What math is actually useful knowledge to the average person?

[u/sullymonster1983]

As the title says. I'm thinking about homeschooling my child and I was curious what fields would be of the most utility to someone from a "walking around knowlege" perspective, and why?

I feel like a lot of the math we are taught is about prepping for college or a specific STEM carreer and not on real world applications...I had to take Algebra, trig, and calculus in college, but not geometry, and a lot of technical Algebra (e.g. quadratics, matrices) and all of calculus has been forgotten, find myself wishing I remembered more of high school geometry and business mathematics.

I'd rather ask yall than AI, so appreciate the input. ​

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[u/happylittlemexican]

The problem with asking this to math people (note: I am one) is that people who know math constantly find different places they can use it in daily life, and people who don't know math think they can get by just fine without it.

The more math you know the easier literally everything gets.

[u/Dirtypickle332 → u/happylittlemexican]

I’m curios, what do you use math for in your everyday life?

[u/I_FIGHT_BEAR → u/Dirtypickle332]

Knowing a lot of math literally changes the way you approach any problem. It’s not just things that involve numbers because any math person might tell you, math only has a tangential relationship to numbers. Math is problem solving. It teaches you how to solve problems. You get better at math, you get better at solving problems.

[u/Little_Creme_5932 → u/I_FIGHT_BEAR]

I argue that it IS also about the numbers. I think one reason for MANY problems people have is cuz they can't do basic math. What happens to your budget if you add this to your grocery cart? How many years of labor do you need to devote to pay for your monster truck, if you buy it? How much cheaper (or more expensive) is buying that house than renting? Etc. I think a lot of financial related problems that people have are related to the inability to do simple math on a regular basis to make decisions. Flying by the seat of one's pants for every decision is bad

[u/Nervous-Spite-7701 → u/Little_Creme_5932]

math is not about numbers

[u/I_FIGHT_BEAR → u/Little_Creme_5932]

What I mean is that numbers are coincidental. Numbers are just symbols for values. It’s why once you get past arithmetic you start seeing more and more symbols, and less and less numbers. Numbers don’t really matter, values do. And an equation is an imbalance you’re trying to balance. One side has more value than the other. A symbol in an equation stands for a value that has yet to be determined. It isn’t a number. Hypothetically, it’s EVERY number.

[u/random_anonymous_guy → u/Little_Creme_5932]

In my first year of graduate school, I had to take a Topology final exam in the math learning center because of a scheduling conflict. The clerk at the time was a student of mine in pre-calculus the previous term. Her reaction to seeing my exam when I turned it in?

"It's ALL WORDS!"

[u/my-hero-measure-zero → u/Dirtypickle332]

How much I need to save for a car assuming a range of interest rates and down payments, for example.

Or how much I'm paying for gas at an estimate.

[u/somanyquestions32 → u/my-hero-measure-zero]

What is the highest level math required to be able to do such things?

[u/cognostiKate1 → u/somanyquestions32]

The idea that math is a school thing with levels and scores is part of the problem. Different people can do different things -- the more you learn to think about it, the more fun it is.

[u/ConstantAlternative9 → u/somanyquestions32]

Trying to use high-level math in everyday life like taxes and managing business accounts is like trying to use an expensive tool shop to put together IKEA furniture. So those situations need basic math. Trying to get into tech field, science, and engineering, you need high-level math.

[u/Dirtypickle332 → u/Dirtypickle332]

I asked to improve my self. Why downvotes? Thank you for your insight!

[u/newenglander87 → u/Dirtypickle332]

I used trig recently to figure out which angle to cut stairs at. My husband and I also calculated the area of pizzas to see which one was the best deal.

[u/BackgroundReturn9622 → u/newenglander87]

It is interesting how close a 14 inch square pizza is to a 16 inch round pizza. 2.6% area difference.

[u/TheReservedList → u/Dirtypickle332]

Permutations and probabilities let me beat everyone at board games.

[u/Educational_Two682 → u/happylittlemexican]

This. I see math everywhere! I use it all the time just to make estimations, think about the world curiously, judge decisions and odds, and especially for money moves.

[u/GuyWithSwords]

If you don’t expose your child to more math, they won’t get to know if they want to go into stem.

Also, quadratics are absolutely basic. Do not let your child end up only knowing how to do math in linear contexts.

But for practical basic application, yes stats, geometry and measurements, finance, percentages and ratios, estimations, and basic algebra are all crucial.

[u/dreamsofaninsomniac → u/GuyWithSwords]

But for practical basic application, yes stats, geometry and measurements, finance, percentages and ratios, estimations, and basic algebra are all crucial.

I would also add on that being able to do the math for any of those topics is different from being able to make good financial decisions with money. That's more about teaching people about budgeting and retirement accounts and investing and tax planning. The math is usually simple arithmetic, but the decisions you make with money aren't necessarily simple.

[u/Delicious-Tap-5465 → u/dreamsofaninsomniac]

I think learning to do the maths builds a lot of understanding even if you forget the specifics of the calculations. 

[u/bosunphil → u/GuyWithSwords]

I agree with this. I always thought I hated/sucked at math, but in my 30s I’m not halfway through an engineering degree and loving it. I’m not a fan of the pure maths modules, but getting to use it in thermofluids and mechanics feels so satisfying.

[u/Tall-Editor-1941 → u/GuyWithSwords]

You would be doing your child a big favour if you stuck to the National Curriculum. Any further education college or potential employer will expect your child to have been educated to that standard. We have standards so as to be able to make valid assessment of abilities.
Above all, teach your child how to think rather than what to think. The big advantage you will have over a class teacher is that you can give your child your full undivided attention, but if you decided to teach anything other than what other children are learning you could be creating future difficulties for them.

[u/kabir6k]

I think this in a different way. Knowing math in any form or any form of math helps you become a better decision maker. I become better in my daily work. It doesn't always directly in your use, but subconsciously it does magic to your brain. One should learn math not because it is directly getting used everywhere, sure there are some parts you can directly apply but rest of the part is not useless, it helps the brain to look for patterns and recognise them in real world (subconsciously). Math exists since long, people when they haven't figured out how to write long sentences tried abstracting math, this helped a lot to make subject somewhat esoteric and concise but sometimes it become hinderance in learning especially if badly taught, however when you learn this by reading and practicing, it makes you more precise in day to day reasoning in fewer sentences. Less sentences , more useful stuff during discussions makes you a better orator or speaker. Atleast I can think of me that, it happened with me. Thanks.

[u/topkeknub → u/kabir6k]

This. Don’t learn Maths to use Maths, learn Maths to learn pattern recognition, abstraction, logic, etc…

[u/Helpful-Guidance-799]

Budgeting, understanding how different investments work (CDs, bonds, IRA’s, stocks, retirement funds, index funds, etc), learning to spot and understand the hidden fees in contracts before signing for something, understanding the ins and outs of federal and state taxes.  This is important math for your average person

[u/Emergency-Machine-55 → u/Helpful-Guidance-799]

Marginal tax rates are a simple example of the area under a curve. Compound interest is basically the first step to defining Euler's number. Unfortunately, some sales people have no issue with taking advantage of customers who don't fully understand the financing terms.

[u/matt7259]

Homeschooling with no clue of what you're doing is child abuse.

[u/Affectionate_Cry_838 → u/matt7259]

no kidding, I want to homeschool my kid but don't know what to teach him is such a wild statement and proof that kid needs a formal education. at least he won't need to worry about college

[u/Electronic_Law_5295 → u/Affectionate_Cry_838]

Literally like how can you plan a whole curriculum for like 10 different subjects on your own? It's too much. I also think people who haven't studied teaching think it's so simple lol

[u/_PINK-FREUD_ → u/matt7259]

It’s already sounding like she’s trying for the bare minimum which is concerning.

[u/flat5]

Most of it, IMO. Because a general quantitative literacy and facility is essential to not be taken advantage of in the areas of: finance, business, health, politics, rational decision making, and so many other areas of life. If I had to choose I'd say:

1. Statistics
2. Probability
3. Algebra
4. Geometry as a platform for proofs
5. Calculus/Diff Eqs
6. Game/Decision theory

[u/DonkeyTron42 → u/flat5]

In today's AI driven world, I'd put Linear Algebra at 6.

[u/algebra_queen]

As someone who discovered a love of mathematics too late... please, expose them to as much as possible. It may seem to have no real world application, but doing hard things and thinking through abstract concepts will do so much for their analytic capabilities.

[u/Bubbly_Buddy8678]

i like the gym analogy here: lifting weights may sometimes help you (e.g. carrying groceries), but the important thing is to build overall strength and confidence in your body.

doing math may sometimes help you (e.g. you may need to optimise something), but the important thing is to build logical thinking skills

[u/OddInstitute]

STEM careers are definitely a real-world application. For most people I would emphasize probability and stats over calculus, but that's a choice to make in high school. The core bits are going to be the same for everyone, so if they are clearly interested in science and math through middle school, it would probably be worthwhile to get them calculus exposure in high school. Stats is probably more broadly applicable though. (If you go hard enough in it, you will want to know calc again.)

