(Slightly off-topic)
It's really sad to me that as of yet there is nothing to compete with paper and a pencil for math. I've used probably 10 different programs/websites, lots of stand-alone software, LaTeX, drawing programs on tablets, etc. for this during my time as a student. All of it feels poorly put together because none of it solves any new problems. Drawing on a tablet is a worse imitation of drawing on paper. TeX is just unwieldy for anything other than writing down a final answer. Even the tools that are supposed to help automate stuff almost always fail to do so. To be clear, I think there is a lot of room for improvement within the next few years, especially when it comes to touch-screen interaction and similar ideas. I'm just hoping someone comes along and invents a decent product that feels just as intuitive as drawing diagrams and writing equations that utilizes the power of the computer strapped to it effectively (i.e. not just attempting to translate and simplify my drawings to text).
I frequent math.stackexchange.com and never write anything on paper. I enter my solution in MathJax either directly in the answer space or use MacDown which lets me enter MathJax offline and view the result as it is entered.
My answers have more detail than most since I am working out the math as I enter it.
I think I do OK since I have over 60,000 reputation points.
Recently saw chalktalk[1] which is designed for a different goal (and very rudimentary from what I've tried), but seems to be a step in that direction.
This is very cool and very much like what I want, but I can see how it's rudimentary. I think the only sustainable approach to these things is to build modular components and keep them separated into different modes/contexts. The advantage of that being that you can easily import symbols/functions from that particular paradigm of math into your notebook and then apply it to what you're doing in order to save time.
A second vote for Lyx - I worked through my OU maths degree using it and barely ever did my working out using pencil and paper. Instead, I'd write up the coursework "live".
You do certainly need to memorize the shortcuts and access keys for your notation, but then I can very quickly write out mathematics that I can still read a week later.
My brother[1] on the other hand does everything by hand. I even saw 7 pages of matrices & wave functions all in biro which was apparently "one equation" - I think even he thought that was a bit too much though and he finally started doing things in Mathematica.
I did two quarters of proof-based math courses recently with pen and paper, then started using an iPad Pro with Apple Pencil, and a program called notability. I think it’s better than paper! I can erase, resize easily, move things around, but it still feels like writing with pen and paper, while making it much easier to not lose all my notes :)
Interesting. Admittedly, I haven't ever used the iPad Pro/Apple Pencil. In my personal experience, it just never felt great using most touch screens. Most styluses feel too heavy and slip too much on glossy tablet screens so it feels ill-suited to writing small stuff quickly. On a Surface Pro + whatever the Microsoft stylus is called, I find myself writing way too large and then having to constantly scroll down in order to comfortably fit things on the page. Also, all the software I've interacted with is awkward when it comes to grouping symbols so that's always an annoyance to me.
I completely agree with this problem. While I haven't solved the full problem you are describing, including graphs and diagrams, I think they will all fit nicely into this application model soon.
The biggest problem with pens is palm rejection, which some recent hardware has gotten right. This actually works find on a screen you can only write on with the pen, like a graphics tablet, but people love their mobile games, so even laptops get capacitive touchscreens in most cases these days.
I cannot wait for good tools for managing mathematical work like we have for prose today, I think it will be a real productivity boost for students as well as professionals. So many workflows get forces into Excel and Word because they are the tools that people know. While they are great at some things and pretty good swiss-army knife products, they just don't work for managing a bunch of floating diagrams/images and lots of equations.
It's definitely early days for me, but I've recently shifted from all pen-and-sketch-pad to just getting more comfortable with LaTeX and entering more stuff directly into LaTeX. I find it makes me think more carefully. I've put some effort into getting immediate rendering on file change using Skim and various little bits of Emacs lisp to make LaTeX editing convenient. (I'm sure I've got plenty to learn about what the LaTeX modes that come with my editor can do as well).
For me, expressing math as code in a high-level language like R is way more intuitive, and faster to read/write/extend/verify than formulae.
This said, my context is always data-analysis/modeling. I’ve never felt intimidated by code, though I spent many years being intimidated by certain formulae. I’m fairly certain that I’d have pursued math to a much higher level in school if the symbolic expressions were pseudo code I could mess with, but this may just be my odd learning style.
This might be a good final ending step, with a society full of code literate students, but currently we aren't anywhere near that. Students and professionals alike use math notation, and I think it is important we find ways to bridge the gap between paper and digital math representations.
Every process that has moved to computers has seen immense productivity enhancements. Production of written text, audio editing, video editing, engineering drafting, all of these things involve producing a ton of unique information in a workflow. Copy/paste, versioning (even primitive versioning saving old docs), undo/redo, and re-arranging large groups of content are just so powerful that you can't go back to life without them once you can use then second nature in a given context.
I’m merely saying that in terms of symbolic representation of math, I’ve personally found code or pseudo-code the fastest to understand (but I’m not a professional mathematician!).
What do you feel is the core problem you are trying to solve? And any concerns about whether the effectiveness of student learning might be affected by using an electronic tool instead of pen and paper?
[1] https://www.npr.org/2016/04/17/474525392/attention-students-...
