All the things I wish I knew about studying at school

My niece reached out to me a few days back asking about tips for studying at school. She was specifically interested in any ideas I had about how to excel in her maths studies. I wrote up my thoughts for her and it occurred to me yesterday that there might be some benefit from putting these notes online as well.

Without further ado, therefore…

Study Skills Advice

As I understand it, your question takes two parts:

1. how do I learn / study better
2. how do I specifically learn / study for my upcoming exams (in particular for mathematics)

I've split my response up into two parts since they're somehow related but also different. Part one ('how do I learn new things') is sort of required for part two ('what do I have to do to get good grades on my exams'), since it's pretty hard to try to cram ideas and concepts into your head if you don't first understand them.

1. Learning to Understand

Something you just have to 'learn'

First off, you'll want to learn the small tiny 'fact-like' things first. Some of this you just have to put in some work and learn them. It'll help you a LOT when it comes to getting a grasp on the bigger-picture concepts. To give an example, if there are certain equations or definitions of concepts, it can help to take a bit of time and just learn those by heart (in whatever way usually works for you for that). Note that this is limited to just small fact-like things. For sciences, maybe there are some facts or properties of something derived from the periodic table, etc, that are important. In the specific case of quadratics that you asked about, it might be simple things like:

• the usual form of a quadratic equation
• the quadratic formula
• 'what is a discriminant'
• what does the completed square form look like, and how do you solve it?
• what does this or that quadratic look like when you graph it out?

The key thing is to isolated and master those tiny morsels of information / facts early on, since a) it needs to be done anyway and b) it'll help you with the big-picture stuff. Sometimes textbooks help out by highlighting or bolding those key concepts. Just make sure you're not just trying to learn EVERYTHING by rote, since that advice is as good as no advice in my opinion!

Learning for understanding: foundations

Something else I'll say early on is that there are some core foundations that will serve you well:

• start with a / the problem — it will help to try to wrestle with the kinds of things you're expected to do with this particular topic you're studying. It can actually help you to do this at the very beginning of starting a new topic: before you even study things, take a look at the kinds of questions that you'll be tested on and expected to answer. Maybe even try to solve them. You'll learn a lot about the subject area just by rolling around in the mud and struggling a bit.
• curiosity — this almost goes without saying, but you should try to find a way to be curious about whatever you're meant to be studying. It'll help a LOT with your motivation and interest, which will in turn help you keep moving forward and give you energy at moments when things get hard. Sometimes the trick to this is just trying to ask questions about whatever it is you're studying: why is this important? how does it connect to topic X or Y we already studied? what is most surprising about this topic? Sometimes it can also help to know a tiny bit about the history of a topic. Calculus is a bit down the road in terms of your studies, but back in the day (late 19th century, early 20th century) there were really epic debates between the various people who were developing this new area of maths. Lots of drama and falling out between people. So sometimes just knowing a bit about the personalities behind things can help.
• growth mindset — I wrote a blog on this a while back but the core thing is just to believe that you have it in you to master this thing. Once you have that, and if you start from that place, then you'll have much of what you need to keep moving forward. And as one teacher once told me, as long as you never give up then you'll eventually master it. Sometimes you just have to be a bit patient. Most things come if you give them enough time :)

Retrieval Practice

This is sort of the core of most learning, in my opinion, and I have a lot of thoughts and practice around this. (Have read a LOT about what research recommends in this area, but I figure you're interested mostly in whatever is practical so I'll keep it mostly at that level.)

The core: if you want to learn something / master it, you have to retrieve it from your memory somehow. (Retrieve can mean lost of things: for German vocabulary it might mean knowing the gender or translation of a particular word. For Maths it might mean a particular formula, or even a high level understanding of how one concept relates to another.)

The important thing about this retrieval is that it will be and should be hard to do. (This is one reason why people don't necessarily enjoy doing this, and even fewer actually do it.) It's hard to struggle to put together a coherent explanation of topic x or y, but that struggle is what helps create neural pathways that cement the understanding going forward.

One possible way you could do this is to write short summaries of what you understood of a particular topic, then check your notes to see if you were correct. IMPORTANT: the key thing is to do this from memory / without notes. Otherwise you're not actually reinforcing materials in your head.