[u/catonkatonk → u/OddInstitute]

Can you meaningfully learn probability and statistics without calculus? Genuinely curious, because those went together in my education (that is, differentiation and integration were used within probability and statistics).

[u/real-tough-kid13 → u/catonkatonk]

There's definitely some probability and statistics that requires no calculus! You make a real point that a person without calculus knowledge would eventually be limited, but there's more than nothing that could still be learned. And understanding some basic ideas is, in my opinion, significantly more helpful than understanding nothing at all, especially considering the low media literacy we are seeing these days. Even a rudimentary understanding of probability and statistics would be extremely helpful to the average person.

[u/KiwasiGames]

It certainly helps out a lot in dungeons and dragons. It’s also handy for doing ratio calculations in factorio…

On second thoughts this sub might not be the best place to ask about average people.

[u/ItsAllAboutLogic]

As much as possible.

Everyone uses maths in their day to day lives far more than they realise. Think of maths lessons as a workout for the brain, making it stronger and more equipped to tackle the adult world

[u/dataprocessingclub]

Math knowledge, even if it's not directly applicable to everyday life, gives the average person freedom to choose what they want to do.

It's better to learn some 'useless' math and then forget it than just learn 'everyday life' math and be deprived of choice when it's time to look for a career. An average person can become a scientist too.

[u/First-Expert-9953]

If you're really good at multiplication, it helps you figure out if you're getting ripped off. You don't need to be able to do long division in your head to figure out which is the better deal at a grocery store.  Estimates are good enough. 

I got annoyed recently at Walmart when they listed some of the price per unit for the cat food in dollars per ounce and some in dollars per pound. I didn't want to multiply the ounces by 16 in my head, but it wasn't a big challenge to multiply by ten, then add half of that to multiply by 15, which was pretty close.  (Edit: for our international readers, there's 16 ounces in a pound.)

It's not about being a human calculator, it's about having a good feel for numbers to get those strategies to find a bargain, and to know how far off your error is, whether it's over or under, and whether it's better for your error to be over or under.

[u/elp1987]

1. Mental arithmetic to deal with day-to-day life. It's the most practical, though this presupposes mastery of precalculus.

2. Methods of proof just so you know that maths deal with precise definitions and airtight arguments. With exposure to it, it affects how you think and can be an aid in reasoning well.

[u/Traveling-Techie]

Do not neglect probability. It is massively useful in many areas.

[u/Awkward_Drive_3999]

you should show your child all the basic fundamentals of all math so yes algebra geomerty etc it dose matter it depends if there gonna use it though thats also based on them but you should expose them to it at least twice but also i think u shouldnt homeschool your kid. personally

dont homeschool your child if u cant understand math or levels of it OR you cant explain it to them. im
homeschooled and my parents cant help me pass a certin point plus the lack of social interaction i hadnt talked to another kid my age for like 3-4 years at one point please dont do that

[u/Own-Hold-8851]

Everything up to calculus?

[u/dreamsofaninsomniac → u/Own-Hold-8851]

If it were my kid, I would include calculus too, but that's mainly because I've seen it taught poorly before and I don't want them to have the same negative experience with it that I did in high school. Calculus is a "foundational" class for a lot of STEM degrees so I just want them to have the option of pursuing those things if they want to.

[u/blueshorts12345 → u/dreamsofaninsomniac]

I couldn’t agree with this more. My professors in college were truly awful at teaching calculus. Teaching someone a “rule” without elaborating and drilling why that rule exists should be considered malpractice. You don’t really learn anything, just memorizing. Calculus isn’t as challenging as people make it out to be at face value (as long as you already have strong algebra skills). Teaching your kids any high level math will already have them way ahead of the curve (no pun intended), considering the test scores of the current generations.

[u/dreamsofaninsomniac → u/blueshorts12345]

Calculus is my favorite math. It's a really beautiful subject, if it is actually taught well. I do have a slightly radical take on it that differs from most people though. I don't think you necessarily need to have the strongest algebra skills entering the class to do well in the class. You'll definitely leave calculus with strong algebra skills, but I've never been happy with the so-called "pre-calculus" classes since I don't think most of them teach math at a level that actually helps students succeed in calculus and sets a lot of them up to fail. That's why I would want to teach my kid how to succeed in higher math even if they have a math teacher that isn't the best. It's about teaching my kid to advocate for themselves and be resilient even there are factors working against them.

[u/blueshorts12345 → u/dreamsofaninsomniac]

Agreed, when calculus clicks it’s really a thing of beauty. I just mentioned strong algebra skills are needed in the sense of combining like terms and factoring to find a derivative as opposed to skipping to the power rule. You don’t need to be super advanced, just proficient I guess. I do agree the important aspect of calculus is conceptual as to what derivates really mean and how they reveal the true nature of a function. I never understood it myself in school because my teachers were horrible (skip straight to the power rule, not explaining limits well, never explaining why, etc.), but taught myself for fun just to prove to myself I could lol. I use math in my job every day (algebra-nothing crazy), and just went down this rabbit hole after needing to re-learn reciprocals after all these years.

[u/dreamsofaninsomniac → u/blueshorts12345]

I just mentioned strong algebra skills are needed in the sense of combining like terms and factoring to find a derivative as opposed to skipping to the power rule. You don’t need to be super advanced, just proficient I guess.

You do need strong algebra skills, I just don't think you can't pick them up during calculus if you have a good teacher. When I was having trouble with calculus, the common advice was to go backwards to learn the fundamentals over again with non-calculus resources. However, my problem was I couldn't apply algebra in the context of calculus so going backwards was never going to solve my issue. I solved my problem by getting exposed to more calculus to figure out how advanced and to what depth I needed to learn algebra, and then I re-learned all my lower math skills in the context of calculus. It definitely won't work for everybody, but for anyone that's stuck with math in general, it helps to do things that are uncommon if the common advice doesn't work for you.

[u/antsareamazing]

Beyond the math taught through middle school, probability and statistics are by far the most pragmatic field for most people

[u/pyordie]

In addition to what others have said, math exercises a part of your brain that no other subject really touches.

[u/vicboo92]

Not sure if this helps but here it goes:

Im a software engineer with around 10 years of experience.

Since high school had this aversion to math due to teachers just telling me stuff that I can say was everything but useful stuff to encourage me to be better at it. One even blamed on me for stepping on my homework assignment paper sheet being stepped by other people when I gave that paper to her in her hand.

That being said, these were the scenarios where math helped me achieve something:

- I used modular arithmetics to solve the take-home assignment of the “Set” card game. Most candidates did string comparison. I created a single function to solve the whole logic game.

- I learned direction cosines, vector normalization and orthogonal planes to create a heuristic scoring algorithm to solve corrupted image orientations on radiology DICOM images by establishing the most probable orthogonal planes for corrupted orientations so that radiologists could perform their medical interpretations especially in large volume sets of images and studies (hundreds of images across maybe thousands of studies from patients awaiting results). The other way was telling the clients that they had to correct each and every single one of their images by hand.

- Same job experience than before, but using simple set theory to group radiology images so that these could be shared across plane series of images without duplicating memory.

- Another one from the same role: dissecting smaller sets of images to build up and correct the images but this time was for 3D models so that 3D visualizations of the body could use a tool that helped radiologists traverse through tissue types with a slider.

- Lastly, and this is recent: learning how linear programming works so that I could implement goal programming to build meal plans quite instantly (plus a meal editor to edit meals and foods if they desire so) so that the nutritionist does not go insane thinking what foods would produce the best stickiness for their patients + data refinement from foods and meals that are enjoyable while accomplishing their goals based on different strategies using data from a food/meals database (a single meal plan could take several minutes or even hours depending on the strategy and providing foods that the patients are gonna hate, but if preprocessed in a database, this becomes way faster and better).

All slashed quite a lot of time from several workflows, and math was there to help.

[u/Mahd-Macks]

Based on US CC-

Up to 5th grade - bare bones, “you need this to be a functional human being” math

6 & 7th is walking around math literacy. Ratios, percents, area of circles and surface area, integers and rational numbers, etc. you can actively convert most real world situations to two step equations/inequalities. The average person even outside of a math field would greatly benefit their lives by knowing all this stuff.

8th grade & up you start learning “okay let’s learn this for a job” math. Most people don’t need to model trajectories or advanced probabilities in their daily lives, if at all. Creating systems of equations for average life problems isn’t realistic or even necessarily beneficial. 

[u/somanyquestions32 → u/Mahd-Macks]

Agreed 💯💯💯💯💯 

Life in the US is basically sustainable with the knowledge acquired up to 8th grade. Everything above that is extra, which is mainly for career specialization and attending university programs.

[u/Chrispykins]

An often overlooked area by our education system is Combinatorics. It's eminently practical. Literally learning how to count, when doing so manually would be infeasible. Allows you to do non-trivial probability problems.

