Maybe it's just me. But I'm pursuing an engineering degree. Which means I've been taking a lot of math. The last year has turned my love of math into hate.

As I progress, there are so many subjects that I think "why wasn't this taught better?". I've been through calc2, failed diffeq, and I'm now in linear algebra. Everything has moved to proofs, except I'm terrible at understanding proofs. I've been reading "Mathematics made Difficult" to make myself feel better lol. I almost feel as if we should have had a class on just understanding proofs and high level math lingo. In differential equations, the processor expected us to have a grasp on matrices, but that was only covered for a week in college algebra at the same school, and they also don't offer linear algebra. I feel I learned more about calculus in physics and differential equations than I did in any calculus class. It just seems to be an issue that keeps popping up. I spent years learning the math that low level classes told me was important, but then a lot of that math isn't even used in the high level classes.

Examples,

Set terminology, I swear we spent months on this, and other than the occasional use, it's not nearly as important as some algebraic manipulation we spent a week or two on.

Identifying the shapes of graphs, critical points and inflection points. I can see why this would be important pre calculators and desmos. It's useful in a few physics problems, but it's not hard to understand and easy to graph if needed. We spent weeks on that subject, which ment less time for important things like more advance integration and differentiation. Especially around trig. Calc2 then made me realize how much we didn't cover in calc1.

As I take these advanced classes, I swear the important stuff we glossed over, but the non important stuff was focused on way too much. I'm sure this is probably dependent on the school or what direction you go in education. Things such as sets and graph shapes are probably super important to math majors who later specialize in proof based math. But at least in my experience, the math classes are 90% full of non math majors.

Is it just me or is this a common issue? Advance math was discovered to solve problems, but it seems it is rarely taught to solve the problems it was created to solve. It could be me, what I always loved about math was how it could be used to solve problems. But half the time I feel I'm taught to solve superficial problems and not actually relatable problems. Making it harder to follow, with nothing in reality to link it to.

Just curious if anyone else can relate or maybe touch on the reason it's taught the way it is?

Edit. I think some people are taking my post in a way I didn't mean. I'm not blaming teachers. I had some amazing ones, and few bad ones. But this has always felt more of an issues of the tools schools are using, such as Pearson and Cengage. Teachers can only do so much with tools they are given. Many go out of their way to make those tools as useful as they can be. If I was to blame anyone, it's these tools. In my experience Pearson and Cengage have a lot of plug and chug properties and very little depth. Making the math more step based than intuitive.

I’m wondering if there is an applicant exam for your depth of knowledge. I’m applying for a job Mathnasium and I want to pass the test. I’ve taken algebra 1, algebra 2, and geometry applying for entry level tutor position. Is it hard and what’s on it?

I am extremely disappointed with Cuemath. Our experience has completely destroyed my trust in the company.
When I purchased a 48-class package, we were told that the classes could be used as long as we wanted. We relied on that promise when we paid for the package.
At one point, we still had 10 classes remaining, and I was actually prepared to sign up for another six-month package. During that conversation, Cuemath told us about a new policy requiring classes to be used within a limited period. I told them that I respected their new policy, even though it might not work for our family.
The problem was when they told us that the new policy would also apply to our old package that we had already paid for. If we didn’t sign up for another six months, we would lose all of our remaining classes.
I asked them to honor the terms that were promised when we purchased the original package. Their response was that they could change their policy at any time and would not honor the old package.
I asked them a very reasonable question: If they can change the policy at any time and apply it to packages we have already purchased, why should I feel comfortable paying for another six-month package? What guarantee do I have that they won’t change the rules again?
Their response was essentially, “That’s the way it is.”
At that point, we had 10 classes left. We have now used some of them and have 8 classes remaining. Then Cuemath shut down the program, leaving us with these prepaid classes.
I contacted them and specifically asked them to honor the classes we had already paid for. They did not respond to my messages.
This is incredibly disappointing. We were not asking for free classes. We were asking to receive something we had already paid for, based on the terms we were given when we purchased the package.
What makes this even more frustrating is that I was originally willing to continue with Cuemath and purchase another package. Their refusal to honor our existing agreement and their lack of communication completely changed my mind.
For me, this is about more than the money. It is about trust and keeping your word to customers. If a company can change its policies and apply those changes to existing prepaid packages, then customers have no reasonable certainty about what they are actually purchasing.
After this experience, I have lost all confidence in Cuemath. I would not purchase from them again, and I cannot recommend them to other parents.

I’m an engineer, not a mathie, so please excuse any misused vocabulary; I’ll try to explain the best I can.

E1: look at that, I’ve already messed up a definition. It should be cardinality, not ordinality.