Another way of testing things (e.g. in your specific case of quadratics) is to do practice examples. Your school or textbook probably gives you some practice examples, but you shouldn't confine yourself just to doing those. Make up your own examples, or go online and find more examples (use Khan Academy or whatever).

It can also help to make distilled summary sheets at some point during your studies which gather together your understanding on a single piece of paper for the entire topic. Here actually you can see the one I made digitally for my own study of quadratics a few months ago:

The key thing with retrieval practice is to get a lot of it, and to try to make it the 'hard' / 'difficult' kind of retrieval. Mostly this starts with a blank sheet of paper and then you try to write down what you know about a topic, or a concept, or whatever specific thing you're trying to understand. Writing things down will help you realise (quickly! painfully!) which parts you don't actually understand. So it's as much to reveal to you which parts you need to work on as it is for anything else.

(There's a much-praised technique named after a well-known American scientist, Richard Feynman, and you can do something like this, too:

1. Write the title of a topic that you want to study / test yourself on
2. Write or map out an explanation of that subject intelligible / appropriate to a non-specialist. Do this from memory.
3. Identify any gaps in your explanation / understanding.
4. Relearn / restudy / interrogate to fill in the gaps.

You can use narrative / diagrams to condense and clarify your explanation. It's basically the same idea. And yes, bullet points or spider diagrams are all possible ways of doing this.)

Developing mental models

There's this idea that the whole thing you're doing when you learn something is developing 'mental models', which I personally find a bit hard to wrap my head around, but it is a thing… It's maybe the next layer up in what's happening when you try to learn something.

Mental models are, for me, about making a topic your own somehow. They're also about making the concepts of that topic manipulable somehow.

The 'making it your own' part has a lot to do with confidence, somehow, but it's also just feeling familiar and effective with the concepts that you feel comfortable solving problems in that area. If you see a problem, e.g., you know which techniques (or which subset of techniques) are needed to solve it. If there are multiple possible ways to solve something, you'll have a good feel for the tradeoffs: i.e. why this way is better than that way etc. In the case of quadratics, for example, we know that there is this amazing thing which is the quadratic formula, but you probably don't want to use that formula the whole time because it's easy to make a mistake with it and it's a bit cumbersome. Instead, we often use other simpler techniques that work for many (if not totally 100%) of the problems that you'll be exposed to.

One way to help develop mental models is to try to explain the topic to someone else. You already did a bit of this in the retrieval practice above: trying to explain it on paper is already some of this. But trying to explain a topic to people at different levels of understanding can be really clarifying. I.e. if you had to explain quadratics to a 5-year old it's probably different to how you'd explain it to a 40-year old. (Along with this, you can test out this approach by chatting with a chatbot about the topic. I'm sure you've heard of ChatGPT, but Claude is also another good option, esp for things like maths. The key thing is to start the conversation by saying something like "I would like to have a conversation about quadratics. I've been studying it and I'd like to test out my explanations of some core concepts with you. I would like you to tell me if things feel unclear about what I'm saying, or if you notice that there are some areas where I could improve my understanding.")

(While we're here, using things like ChatGPT to develop mental models can be useful. I will often have conversations that begin with something like "What is a good way to think about the discriminant in relation to quadratic equations? Please make your explanation simple to follow and use some concrete items in your reply, like only items that you'd find in a kitchen.")

Making mental models is hard! But the work you do to solidify things and make them your own is really worth it!

Anyway, the big point here is to reflect on what you're studying. Make sure to also give some time to connecting it to other things either in your maths studies or outside, or even life in general. It's not the best to just view everything completely isolated and disconnected from the other topics, so try to take a step back from time to time! (Unfortunately, most schools aren't built to encourage that process much, but it's important!)

Specific contexts

There are some other specific contexts that require different / more targeted advice, but you didn't mention them so I'll ignore them a bit. But language learning is one of them, and learning some kind of 'motor skill' is another (i.e. that requires coordination or physical movement like playing golf or the yoyo or whatever).

In Practice: Understanding Quadratics

To summarise the practical points listed above:

• learn the small fact-sized pieces early on
• get lots of retrieval practice (a mixture of examples of doing whatever the skill requires of you, and/or writing or explaining the topic at various levels)
• develop mental models where you can.