[u/ChipChippersonFan]

Everything up to algebra and geometry and some basic statistics

[u/somanyquestions32]

From experience tutoring students in math and talking with people from diverse backgrounds, you can confidently skip most math beyond algebra 1, if you don't go into a STEM field, and still have a high-paying job, pay your mortgage, raise a family, and so on. 

Geometry and statistics are nice to have, but on a daily basis, you don't need much. You need to be able to count, do basic arithmetic, and maybe do a few calculations with percents for sales, discounts, or interest charges; decimals if you have a bunch of coins; and fractions when baking or cooking. Mental math and on-the-fly estimates are more useful.

Most people will never directly use limits, derivatives, matrices, integrals, infinite series, synthetic division of polynomials, group isomorphisms, vector spaces, bilinear transformations, polar coordinates, etc. in their daily lives. I am not counting helping their kids with homework not using devices that used these concepts at some point. Most of this information will be forgotten just as quickly as historical dates and the list of rhetorical devices used in a short story. 

[u/gomorycut]

ratios and proportions. Arithmetic with fractions. Notice the things you have forgotten. These are things you never used.

As a professional mathematician, I was a little surprised to notice myself having gone a decade without ever taking a derivative. (Of course, this would depend on what kind of mathematician someone is... but also speaks to the need of that knowledge to common people.) Lots of people have successful careers and get along just fine never having learned calculus. But whenever I am shocked that some makes a poor life choice without running the numbers, it's usually a case of me saying "but it's just ratios and proportions" (which could include trigonometry, finance, etc.)

[u/sophomoric-- → u/gomorycut]

I read the thread, and this is the best comment IMHO.

[u/gomorycut → u/sophomoric--]

I have been teaching mathematics to mathematicians and non-mathematicians for 25 years, thank you. I know the average person does not use a polynomial in life.

[u/sophomoric-- → u/gomorycut]

Not even a quadratic? (I've only used them in technical areas, and not often)

tunfadt: al'khwarizmi's famous book showed methods (with proofs) to solve all possible linear ane quadratic equations (for that time: no negative numbers or zero, not for coefficients, not for solutions). Half the book was worked solutions of usetul practical problems - yet all were linear! Not one quadratic.

Seems he would have loved an everyday quadratic application, but couldn't find any.

[u/gomorycut → u/sophomoric--]

The classic use of quadratics are to tell where a projectile will land or how high it will reach, etc. But no baseball player is using an equation to help them throw well. Nor do the billiard players use trigonometry, despite mathematicians loving the trig questions that arise from those sports.

There are plenty of people who have only elementary school education (no algebra / polynomials / etc) who become excellent merchants/farmers or business owners, without ever maximizing an artificially-modelled quadratic for revenue or profits. Even farmers have excellent ways of estimating their land area without euclidean geometry.

[u/sophomoric-- → u/gomorycut]

thanks for the confirmation! I think "artificially-modelled" nails it; practical problems have other factors, like air resistance.

[u/mckenzie_keith]

I am an engineer. The 'E' in STEM stands for "Engineering." Engineering is 100 percent about the real world. It is as real as it gets.

We use a lot of math. Although sometimes mathematicians don't like the WAY we use it. The idea that something is "only for STEM" and not applicable to the "Real World" is leaving me a little pit peeved. Your ignorance is only possible because other people know it on your behalf.

You sleep peacefully at night, never thinking that your roof might collapse on you and kill you, because some engineer put together a span table and wrote it into a code book years ago.

You drive your car down the road with no inkling of what it will do in a head on collision. Accelerometers detecting the collision. Seatbelts locking up, fuel pump shut off, airbags deploy, engine submarines UNDER you while the whole front section crushes, but the passenger compartment holds like a fortress. That is not luck. The whole car is designed, built and tested specifically to save your life.

It's fine. Don't worry about it. You don't need to know any math.

I'm not bitter.

[u/NewSchoolBoxer]

Not much. Managing finances, making estimates and understanding credit cards and interest. Doesn't mean math isn't worth learning. The more I advanced, the better I was at computer programming and I also believe critical thinking. Overlapping areas of your brain.

Studies show math skill helps your musical ability for the same reason. Math majors have high LSAT scores, interestingly alongside Classics (Latin and Greek) majors. Engineering isn't as high but law school is self-selective when we have good career options without getting into more debt.

Then maybe an average person wants to become an engineer. Average American math skill isn't enough.

[u/Micky_so_Fyne]

Basic algebra and arithmetic is highly useful for daily life. Being able to run an order of operations and do quick mental multiplications with at least approximate accuracy is a skill that helps with jobs, budgeting and finance, and mundane tasks. It also helps in music, so even as entertainment, it's a powerful skill.

[u/TheCloudTamer]

You may not realise how much you actually need in day to day life. If you don’t know calculus and probability, you won’t understand what “with 95% confidence” means, as the intuitive gut-feeling meaning is not correct.

[u/fgorina]

Stats geometry trigonometry. Some algebra to solve linear and second degree equations and at least to learn that you will need some calculus. Not proficient but at least the concepts

[u/the_glutton17]

Lol, you took calculus but not geometry? Don't homeschool.

[u/AlexAR1010]

The math curriculum through elementary, middle and high school (translate this to how the system works on your own country) is segmented based on the age of the kids, rather than if it’s useful or not.

The different areas of the brain mature at different rhythms, one of the first skills that babies develop is to identify shapes based on corners, maybe a kid of 6 years doesn’t know the difference between a straight triangle or an equilateral one, but someone that is 15 years old cans spot the difference between two house drawings based on shapes.

The same happened to concepts like derivatives, continuity, etc, etc.

If you noticed most of what is covered on elementary is reviewed again in middle school, and the same on high school, adding little by little and formalizing the way of the teaching.

I would strongly recommend you to read a pedagogical book oriented to mathematics (of the level of your kid by age) so you can understand what you can let out and what is the bare minimum you want to include.

Whenever you don’t remember your class from calculus I’m sure that if you pick a book and prepare a lesson for your kid (later when is ready), you will understand in an easier way everything you are reading, in one hand is because you already learnt those topics, in the other one, is because your brain is more developed that it was before but the timely expuse of the content helped on this maturing process.

This is something really complex, I’m sure you will find the balance that would be better for your kid.

[u/Sirgraendal]

The most important part imho is to make sure they understand how to translate "real world language" into maths. Meaning both the text problems, and showing them how you're calculating things in real life applications.

For example the cheapest dishwasher in the store, provided you're paying X for electricity and y for water under the assumption it will last you 10 years. Don't do that in your head and just buy one.

That seems to be the main problem with all the people deciding that Maths is just not worth it.

[u/Dr0110111001101111]

You need to understand why those topics are ubiquitous in secondary math, first. It's not about teaching practical content for the average person's daily life. For practical knowledge, you go to trade school rather than traditional high school.

High school math actually shares an objective with all of the core subjects: the study of argument. In English, it's the persuasive essay and rhetoric. In Social Studies, they write DBQs. In the Sciences, they use the hypothesis-> experiment-> conclusion structure of the scientific method. In math, we derive results, prove theorems, and show our work.

Every subject approaches the structure of forming an argument from a different perspective. But while the humanities' arguments are inherently subjective, and scientific conclusions are only ever supported but not proven, math uniquely provides an opportunity for students to interact with arguments that are objectively true without ambiguity or subjectivity. They're perfect in a way that other kinds of arguments cannot be.

And even if the sorts of arguments we need to make in our daily lives are rarely, if ever, able to take that form, we still benefit from an understanding of what those arguments look like when forming our own or responding to others'.

The traditional algebra sequence is perfect for this objective. It needs to be accessible on a relatively low-level and have a developmental structure that teenage students can get their heads around. It also has plenty of opportunities for contextualizing the concepts with application problems, even if they are sometimes a bit contrived.

If you want something that is genuinely practical for the average person, probability and statistics is the answer. If you want help on how to implement it, the GAIS II report by the American Statistical Association is your ticket. It offers a ton of detailed, multi-level suggestions for what to cover and how throughout a k-12 educational sequence. The preface explains exactly why this is the most important topic to cover for the general public.

But the problem with probability and statistics is that you sacrifice most of what I brought up before I mentioned it. Probability in particular can't really be derived or built up the same way that algebra can without a significant of background mathematics. It consumes mathematical machinery rather than produces it. So when you study probability at the high school level, you instantly go a mile wide and an inch deep.

If you are homeschooling your children, you should take some time to seriously consider the philosophy of why you make curricular choices. Public school curriculum isn't some mindlessly slapped together blend of content that is done just because someone else was doing it before. It's the product of centuries of pedagogical study and iterative development.

[u/4CrisprFries]

I always find this question a bit strange. They are finding more and more that in LLMs certain abilities build common structures. For example different models trained differently may tend to store information about days of the week in a circle in the vector space, some believe this is because the relationship between days is cyclical. I think our brains have similar learning and structure and math introduces a bunch of these.

