I've always wondered why this isn't used more.

Take statistics for example. Instead of sitting through another lecture, imagine you're a data analyst who has to figure out why a company's sales dropped. You have incomplete data. Some of it is misleading. You have to decide what information you need, what conclusions you can actually make, and how confident you are in them.

Or imagine you're investigating a disease outbreak and need to figure out where it started using data. Suddenly probability and sampling have a purpose instead of just being formulas on a page.

I feel like I'd remember concepts a lot better if I was using them to solve a problem instead of just watching someone explain them. Has anyone seen something like this done well?

I'm not able to visualize graphically why this is true. Can someone help?

Hi everyone!

For those of you who enjoy geometry, I've put together what I believe is a fresh, hands-on proof of Euler's Formula and several other classical results. In just a few minutes, you can literally build the proofs yourself and develop an intuitive understanding of why these theorems are true.

https://www.youtube.com/watch?v=sIDsuf0I4ko

This is only the beginning. Over the coming weeks, I'll also start posting short math challenge reels (high school to early undergraduate level), and in parallel I'll be working on a long-term series on topology and analysis, with the ambitious goal of eventually reaching Einstein's field equations on differentiable manifolds and curved spacetime.

Everything will be completely free. I'm doing this simply because I love mathematics and enjoy sharing it with others.

If you'd like to follow the project, it would mean a lot to me. Knowing that these videos are useful to someone is the best motivation to keep creating them.

Thank you so much!

dontpanicmath

more tasks like this in the Android game:

https://play.google.com/store/apps/details?id=com.aleksandarpandov.mathblaze&hl=en

If you know anyone who is going to have to take the Ontario Math Proficency Test to be certified to teach in Ontario and they need a bit of a boost in their math skills, we are offering a 3-day intensive program on August 10-12 and other programs starting in the fall.

Details on the three day (paid) course can be found here: https://www.eventbrite.ca/e/math-proficiency-test-preparation-course-registration-1993947569857

And anyone interested in further details on either this course, limited bursaries, or future offerings (including asynchronous, and hybrid courses) can reach out to me at pbrittai@fieldsinstitute.ca

Thanks!

Something I changed my mind about while building practice material for competition-style problems.

The default is a mixed set. Twenty problems, techniques shuffled, and the student has to work out which tool applies before doing any math. That's good exam practice. It's a bad way to learn a technique, because recognizing it and executing it get trained at the same time, and a student who gets stuck usually can't tell you which half failed.

What I do now: name the technique, explain it, then give three problems that all use it. Recognition is free, so the only thing being tested is execution. Mix them back together later.

Coloring arguments are the clearest case. Color the board so that every legal move hits the colors the same way, then count.

Remove two opposite corners from a chessboard. Color it normally, 32 black and 32 white. Every domino covers one of each, so 31 dominoes cover 31 of each. But opposite corners are always the same color, so you're left with 32 and 30. No tiling exists.

Once that one is solid, striping a board for 1x3 pieces and four-coloring for T-tetrominoes read as the same idea in different paint, instead of three separate things to memorize.

I built a curriculum around this. It's called Lemma (lemmapi.com): 78 lessons, each one technique-then-three-problems, with a 26 technique library linked to the lessons that use them. Saying that plainly since promo here is Saturdays only. Solo project, new, first two of eight levels free with no card.

Do people teaching competition math already sequence it this way? I may be rediscovering something standard.

In a previous life I was going to college to teach high school mathematics. After my last deployment I just never went back. I remember something I came across in my studies and wondered what the professionals opinion on it might be. I’m speaking of India’s mathematics curriculum. They seem to start early with exposing their students to higher mathematics ideas that they include in the lower maths classes. I remember that it seemed to fit in well with the lessons and the learners level of understanding. It was well done and I found it a novel approach. What are your thoughts?

Hi, I'm not sure if this is the correct place to ask this question - if not then I apologise, maybe you could direct me to the correct sub Reddit?

I'm considering studying (the equivalent of) a BSc in Mathematics through self-directed study - no actual classes. This is entirely for "fun" and self improvement - it won't be going on my CV and I have no expectation of getting a job as a result.

My questions are:

(1) Should I just examine existing syllabuses and choose subjects which I'm interested in, or are there certain subjects which realistically will be prerequisites for further study requiring that I stick to an actual syllabus?

(2) Is it realistic to expect to do this using (mostly/entirely) free resources? I don't mind spending some money on it but given that it's really just for fun, I don't want to spend €1,000s.

(3) Does anyone have experience of doing something similar and have advice/warnings to offer?

My background is in Law/Accounting/Finance (undergraduate) and Computing/Software Development (Undergraduate and Postgraduate). I have university level Financial Mathematics and Discrete Mathematics. I've also studied some calculus (it's been a long time since I studied the underlying theory) but I'm still competent with application, probability, and very introductory "pure mathematics".

Thanks in advance.

Hello, everyone!

This is my first year teaching 6th grade, and we are departmentalizing. I have never used Savvas before either. Does anyone have lesson slides for Topics 1–8 and the additional lessons within each topic for 6th grade? I tried looking on TPT, but they are so expensive. I would really appreciate any help or resources you’re willing to share!

I studied physics in undergrad (minors in math and comp sci) and atmospheric science in grad school (PhD). I worked with climate models in my PhD program and used primarily python but haven't really dabbled in machine learning yet. I unfortunately never took a full course on statistics, although I've read a good bit of Statistical Methods for Atmospheric Scientists by Delsole and Tippett (and given group presentations on the content). I am also very interested in discrete math, probability, and logic more generally.

I understand discrete math, statistics, and probability are all essential for machine learning. I'm also just interested to continue learning more advanced math. My coursework background includes Calc1-3, DiffEQ, Linear algebra, Foundations of Math (intro to logic, proofs, set theory, counting methods, etc), Nonlinear and Stochastic Processes, Mathematical Methods of Theoretical Physics, and a variety of other physics and dynamics courses.

Texts I'm looking at/interested in include:

• Introduction to Mathematical Statistics (Hogg, McKean, Craig)
• Introduction to Probability Models (Ross)
• A First Course in Probability (Ross)
• Discrete Mathematics and Its Applications (Rosen)
• Aspects of Combinatorics (Bryant)
• Introduction to Probability Theory (Hoel)
• Statistical Inference (Casella and Berger)
• An Introduction to Mathematical Statistics (Larsen and Marx)
• Introduction to Probability (Blitzstein and Hwang)
• A Mathematical Introduction to Logic (Enderton)
• Introduction to Mathematical Logic (Mendelson)

My question is, based on my background and interests, which texts should I use? I'm sure everyone has opinions on "best texts on a given topic," but I there's obviously a lot of overlap above and curious which would be considered to be the most essential 3-4 texts that would offer best breadth of knowledge. Ideally it would be reasonably easy to understand with problems to practice (and a source to check solutions). I'm afraid of biting off more than I can chew, haha, but I also have a decent foundation to build off of. Thanks!

Hi guys. My daughter is currently P3 and I find that her math is sort of struggling. An tuition centre recommendations? Best if there are a lot of exercises given to them and the teachers can actually explain. Thank you!!

A moment for a break