2. Studying for Exams

I'll take it for granted that you agree that you can't study for something without properly understanding it, so somehow the things in part 1 are sort of a prerequisite for this section; you can't get ready for an exam if you don't understand what's going on.

That said, there are some tactical things you can do to help your chances of success once you do have an understanding of a particular topic. Note that for all of this, it's a bit of a question of picking which parts seem doable / manageable. It's probably unwise / counterproductive to necessarily try to do EVERYTHING :)

Ground rules

You should understand the requirements of the exam. Take a bit of time to read through some previous exam papers. I'm sure your teachers have also given you clear guidelines on what kinds of things to expect. That will give you a map for how to prepare, so be sure to do this.

Foundations: Exam Study

There are some basic foundations here which for various reasons get forgotten when you're under exam pressure, but it's good to remind yourself of these, since if you neglect these it'll negatively affect your ability to study etc.

• sleep
• eating things that nourish your body instead of just feeding cravings
• taking breaks (every hour, ideally, get up and walk around for a minute or two)
• minimise distractions (put your phone in airplane mode or in a lock box while studying)
• movement in general / going out of the house for walks a few times a day is a good minimum.
• 'managing your energy' — this one's a bit hard to quantify / explain, but I'd say it's worth trying to embody the principle that you should only study as much today as allows you to keep studying tomorrow. I.e. if you overdo it and you study a lot today, but it's a bit too much and tomorrow then you can't do any study etc, then that was counterproductive. (Hope that was clear!)

Mnemonic / memory tricks

There are a TON of memory tricks out in the world. All of them are useful, but not all of them are equally useful for every situation :)

Things like the major system, the link system and the peg system are all useful, but they require a bit of time and probably also someone who knows how they work to explain them to you.

If you already have a bit of experience with these things, then I'd encourage you to use them in your studies, but if you don't have much experience then I'd say probably that it's not going to be the difference between an A and a B grade so probably it's a waste of your time to try to get into that in the run-up to exams.

That said, it would TOTALLY be a really useful investment to learn a few of these during summer holidays in a non-stress / fun way. You can play around with learning the order of decks of cards etc — I can explain all this if you're interested — and then you'll have that skill available to you if you need it next year or throughout your life.

There are some general memory principles that you can rely on in general terms:

• when trying to remember something, make it memorable in your mind! so maybe try to imagine the concepts as characters in some kind of image in your mind, and use all your senses and bring in some shock or drama etc etc. (LMK if you want more of these kinds of advice. I have a lot, but not sure how useful it is for you right now.)

Spaced Repetition

This is a really useful tool, but it requires a bit of upfront (time) investment and unless you're feeling super comfortable / not stressed at all, I might suggest to add it to the list of 'things to learn about over summer / winter (?) holidays'.

Basically this means testing yourself with (digital) flashcards, but the twist is that you only get shown the flashcard at exactly the optimum time / day when you need to be tested on it. (There's a whole science to this which I won't go into, but there's a TON of backing to the fact that this is the way to make things get into your memory.)

The best option for this is a piece of software called Anki. It runs on your laptop and phone etc, but it has a bit of a steep learning curve mainly because the defaults it comes with aren't great. So if you were interested I could help you set that up, but the key thing to know is that using this requires a bit of extra work.

The main idea is that you create (digital) flashcards for all the things you need to know, and then every day you check in with Anki to review whatever cards it says you need to know. There's an algorithm that calculates which cards you should review. It should mesh well with your intuitive sense of how memory works: i.e. over time you slowly forget things, so Anki will prompt you to recall a particular concept just at the point before you forget it, since that exact moment is the best time to review it. When you review it at that moment and you get it right, it'll really strengthen your memory for that thing. If you don't remember it, then it'll reset the status of that card and it'll know to show it more often for a few days etc.

There are more manual ways to get the same effect, but (for a lot of reasons) they're not as effective since humans don't work / behave like computers so really using a digital tool is the only way to go.

For quadratics, to use my experience, I have a bunch of cards relating to that that I get tested on. Writing a 'good flashcard' is a bit of an art, and we can get into that if you're interested, but I'll just lay it here as an option for now.