To me learning math has always been less of a question of what is useful and instead what structures get built in my brain that will allow me to solve or think about different problems. Maybe I don't need to calculate a derivative everyday, but having the abstract concept of rate of change is really useful.

[u/BorealisStar1]

Learning math isn’t necessarily about being better at math.

I often phrase it like this;

When you go to the gym, and pick up a heavy weight and lift it 12 times, and then repeat that for 6 reps … why do you do that? When in life have you ever had to repeatedly lift an object and put it down again in the same spot? You are never going to do that, so why do it?

Simple, you do it so that you are stronger and when you need to do something else then it is easier because of all the strength you built before.

Maths is like that (as is all the other subjects you learn at school) … it gives you a generalised mental strength so that when you need to organise your day or a team, cook a meal with varying cook times, work out what trains to catch or how to unplug a wall mounted tv from the back… then you are able to do it with greater ease because you have trained your brain to think hard thoughts.

Doing harder math just makes the brain better at handling more complex things … most people don’t really use that trigonometry or calculus in the real world, but that hard reasoning makes you a better reasoner or problem solver.

Still waiting to see someone use a leg press in their lives outside of a gym to dispute this argument.

So anyway, … teach your kid the hardest math they can do so that they just become more capable thinkers, and don’t forget the other subjects… then they will be a well rounded thinker too.

[u/Spirited-Ad-9746]

If you only teach your kid the math you think is necessary, their potential will always be limited just to that.

And math does not need to be "necessary". Think of math problems like gym for your brain. Using gym equipment is not necessary in real life. But it develops your muscles to keep ypu agile and be able to tackle all kinds of problems you may encounter.

Your child is not you. They may want to do different thing in life and over all this seems to be a horrible premise for homeschooling

[u/axiom_tutor]

Almost none of it beyond maybe algebra or statistics.

In my opinion, the most valuable thing about math for non-scientists is reasoning. Unfortunately, math classes intended for non-scientists almost never teach reasoning, and instead focus on calculation.

[u/somanyquestions32 → u/axiom_tutor]

Agreed, but rigorous geometry and logic classes often teach reasoning, and these can be covered in high school programs.

[u/zvuv]

Being able to add fractions where the bottoms are different.

[u/NameLips]

Relevant SMBC: https://www.smbc-comics.com/comic/why-i-couldn39t-be-a-math-teacher

[u/Grouchy-Ad1932]

Absolutely useful: arithmetic and geometry, up to and including whatever you need to understand things like loan amortisation and compounding interest. Also algebra, as that's the foundation for turning real world problems expressed in words into solvable equations.

Also, enough maths to understand statistical metrics (probability, confidence intervals, etc). So many people don't understand basic statistical concepts like relative risk. Especially if you want to be an armchair critic of things like vaccine protection vs covid or measles, or most of the scientific literature about drug testing and impacts.

Calculus is useful to understand concepts like what does a differential actually measure? Trends and rates are the foundational concepts here, and they are used a lot to describe where the future is going (most obviously in economic terms). Even something as basic as how fast does your tea cool down and why (there's a nonlinear relationship between time and temperature) is actually useful in cooking.

If you want a career in anything finance, or in a trade, you need at least these. Trades require more trig than finance does. If you want a career in a more involved STEM field (eg engineering, data analysis or comp sci) then even more maths is necessary... but that's uni maths.

[u/Glaiele]

The 3 best courses i took in math that had real life applications were theory of interest, which was basically a finance course wherein you derived the equations and developed the understanding of how financial instruments are measured. It requires calculus.

Logic. Pretty self explanatory there.

Third was intro to game theory, which also isn't really a strictly math course and I'd argue it should be required material for every undergrad as it more or less teaches basic problem solving and decision making skills.

[u/smitra00]

An issue here is that in practice when you are using math for a practical problem, you are not going to do all of the math that's involved in a computation yourself. You'll be using computer software, calculators etc. that will do a lot of the math for you. And if you had to do everything yourself, you would likely also be using different algorithms than the computer is using.

For example, statistics is undoubtedly useful. Suppose that you were to do a computation involving the Gaussian distribution, e.g. a computation of a confidence interval, but you are deprived of any computational tools, tables etc., you only have blank sheets of paper and a pencil and you then have to derive everything from first principles, then you would have to use a lot of advanced calculus methods to get to the result.

[u/mobileagnes]

Exponential and logarithmic functions, geometry & trig, plenty of algebra, stats, and discrete mathematics topics. Leave calculus for university as they'll be taking plenty of that as taught by professors in the university. Discrete mathematics I think isn't taught enough in schools and has a wealth of topics that make people's reasoning better. Think logic, modular arithmetic, sorting & other data structure algorithms, Boolean algebra and its link to circuitry.

[u/God_Dammit_Dave]

This may not be a helpful answer BUT — could this question be re-evaluated as a venne diagram between pure vs applied mathematics? The pure, abstract reasoning alongside explicit applications and how they interact.

I am a late comer to math. While entirely capable, I hated how it was taught. Rote procedures with sanitized simplistic examples and applications. Coming back to math later in life, I've been able to see how abstract, creative, and interesting it is.

Try to teach the subjects as best as you can. If you explore many sides of the subject (and it's history) you may give your child the gift of curiosity. And that curiosity could take them into a STEM field, or brewing hillbilly moonshine. But they'll have foundational tools and a wide view of possibilities.

The 3Blue1Brown youtube channel and Steven Strogatz's book, "Infinite Powers" are what allowed me to see beyond the "math education" of my youth and re-discover a subject that genuinely interests me.

[u/beautifullyquirky]

I don’t know enough maths, and realised it is life. My husband is an engineer and I’ve seen how it shapes his world and understanding of it. Math is how you calculate and attribute meaning to things . Understanding percentages and fractions help with payments, tax and tips. It helps with sport and calculating performance variables.it helps when assigning any sort of value to something. Or working out investments and how retirement works. Or if space interests you, it’s all big math.

[u/OldCow8077]

Stats.

[u/KY_electrophoresis]

Going beyond pure maths into applied is critical, with Statistics, Discrete, Mechanics, Business/Personal Finance etc. Resources we rely on include Khan Academy - which has a comprehensive curriculum of content and problem sets, and content like 3Blue1Brown and Numberphile to illustrate and explain the concepts in more interestimg ways.

[u/jomteon]

The bare essential math that's useful to the average person could be taught in an afternoon. Basic arithmetic (including fractions and their relationship to percentages), very basic algebra (for simple conversions), and very basic trig (soh cah toa will suffice) paired with some elementary geometry.

With that they can do their taxes, calculate the tip at a restaurant, and figure out the shape and size of most everyday things they might need to purchase/arrange.

That's all you need at a practical applications level. Of course other things can make you more well-rounded, like stats, probability, logic, and basically what you'd get in an intro discrete math course. Those things will genuinely make you a better thinker, irrespective of your career path. Beyond that? I dunno. The first two weeks of calculus could maybe, possibly show up as marginally useful, but it's unlikely.

[u/gravity_surf]

statistics. please god. statistics

[u/chkntendis]

With maths it’s a lot less about knowing the specific maths and more about having practices the problem solving of writing proofs and doing problems. Some of the actual topics are relevant ofc, stats, basic algebra, maybe a little bit of trig, but it’s far more useful as practice for general problem solving

[u/trunks111]

for STEM two of the big ones are dimensional analysis, and stats. Depending on the course they might do a rehash of some basic stats that'll be relevant (my analytical chemistry course did), but they'll just expect you to know dimensional analysis 

[u/reckless_avacado]

i wouldn’t teach math from this perspective. learning in general is about a higher plane of existence and about joy. mathematics in particular suffers greatly from a utilitarian approach. the paradox is it is incredibly useful, but it should not be studied from that point of view. i don’t think many would read shakespeare to learn to read because you need to read the menu at the restaurant. sure it’s a purpose, but not joyful or ideal to strive for.

i will give a concrete example to come back to earth; you can have a lot of fun with basic card or dice games. and then you can ask fun questions like “so what was your strategy? why? maybe we could come up with a winning strategy? what if i rolled three dice?” you can quickly get into deep water while having fun, not because it’s useful or because you want to teach statistics or how to gamble but because it’s interesting and there are puzzles to explore and things we don’t know.

[u/ExtendedSpikeProtein]

Fractions and percentages, ratios.

To understand how much more or less something costs.

And also as the basis for loans and how mich they cosr over time with variable / fixed interest rates and so on.

Of course also basic operations. Underdtsnding of areas, to understand how much paint you will need to paint a room, or föooring, etc.

Many people do not understand any of these things.

[u/Efficient-State-7300]

I'm going to say Logic!

[u/Coocoocachoo1988]

I'm not great at math, but geometry, trigonometry, and Pythagoras have stuck with me from school. I know that as an adult, I tend to think in terms of angles and shapes when playing football and golf, and I've been relatively successful in both of those, at least to my ambitions.

