I was talking with friends recently about an interesting phenomenon that all self-taught programmers have observed, which we ended up calling “learning loops.” A learning loop is a process in which learners are motivated to advance their knowledge thanks to the positive feedback on their performance.
In this blog post, I want to look at the mechanics that make learning loops work and think about ways they could be used by teachers, private tutors, and publishers to build learning experiences in which learners have more agency and control over their learning. We’ll also look at the related phenomenon of game mechanics that exists in certain “addictive” computer games. Figure 1 contains a visual summary of the ideas we’ll discuss in this blog post. The two main questions we’re interested in are: “What can teachers within the formal educational system learn from autodidacts?” and “What can autodidacts learn from the gaming industry about staying motivated?”
In the second part of the blog post we’ll think about the role of teachers and educational resources in supporting and reinforcing learning loops. I’m writing this mostly as a self-reflection and welcome comments by other educators, content creators, and learning experience designers interested in this phenomenon.
Figure 1: The main question I’m interested in thinking about is how to introduce aspects of self-directed learning into the formal educational system, in order to give students more agency over their learning process.
Continue reading “Learning loops” →
Over the years several readers have suggested (sometimes demanded!) that I write a book on statistics. Indeed, since the company’s mission is to make the most useful parts of math accessible to the people, it makes sense to pursue statistics as the next title. Statistics is some of the most useful math out there! The 21st century is going to be all about data, so it makes sense to learn about the concepts and tools you need to analyze data, discover patterns, and make decisions.
I’ve now been working on the No Bullshit Guide to Statistics for three years so I figured it’s about time for an update to let y’all know how it’s going. My goals with this blog post are to share with you the detailed book outline and chapter previews, and also ask for your help to validate certain assumptions about the readers’ background (math and programming skills) and their motivation to learn statistics. Please jump to the short survey before continuing with the rest of the blog post. It won’t take longer than 2 mins.
Continue reading “No Bullshit Guide to Statistics progress update” →
Let’s talk about the problems with the teaching of statistics. Understanding statistics is essential for many fields of academic research, and also useful in industry. Why is it that first-year statistics courses sucks so bad? It seems that conceptual understanding of statistics ideas only marginally improve after taking a STATS 101 course. Is this because statistics is a really difficult subject to teach, or are we teaching it wrong?
I’ve been looking into this question for the last three years and I finally have a plan for how we can improve things. I’ll start wiht a summary of the statistics curriculum—the set of topics students are supposed to learn in STATS 101. I’ll list all the topics of the “classical” curriculum based on analytical approximations like the t-test. This is the approach currently taught in most high schools and universities around the world.
The “classical” curriculum has a number of problems with it. The main problem is that it’s based on difficult to understand concepts, and these concepts are often presented as procedures to follow without understanding the details. The classical curriculum is also very narrow, since it covers a slim subset of all the possible types of statistical analysis that can be described as math formulas that can be used blindly by plugging in the numbers. In the end of the introductory stats course, students know a few “recipes” for statistical analysis they can apply if they ever run into one of the few scenarios where the recipe can be used (comparison of two proportions, comparison of two means, etc.). That’s nice, but in practice this leaves learners totally unprepared to solve all stats problems that don’t fit the memorized templates, which is most of the problems they will need to solve in their day-to-day life. The current statistics curriculum is simply outdated (developed in times when the only computation available was simple algebraic formulas for computing test statistics and lookup tables for finding p-values). The focus on formulas and use of analytical approximations in the classical curriculum limits learners development of adjacent skills like programming and data management. Clearly there is room for improvement here, we can’t let the next generation of scientists, engineers, and business folks grow up without basic data literacy.
Something must be done.
Continue reading “Fixing the introductory statistics curriculum” →
I have been working on a French translation for the math book and in the process I stumbled upon some really powerful “authoring hacks” that I would like to describe here in case they might be useful for other bilingual authors and educators.
Let’s see les maths!
