{"id":1241,"date":"2026-10-05T07:06:15","date_gmt":"2026-10-05T06:06:15","guid":{"rendered":"https:\/\/blog.lboro.ac.uk\/cmc\/?p=1241"},"modified":"2026-10-05T07:06:16","modified_gmt":"2026-10-05T06:06:16","slug":"two-minute-math-mathematical-explanations-using-animations","status":"publish","type":"post","link":"https:\/\/blog.lboro.ac.uk\/cmc\/2026\/10\/05\/two-minute-math-mathematical-explanations-using-animations\/","title":{"rendered":"Two-Minute Math: Mathematical Explanations Using Animations"},"content":{"rendered":"\n

In this blog post, Professor Colin Foster describes his recent project, producing over 160 short video explanations of mathematics, for school and university age students. You can watch the videos at twominutemath.org<\/a>.<\/em><\/p>\n\n\n\n

Introduction<\/strong><\/h2>\n\n\n\n

As they gain experience, school mathematics teachers and university mathematics lecturers get very used to explaining the same things over and over again. Each year, a new set of eager (or not so eager) students appears, but the mathematics we teach hardly changes. As time goes on, teachers and lecturers develop ways of explaining various concepts, informed by the difficulties their students present with. The knowledge we develop doing this might be categorised as an aspect of pedagogical content knowledge<\/a>.<\/p>\n\n\n\n

While the content of mathematics taught at school and beginning university may change less than the content of other subjects, one thing that does<\/em> change is the technology available to learn it. Mathematics teaching at both school and university level has come a long way since the days of \u2018chalk and talk\u2019. Teachers generally now have easy access to free technological tools, such as GeoGebra<\/em> and Desmos<\/em>, which allow live graphing, geometric construction, visualisation in 3D and handling large data sets and running simulations.<\/p>\n\n\n\n

The power of animation<\/h2>\n\n\n\n

In this context, I\u2019ve become increasingly aware of the power of an extension package called TikZ<\/em> that runs inside LaTeX<\/em> (a document preparation system and markup language) to generate vector graphic animations. University mathematics lecturers will be very familiar with LaTeX<\/em>, as the standard way of formatting mathematical text, and TikZ<\/em> as a convenient way of drawing diagrams and graphs, whereas school mathematics teachers are likely to be more familiar with Word<\/em> and PowerPoint<\/em>.<\/p>\n\n\n\n

But although I have used LaTeX<\/em> and TikZ<\/em> for many years, I only recently realised how easy it is to use TikZ<\/em> to generate animations. It is quite accessible, even if you don\u2019t have previous experience of these languages. (See the notes<\/a> at the bottom for technical details if you want it.) Because the generated images are vectors, the animation file sizes are tiny<\/em> \u2013 often just kilobytes, or a few megabytes, so they are very quick to download and watch in a web browser, on a computer or even on a phone.<\/p>\n\n\n\n

The role of AI in coding<\/h2>\n\n\n\n

A big part of what now makes this so easy is the ability of AI to help with writing and debugging code. Gone are the days of spending half an hour hunting down a missing semicolon! My most common prompt to AI these days seems to be, \u201cDebug my code\u201d, which I find it now does with impressive efficiency.<\/p>\n\n\n\n

Over the summer, I have produced more than 160 short video explanation of mathematics. I\u2019ve called the website Two-Minute Math<\/a><\/em>, although some of the videos are a bit longer than that \u2013 occasionally up to 5 minutes. Not all the videos use animations \u2013 I have tried to avoid being \u2018a hammer in search of a nail\u2019 \u2013 but many do. And I could not have produced anywhere near so many videos over such a timescale without AI help with the coding.<\/p>\n\n\n\n

The style of the videos<\/h2>\n\n\n\n

The videos are minimalist in style, and I\u2019ve tried to be informed by the design principles we used in developing the LUMEN Curriculum<\/a>, including the Cognitive Theory of Multimedia Learning<\/a>.<\/p>\n\n\n\n

I have been very inspired by the classic mathematics videos from the Open University produced under John Mason, which I first watched 40 years ago, and by Dave Hewitt\u2019s writing about the pedagogical power of \u2018canonical images<\/a>\u2019.<\/p>\n\n\n\n

Below are three examples, one on algebra, one on geometry, and one that tries to explain what correlation is in statistics. I\u2019d be delighted if you would pick one and take a look, and see what you think.<\/p>\n\n\n