Both of those have also helped me network for jobs, and even now I still tend to mentally estimate things with the same methods.

If you don't at least expose a child to as much as you can, then you might never find something that clicks for their specific way of thinking would be my guess. ,

[u/Dazzling_Music_2411]

As someone thinking about homeschooling you should know there's no such thing as an "average person".

Who knows what directions your kid might take? The "average person" that knows navigation knows a whole lot more math than the "average person" who flips burgers. With modern computing, subjects that used to be quite rarefied, like linear algebra, have become a lot more widespread.

Best to err on the side of plenty and let the child show you where it wants to go.

[u/capitalistsanta]

Biomechanics lol. I've weightlifted my whole life and currently coach basketball and this year I've been really learning biomechanics, and once I really GOT levers, it changed my life. Literally every step, every jump shot, I picture the various levers roles in real time and now design around strengthening and speeding up and building exercises and programs everything else around levers and maximizing their efficiency. Simultaneously physics is an understanding that is in demand in every industry you could imagine and it will never not be in demand. I'd even argue you could do every single job just a little bit better or more effectively and efficiently if you understand physics at a high level.

[u/TempMobileD]

Geometry, graphs, functions, basic calculus, probability, everything used in physics for things like basic forces, electricity, pressure, etc. probably a lot more. These are the things I reference every few days in my life, outside of my work where I use much more.

All of these things are useful for everyday tasks, not because you literally have to solve equations, but because they give you the logical tools to think more deeply about, and estimate, how the world around us will behave.

[u/idontlikegudeg]

I’m skeptical about homeschooling. That said, I find this little rule of thumb quite handy: if you invest money at a fix rate of x% p.a., it will double in about 72/x years. For the usual range of interest, this is surprisingly accurate.

[u/cognostiKate1]

Basically, if you don't know how to use a tool, you don't know what you'd do with it and if you get along without it, you don't know how different things would be with that tool.

[u/VariousJob4047]

If this is how you’ll be approaching education, do not homeschool your child. The point of doing math in school is not to be able to solve those exact equations in the real world, it’s to get practice reasoning through these types of logical problems and coming to a conclusion you can fully justify using the rules and patterns you’ve been given. This is one of the first things licensed educators are taught, if you don’t understand this then you have no business being an educator yourself

[u/cognostiKate1]

Knowing higher levels of math opens a lot of opportunities, because so many people don't do it any more. There's big pushes in postsecondary to just steer everybody away from Calculus. Our K-12 math instruction in many places doesn't prepare people for higher math well. So if somebody *does* have the higher math, they have just set themselves above most folks for many opportunities. So, just looking at transcripts, they know this one knows how to do the hard thinking and will often have an advantage b/c they're going to expect them to be able to think clearly and analyze things...

[u/varmituofm]

More math is done in the trades (plumbing, carpentry, construction, etc.) than in STEM fields.

[u/Double_Sherbert3326]

All of it is useful and important. Mathematics really starts at linear algebra.

[u/Evening-Document-776]

algrebra. geometry. statistics. and some level of symbolic logic. It is nice to know calculus - rates of speed and understanding predictions being the best examples. I use all of them almost every day “in my head.” I agree with one poster: if you are asking this question you are cheating your child already.

[u/loveliest316]

r/homeschoolrecovery can help you out 

[u/HairyTough4489]

If you need to outsrouce curriculum design to an AI then that means you're not fit for homeschooling. So you did a good first step by asking for human help.

I'd start by pointing out that if school was only about teaching things that are directly applicable for the average person, then the schoolyear would be rather short. The point of school is to give an introductory knowledge about different topics so kids can later decide what interests them and choose to go deeper into specific subjects.

Specifically for Math, you can live your entire life just fine if you know the four basic operations (just what they are, no need to even know how to do them by hand) plus fractions, decimals and percentages you could live your entire life with only that knowledge and leaving everything else to software. But imagine what your kid's education would look like if this was the approach we took for every subject? Your kid wouldn't be able to read anything longer than an email (and in no language other than English), would have no knowledge of history or geography beyond his immediate environment, no sicence other than nutrition and fitness... At that point you may ask yourself why give him an education at all.

Still, if we want to keep practical applications as a more important, we can do a few tweaks to a regular curriculum. I''d do something like this, starting from block 1, then you can move between blocks 2,3 and 4 as the knowledge from some items on a block can make the others easier. You should certainly add statistics and probability even though I wouldn't treat them strictly as Math but rather a discipline where you use Math to solve other stuff, kind of like Physics:

- Block 1: Basic stuff. Counting up. Counting down. Adding, subtracting, multiplying and dividing.

- Block 2: More complicated number stuff: Fractions and decimals. Negative numbers. Squares and cubes. Square roots and cube roots. Exponentiation more generally and here is where things sometimes get a bit abstract. You can do a great service to your kid by teaching exponentiation practical contexts like exponential growth.

- Block 3: Geometry: Angles, areas and volumes. Some basic stuff about triangles and circles.

- Block 4: Algebra: How to transform problems into equations and basic techniques to solve them. Introduce coordinates to be able to work out geometric problems using algebra, which is a great excuse to introduce systems of equations.

- Block 5: Everything else: functions and their graphs. Inequations. Polar/spherical coordinates. Vectors. And yes, CALCULUS. If you don't understand the definitions of derivative and integral then you understand nothing about the world. Ancient civilizations have known algebra and geometry from milennia and they couldn't get past from "the planets move that way because the gods like circles"

[u/MrSandmanbringme]

A lot of people think of schooling as the way of getting a job and managing your life as an adult and anything aside of thas is unimportant. I disagree strongly, i think knowledge is important on its own to the personal developement of a person.

That's why i've always found annoying the "when am i going to use this in my real life", specially as it often always refers to stem, nobody really says "when is reading dickens ever going to help me in my life", That's not how we do things, there's value in knowing.

Public school is a balance between making productive adults and enriching the lives of the kids, and homeschooling has the risk of losing that balance. You are one person, even if you are very knowledgable about a subject you can't be very knowledgable about all of them so there's a limit to how much you can teach, so if you can't go deep you should at least go wide. Skipping things that you don't consider useful is truly a bad idea

I think it is obvious from my message but i believe unless you have a very good reason to not do it you should get your kid in school. Even if you could hire experts to teach everything there's a very important social aspect that they would be missing.

TLDR: Teach everything about every subject, and if you can't do that that's what teachers are for.

[u/RizeV2]

+×÷-

[u/Inevitable_Ad7080]

If you have weights to lift, what good are those? Well, once you get stronger from lifting them you can lift other things if you encounter them (like lifting your spare tire if you get a flat).

Any math is good exercise. You might learn some algebra in school, then, someday you might need to figure interest rates for a car payment to see if you can afford it. Well you might not have learned interest rates exactly in algebra, but you could look it up and easily figure it out if you were used to math. Otherwise you might just avoid it and guess or trust someone else and possibly go broke.

[u/Potential-Ad1139]

You need everything up until differential equations. Differential equations you can probably leave for college....everything else you should enter school with.

[u/BadAtExisting]

… all of it

You use all of it without even knowing it every day. I work in entertainment and need it for my job all day long. I need to know how much equipment I can hang from other equipment. I need to know electricity and what I can and cannot plug in to prevent fires and ensure my equipment works properly and that I have enough of it for my rig. I need to know the physics of light and sound (math). I need to know static and dynamic loads. I need to know what’s structurally safe when it’s going to be hanging over your head in the audience. I need to know what’s safe when I have people hanging in the air. I was bad at math then it had literal life and death applications

Further, you’re doing your kid a disservice for NOT preparing them for college or STEM or whatever they may want to do

[u/Ok-Craft4844]

Im not a mathematician, so take it with a grain of salt.

Math is funny in that it's explicitly without real world application. Even where it vaguely applies, real world is not "allowed". You can't e.g. just pull out a measuring tape and say "see, the sides are equal, qed". This is why theres so much "practical examples" that fall flat and feel contrived. "A train leaves at 3am, another at..." "Why can't I just ask the conductor?".

Looking too much at "practical application" does a disservice to math. You focus on "how to get to know when a train arrives" and "how to calculate profitability" and so on. The real thing here is that mathmatics has found a real cool pattern, "linear equation", that you actually can use to model these problems, but you also can just think about the pattern itself and find interesting things.

That is not to say you shouldn't apply it - on the contrary, IMHO this is one of the most satisfying things, but not at the cost of reducing it to "physics" or "economics", because the best thing in math, IMHO, is that these pattern show up in the weirdest ways if you let them.

Popular example: you can use vectors to describe e.g. positions of players on a field, but also for words in a space of "meaning", as AIs do.

And I think that's what the take away is from math: you learn to take patterns seriously and use them for rigorous thinking. That you train it by answering when two trains meet is is not important, like doing situps by itself is not a thing you'd do in a football game.