Interleaving

This is a fancy word for saying: 'don't study just one topic on its own'. When you're testing yourself on things that you'll need to know for exams, make sure to switch things up a lot. This means doing one problem from quadratics, then another relating to trigonometry, and another relating to topic z etc etc.

There is again quite a bit of evidence that this makes you much stronger in your understanding / learning, even though (or maybe because!) it's a bit harder to do.

If at least part of your review of topics / facts are handled by Anki it'll take care of giving you random flashcards anyway, so this more relates to things like solving maths problems by hand.

So don't just do 50 iterations of the same maths problem, in other words. Make sure you're switching topics etc.

3. Next Steps

• Check the practical suggestions above
• let me know if anything's unclear / or you want to know more about how to do thing x or y
• gather some problems to solve so you can make sure you're practicing the things you need to study
• get into some good habits around retrieval practice (i.e. writing things down to test whether you know them or not)

Spaced Repetition Without Computers

I wrote a little something over for the Spaced Repetition Foundation about getting the benefits of spaced repetition without relying on technology. Check it out here. Also give Matt's recent post on spaced repetition and creativity a read.

The ways memory skills augment your life

I released a new episode of Sources and Methods today. This week I spoke with Lynne Kelly, author of ‘The Memory Code: The Secrets of Stonehenge, Easter Island and Other Ancient Monuments', a fascinating exploration of the intersection between history, archaeological sleuthing and memory techniques. We delved into the contents of her book as well as the practical applications she found for these ancient skills.

I’ve been fascinated with the work that Lynne has been doing on the history of memory and her own personal memory ‘experiments’. If you need some inspiration as to things you might learn (or ways you might learn them), head over to her blog and the page entitled ‘My 33 Memory Experiments’. She generously includes photos and explanations of how the various systems work. Her latest groups places them in even further context. As someone who’s been following her memory experiments for a while, I found the book really useful to understand why she was picking a certain technique over another.

She’s about to start a new project involving memory skills, education and schools (she discusses that in the podcast around the 34-minute mark) and I look forward to reading about the outcome.

Positive feedback on my Memory Skills course

I haven’t written much on this blog about the memory course I wrote and launched a few months back. Its target audience is Muslims hoping to learn the non-canonical Asmaa al-Husnaa or 99 Names of God.

The point of the course isn’t so much to learn the 99 Names. They have their uses, to be sure, but I chose them mainly as a proxy to teach some basic memory techniques and skills that will have relevance and use throughout your life.

The course of emails lasts for a week, but as part of the package you get:

• daily emails containing the course’s core lessons
• 13 custom worksheets and handouts to practice the daily email lessons
• a summary sheet at the end of the week with an overview of the main principles of the course
• recommendations for ways to apply the principles in your daily lives and in other studies
• support through the Incremental Elephant community on the forum

I haven’t done that much marketing or outreach except what has been easily to hand, but I’ve been pleasantly surprised by the numbers of users trickling in bit by bit. Some recent feedback from users:

“Thank you for setting up this helpful course! It's been fascinating to learn the memory techniques and tips you've offered.”

D.N., Singapore

“Overall, I'm quite pleased that this course gave me the incentive to memorise the names properly and I also learnt other interesting things (can see now how this could easily become an obsession!). The emails were readable and contained about the right amount of information to make it doable in one week. Your didn't make any grandiose claims and the price was very reasonable. Jazakallahu kheyra. I'll recommend this to others.”R.H., United Kingdom

R.H., United Kingdom

I’ve also been pleased how those who finish the course have gone on to develop interests in more advanced memory techniques beyond the foundations contained in the email lessons.

If you’ve ever been interested in having a better memory, being able to learn longer lists and complex ideas for school or daily life, head on over to Incremental Elephant and give it a try!

Different Uses for Spaced Repetition

[This is a cross-post via the Spaced Repetition Foundation blog, where it was originally published]

Maybe Spaced Repetition isn't the best word. It's only descriptive after the fact, once someone has explained to you about Ebbinghaus and his experiments learning sheets of random numbers during the 1870s. For a general audience, we probably need a better term to help people understand what you can do with Spaced Repetition. We also need better examples and models of people who use it in a variety of domains of their life.

