I loved math in school. I majored in math in college. I taught middle school and high school math for six years, including geometry for at least three, before changing careers 15 years ago. A trapezoid always, ALWAYS had exactly one pair of parallel sides.

Tonight, my 7yo was doing an online math quiz, and a rhombus was classified as a trapezoid. Lo and behold, trapezoids now have AT LEAST one pair of parallel sides. So previously trapezoids were defined in opposition to parallelograms, and now parallelograms are a subset of trapezoids. Honestly, this feels about as destabilizing as when Pluto was demoted to dwarf planet status.

The internet tells me this was a common core change in the 2010’s. It also tells me that until the early 1900s, all the shapes we think of as “special parallelograms” were defined as not being parallelograms. So I guess there’s precedent for this kind of change. But also, I’ve seen a LOT of online math resources today still defining a trapezoid as having “exactly one” pair of parallel sides. Maybe those resources are written by people my age who are clinging to the past?

My question is for the geometry teachers who were teaching during this change. How long did it take you to stop thinking of parallelograms as not-really-trapezoids? Did that transition actually make sense to you, or do you still secretly have a trapezoid bucket in your head that’s fully separate from the parallelogram bucket?

A bit about me. Finance and math background, CFA Level III, Treasury funding experience, and I know ML well enough to build and ship models. I'm retired (FIRE) and have time on my hands. I love teaching and explaining things.

I'm thinking of doing some free explanatory posts here or in r/learnmath. But I don't want to guess what's useful. For those of you learning math or ML: what's the one concept that, no matter how many times you read about it, still doesn't click? Or what's the most frustrating part of the learning process for you right now?

Just trying to figure out where I can be most helpful. Not selling anything, no app to promote, just genuinely curious.

I want to know if I will be okay if I take abstract algebra before real analysis.

My university allows me to take abstract algebra before real analysis. If I take real analysis first, due to scheduling issues, I would have to wait 1 extra semester. I don't want to do that, but I also don't want to get absolutely demolished, or be at a significant disadvantage.

Description of my university's real analysis class:

"Sets and functions. Induction. Axiomatic introduction of the real numbers. Sequences and series. Continuity and properties of continuous functions. Differentiation. Riemann integral."

Description of my university's abstract algebra class:

Groups and their homomorphisms; commutative rings and modules; fields and vector spaces; subgroups and quotient groups, permutation groups; modules, submodules, quotient modules; polynomials rings and their ideals, modules over polynomial rings.

As a kid I slept through almost every class and used my nights to teach myself other things. I ended up skipping a lot of school and building my professional career from a young age. I'm very happy with that path and have no regrets.

The one important thing I skipped along the way was math.

Lately I'm in a lot of settings where numbers come up constantly, and where things like percentages have to be worked out quickly, mid-conversation. I can't answer fast enough, and it's starting to bother me.

If you believed someone could learn math quickly, what roadmap would you suggest?

I know I could ask an AI and get a pile of suggestions. I'd end up going through whichever resource is best at "AI SEO", which may not even suit me. Many of you may think this is a pointless post for that reason, but that's exactly why I'm asking. I'd rather hear from people with real experience.

Thanks in advance!

In my first year of University as a Mathematics major, I’m looking for advice on finding a good popular mathematics book.

Starting mech eng soon. First-semester Mathematical Analysis I covers functions, series (ratio/root tests, Taylor/Maclaurin, nth-root, etc.), limits, and derivatives (no integrals). It’s quite different from the usual Calc 1 track, so I’m unsure what to prep.

My algebra is mediocre—not terrible, but not solid. I don’t have time to grind prealgebra → Algebra 1/2 → Precalc + Trig properly. A lot of Algebra 1/2 feels irrelevant to the course beyond a few key skills.
What should I actually focus on? Is there specific algebra/trig topics that matter most for this course?

Edit: Is Just-in-Time learning a good approach here—working through lots of problems and only drilling the specific algebra gaps that actually block me when I get stuck? It seems more efficient and better at exposing real weaknesses than trying to relearn everything upfront.