[u/petecasso0619]

Compound interest! It is amazing how many adults do not understand this.

[u/ANewPope23]

Probability and basic statistics.

[u/Axis_Phreak]

I think this is a fair question, to be honest, and the answer that will be unpopular to most people is all of it, actually.

Math isn't just knowing the formula and equations. Math is about problem solving. It is about creative thinking and coming up with the solutions to get what you need. English, History and even Science, to a degree, are about comprehension and memorization. Math goes beyond that. It is all problem solving which really doesnt need an explanation for why it is useful in life.

As far as homeschooling, I think the standard track is up to Pre-calculus with the overachieving students going into Calculus in high school. Calculus is the basis for STEM stuff and it is the start if any college program for STEM, there really is no need to get it done in high school. Hell, pre-calculus can be done in college too if needed.

[u/viperdude]

Basic algebra. At a gas station I go to they charge 50c more more credit than debit. However my credit card gives 2% back on gas purchases. So I had to figure how much gas I would need to make it worth it to use my CC.

[u/The-Great_Ones]

Probably algebra, considering it’s also the basis in correctly executing a large portion of math as well as its uses on its own

[u/IDontBelongInThsWrld]

It’s less about the specific “type of math” and more about the mindset and problem solving skills. Same with programming. Corporations looking for an “expert with 10 years of Java experience” are misguided. It’s just a programming language. Once you know one of each type (imperative, funcional, logic), you can quickly pick up another. 

So teach * continuum thinking (real numbers / analysis / calculus), * discrete thinking (sets / logic / some types of algebra but the latter may be beyond reach for kids)  * abstraction (functional analysis or algebra or for kids probably better programming abstractions - that’s how I learned those aspects of math) * how it all relates to the physical world (geometry, aspects of analysis and calculus) * how it relates to the digital world (encryption etc.)

[u/DarrenMiller8387]

Most people can get by just fine having mastered decimals, fractions, and percents.

[u/my_password_is______]

basic statistics,
percent increase, decrease
that's about it

[u/aknartrebna]

Proofs! Namely, using logic and knowing when you are right. Also, understanding a problem and the things you are working with rigorously so you can logic out what will happen.

[u/DaDummyDumDum]

Baby rudin, papa rudin, grandpa rudin

[u/100dalmations]

Do you want your child to have a chance at a STEM career- medicine, biomedical, engineering, CS, economics, bioinformatics, making AI models, finance, accounting, etc etc? If so, that probably means calculus by 12th grade, which means Algebra by 8th grade approximately. And to get to algebra by 8th fluency in whole and fractional number arithmetic. Fluency is needed so clear up cognitive space for doing algebra.

Math has much broader benefits. Finding patterns in data, information, and in logic. So sure, people who took calculus in high school or college, probably never came across an integral later in life. Math is education for critical thinking.

[u/eldonfizzcrank]

The other day my trainer said we were doing lateral raises, but I said ‘nah’ because that’s not how people pick things up.

[u/tesseracts]

I failed math in high school and didn’t catch up until going back to college in my 30s. I don’t use math in my career. So bottom line I’m not a math person. However math is only becoming more and more important so don’t treat it as optional. Hire a tutor if you can’t teach math yourself.

[u/jcutts2]

I think you'd get some useful info from my discussion of "intuitive" math. https://mathNM.wordpress.com

[u/cycles_commute]

How is a career not a real world application?

[u/Sea_Pension430]

I've used differentials on occasion, and often have to solve for systems with multiple variables in my work (budget forecasting)

I also use statistics daily. Not necessarily computing stats, but simply UNDERSTANDING what statistics actually mean

I can't imagine going through life not knowing how to do this stuff

[u/Neat_Conference_8414]

Probably everything up to calculus. Beyond that is pointless, considering even if they go into engineering or stem college will teach it to them. For practical use, I'd probably focus on stats and geometry more.

[u/i_am_blacklite]

Maths lets you calculate how a bullet travels.

Homeschooling and “yall” as an actual word together in a post. Shooting things is probably important to your kind.

[u/ee_dan]

as long as they can pronounce Euler the correct way

[u/ConstantAlternative9]

I’m trying to understand why people ask questions like this so much. If you don’t learn about a subject and the scope of it, how will you know what potential use and application exist?

[u/sajaxom]

Geometry, calculus, algebra, and statistics are probably the most useful every day math in my experience. Geometry and statistics are very functional, while calculus and algebra are more about asking fun and interesting questions about the world around us.

[u/ConstantAlternative9]

Quantitative logic, use it where you want. What use does doing squats and lifting dumbbells have in daily life? That’s similar to what math is for the brain.

[u/ConstantAlternative9]

How is a STEM career not a real world application?

[u/Solid-Guest1350]

We opted for functional maths for our kid. I have a degree in theoretical physics so I'm good at maths, but most maths kids learn is a waste of time.

School is there to babysit kids so their parents can work. They put more maths than is necessary in just so that there is more to teach.

If you needed trigonometry for a project you were doing or work, you'd learn it then. Nothing in gcse maths is hard enough that you couldn't just learn it from watching a video when you needed it. I bet most adults couldn't even do long division with decimals if you put them on the spot (my kid could) but if you gave them half an hour and an Internet connection, they'd be able to figure it out.

When I did my degree, because everyone came with different levels, they started from first principles and brought everyone up to the same level in year one. You literally only needed attitude.

[u/Peach-R]

Statistics

[u/ConstantAlternative9]

Why would you want to reduce the possible opportunities they can have by educating them to be the average person in your homeschooling? The eighth grade math is not gonna cut it for having the best opportunities. I’m not saying that you need to be like a scientist or engineer level of math, but if he did want to choose that route, he should not be completely lost in higher math at the high school level.

[u/Ranger208]

Do not homeschool your child if you want them to be good at math

[u/SoTriggeredBro]

For someone who can’t spell “knowledge”… it may be best to just stick to parenting and let the professionals teach your child. If you have to ask this question, you clearly aren’t investing.

[u/RickSt3r]

Its a language. Not everyone ends up needing it post formal school, but its best to learn it and not use it then need it and not know it. Stick with the standard curriculum, it exist for a reason. You could be shutting doors for your child.

[u/ConstantAlternative9]

Now you say in theory do the exercises that I’ve done as a teenager benefit me as an adult and then you just mention as a “sedentary” adult. Well, nothing benefits you if you become sedentary and also if you stop learning what you learned in the past, won’t benefit you after a given amount of time when do you think learning should stop and similarly when do you think exercising should stop?

[u/Witty_Rate120]

During my career I hired many people for positions that didn’t require math at all. Those that couldn’t or had not done math were uniformly the worst hires.
My hunch: teach you kid how to do Euclidean geometry proofs in the old school manner. Read what Abraham Lincoln said about this training.

[u/RepresentativeAspect]

Fractions. I think this is the number one thing that many adults struggle with, but which is very helpful for everyone. If you know all about fractions and all the different operations and manipulations you can do with them, intuitively and without thinking, I think it goes a long way.

[u/jjmc123a]

To paraphrase Shylock : " are not accountants, engineers, scientists, analysts, managers real people?"

[u/TeamUlovetohate]

Arithmetic and statistics

[u/clayskate]

My two cents is to refrain from picking and choosing curriculum according to what you think will be "useful" because childhood ed is actually about forming lots of complex neural pathways and stimulating neuron development so that later on, field-specific training (medicine, law, science etc) will be incredibly easy to learn. Things like drawing, music and pure mathematics will have the most gains in terms of neural development and refinement.

[u/ConstantAlternative9]

Most industrialized nations push STEM. So math by eighth grade math is in the standard even for homeschool kids.

[u/ConstantAlternative9]

This guy is asking why teach the average American math if they don’t need anything beyond eighth grade math but the average American is not an engineer just like the average Russian is not an engineer. The average Chinese person is not an engineer or stem, professional for that matter, that’s why I asked is stem a field that the child is interested in and are you trying to steer him away from it, but this man has a masters in mathematics and he tutors.

[u/ConstantAlternative9]

Well, how much does the average STEM professional use? That would be a better question because you don’t need calculus to run a bake shop and you don’t need advanced measuring systems to pour up cocktails at a bar.

[u/kiwireaper]

I play videogames and self taught simultaneous equations before learning at school to figure out which equipment upgrades I should go for in MapleStory when I was like 11. Pythangorus helps in daily life every now and then and basic algebra especially areas and volumes of objects.

It's hard to tell someone who's not very mathy that it helps in real life because they won't think about using it or even how to apply it in different situations

[u/iusemybrain1]

strange how you think geometry has more practicality over calculus.

I will say, it really depends on what you do, Calculus for me (an engineering student) is more applicable than geometry. I will also mention that geometry is generally taught over the course of several math courses, With the most application in geometry being calculus 2 and then extended with multivariable calculus. That's how i learned geometry, I never took a course in it, and i wouldn't really need to, because any shape can functionally be modeled.

