Are there high schools where absolutely no algebra is a possibility? I didn’t go to a fancy pants school, but even the lowest track of students—there were four tracks— had to take some basic algebra courses.
Because it is obvious some students are not getting through high school with the math knowledge needed for tech school anyway. By trying to not limit their choices we make them waste a lot of time practicing quickly forgotten rote learning of tricks and techniques to “pass a math test”. They leave high school with a disdain for math, and with poorer grades in subjects they actually care about.
Rather than “not limiting” them by making them take inappropriate classes in high school the system should have options to change your mind. Building understanding in math requires students who are motivated by a desire to learn math, not just a motivation to not fail.
A good argument could be made that everyone should have some familiarity with the basics of probability and statistics.
But geometry is useful too, not just for its practical applications, but because it’s a way of teaching logical reasoning and deductive proof, by working with concepts that (1) can be drawn and visualized, and (2) are noncontroversial and not obscured by emotion.
They need one beginning middle school math class that teaches:
- Solve for “X” for fairly basic 1 variable equations. Move things around and manipulate the equation to solve for X.
- Use that knowledge to do basic SOHCAHTOA trig. Give them 2 things and they should find the rest.
- Expand on that knowledge for basic carpenters geometry.
After that you can have different classes or higher level classes or different directions. We do a disservice to the students by treating these skills as the entry skills of these huge math disciplines and not the culmination of arithmetic.
I took everything through Calculus in high school and have used virtually none of it in the intervening 45 years beyond basic algebra/geometry. Most students would be much better served by a practical math class that folded in probability and basic statistics.
And please teach them that you can solve for anything, not just for X, and that your “variable” can have a long-ass symbol, and that you can always say “you know what, since this variable’s symbol is kind of clunky, I’m going to rename it ‘x’”. Or ‘chocolate’. Or ‘©’. The biggest problem most of my chemistry students had wasn’t with chemistry, it was with not knowing that you could solve for [HCO[sub]3[/sub][sup]-[/sup]]
All the math taught by teachers who actually understand what they are teaching.
Every time I see someone moaning about new math, or about not understanding the practical applications of what they are learning, I know they have not had a good teacher.
(Do we demand the practical applications of writing 1,000-word essays? No, because we all get that it’s about learning how to understand a text, analyze a problem, and express yourself.)
Math is about problem solving in a ruthlessly logical fashion and being able to apply this to other aspects of your life, be it felling trees, repairing escalators, or figuring out how much dirt to buy to fill a garden box.
In practical terms I tell high schoolers to take the most advanced math they can handle otherwise they’ll end up like a relative of mine who finished high school knowing she wanted to be a dentist for a living. She then had to spent two years doing catch-up math courses in order to enter dental hygienist school (at which point she stopped. Happy!).
Quite frankly, unless a HS student plans to go into some field like science or engineering, they shouldn’t have to learn anything beyond algebra. I’d much rather see high schoolers be taught a lot more practical math related to personal finance, household budgeting, etc. these days; there’s far more need for that.
For those who are advocating this: I’m wondering what specifically you think high-schoolers should be taught. Can anyone either spell out or link to specifics?
Echoing Kimstu here, but the problem with the argument that we need more “real world” math is that the reason why most people struggle with those real world examples (taxes, balancing books, understanding loans/mortgages/hospital bills etc) is not because they require difficult math, but because they require sophisticated problem solving, excellent language skills, and complex understanding of many moving parts that are in a constant state of change, and may require active management of many different communication streams.
I’m a “smart” guy who took all the advanced math classes in high school and did some more advanced calc in college. Doing taxes or managing my medical bills is complicated and difficult not because I can’t do the math, but because the systems are not designed to be user-friendly, are ever-changing, and are in fact developed to meet the needs on the entities administering them and not the needs of the end user.
Also, I have to ask, with no snark intended, is trig really required or is that just a made-up statement? In my experience, which I concede is now 20+ years out of date, trig was only “required” if you were in an advanced, college-placement math track. In which case we’re not talking about general education at all.
Frankly I have always thought a students basic education should end by 10th grade and after that, most school time should be spent on what they want to do in life. So in some kids cases that might be all automotive. For others, lots of math. For others lots of biology.
I’ve never met anyone who could factor a polynomial but couldn’t balance a checkbook. (Met plenty who didn’t balance their checkbooks - but not because they couldn’t understand the math.) What I see is kids failing to understand factoring polynomials because they can’t factor numbers.