Fairly straightforward- does anyone here have any recommendations of what I can do to essentially "teach myself" math again from the ground up (online resources or anything that could also be of use to me)? I want to spend the rest of my semester studying and improving rather than continue to let this problem go on. I considered Khan Academy for a sort of "gamified" structure but I read on other forms that it's very unhelpful beyond 10th grade mathematics. I'm not looking for a way to "gamify" my education, I was only saying that in terms of finding something with structure- I was also considering tutoring... but for now just things that I can begin at this moment in time.

Background information:
I'm constantly struggling with my math classes: I had to retake pre-calculus I twice before I passed with a C and I'm currently going to drop pre-calculus II because my grade is too far gone to save. What made it worse was the regretful decision of leaning onto Chat GPT as a form of "tutoring" / cheating (something I'm trying to stop).

A major problem I've had all my life is my ADHD, I would constantly use it as a crutch throughout high school... but as an adult I'm honestly sick of it; my best friend with similar "problems" as me has a 4.0 GPA while I'm barely scraping by at around 3.0 simply because of my lack of knowledge in math (it used to be 1.6 before I created a better study routine and after this semester it's bound to get lower than a 3).

It isn't like I cant pass a class- last semester I almost got all As while taking 6 online courses, but that's also because none of them required me to write a+bi in terms of r, (cos(theta) + sin(theta)i) lol.

My goal in life has always been to become an engineer or something music related (I'd like to design instruments or make sound equipment for studios), however I let my insecurities knock me down and lost sight of my priorities since high school up until now (currently taking general education at community before I transfer credits to a university to pursue a bachelor).

If I can boost my GPA up from a 1.6 to a 3.0, I believe that I can do the same with my struggles in math because I'm dedicated to do the work.

Thank you to whoever took the time to read all of this, and whatever response is much appreciated!

Im in my early twenties, during highschool I struggled immensly with math, not being able to graduate with even a pre calculus course under my belt and failing the easier math courses multiple times before finally succeeding barely, I want to pursue post seco dary education, one of the Universities I really want to go to is very competitive to get into. I want to give myself to be accepted by the university and others so I plan and retaking my highschool math courses at an adult learning center/school soon and aiming to get the highest marks possible. In the meantime before i enroll at the adult learning center I want to study math at home/with a tutor to make my ability to get high marks while taking my highschool courses as high as possible. I want to buy workbooks/textbooks that use my provinces corriculum for the appropriate grades, how much time per day should I spend working on these books/with a tutor?

Pre Calc student here, I hard a hard time on this problem last quiz I took and was wondering if anybody could help explain what to do in a case like this. Thanks!

problem: 4^x-6(2^x)=16 solve for x.

Im really not good at math and physics but have them at university in the first year. My question is, are there any tips on how to get good at math or is it mostly just doing exercises after exercises each day? Or are there any specific learning techniques for it? I’m already trying to do some exercises each day but Im really bad at visualizing the problems and knowing how to find the right formula for the specific question. I know it might sound stupid but it’s a genuine question. Thanks in advance! 🫶

Like in the title, the most math I know right now is 10th grade things and some 11th since I'm ahead. I sometimes read proofs for better understanding on certain topics and also do programming and I am more and more realizing I don't have any idea on how logic works. For example I was reading something about parabolas, saw the `->` sign and just came upon material implication on Wikipedia and I just saw all these terms that I had no idea on 😭

What's a good introductory course to logic, for mathematics and computer science. I feel that I may be lacking a lot of foundations so really introductory but still rigorous. I came onto 2 things

ForAllX's open logic project and mathematical logic 6th edition by Elliott Mendelson, would you recommend those or something else?

I’m currently in school to get a bachelors in electrical engineering and minor possibly in materials science. The college I want to go to actually doesn’t take these classes under their engineering program because they have them wrapped into one class along with engineering analysis. I figured if I take these 2 extra classes along with some classes that would transfer then I would be in then with the math part of the class and could focus more on the theory. Is it worth it? Or are these topics that can be learned along side what I assume are applied applications problems in the engineering analysis class?

I've been having this problem for a while now, especially in math, and I'm honestly struggling to figure out what's going wrong.

Whenever I have an upcoming math test, I spend a lot of time studying. I go through the homework questions, practice different problems, and make sure I understand the concepts. I also use ChatGPT to help explain things, but instead of just asking for answers, I have it explain the logic behind the math, why certain methods work, and how to approach questions step by step.