\n
\"\"<\/a>
How do I solve a linear equation?<\/a><\/figcaption><\/figure>\n<\/div>\n\n
\n
\"\"<\/a>
What is the volume of a cuboid?<\/a><\/figcaption><\/figure>\n<\/div>\n\n
\n
\"\"<\/a>
What is correlation?<\/a><\/figcaption><\/figure>\n<\/div>\n\n\n

Ways to use the videos<\/strong><\/h2>\n\n\n\n

I could envisage the videos being used in a few different ways:<\/p>\n\n\n\n

1. For Students<\/em><\/strong>: Students could watch them to help with concepts they have found difficult \u2013 either from their current learning or from some time previously. I have suggested on the site a possible workflow for this based around self-explanation<\/em>. It is easy to engage passively with videos, whereas if students are pausing, rewatching parts, making notes and asking themselves questions, it is possible that more active engagement is happening that will lead to longer-term learning.<\/p>\n\n\n\n

2. For Teachers<\/em><\/strong>: Teachers might watch them together and consider what they like and what they don\u2019t. Perhaps a continuing professional development opportunity could consist of going away and making notes on what they would do differently (or perhaps even making an alternative video), and then coming back together and comparing and discussing. The discussion aspect might be more valuable than any of the individual videos produced.<\/p>\n\n\n\n

3. For Trainee Teachers<\/em><\/strong>: Trainee teachers might get ideas for their own explanations from watching them. They might craft an explanation of their own, in their own style, based on some of the ideas used in these.<\/p>\n\n\n\n

4. For Experienced Teachers<\/em><\/strong>: More experienced teachers might use the videos with their students without the sound<\/em>, pausing where necessary to support their own explanation and to invite discussion. I think that\u2019s how I would use them myself.<\/p>\n\n\n\n

What should I animate next?<\/strong><\/p>\n\n\n\n

If you have comments \u2013 or suggestions for additional videos to make \u2013 please let me know!<\/p>\n\n\n\n

About the author<\/strong><\/p>\n\n\n\n

Colin Foster<\/a> is a Professor of Mathematics Education at Loughborough University. His research focuses on the learning and teaching of mathematics in ways that support students\u2019 conceptual understanding.<\/p>\n\n\n\n

Technical note: How the stop-motion pipeline works<\/h2>\n\n\n\n

The way the animations are produced is based on traditional stop-motion animation. The .tex file acts as the \u2018digital flipbook\u2019 generator: instead of drawing shapes or graphs by hand in software like PowerPoint<\/em>, the TikZ<\/em> code instructs the computer where every axis, dot, line and text label should sit across incremental steps.<\/p>\n\n\n\n

You then run an R<\/em> script that automates the entire video pipeline \u2013 compiling the document rapidly with LuaLaTeX<\/em> (via tinytex<\/em>), extracting the high-resolution PDF pages as frames using pdftools<\/em>, and stitching them into a crisp 60 frames-per-second 1080p MP4, using the av<\/em> package (powered by FFmpeg<\/em>).<\/p>\n\n\n\n

Finally, I add a bit of voiceover, and it\u2019s good to go!<\/p>\n\n\n\n

For more details see https:\/\/www.luatex.org\/<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

In this blog post, Professor Colin Foster describes his recent project, producing over 160 short video explanations of mathematics, for school and university age students. You can watch the videos at twominutemath.org. Introduction As they gain experience, school mathematics teachers and university mathematics lecturers get very used to explaining the same things over and over […]<\/p>\n","protected":false},"author":770,"featured_media":1249,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"lboro_blog_alternative_thumbnail_image":"","footnotes":"","_links_to":"","_links_to_target":""},"categories":[26],"tags":[250,239,151,247,24],"class_list":["post-1241","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-teaching-practices","tag-ai","tag-explanations","tag-mathematics-education","tag-teachers","tag-teaching-practices"],"_links":{"self":[{"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/posts\/1241","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/users\/770"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/comments?post=1241"}],"version-history":[{"count":4,"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/posts\/1241\/revisions"}],"predecessor-version":[{"id":1250,"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/posts\/1241\/revisions\/1250"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/media\/1249"}],"wp:attachment":[{"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/media?parent=1241"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/categories?post=1241"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/tags?post=1241"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}