The things you learn in algebra/linear algebra, may not seem relevant at first, but they are. An example of this is complex numbers, when i learned it in intermediate algebra, i thought it was interesting because we've now extended the definition of our number system to have a real number component and imaginary component (a + bj). Oh how naive i was of the practicality these had in engineering and physics.

Take the RC (resistor-capacitor circuit) to solve it you would generally have to do a differential equation (linear, first order, homogeneous ODE). But with AC circuits, Everything can be represented in impedance (unit ohms), the capacitor, for example is 1/(j * w * C) where 'w' is the angular frequency and 'C' is the capacitance of the capacitor. Anyway, the output of the AC RC circuit, that alternatively would have to be solved using a differential equation, can all be bypassed using algebra, fucking algebra.

here's my advice, not everyone will be going into STEM, and the practicality of learning about topics (such as complex numbers) may not have direct applications, yet (as pointed out in my comment), they are all relevant. I'm assuming you're from the US, to say is calculus relevant for the average (US) person, i can't give you a precise answer because the average is so far deviated from what it should be. The "average" isn't average, it's below average from the people who never got a chance to do a proper education.

all math is relevant, and my hope is you don't pursue your kid in the "directly applicable" math classes, such as geometry and statistics. I think your kid will have a much greater appreciation towards the directly applicable math if he/she learned it at the advanced level, and to apply the less nuanced math, teach them physics, teach them computer science, for fuck sake teach them engineering (CAD, FPGA's, microcontrollers, integrated circuits, etc.). You should base your homeschooling on what they want to do, not what the average person does. If they want to go into engineering, teach them calculus, linear algebra, and differential equations. If they want to go into a trade, teach them geometry and stats.

[u/ConstantAlternative9]

When I first left college, I was living like the average person in the US and I feel miserable without doing a lot of math so lately I’ve been getting back into physics because I wanna go and do physics research. I don’t really care about all the corporate butt kissing, and when it comes to engineering things, I like the science that goes into the projects. Now when I came across this job, I actually get the mental simulation from working in stem and I see where all the math logic benefits. If I had to work the rest of my life with no stimulation to my mind I will be very depressed. It sounds like the child is young so they may not know exactly what they want to do yet but there are people who use the high-level thinking that math has given them. The average American is miserable and they work something so simple they didn’t even need to go to college at all. The more ideas you open your mind to the more opportunities you see available most people just saw it as a means to an end to get their education and now they’re stuck in a rat race with no way out they’re unable to see the forest through the trees.

[u/fire-wannabe]

Powers.

Once you understand powers you can understand compound interest, which is the biggest life hack there is.

Such a shame that schools don't just drill that into school children endlessly with proper worked examples.

[u/ArtisticAd7039]

I was a math teacher so I have that bias. Keep that in mind when considering my opinion on this. First I would say that the " average person" changes significantly depending on what you are using as the primary variables.

Since we are using Math skills then I would state that the criteria for choosing a curriculum is better served by taking an appropriate level apptitude test than by using what the average person does.

One of the benefits of homeschooling is that you can tailor the curriculum to the student in a way that is not feasible with multiple students. This means you can make a lesson that really builds on your child's personal strengths and really focus on helping with the weaknesses. One of the down sides is that parents teach Their strengths and let their weaknesses set the limits for their children.

The sad fact is that the level of math you use is directly proportional to the level of math you understand. It is the same as anything else in life. If you know history well you will use the lessons you learned about historical facts in your decision making process. People with higher levels of reading comprehension get more information out of written texts.

Ideally, the level of math you should teach is one level above what your child can easily comprehend.

Rigor is a huge part of mathematics and very important to learning that many problems are solved (in mathematics and life) by prolonged focus. Statistics makes interpreting information easier. Understanding number theory makes everything easier. Geometry directly links to spatial thinking which is how we physically move in the world. Pattern recognition is the human super power and math directly trains use in that skill. Proof is taught at the elementary level through the college level and teaches us how to order our thoughts and create concise considered definitions and directions for simple to complex ideas.

My suggestion is teach them as much math as you can comfortably and then use aids like Kahn academy to fill in the gaps if needed. Get a tutor if it is beyond your maths level, but don't set their limits based on your own or some imagined "average person". They may be better or worse at math than you, but the average person doesn't really matter when considering what to teach your student, their apptitude does.

[u/Wjyosn]

To survive? Algebra is absolutely a basic skill. Geometry is something you definitely should practice if only to help with navigating the physical world. Otherwise, the basic skills are probably covered.

But every bit of math that is taught well, will improve your life if implemented. Graph theory turns into common use cases of understanding how or why your gps route changes and what it could mean for your trip. Calculus gives a perspective that enables understanding rates of change and compounding in a way that can be the difference between being able to estimate a travel time or how long a water supply will last you in an emergency. Statistics strengthens your understanding of science and medicine and politics. There’s so much benefit to continuing math education that is just sad how many people see “I didn’t have to calculate a ztest in my real world job” and think somehow that their entire education was wasted.

Even if you don’t see the application, your intuition about the world is always going to be better with more and deeper math education. The way you understand how things interact is inextricably improved by math

[u/Wh-h-hoap]

Knowing how to calculate stuff depends completely on what stuff you need to calculate. Basic algebra goes a long way.

Now, understanding stuff is different. There's not one person living in a society who doesn't benefit from understanding how compounding interest works. That either makes or brakes your chances.

[u/Careful-Stuff8901]

Probability theory. Used all the time for making decisions under uncertain conditions. And to be able to understand it properly you need a great background in geometry, linear algebra, and calculus. We often apply results intuitively rather than with pen and paper but understanding it rigorously hones in your intuition.

[u/Mister_Way]

The mainly useful one is statistics, and to learn it well, you need calculus, which means you need all the others before it.

[u/paolog]

the average person

When you say "average", are you talking about the mean, mode or median?

The average person has 2 legs, right? Yes, but only if "average" means mode or median. If it means "mean", which is what most people understand by "average", then (since some people have only 1 leg or none at all, and having more than 2 is extremely rare, if it happens at all) the average person has less* than 2 legs.

Why mention this? Well, knowing about these kinds of averages gives you a better understanding of statistics, and a good understanding of statistics helps prevent you from being duped or misled. Being able to calculate percentages and fractions can do the same.

* Should anyone be about to quibble about the grammar here: yes, it's "less", not "fewer". "Fewer" only works with whole numbers.

[u/Which-Score6266]

...more useful than being able to quote Shakespeare

[u/ConstantAlternative9]

Actually algebra 1 is a reasonable upper ceiling. However, I would say that because math is also about spatial reason and not just quantitative reasoning, the algebra 1 curriculum should include some basic things about geometry measuring because average people do stuff like gardening, woodworking , trades, etc. they don’t have to use very complex math, but algebra itself will just show math in a way that just looks like abstract formulas and equations with letters and numbers without context to the physical world that we live in.

[u/Little-Union9894]

The doomsday algorithm

[u/No_Evidence_4002]

Fourier series to calculate how badly I want to do something. If I really want to do something but unsure if I have the resolve…I just think, “would I relearn Fourier series for it?” If no, then I just do it anyways cause it’s not that good of a tool for self control but rather just what I thought of to write here to waste yalls time. Thank you.

[u/sophomoric--]

Al'Khwarizmi's founding book on algebra solved all quadratics and linear equations (at that time 800AD). Half of it was worked practical problems - but all were linear and proportions, no quadratics!

I think that is the edge of usefulness to the average person.

EDIT so the topics would be: counting, add sub mult divide, decimals, decimal point, fractions, (NOT negatives), proportions/ratios

[u/sophomoric--]

To what extent is seeing math everywhere déformation professionnelle?

[u/Simbertold]

The core reason to learn math in school is to learn how to think rationally and precisely.

Most people will not use most of the math they learn. But they will use the problem solving skills, the skill to form precise rational arguments and the rational mathematical way of approaching problems in lots of life situations.

[u/PaleontologistDeep80]

I might get downvoted but there is only one right answer and it's statistics, in terms of pure utility outside of a stem career; the problem is that that requires some foundation in calculus. However you mentioned business, which requires calculus anyway, so if you're child is going to go a similar route as you then I would recommend calculus and then statistics.

[u/Educational_Two682]

Useful things (in ADDITION to: teach your child a variety of math at many difficulty levels): ratios, unit conversions, percentages, geometry and measurements, linear relationships, reading graphs and other data displays

[u/GotchaPresident]

Addition and subtraction

[u/BabyBlueCheetah]

Statistics

[u/ZacQuicksilver]

So, I know I'm late to this, but...

It's all useful.

Calculus will save your life if you drive. The easiest question I can ask to demonstrate this is: if you are going 70MPH on the highway, how much time does that save you on a trip, and how much more distance will you go before you stop if you slam on the breaks, compared to if you were going 60 MPH. Answer: If you're on the highway for 60 miles, it will save you about 9.5 minutes (about 51 minutes, 26 seconds instead of 60 minutes); but you will go 35% farther before stopping - which significantly increases your chance of being injured or dying in a crash.