The thing is, I genuinely feel like I understand what I'm learning.

For example, I recently studied a lot for a math cumulative exam. I went through the material, practiced the questions, and made sure I understood what I was doing. When I actually wrote the exam, I felt pretty confident. The questions didn't seem particularly difficult, and I even had time to go back and check my answers.

I walked out thinking I had done pretty well.

Then I got my mark back, and it was 55%.

I was genuinely shocked. I wasn't expecting a perfect score, but I definitely wasn't expecting something that low. I was so confident in how I performed that I initially wondered whether there had been a marking mistake.

What's even more confusing is that this doesn't happen nearly as often in my other subjects.

I've experienced something similar in chemistry before, but recently my chemistry marks have been improving. Physics, on the other hand, has always been different. Whenever I studied for physics, I usually performed about as well as I expected. I could understand the concepts, apply them to questions, and get decent marks.

But for some reason, math is completely different.

I'm starting to wonder whether there's something wrong with how I'm studying. Maybe I'm understanding the explanations but not developing the ability to solve unfamiliar problems independently. Maybe I'm making small mistakes that I don't notice, even when checking my work. Or maybe I'm just not preparing for the types of questions that appear on tests.

The most frustrating part is that I don't walk out of these tests feeling confused or unprepared. I walk out feeling like I actually did well, only to find out that I didn't.

I don't mind putting in the work. I'm willing to spend hours studying and practicing if that's what it takes. But I want to make sure I'm studying effectively instead of repeating the same mistakes.

Has anyone else experienced something similar?

If so, what ended up being the problem, and how did you fix it? Is there something I should change about how I study, practice, or check my answers?

I'd really appreciate any advice, especially from people who have struggled with this and eventually figured out what was going wrong.

Ciao a tutti! Sono un insegnante della Scuola Secondaria di Primo Grado e sto sviluppando il progetto profwico.com

Raccolgo e creo schede didattiche, diapositive per la LIM ed esercizi guidati passo-passo pensati in ottica inclusiva (con particolare attenzione agli studenti con BES e DSA), per aiutare i ragazzi a visualizzare i concetti matematici e scientifici (come le proprietà delle potenze, la semplificazione delle frazioni, la geometria e molto altro).

💡 Cosa trovate sul sito:

• Schede ed esercizi pronti da scaricare gratuitamente in PDF.
• Spiegazioni visive e schematizzate per le lezioni in classe o a casa.
• Materiale diviso per materie e classi della Scuola Media.

Mi farebbe molto piacere ricevere pareri, consigli o feedback da altri colleghi ed educatori per continuare a migliorare la chiarezza di queste risorse!

Hey I am a class 12 pcmb student..I want to take cuet for eco hons..so is brillaint coaching good for CUET prep as it is starting from Nov 1

Hey y'all

My last post didn't get a ton of traction and I believe it has since been deleted but I still felt like giving a quick update because I think it's an interesting case

tl;dr of my last post: "I need to relearn all of math up to calculus to graduate on time. I tested into calc over 2 years ago and haven't touched math since, so my entire foundation is super shaky and I basically need to relearn everything up to calc 1."

The comments on that post were telling me it was basically impossible and that my best bet was to drop the class and restart from a lower class, and to just accept I was going to graduate late.

I decided to just try my best anyway and stuck with it, and it seems to be a great decision so far because we just started midterms and I got an (admittedly pretty sad) passing score on the first exam (~70%) and I am passing the class as a whole and doing way better than I ever thought was possible.

On top of that, I'm realizing that math is actually crazy fun, which is something that I never thought I would say.

We are doing pretty elementary stuff right now, mostly focusing on derivatives, but the more I learn about these topics the more I realize how genuinely useful they are in real world applications. For instance, I'm a chemistry major and just yesterday I took the second derivative of my IR spectra which let me more easily identify the functional groups in the data. I would have never thought to try that without this class!

For anyone in the future who reads this and who might be struggling or in the same boat as I was:

Take a few moments to calm yourself. This class is not as hard or overwhelming as people make it out to be. It can be tricky at times, yes, and the math can feel very difficult when you look at it without thinking, but I promise you that calculus is easy.