The first use case or scenario in which many encounter spaced repetition software or uses is language learning. And yes, it is great for learning vocabulary in an efficient manner. You can see how people have found ways to blast through large numbers of words by using things like Anki or Memrise.

But it would be a waste to limit our understanding of what Anki or spaced repetition can do to just learning vocabulary lists. It can be used for so much more. Indeed, expanding people's awareness of the various possibilities is an important reason why Matt, Natalie and I decided to set up this foundation.

With that in mind, I wanted to take a few moments to write down some thoughts on how you can use Anki and Spaced Repetition in other areas of your life. This list isn't in any particular order. You'll find that most things involving information or learning can be somehow coupled with the use of spaced repetition software, and the extent of your use is basically only as limited as your creativity.

- Birthdays -- learn all the birth dates of your friends and family. This probably works best in conjunction with some other system like the major system for remembering numbers, but you might be able to brute force this through.
- Kindle Clippings -- using Anki's in-built cloze deletion tool, you can blank out key parts of your kindle clippings to remind you of things you read in previous months or years. This way, books that you've read needn't be confined to vague memories. You can be more deliberate about what you're learning. Even things like book titles could be something you could learn with Anki. Consider a card which tests me on the author's name and the title (based on a short description). This way I avoid having those moments where I forget the title of the book but remember the contents pretty well.

- Magazine articles / things online as you're reading
I do this a lot. Whenever I'm reading online articles -- in Instapaper, let's say, which is the place where I read most things -- I'll save the highlights of passages I want to keep in my reference library. At a later date, I'll go through those highlights and see what I want to remember for the longer-term. I'll then transfer the clipping or highlight into my Anki library.

- New English words -- I'll occasionally come across technical vocabulary that is new to me while readying. If it's a word that I find myself looking up often, I'll save that entire sentence into Anki and use the cloze deletion method to set up an appropriate test.

- People / Faces
Matt seems to use this far more than me, though I'm starting to do it more often. The idea is that you find a picture of people you meet in meetings or in work contexts (Google Images or Facebook works well for this) and test yourself on their names and maybe one or two key facts about them -- that they're a vegetarian, perhaps, or that they just had a baby, or whatever it is. You can even do this pre-emptively. I once did this prior to a conference/event on Afghanistan. The conference home page had everyone's name and photo (those who were speaking / attending) so I just downloaded the lot, made cards for everyone as well as what their job/specialism was. By the time I arrived at the conference I knew everyone's name and who they worked for and what they worked on. It was a far more relaxed and personable experience than previous events of that kind. I don't get invited to speak at such events any more really, so I have no use for this, but I imagine many readers would find this useful.

- Reference materials -- You probably have things in your life that you're perpetually looking up. The time in-between looking-up probably is a matter of months (or maybe years). Just long enough to forget, but not long enough to forget that you once knew this thing. With Anki, those tip-of-the-tongue moments can become a feature of the past. No more remembering that you once new something.
Some examples: perhaps the precise proportions of a recipe you make every  month or two. Yet every time you make the recipe you have to look up whether it is 1 part flour to 2 parts water, or 1:3. Anki can keep your memory fresh.
Similarly with important medical data, or phone numbers, or points of contact for certain work projects or people.

- Coding language -- I used this while studying coding this past summer, and have found it great for making sure that the conventions I learnt for one language didn't get forgotten while I worked on the next language / scenario.

- Revising things you should probably already know but maybe have forgotten
This, for me, is the subject of mathematics. I studied it at school, but since then have had less need for it. This past year I've returned to mathematics with the somewhat embarrassing realisation that even things like my times-tables aren't as solidly in my brain as I'd like. I can tell you what 6x7 produces, but I'll probably need to think about it for a few seconds. Enter, Anki. I've been drilling myself on times tables for a few months and have found a real uptick in the speed at which I can recall those answers.

- Geography
You probably did a certain amount of this at school, but since then haven't added to the knowledge (or some maybe has been forgotten). Learning all the capitals of all the countries of the world (and being able to locate them on a map) isn't just an abstract skill. Things like this enhance your ability to understand and interact with the world. Instead, when you read a news article referencing a number of countries, you can place them on a map and realise that Ouagadougou is the capital of Burkina Faso and that it's included in the article for that reason.