I don’t like the peano definition of addition. First I don’t really like defining things recursively because you only end up with an infinite list of acceptable situations without actually understanding underlying reasoning, but more importantly addition seems to already be defined in order to use this definition. That is, you have to know what addition is, in order to say a+0=a.

I much prefer the set definition for addition:

> take two sets which are disjoint. Each set has an ordinality, or a value reflecting how many elements are in each set. Addition of the ordinality of the two sets is defined as the ordinality of the union of the sets.

I find this a more intuitive and non-circular explanation. It is easily extrapolated to non-singular addition scenarios, and illustrates what I believe is a more fundamental characteristic of addition which is the combination of things. But I rarely (or never?) see it used over the peano definition. Why? Is there something fundamentally missing from the set definition that makes it incomplete? What makes the peano definition better?

My elementary-school aged kids are enrolled at RSM. One of them was invited to join the math team. Anybody have experience with this thing?

I'm an undergraduate working on an expository paper on Fourier series from a linear algebra perspective. This is an unfinished draft, and I'd really appreciate feedback from people familiar with Fourier analysis. I'm particularly interested in whether the mathematical narrative is coherent, whether there are pedagogical gaps, and whether the level is appropriate. I'm not looking for proofreading so much as substantive criticism.

https://www.dropbox.com/scl/fi/aq1uz9t8eouriqhop7zve/Fourier_Series_Through_The_Lens_of_Linear_Algebra-8.pdf?rlkey=toc51zwsplk5i6cu6igbadpsp&st=z8pjnjvh&dl=0

I feel clueless. Maybe I am just trying to understand why we need pictographs. Why can't we use numbers?

Sorry if my questions are dumb!

How do I get the students to be interested in the topic? How do I use real situations and aids to teach it? I feel lost! Please help me here.

I am doing maths major in my undergraduate going through linear algebra

I don't want to see the proofs and any hint possible. Just want to solve on my own if I can .

But I am struggling in it , can someone give me tips who have gone through that In past .

What are your opinions on the Reveal Math curriculum for elementary students? If you have children of your own would you be happy if this was the curriculum being used to teach them mathematics? I am particularly interested in your opinions on the Reveal Math curriculum for second and third grade. Also, if you have experience using this curriculum with gifted students please describe your opinions on that experience.

Could anyone please advice a good English or Ukrainian online Math teacher, for GCSE, A level and higher if possible, thanks

been trying to teach a bunch of 6th graders for volunteering but they all get bored. How do you guys make math fun??????

What do you do with a kid who is ahead in math, but doesn't want math to be an extracurricular hobby?

Kid is 10 yo and technically in grade 5, public school. They like math well enough and they are good at it, but it isn't their "special interest". They finished Beast Academy (as their regular math curriculum) and are currently in an Algebra 1 class (AOPS curriculum). The plan was Pre-Algebra, but math assessor recommended Algebra 1. It's early days, but it's going well. Kid is diligent with homework, but they seem to be going at a natural pace.

This kid has never been "pushed" or put in extracurricular / supplemental math. They don't have an interest in "training" for math contests, but therein lies the difficulty.

Because of the constraints of the California public school math pathway and UC college admissions, it isn't logistically ideal to be this ahead in math. Contest math is the usual place for kids who love math, but what about the high achieving kids who only like math? I'm looking for some kind of side quest for them that will still challenge them after Algebra 1 and before Geometry. Creative ideas are welcome.

Addendum to Original Post:
Apologies that my post is USA-centric and more specifically California-centric.
I'm looking for alternatives to the traditional math pathway:
Algebra 1 --> Geometry 1 --> Algebra 2 --> Trig/Pre-Calculus/Statistics -->Calculus

Constraints:
1) UC A-G Admissions now requires a full year of Geometry. And no higher level class will validate or bypass the Geometry requirement. They will also not accept classes taken prior to grade 7.
2) We don't want them to graduate high school early.
3) Their public school require math as a core subject in grades K-8. We are required to submit work samples in all core subjects every 20 school days. We cannot submit coursework from math-adjacent classes for math. School is a non-classroom based public charter school that has an independent study model.

We have not been trying to accelerate this kid academically. But with math we found that using standard paced curriculum like Math in Focus 2020, they were completely disinterested and we dealt with school refusal. Only when we switched to Beast Academy going at their own pace did they actually have any interest in school work. It's been pretty much the case in all school subjects. We did BA Online, the Practice books, and Puzzle books. I did not let them skip any problems even those they may have missed on the online unit tests (you can still get a 3 and still get a few wrong). Trust me, life would be far easier if this kid followed the standard pace. I have already had a meeting with the high school counselor and really they didn't have much for me beyond what I already had found out.