Your first goal needs to be to solidify your algebra foundations. Make sure you understand everything you can from algebra. 99% of everything you do in calculus is just applied algebra, so if you can't simplify equations, solve for variables, or you don't understand functions then that needs to be your first goal. Kahn academy was the biggest help for me here. I religiously studied Kahn for a week straight before feeling confident enough in my algebra to move on.

Your next goal is gonna be to understand the basics of all the other stuff leading up to calc. For me so far things like trig and geometry have not been important at all other than the rare sin(x) in a problem, so those can be on the back burner until you feel like you need them, but for the most part algebra is your most important tool.

Your final goal is gonna be to study your butt off in calculus. Do every optional problem, solve extra problems that aren't assigned to you, research the different rules that make finding differentials easier, and memorized it all. Your goal is to build intuition for these things, and the only way you are gonna get this stuff down and Internalized is through practicing until your fingers bleed. I have not had a night in the past month where I did not dream of calculus problems. That is how much you should be practicing.

Once you have done all that, you should finally start to feel confident and comfortable in calculus. If you still aren't, this is when you need to see a tutor.

Im pretty confident now that I can say for certain I love all of STEM. In the past I had a certain hatred for engineering and mathematics because I honestly struggled in math growing up, but now that in finally having fun and realizing the applications of the things I'm learning, math as a whole has been recontextualized into a fun and interesting subject for me.

I'm 24 and trying to rebuild my math skills from the ground up so I can pursue mechanical engineering. Where should I start?

Hi everyone,

I'm 24 years old, and I'm trying to improve my math skills after struggling with math throughout much of my education. I'm hoping to get some advice from people who understand mathematics and might be able to point me in the right direction.

I have an autism diagnosis and had an IEP in school. Looking back, I feel like I was moved through grades without fully understanding some of the material. As a result, I have gaps in my mathematical foundation that I'm now trying to address.

I would estimate that some of my foundational skills are around the elementary-school level, although I can solve certain problems beyond that level. I can handle basic arithmetic, decimals, simple equations, and some geometry, but I struggle with other topics, especially when several steps are involved.

Some of the things I have difficulty with include:

• Simplifying fractions and finding common factors mentally.
• Adding, subtracting, multiplying, and dividing fractions.
• Long division and doing calculations efficiently.
• Ratios, proportions, and percentages.
• Negative numbers and algebra.
• Unit conversions and more advanced geometry.

For example, I might understand how to solve a straightforward problem but struggle when the numbers become less familiar or I have to figure out which method to use on my own.

My long-term goal is to study mechanical engineering, so I know I have a lot of work ahead of me. I'm interested in aerospace, robotics, aircraft, and hands-on engineering projects, which is part of what motivates me to keep learning.

I'm not looking for shortcuts or a way to avoid the work. I'm willing to start at the beginning and put in the time. What I need is a sensible path that helps me build a genuinely solid foundation instead of constantly discovering gaps in what I thought I knew.

My questions are:

1. If you were in my position, what exact sequence of math topics would you study, starting from the basics and working toward calculus?
2. What textbooks, free courses, websites, or other resources would you recommend for an adult rebuilding their mathematical foundation?
3. How can I get better at recognizing which method to use when solving a problem, rather than simply memorizing procedures?
4. Is it realistic to work toward a mechanical engineering degree starting from this point, and what should I prioritize to prepare myself?
5. For anyone who struggled with math earlier in life, what helped you finally understand concepts that previously seemed difficult?

I'd especially appreciate advice from mathematics teachers, tutors, engineering students, or people who have successfully rebuilt their math skills as adults.

I know this will take time, but I genuinely want to learn and understand the material rather than just get the right answers.

Thank you for reading!

I used a calculator I found on Google to get the answer but it didn’t actually show me the process and I’m curious!

My job is managing performance data for a hospital, and we have an operational standard to meet. The standard is 96%, and currently we have 99 compliant patients out of 105 total patients. This means we’re non compliant at 94.3%.

I would need to either turn 2 of the 6 non compliant patients into complaint ones, or find a number of additional compliant patients. The calculator I used just asked for the input of “what is ‘99’ ‘96%’ of” and gave me the answer of 4.

I know how to calculate a few things regarding percentages, very basic stuff, but not this. Could someone please explain the formula? Google is of no help here, it just keeps leading me to calculators!

Thank you in advance 😃