Resources for Studying Math with RemNote

Resources for Studying Math with RemNote

NB: This is a wiki post. Please feel free to contribute. In particular, add your own resources under “Resources”. External resources also are appropriate, but should be marked as such. You could post underneath as a reply and then link to that reply in this main text. See Jay’s notes as an example.

So far in Mathematics with RemNote…

Hello fellow RemNoters.

In service of the new study groups created for the Discord server, this post is a compilation of all official and community Math relevant resources produced so far for RemNote.

In the forum thread, “Has anyone ever studied maths with RemNote?”, brunntobi asks us what role spaced repetition plays in studying Maths with RemNote. Resident CSS wizard Hannes reminded that mastering the fundamental parts first allows you to develop your expertise on solid ground, implying the use of the queue, RemNote’s spaced repetition component, for keeping definitions and core concepts on roll call and leading us to the question of “what’s most important in Maths to internalise/master?”

Ingelbertph from the University of Hong Kong linked to his developed set of notes, explaining that his workflow omits the queue and utilises daily notes, emphasising a considered approach that asks when and how to apply structure to your notes. Math teacher 88DM88 also stepped in to reveal their workflow after a period of experimention with RemNote, demonstrating a trial-and-error approach that suggests “what works” isn’t always arrived at immediately, and that through determination we can build our own insights from the ground up. The thread came full circle when Tobias posted his own answer in a write up on Medium, but that in doing so explored much more. You’ll have to read the full post for a spin on the Zettelkasten concept of permanent notes by blablagang.

While it is usually recommended to run through the excellent RemNote tutorial first, once comfortable with RemNote here are the community resources specific for Mathematics. Below is what is intended as an exhaustive list. If you know of a resource I’ve left out, please mention it below!

Resources

Articles and videos, example notes, and CSS snippets. Lightly annotated.

Articles & Videos :page_facing_up: :video_camera:

  • @brunntobi’s article on How To Study Maths With RemNote. A slim article that packs a helping punch. Touches upon the utility of the concept-descriptor, creating exercises and his idea of “feedback flashcards”, keeping a todo list in the style of Ali Abdaal’s revision timetable, tips on writing LaTeX and more. (NB: Requires a Medium account.

  • @penolopiedavid’s video on Active Recall and Spaced Repetition. As a Math and Econ grad, Penelope showcases a hindsight-rich four step workflow. Includes example notes for various components of mathematical knowledge like graphs and equations.

Example Notes :memo:

CSS Snippets :scroll:

  • @HannesBigger LaTeX. Keep squinting at LaTeX? Hannes has you covered with CSS to increase the font size.

Misc.

TODOs
O Featured tips section
O Common questions and issues
O Quick LaTeX tutorial gif?

Edits
01 May, 2021: Added message to encourage new edits.

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I love the community spirit here :heart_eyes: thanks for compiling this!

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Michael Nielsen’s article on creating flashcards in multiple passes to deeply internalise the concept.

RemNote uses KaTeX for its LaTeX, here’s the reference. For chemical formulas (math adjacent I guess) mhchem is used, here’s the reference.

Some hot LaTeX tips from hannes: using a text expander form to fill in arguments and colouring the formulas.

This post could also be made into a wiki so people can write directly into it, if you’re up for that?

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That’s a great way to flesh out one of the two core sections of this post. I’d be for it on the basis the two purposes are respected (as in discussed, not necessarily kept). The two purposes are:

a) highlight all relevant community-made resources and contributions, and b) trace the common discussion points around studying Maths with RemNote.

The reason I excluded links to external resources in the initial version was to set the tone as a community-driven enquiry. However, I see that “resources” as a word implies content from a variety of sources, and including them better kickstarts study of the subject as well as addresses the implications of the discussion points.

The main benefit I see to a post like this one is the evolving history of thought from the community, allowing new RemNoters to get up to speed with identifying their upcoming learning points and to keep an overview resource to help synthesis the discussions. Like a public MOC, perhaps.

So for the wiki contributions, if I could suggest we distinguish community-made resources from external resources, either through separate sub-categories or visual indicators for example, and we stay privy to the beat of the Conversation, then I’d be happy for the post to be driven by our hive mind.

TL;DR Yes, let’s go ahead and do that, and maybe we can make a real history of thought from it.

Hey all, I’ll post a couple of things I’ve been working on, feel free to contact me about it here, or post in the #math-users-group Discord .

Example of using Image Occlusion to recall labels of different parts of a diagram. And using Front-Back flashcards to review basic definitions, nothing too fancy: RemNote

And here are my scrap notes on tools and the limits of typesetting/drawing math in RemNote (please support Category Theory!) RemNote

Experiment Using RemNote to TEACH Math (high school)

I put all the ‘basic facts you need to know’ for a particular topic (Straight Line Graphs) into a RemNote format, to share with my pupils to revise: RemNote

I also made similar content for teaching Inter-Quartile Range: RemNote

TL;DR:

· Works best for the sort of brief facts you’d squeeze into a revision summary cheat-sheet (heck, just find one of those and image-occlusion the entire page!)