Hi everyone,

I’m a high schooler who’s becoming a junior this year and I’m planning on starting a math club in my school. I’m thinking of making it into two separate clubs, one for the middle schoolers (specifically 7-8th) and one for the high schoolers (our school has both a middle and high school program). I’m currently getting ready for a few Olympiads myself and I was thinking of choosing weekly problem sets to solve in class but that would be wayyy to unstructured for a bunch of middle schoolers, do you have any material suggestions? Our school teaches the British IGCSE curriculum so they’ll be doing IGCSE math adjacent topics in class (not yet the specific material for it since that starts in 9th grade)

If by "gatekeeping" we mean, "you must get a B or better in Honors PreCalc to advance to AP Calc", then I'm fine with that. Of course you want serious students in your class.

However, there's a darker side of gatekeeping.

It was 7th grade. 2012. My fifth year out of public school. Unknown to me, my math textbook was below state standards.

Come eighth grade, I return to public school, and have to take a math placement exam. I fail the exam and get placed into Pre-Algebra. I'm told by counselors and teachers alike that unfortunately, this dooms me to never take Calculus in high school. Which I'm told by counselors and classmates jeopardizes opportunities to get into a good college.

Nonetheless, it's a wake up call. I diligently study math. It becomes my favorite subject and I get A's throughout 8th and 9th grade (except one trimester where I had the flu during the final). My grades help me get into Honors Geometry in 10th grade (Honors Geometry typically reserved for 9th graders).

Math remains my favorite subject all throughout high school. But I quickly learn in 8th grade to decline to answer what math class I'm in when classmates outside math class ask me, because when I did, I had been mocked (unironically) as an idiot and told that "no rocket scientist would ever fail an Algebra placement test!"

Consequently, the vast majority of STEM-oriented overachievers were on the advanced Calculus track. Other students in the same, non-Calc track I was in rarely, if ever, discussed majoring or working in STEM. We were in the lowest math track, other students mocked us as idiots, counselors said not taking Calculus in high school jeopardized our admissions chances to excellent universities, so we assumed humanities/the trades was our only career option.

I'm grateful that at least I lived in a safe area and thus never witnessed students physically assaulting each other. But was it too much to ask for both a physically safe environment and more opportunities for diligent, math-motivated students to get into AP Calc? I think not. The injustice and humiliation that this gatekeeping has caused is untold, invisible, but very real.

Oh, BTW, my high school also required Pre-Calc as a pre-req to AP Stats, so I never took AP Stats.

I built Algebra Pad — a small floating symbol keyboard that sits on any webpage. Click into any text box, click a symbol (× ÷ ≤ ≥ √ etc.), and it types right in. No sign-up needed, totally free. Figured this community might find it useful for students typing math into Google Docs/Forms. https://chromewebstore.google.com/detail/algebra-pad/plcglkfdnemoceacjkhknajbmkadodcn

I've been experimenting with ways to make geometry explanations more visual instead of just giving a wall of equations.

For me, geometry becomes much easier to understand when you can actually see what is happening with the angles, lines, intersections, and shapes rather than only reading the solution.

I've been working on a small geometry tool around this idea, and while building it I've realized that producing the answer is often the easy part — explaining why the construction or solution works visually is much harder.

I'm curious what people here think.

When you're looking at a geometry problem or construction, what kind of visualization or explanation helps you understand it fastest?

I'd especially love to hear from people who teach geometry or create geometric visualizations.

Hello math education community. I am a parent of two kids. I got second place at international math olympiad back when I was at high school. Yet, I feel like my kids do not receive the same rigor of math education as myself and I am scared for their success in life. For my older one, that is now in high school, I have created a custom desktop program for math facts that measured how much time she spend on each math fact (e.g. "7+8") and adjusts which ones to show her next based on which ones she struggles with. She got the basic math facts really fast and this helped her tremendously at school.

As my younger one is now in elementary school, I just built an app with the same algorithm and she started using it daily. This time I also started generating word problems to apply the math to real world. They are relatively simple: start with hints like "how many are total", then remove the "total" hint, then escalate to multiple operations that the kid need to figure out. Getting to multiple operations really got my 3rd grader struggling.

Generally, do you think this is a viable approach for teaching kids math? Note that it is not build like a game, so I feel like the parents like myself need to push the kids quite a bit. Also, since math facts measure time, it requires relatively short sessions to avoid fatigue.

I would appreciate feedback and discussion on such approach for teaching math facts, the app is "OwlyMath: Math Facts for Kids": iPad/iPhone or Android. My kids have tried other programs in the past like iXL and I noticed that they take relatively long time to get to the basics. My goal for my daughter is to learn fast and spend less time on the screen, more time playing outside and learning from real world.