Before we begin with the “How it’s made” episode, let me show you some examples of the final product. I have selected the best four “backports” — explanations that now exist in the English version thanks to the additions in the French version.
- Reader feedback was consistent at pointing out the algebra sections as boring and TL;DR. Readers are willing to learn algebra (the rules for manipulating math expressions), but then when it comes to algebra “techniques” they are not sold on the concept. One solution to this problem would be to drop the “boring stuff” (lower the expectations of the reader), but I was having none of this. Instead I decided to just improve the explanations and add pictures: Completing the square en Français et in English.
- Functions (modelling superpowers) are the best thing ever, and probably the most powerful tool readers will develop in the book. This is why proper definitions and examples of functions are essential.
- Polar coordinates are super important—for both practical reasons and for the “aha” moment (knowledge buzz) that occur when readers understand $(x,y)$ is just one example of the many possible representations of the points in the Cartesian plane and $r\angle \theta$ is an equivalent representation (instructions that specify the position of a particular point int he Cartesian plane based on the distance $r$ and direction $\theta$).
- Speaking of knowledge buzz through representation theory, the book now finally has a proper motivation why readers need to think about the concept of a basis (a set of direction vectors that is used as the coordinate system for a vector space). On this one I go back to the basics—explain through an example.
Contuinuez à lire si ça a l’air intéressant. Read on if you’re interested.
Continue reading “Multilingual authoring for the win” →
Two months ago I was on a train going from Montreal to New York City. It’s a long ride, but I used the time on the train to triage all the coding project ideas I could work on while at the Recurse Center (RC). So many projects; so many ideas.
Today I’m on the same train heading back to Montreal and have another 10 hours to triage the thoughts, experiences, and observations about the big city and the social experiment that is RC. Here is my best shot at it—stream-of-consciousness-style—before I forget it all.
Continue reading “Impression from NYC and the RC” →
This is a followup on my previous post about the challenges of open educational resources (OER) production and adoption. I’ve come to the conclusion that the key aspect holding back the “OER dream” is not the lack of collaboration tools or the ability for teachers to discover material, but the quality of the content. You can’t write a textbook by committee. It’s as simple as that!
Continue reading “The textbook business” →
The goal for the NO BULLSHIT guide to MATH & PHYSICS was to make a concise textbook that teaches university-level calculus and mechanics in a nice “combined package.” The math fundamentals chapter grew out of the need to introduce the prerequisite material that many students often lack. I didn’t want to be like “y’all should remember this math from high school,” because if you don’t remember the material such comments would not be very helpful. A review of high school math would be more helpful.
Continue reading “Improving the math chapter” →
A reader recently suggested I should write more articles that introduce math specifically for different audiences. Math for doctors (although I’d hope they already know math!), math for artists, math for musicians, etc. I like this idea.
Continue reading “Math for lawyers” →
Yesterday I read the fascinating essay titled The Aims of Education by Alfred North Whitehead (1861-1947). It was written 100 years ago, but every line of it rings true in the modern context. Below I’ve extracted the best quotes from the essay and added some personal comments.
The OP gives a detailed blueprint of how to structure formal education, making a distinction between “general education” (primary school and middle school) and “specialized training” (high school and college). The essay discusses learner psychology, learner user experience, curriculum customization, student assessment, and even proposes a new structure for the educational system. The essay is so full of good stuff that nearly all of it is worth quoting.
Continue reading “The aims of education according to Alfred North Whitehead” →
I just read this excellent article Pragmatic Learning: It’s not “fun” on Roger Schank’s blog. It’s a very good post that calls bullshit on the “gamification” cargo cult which is widespread in the edtech and corporate training world. Just adding points, badges, and levels to a corporate training program that teaches you something boring is not going to suddenly make it fun. The author’s main observation is that forced learning is not fun and we need not pretend it is. Consider an employer who wants their employees to know X because it is required by law, or a bunch of students forced to learn Y or else they’ll fail. These “forced” trainings are not fun, and gamifying them is akin to putting lipstick on a pig.
Continue reading “Learning can be fun” →