more about TPCK here.

The TPCK model is useful when answering questions like: what does a teacher need consider when designing tasks and selecting technology in a particular subject area? A teacher draws on understanding of content, pedagogy, and technology - and most importantly an understanding of the interplay between these.

The Triple E (3E) framework takes a student learning perspective. You can learn more about 3E here.

The 3E model is useful in answering the question: how is the technology affecting student learning in this particular task? A 3E analysis may reveal that it is primarily promoting engagement but technology, when used effectivel,y could potentially enhance student learning, or even help facilitate its extension beyond the classroom.

The SAMR framework takes a task-design perspective. You can learn more about SAMR here.

How do we use SAMR? You may want to know concretely: How is the technology actually employed in the task, and how does this affect learning outcomes? Some technology acts primarily as a substitution for another, but it may also be augmenting, modifying, or even redefining what can be done in a particular task. 

Linking the frameworks
As these three frameworks approach the effective use of educational technology from different perspectives, they can be seen as complementary: each provides a different lens. The frameworks can also be viewed as being concerned with overlapping stages in the lesson/task design process: from teacher knowledge, to task design, to student learning outcomes - each framework offers insight into all these stages, but each has a particular focus. Teacher knowledge, described by TPCK, provides the foundation for the decisions made in task design, SAMR describes how the technology is used in the task design, and Triple E provides a concise description of how the knowledge and design choices affect student learning.

References

Kolb, E. (2013) Engage, enhance and extend learning: Find out what these terms really mean when you integrate technologies into your lessons. Learning & Leading with Technology, 40(7), 21-27. Retrieved from http://www.learningandleading-digital.com/learning_leading/201305?pg=22#pg22

Mishra, P., & Koehler, M. J. (2006). Technological Pedagogical Content Knowledge: A Framework for Teacher Knowledge. Teachers College Record, 108(6), 1017–1054. http://doi.org/10.1111/j.1467-9620.2006.00684.x

Puentedura, R. (2009). The SAMR Model. Retrieved from http://hippasus.com/rrpweblog/archives/2015/10/SAMR_ABriefIntro.pdf

computational thinking

The 2017 NMC/CoSN Horizon Report (K–12 Edition) identified teaching computational thinking as a persistent and difficult problem.

Although correctly highlighting its importance and the challenge that educators face in teaching it, the report, like some of its sources, perpetuates some common fallacies about the nature of computational thinking and its relationship with modern computer technology.

The report strikingly asserts that "The roots of computational thinking can be traced to algorithmic thinking of the 1950s and 1960s..." making the fundamental mistake in assuming that understanding computational thinking is a response to the sudden arrival of digital computers.

The truth is the reverse: the advent of digital computers in the 1940s and their wide adoption in the decades that followed was the result of humanity's centuries-long study of computational thinking, and in some senses, modern computers represent the crystallisation of a very elaborate understanding of what computational thinking is.

In other words - mathematicians, linguists, philosophers, engineers and scientists had been working on gaining better understandings of computational thinking for a very long time. The results of this research included several mathematical models of computation (Turing machines, and the Lambda calculus are examples), understandings of the logic and workings of formal systems (Boolean algebra, for example), the limitations of computation (Godel's famous theorems), an understanding of formal languages (Chomsky hierarchy), and also key results in how to express problems and ideas computationally. One of the fruits of this long research programme, that dates back at least to Leibniz, is the digital computer.

When Ada Lovelace wrote programs for Babbage's Analytic and Difference Engines, she was

applying, and developing, our growing understanding of computational thinking.

A helpful reminder that computational thinking predates our notion of computers, is to remember that computers used to be humans. The book and film Hidden Figures provides a nice window into that time, not so long ago, where people were employed to do the sort of problem solving and calculations that today are solved using software and hardware.

People solve problems and do calculations - but how do we do it? This is the basic question that fuelled the interest in studying computation itself, beginning hundreds of years ago. To the surprise of some, it was found that there was no magic spark within the human brain that allowed us to add numbers together: a formal system (a system with no deeper meaning, only symbolic manipulation) could express all of the operations of arithmetic. In fact, machines could be developed to carry out calculations.

Understanding computational thinking is not something that needs to happen in response to computer technology - computer technology is the result of our already deep understanding of computational thinking.

Why do so many people treat computational thinking as a new problem, one that is forced upon us by the advent of new technology?

We all like new problems.
New problems give us a chance to come up with new and exciting solutions. We don't like to be reminded by historians and other scholars that there is really nothing new under the sun. Coming up with a new solution to a new problem makes us a creative genius; recognising something as an existing problem conveys far less excitement and prestige.

We like to think of technology as something new.
Although the consumer aspects of computer technology are new, the underling ideas that modern consumer technology is based, particularly at the computational level, are not new. We think of computers as having emerged, as if out of nothing, sometime in the 1950s - an iceberg analogy might be useful: the applications that we have seen more and more of in the last 70 years are the tip of a large structure that previously went unpercieved, except by a minority. Our job is not to invent a new way of understanding the tip, but rather to look beneath the surface and appreciate what we were not previously aware of.

We don't like the answer to "what is computational thinking?"
We'd like it if there was something new here, but computational thinking is about using mathematics, logic, language, and problem solving (using, for example abstraction, modelling, and methods of representation).


Bringing computational thinking into the mainstream is an ongoing challenge. Computational thinking involves topics that have always been among the most challenging to teach: mathematics, language, logic, problem solving. From these subjects, we can use what we already know about computational thinking to structure their curriculum in a way that emphasises the most relevant parts of computational thinking.