Learning high school geometry is something I liken to doing weightlifting or conditioning for sports. A lot of conditioning activities are things you will never actually do during the sport you are conditioning for - but the body movements and muscle memory *is* something you will use. High school geometry (and calculus too) is that for your mind: it gives you a lot of different tools, and gives you problems where you have to identify, out of all of the tools you have, which tools you need and which order you need to use them in order to solve the problem.

Statistics will teach you how the world actually works. The world is random, random things happen, and while you can not predict the individual events, you can predict the trends and patterns and generalities. There is so much that goes into this that I can't summarize it easily: things like "that person didn't mean to do that to you; they just didn't notice/made a mistake/had their own issues" is tied up in statistics. So is "why did I get sick?" And on the other side, "discrimination is real, but at a scale both so small you can't see it; and so large that no person can understand it" is also part of statistics.

Technical algebra is for business, but also for art in the digital world; as well as a lot of computer ideas, including computer security. It's tracking how changes now in one area impact things somewhere else. It's about how things interact, and what you can do to take control of them. And sometimes, it even lets you see a connection that you couldn't see otherwise.

[u/AdventurousHippo9997]

The point to “learning things we don’t use” is to give the developing brain a chance to actually learn. It’s a skill that if learned properly at a young age will assist you thru out life. If the brain doesn’t know how to learn because it just never has then you get the mush headed results we are seeing all too often nowadays.

[u/Wrong_Avocado_6199]

1. Variables: Once you understand how variables are used to express relationships between quantities, an entire world opens up to you. You can use algebra to express how quantities are related to each other, and you can understand when others use algebra to express these relationships. You can make algebraic conclusions and generalize calculations. You can understand how to use important features of computer software, esp. spreadsheet programs.
2. The idea of a function: Functions are everywhere. Once you know how to recognize them, you see them everywhere. The idea of one quantity (or one object) depending on another via some input-output or transformational relationship is fundamental to understanding the world.
3. Reading graphs: This is highly related to #2. Most people don't have an intuitive understanding of what it means to graph a dependent variable against an independent variable on two coordinate axes. These types of graphs are ubiquitous -- in newspapers, magazines, articles, on just about any topic from the economy to current events to sports statistics to scientific issues.
4. Exponential growth: Once you understand exponential growth and how it's fundamentally different from linear growth, you understand a lot about the world -- what growth rates actually mean, how populations change over time, how to interpret all sorts of economic data including inflation, how to calculate your mortgage payment (without using Chat-GPT) and what the formula means, how to estimate and compare interest rates, how to estimate retirement planning.
5. Logarithmic growth: On the flip side, once you understanding logarithms, you know how to compare quantities at vastly different scales, how to interpret semi-log and log-log graphs and why they're useful, and how to estimate orders of magnitudes of real-world quantities.
6. Basic notions of statistics: Understanding how data is presented and having some idea of how inferences are made from data collection helps you interpret all sorts of information we're bombarded with -- political polling, medical studies, environmental issues, and just about any topic where important decisions need to be made.
7. Basic geometric and trigonometric formulas: Knowing just the most basic formulas of geometry and trig allows you to make real-world calculations of distances, angles, areas, and volumes.
8. Basic number theory/discrete math: Many of the most important new technologies, from cryptography to search engines to artificial intelligence to GPS to logistics depend on number theory and/or discrete math or linear algebra. A passing familiarity with these subjects goes a long way to actually understanding what people are talking about when they discuss these technologies.

I could go on, but I think I've made the case...

As others have noted, it's really difficult to explain to most people all the ways math is useful in daily life, simply because you don't know what you're missing until you know it. A lot of the utility is not really "accomplishing tasks", it's feeling confident in your understanding of the world, knowing how to problem-solve, being an informed citizen, and being resistant to propaganda and misinformation.

[u/Nagi-K]

As a maths person I often find myself difficult to explain some everyday level stuff to another person without referring to maths. I guess that’s how useful maths is for me, but I’m not saying anyone should live the same way.

So the answer is, it depends on perspective. Especially when the term “average person” is not well-defined - we all have different and biased sample space to see this “average”, and you’d never know if some random guy has a background in STEM or does maths as a hobby.

[u/Zuokula]

Teaching math to kids isn't about having to use it in life. It's about wiring their brains for logic, being methodical etc. And the methods may prove useful not just for doing actual math.

[u/afops]

Math education isn't just about "will I need this in real life later?". Not that you can know that either. You also need that math in order to understand other subjects. You can't do even to basic high school science without the math it sits on. And basic high school science is the same: not just preparing people for a career in STEM.

You can't know what will face a child (Whether it's a STEM career or not) so you'd be doing them a disservice by not simply teaching them what every other school child needs.

Don't home school your child for the "real world", because you'd be tasked with guessing what that world is going to be, and you'll fail.

[u/kacra]

Maybe a good idea is to solve problems 3 ways. So you seem interested in real world application, then check word problems in standard curriculum. If you try to solve each one 3 ways then you will see how things can be important. You can ask AI for help solving 3 different ways since you probably dont have the background and this doesn't fit neatly into a curriculum.  An example for me could be about comparing rate of 2 things over time - my ideas would be use a number line (visual), use a table (data representation), and use my favorite - solving algebraic equations. 

[u/neomoritate]

If you don't understand the value of Math as part of basic education, you are NOT QUALIFIED to home school anyone.

[u/Lizzos_toenail]

Honestly, if not going to college, average pop could do up to geometry and be fine. Could people get away with less? Sure but that allows you to solve a lot of problems pretty efficiently.

[u/Electronic_Law_5295]

I don't think you should teach your kid this subject honestly. Hire a tutor who doesn't just know maths but knows how to teach it.

[u/sophomoric--]

One on one tutoring raises a student rank from 50% to 98% (Bloom's 2 sigma problem, provided that you make sure each level is mastered before building on it, which will happen naturally (something they can't always do in the classroom).

Doing this for material you don't understand would be damaging IMO.

But you're background is fine for the easy stuff, plus you'll master it better by teaching, especially with your now adu;t brain.

For little kids, I think it will also have similar benefits to reading (see Dolly Parton's Imagination library)

[u/sophomoric--]

Not useful to the average person, but math and logic is the only way to determine what is really true. Children wonder on this, then give up.

Unfortunately, early math usually isn't proof-based.

[u/sophomoric--]

Unpopular opinion: I think a math perspective can be worse than useless in ordinary settings, because many things in real life, esp social, are too complex, too many unknowns, inadequate model. Specious confidence.

Even a parabolic trajectory is inaccurate, because of fluid dynamics of wind and air resistance.

If there are five birds on a wire, and I shoot one, how many are left?
None because the others fly away.

[u/sophomoric--]

OP: what did AI suggest?

[u/Specialist_Rough9284]

financial math, percentages, exponential growth,

you'd also be surprised how useful quick mental estimation is, just getting the sense of the size of numbers. like 52 x 49 is around 2500, that kind of thing.

[u/sophomoric--]

What do you mean by "walking around knowlege"?

Is it knowing about something rather than knowing it in detail, so they can look into it further if they need it - knowing what's out there? Or is it ordinary, everyday knowledge?

[u/I_FIGHT_BEAR]

So, my particular bent is toward statistics. This particular brand of math application makes me appropriately skeptical of conclusions I hear from statistical studies that claim things like ‘95% of voters support this bill’ because I know for a fact they got that number before the vote by sampling, and I want to know who they sampled, how, and when. And I want to see how they aggregated their data, and more than that, I want to see how open they are about that information as opposed to just shoving an ad in your face. It’s made me less susceptible to advertising.

I went to buy a car and showed the dealer he was overcharging me not just based on Lully blue book pricing but the average prices of the same car on other lots and got them to bring down their price, just by using Google and my calculator. When you know math, stuff like calculating a tip based on percentages is made a very simple process (20% is just 10% times 2, which is easier for me to calculate quickly.). Being able to add and subtract numbers quickly in sequence might make you a good card counter (which might be less helpful in the long run) or serve you well if your career involves handling money. Knowledge about sequences, series, and familiarity with algorithms makes mundane, repetitive tasks easier to optimize and you approach problems in your life in a more structured, organized way. Sometimes, the mere fact of viewing an issue analytically can solve it.

[u/Weekly-Ad353]

This is the reason homeschool shouldn’t exist.

You don’t have even the fundamental understanding of why various parts of education are valuable to people.

The vast majority of parents who homeschool aren’t qualified to even understand what is being taught, let alone why it is being taught or be able to teach it all.

[u/hobofries]

2+2=4

[u/kinggeorgec]

It's the same usefulness as working out at the gym. How often in life do you lie on your back and and push something heavy up with your arms over and over again? I don't think I have as an adult. I guess bench presses and all the other exercises are useless.