For better or for worse, tech is being forced into classrooms by textbook companies. At least this project emphasizes students working on good old complete assignments, rather than tiny bite-sized activities. It is also free, rather than $100 per student per year/semester.
Computers are okay at deciding if an answer is correct, but they are not good tutors. Teachers can use Free Math to find the gems in their students work that demonstrate their misunderstanding. Currently there is no way for them to process all of the data and work produced by their students every day and have access to this granularity of information.
I considered having an app that would take pictures of student work, but OCR just seemed unrealistic for math. Bad handwriting and symbol ambiguity are almost guaranteed to make any automated transcription of math work buggy. Unlike with natural language, which you can produce on your approximate mobile keyboard, there is no way to auto-correct a symbol or number based on the context.
Hi, I'm an investor from China. Instead of forcing students to use cumbersome computerized inputs for equations, we are seeing multiple approaches to revolutionalize how math homework is being marked in China, including professional scanners in schools, taking photos using apps, writing equations on iPads and using digital pens with special paper. The are multiple hard parts for this process, such as OCR for complex symbols, solving the problem itself using deep learning and theorem provers, and checking if the students work per line is correct. I haven't seen anything like this in the US, other than a few work in automatic solving the SAT exam(geosolver?).
I'm sceptical that this will improve the classroom climate for that I'd have to be developed with actual teachers and students.
Digitalization just for the sake of it is considered harmful.
Also I'd be wary to trust the similarity metric, IMO it is best to assume good faith until you have evidence of cheating.
Anyway I think this can turn out great, like other have said, if it gets some polishing here and there.
I also want to assume good faith, but some people in education are far more skeptical. I have been in meetings where those in charge or enforcing policy said things like "officially we have to have logins for each student", when a teachers said they preferred a simpler platform with a single quiz URL and students putting in their own names to identify their submissions.
I think one of the major problems with other products, is that they come out swinging with an accusation that all students cheat. Most tools these days have unique problems per students, which can make it harder to go over an assignment, because no one did the same problems.
I know there are varying opinions for what constitutes technology for improvement of a process, vs tech for the sake of tech. I think the world needs a digital way to represent symbolic math, it's one of the last complex processes done daily by millions that is locked out of a computer. Making something digital allows you to have undo/redo, and could eventually lead to a lot of interesting productivity enhancements. Nearly no one writes large amounts of text with pen anymore, because there is just so much more flexibility with a word processor.
One of the few things that forces people back to pen and paper is if part of what they need to write involve math formulas, because the current editors that include equation editing aren't fast enough. This platform isn't currently designed for mixing text and math, but it isn't too hard to add soon.
I think this is great! The offline first approach will clearly help to adopt this in a case when there is not central class management system in school.
Thanks! Definitely one of the hardest things to do getting products into a school is having them approved for support by IT. This doesn't apply to websites, unless they need to manage logins. While there would be some workflow optimizations with a fully managed web app, most districts wouldn't want to have a special gradebook for a single subject/department. This also simplifies development for me early on, so I can focus on the rest of the user experience without a bunch of dev ops work to keep the service up.
On a different note:
I think for grading purposes of student math home work which is done on a paper, Deep Learning neural network programs will be advanced enough in 5 years that is by 2023
- we will have a $200 flatbed scanner in every class room, as student finish his school work/home work, she can put the papers on scanner, it will sent scanned image to school server which is running Deep Learning software which Grades and home work and record scores in Database for teacher to view .
I think this might be a way that such a project could be accelerated. Machine learning is good, but math is extremely ambiguous. Symbols are re-used and their orientation relative to other symbols changes their meaning. Some problems want you to simplify, others want you to expand something. This project at least removes symbol ambiguity in written work.
Even if you could make a computer understand how to solve a bunch of problems, I'm not certain that blind machine learning would produce a good feedback system for getting students back on course when they misunderstand something. They could probably find some likely candidates where students may have made a mistake, but I don't think anyone has tech anywhere near this right now.
A flatbed scanner? Why not just make an app? The student snaps a photo of the page and errors are overlaid. Every kid has a phone today and I assume that isn't going to change in the next few years.
I have kids in high school and 90% of the time when they ask me for help because they are stuck, it's usually due to small arithmetic errors.
Very cool idea. It's so much better to see the steps of the solution rather than just ask for the final answer.
With a little polishing, this could be better/faster than solving homework on paper!
It would be really interesting to somehow connect the homework notebook with other "homework tools" like http://live.sympy.org/ as calculator, or geogebra for geometry, or just a generic diagram editor for doing diagrams (a bit like the scratchpad in khan academy exercises).
I totally think this would be a good container format for these various interactive tools. I think one of the reasons why they are not daily tools for many classes is that so much of math is symbolic. So far symbolic math has been confined to paper, even if a district decides to pay $100 per student per year for access to one of the existing services that will nicely collect your students final answers and machine grade them, students still do their work on paper, and the software is oblivious to it.
On tools like Geogebra, I think we need more interactive tools, but they need to exist alongside the symbolic work that everyone needs to do in most of their classes. Managing a classroom full of students working on computers (which can be distracting), is hard to justify if it is only displaying supplemental material and you also need to transition to "normal homework time".
I definitely need to add a generic diagram editor to make this useful for classes like physics.