Other niche things I've used Anki to help me with:
- brewing times for different varieties of tea, and also the ideal temperature of the water
- Ayas for the Qur'an (i.e. learning to recite these by heart). I know many use Anki for learning Bible verses, too.
- Learning the periodic table (alas, many years ago, in a deck now since deleted from my phone)
- The Japanese Kanji

Others use Anki for learning med-school data.

As I wrote above, the limit to what you can use Anki for is basically limited only by your creativity and imagination.

Learn all the districts of Afghanistan with Anki!

A friend was asking about using Anki to learn to recognise the districts of Afghanistan so I made her a deck that provides tests in the following way;

On the front of the card the question is presented along with a computer-generated audio pronunciation of the district name:

Then if you know it, you'll answer Badakhshan and then you'll click/tap through to the next screen to see if you got it right. You'll see this:

Then you can mark whether you got it right or not. There are around 400 districts to learn, so if you learn 13-15 new cards each day you'll finish the whole lot in a month.

Why learn all the districts of Afghanistan? Sometimes you'll hear someone talking about a particular place or part of the country, and without knowing which province they're talking about you might not understand the context or the conversation. Plus, a little bit of geography never hurt anyone.

Give it a try. And let me know if you manage to complete the deck. You can download the full Anki file here. Enjoy!

Jordan Diaries: Start with Geography

I arrived in Jordan this morning and am beginning my attempts to get to know the lay of the land. First thing is always geography. If I don't have those mental hooks to know that someone is talking about a particular muhafadha  / governorate, I can't properly engage in the conversation / information, so the only way to do this at the beginning is to learn a bunch of those initial hooks in a more deliberate fashion. Later on, you can learn things naturally, incorporating new pieces of information as you hear it, but at the beginning you need that initial scaffolding.

To that end, I'm starting off with Memrise's Governorates of Jordan course, which teaches you all the names, plus their administrative capital town. I'll be doing the same with Amman's geography over the coming days, too, though no pre-written course exists so I will have to make one myself. For Amman, I can combine the more abstract map-work with travelling to see the various places with my own eyes. Then I can combine the two together for a solid grasp of the geography and different neighborhoods. In due course I will also be travelling around the various parts of Jordan for myself, but for now I have to content myself with learning all their names.

How to become a memorisation and language ninja

I’m very glad to be able to announce two new things I’ve been busy with over the past few months.

Firstly, I’m launching an email course showing how to learn long lists of items by heart. This course is outwardly directed towards Muslims, since the list that you learn over the course of a week, is a list of 99 Names of God — the so-called Asmaa ul-Husnaa. But the broad principles are the same for learning any long list of things, so don’t think you need to be a Muslim to take the course. The materials come with lots of handouts and supplementary information about memory and the like.

Note that this first course is part of something new I’m calling Incremental Elephant, a place where I can offer more courses related to memory, language-learning and productivity.

Secondly, as regular readers of this blog will know, I’ve been blogging about technology, productivity, language learning and the intersection between the three for several years. Along the way, I’ve fielded dozens of questions from readers about which programme to use for this or that scenario, or which textbook to use when starting out with language x or y. I’ve increasingly been taking on longer-term clients to coach through these issues, so I’m taking the opportunity now to announce officially that I offer one-on-one coaching for language learning or productivity-related issues.

The language you’re learning doesn’t need to be one that I already know, because my coaching is usually targeting the meta-issues of how you’re studying rather than what you’re studying.

I offer weekly or biweekly Skype coaching sessions. This will include a mix of reviews of work you did the past week, planning your studies for the coming week and brainstorming techniques to get you over specific problems that are preventing you from moving forward. (For example, I’ve recently been working with someone who has problems declining verbs, so we’ve been tackling that from several angles using a variety of techniques).

More news on the Ph.D. front in a few months, I hope, but for now, go check out the 99 Names course and get in touch if you would like to discuss working with me to improve how you go about learning languages.

UPDATE: I've written up a more extensive explanation of what one-on-one language coaching involves, and what kinds of problems it's best suited to tackling. Read more here.