Pros:

· automates the process of regular spaced revision of basic facts (e.g. state the formula for calculating a line’s slope)
· makes you select what exactly are the core facts from a topic, and how the concepts are arranged hierarchically
· pupils enjoyed the click-reveal dynamic, made revising more fun and clearly actionable (reduces overwhelm)
· worked well for simple unambiguous facts, like definitions or equations
· great way for you to store and efficiently re-access your notes and material, gradually building your own custom database, much more search-able and feature-rich than .docx or even ShareLatex

Cons:

· took 3hr to make just one topic, and the entire syllabus is ~100 topics, so too much effort unless it can be done more efficiently
· if people don’t actually use it there’s no scaling benefit
· needed to take time to train pupils in how to use the RemNote queue
· content siloed, without collaborative authorship (colleagues can’t chip-in something)
· needs practice problems and worked solutions (hide-reveal using image occlusion!) but those are limited by copyright, and putting in tons of screenshots can bloat the filesize of your database
· didn’t work so well for more complicated concepts, or things you’d need to take more notes on, because for those you have to figure out how to type a written explanation
· needed progressive disclosure — at the first pass you only want people to see the the basics, then you want full detail, then once you’ve learnt it you only need the basics again as a summary. But the queue just throws everything at you at once with no sorting or ordering (though I guess you could have some custom DoFirst DoSecond DoLast tags to subdivide the content’s sequencing)

Conclusion:

· Making front-facing content suitable for other people’s consumption is much harder and much more work than scrappy personal notes
· Works best for bite-size facts needing little explanation — think summary sheets of equations
· RemNote is great for building, curating, and accessing your own databse of math notes

QoL Improvements Feature Requests:

  1. Make the Latex input box larger/resizable (does anyone have some CSS to do this?)
  2. Please build support for all the environments that Katex supports, namely Category Theory Commutative diagrams Supported Functions · KaTeX
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You may find this writeup about using flashcards in the classroom useful, despite it being a different subject (his older posts are linked at the top as well).

Thanks @UMNiK ! These ideas are largely inspired from summarizing that article

Disclaimer: feedback and discussion welcome, these ideas are not only mine, they’re largely inspired from just summarizing this: Seven Years of Spaced Repetition Software in the Classroom - LessWrong

Why Start Using SRS Flashcards in the Classroom

  • The recall step (the ‘card front’) is where learning and retention actually happen. You need to strongly emphasize the need for going slow and making the effort to recall, rather than simply skipping through the cards.
  • You can consider supplementing note-taking knowledge-delivery “I write up, you copy down” exercises with “I write those facts into the cards”, so that
      1. pupils have a reliably good-quality copy of the material,
      1. which they can reliably access (no more “sorry I forgot/brought the wrong book”)
      1. when accessing those notes, they are prompted to actually study them
  • Providing individualized SRS for revision material can tick lots of important teacher boxes (differentiated instruction, regular recall, reliable notes etc.).
    • Especially if you collect data analytics to quantifiably compare a particular students’ average study time/success-rate to that of your overall class or your high-performers.
  • And at the end of the day, the mere fact of having introduced students to SRS gives the chance for massive payout for those few who adopt it independently.

How to Start Using SRS Flashcards in the Classroom

  • Use Flashcards for bit-size facts, which have already been taught in-context.
  • Be demanding and aim for reliable high automaticity, drilling for speed so that students don’t get stumped when needing to draw on that knowledge as part of a longer procedure.
  • Easy cards are really important, to low-ball easy wins and build engagement with the pupils who are otherwise overwhelmed.
  • Any time there’s something positive or happy, build those good moments into your particular class’ cards — even just a picture of a funny drawing someone made.
  • Review the flashcards with a designated study routine (lasting 2–8min) both as Individuals, or Whole-Class out-lout or mini whiteboard call-and-response (especially helpful for low-motivation students).
  • Have frequent low-stakes quizzes of the flashcard material — setup some sort of workflow to port RemNote content to Google Forms (potentially via Google Sheets)?

Setting Up The Cards (copy-paste these into RemNote)

Concept name :: definition

  • :: example of applying the {{term}} to some contextual material

EXAMPLE:

Straight line gradient :: the ‘steepness’ of the line, the vertical (y-axis) change caused by each horizontal (x-axis)

  • :: in the equation $y=-5x+3$, -5 is the {{gradient}} and $3$ is the {{y-intercept}}

.

.

Procedure Strategy Cue :: response of ‘what approach to take here’

  • :: mnemonics or good advice top-tips pupils should recall when facing this topic

EXAMPLE:

State the gradient of this straight line $6x-3y=9$ :: re-arrange it into the form $y=mx+c$ by 1. adding $3y$, 2. subtracting $9$, and 3. dividing by $3$

  • :: you can only read-off $m$ and $c$ if the equation is in the form $y=mx+c$ i.e. $y$'s coefficient is $=1$. Remember “I’m not ready until $y$ is by itself.”

.

.

Sequence Image Occlusion :: reveal the occluded step in the problem-solving sequence

EXAMPLE:

Re-arrange $6x-3y=9$ via {{$6x=9+3y$}}, {{$6x-9=3y$}}, {{$(6x-9)/3=y$}} into $y=2x-3$$

While balancing the risk of displaying ‘false’ answers, it is possible to make multiple-choice quiz cards like this:

Prompt ::1.
	choices:::
		Option 1
		Option 2
		Option 3
		Option 4
	Answer

Potential Issues

Summary

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  • You avoid the risk of pupils remembering ‘incorrect’ deliberately-wrong distractor prompts, if you just stick to only displaying ‘correct’ recall prompts.

  • Overlearning specific examples means you could just memorize that particular answer rather than generalizing your knowledge of the overall process. Reduce this by intermittently going back and re-jigging the numbers?

  • Avoid using it on phones, the more-visible the screen, the less likely they are to get distracted.

  • Potential barrier: tedium of porting new cards to the pupil’s account. Could be minimised by making the entire class only use one set of login details, and each week the teacher manages that account’s content and manually imports new material.

  • Issue to solve: until RemNote support classroom dashboards to manage pupils’ learning, how do you quantify how much pupils have revised, and what level they’re at?

  • Feature request: implement some basic Teacher/Classroom learning management features, allowing the teacher to push updates to pupil’s designated ‘Study Decks’, and showing a dashboard aggregation of “recall success status” (image from AnkiApp) for individuals, and the whole class

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