Framing these topics in in the context of computational thinking does represent a shift in emphasis. For example, Calculus has traditionally been treated as the pinnacle of highschool mathematics - it makes sense, given the applicability of Calculus such a wide range of real-world problems, and the importance of the mathematics that an understanding of Calculus allows students to develop. However, a high school mathematics curriculum more interested in computational thinking might nudge Calculus out of its revered place in favour of mathematics that is more focused on discrete functions and other topics more aligned with computational thinking.  As Arthur Benjamin puts it in his TED talk "Teach Statistics Before Calculus":

Look, the world has changed from analog to digital. And it's time for our mathematics curriculum to change from analog to digital, from the more classical, continuous mathematics, to the more modern, discrete mathematics -- the mathematics of uncertainty, of randomness, of data -- that being probability and statistics.

emergence

One of the clearest examples of emergent phenomena is provided by the mathematical concept of cellular automata - a cell has one of a number of states (the simplest might just have states on and off), and is aware only of the states of its immediate neighbors. Different types of automata have the cells change their states based on simple rules - the most famous example is Conway's Game of Life, which has a rule that if a cell is turned off but has three neighboring cells that are on, it should turn on. Although the rules for automata are small, simple, and local, surprising large-scale patterns can emerge - patterns that are neither intended nor predictable based on the local rules themselves.

patterns that emerge
in Ulam's two-step automata

Often when we think of emergent technology, we imagine new technology: technology being born, emerging into the world as an entity onto itself. The notion of emergence provided by cellular automata and other models of emergence tell us something different - the elements at the local level (think of this as individual technologies and their intended uses) do not prepare or inform us about what patterns will play out at larger scales.

A similar caution about identifying what is important about technology with what is new is provided by David Edgerton's book The Shock of the Old (see a review in the Guardian, here), which reminds us that the impact of new technology is dwarfed by older technology, and that "invention is not the same as utilization". In looking at the phenomena of emergence, utilization - how technology interacts with people, systems, and life, is what matters.

Attempts to predict large scale patterns that will emerge from technology show how hard it is to anticipate emergent phenomena.

In 2010, then Google CEO Eric Schmidt authored an article for the magazine Foreign Affairs entitled The Digital Disruption: Connectivity and the Diffusion of Power (available here), which attempted to peer ahead into how connection technologies (Google, Facebook, Twitter) would impact geopolitics. It is instructive to read this article in light of how these connection technologies have since been used to undermine democracy - from the scandals of Brexit, the 2016 American election, and the use of data obtained from Cambridge Analytica to fuel the false news supplied by troll farms. Schmidt's insistence that governments should get out of the way of corporations so that connection technologies can be allowed to promote transparency, freedom and democracy, seems worse than self-serving.

Futurists, techno optimists and pessimists cannot be blamed for being wrong - emergent technology is more than the hardware and software that corporations are selling, and technology use is not directed by our intentions, good or otherwise.

hello world

Why blog?

After about 10 years of working in the software industry, I am easing back into working primarily in education (I am a secondary mathematics and computer science teacher). I'm working as an occasional teacher, teaching online, and doing other education-related work.

In some ways I've never left education - I have taken on a few curriculum writing contracts, have led some workshops, but mostly I have stayed involved with teaching by hanging on the periphery of online education communities.

When I left teaching, I still found myself thinking about math - math done for fun and education, so I started a blog mathrecreation to share the math I did for fun, and a twitter handle @mathrecreation to follow mathematics practitioners and educators. My social media presence has been somewhat anti-social: as someone on the periphery of education doing other work, I didn't insert myself into education-related discussions. My posting also was not focused on education in the strong sense - mostly on sharing what interested me, which occasionally included things that might be of interest to educators. Although on the outside, and somewhat anti-social, I have still made some great connections with other educators and enthusiasts, and this has helped me keep the education-side of my life alive.

Part of my re-entry into education is taking courses about education - I hope to use this blog and a new twitter handle (@danmackinnon7) for posts that are related to coursework and other aspects of my education journey, and keep my "math recreation" posting on mathrecreation.

How blog?

While beginning to look at resources for one of my courses, EDU5287 at UOttawa, I was reflecting on how I currently create digital learning resources, and how I engage with online communities of educators and enthusiasts.

I have started publishing the code that I write on Githhub. This is for convenience - I use Git as part of development and like having access to code anywhere, but it also has connected me to others that share similar interests - a social side effect that I was not looking for, but is nice. Most of the code I write is related to my recreational mathematics interests, or related to learning new (to me) technologies. My Github repositories are at github.com/dmackinnon1, and my Github pages are at dmackinnon1.github.io. Although Github is not primarily associated with education, I am interested in looking into how it can be used as a platform for publishing online learning resources.

Whether it is about a piece of math-related code I have written or some other topic, I use the Blogger platform to post. My blog is hosted at www.mathrecreation.com.

A long while ago, I used Google Reader to keep track of articles about math and math-education. Unfortunately that service ended, and I switched to keeping interesting links on a Tumblr blog, mathrec-links.tumblr.com.

Many of my recreational mathematics interests are in the area of geometry, and sometimes generative geometric art. I share math-inspired images that I create using code or software packages on another Tumblr blog, mathrecpics.tumblr.com.

The Blogger and Tumblr blogs automatically publish tweets to the Twitter handle @mathrecreation. Most of my tweets there are automatically published - I don't generally tweet about opinions or personal things.

I'm not quite sure how I will use this new blog and twitter handle... we'll see how it evolves. :)