Ideally, algebra teaches you a method of solving problems (take the information you have, manipulate it into figuring out the information you’re looking for using a few rules). Geometry teaches how to start with a situation and some true statements and use logic to prove other true statements about that situation; it also teaches how to spot faulty logic.
I’m also not sure why accounting is considered more practical than figuring out how much butter you’ll need (and whether you need to buy more) when you have a cake recipe for a 13"x9" pan, but all you have are 8" round cake pans (because your 13"x9" is where you’re cooking the lasagna - speaking of which, two of your guests are vegans, so how do you change this entree that serves 6 into an entree that serves 4? and what time does it need to go into the oven so that everything is ready to eat at the same time since they all have different baking and resting times?)
1- I don’t remember
2- 3-4 years of math seems about right.
3- As a separate class, no. But, I do suppose checkbook balancing could be part of learning how to add and subtract. And I am surprised that compound interest isn’t covered when kids learn about exponential functions.
I don’t remember how many classes I was required to take, because I took them as electives after they stopped being required.
Like others, I’m all for a “life skills” class and I’ve seen some of the schools around here have them (I was a substitute for a couple of months, so I could see what different schools needed a substitute for in the district I worked in)
How I view learning math as a necessity and the people who say “they’ve never used it” - I think that math is in part like the football player training that involves running through tires. No football player has ever run through tires when they’re actually playing football, but doing that trains necessary muscles.
Or, you know, like the kid painting the fence in Karate Kid…
As far as actual classes - I think they need algebra, and more statistics & probability than I got (with a whole section on how people use statistics to lie). And computer programming, which is probably now taught in most schools. But there are probably thinks I learned in geometry and pre-calc that I don’t realize that I use, but I do use.
Here’s a counterexample. My son-in-law is German, and they track kids early there. Because of various reasons he got put into a vocational track for high school. He then got it together. He was blocked from going to a regular college because of this, and had to go to a secretarial college to get the classes needed to eventually go to a regular college. He got a Masters in International Business and is now making tons of money.
9th grade is way early to decide this stuff. If a kid demonstrates that they can’t handle regular math, sure, track them into a simpler math class. But there should always be a path back.
That’s not a counter example, it’s an anecdote of a system that works like I suggested. Your son-in-law has a Masters and makes tons of money, so obviously the system worked for him, even if it was not perfect. Note I specifically wrote that early sorting requires a system for changing your mind later.
Meanwhile practically every high school math class at the slowest and lowest possible level for students is full of students who’re not learning math, they’re learning how to pass math class. The idea that not teaching them about factorising polynomials is taking options away from them is evidence of a broken system, not of a system that is the only way to ensure kids have opportunities to use their talents.
I would start with how interest rate and loan repayment work, and why it takes years to pay off a high interest CC making minimum payments. The class should also cover how insurance works, and the basics of the payroll and income tax systems. Top it off with saving for retirement and the basics of the stock market.
I think the math program should build to a knowledge of how to handle probabilities in a logical fashion.
For example, I’d be over the Moon if the average person on the street could work out what they need to know to answer this question: “If there’s an X% chance of A happening given B, what is the probability of B happening given A?” That is the kind of mathematical question which has some real implications for the lives of humans living in the world, regardless of what specific jobs they take on.
Presently, our math curriculum at the high school level builds to integral and differential calculus. That’s why algebra leads into trigonometry, and why logic isn’t really treated as its own subject, and why statistics is taught as an application of fractions as opposed to something worthwhile. That is what’s pointless, and saying that calculus builds better brains an infinite number of ways doesn’t save it: Probabilities are much more likely to be useful even if the kid grows up to be a civil engineer.
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A lot more focus on debt - just how much your credit-card debt swells with interest, or how staggering a burden student-loan debt can be in college. Mortgages, investments, etc.
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Things like 401ks, Social Security, etc. How contributing a thousand dollars in your 20s grows to much more than contributing a thousand in your 50s.
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Budgeting - how much various things cost.
On the same track, mental math and using mental references to calculate distance and volume.
For example, have the kids walk across the room in a way that over time and with practice, they can pace out a yard. Then they divide by 3 and have a distance in feet. Do it again diagonally and multiply and you have square feet. Now they can figure the area of a room or the front lawn.
Or by measuring their fingers (or 2 of them) figure out about which finger is one inch across.
I mean we use “length of 2 football fields” because most people can relate so why not teach some other useful measuring references.
Accounting isn’t really math - it doesn’t require anything other than arithmetic. It’s comparable to doubling a recipe to make 2 - 9 inch layers rather than 1. Deciding which accounts to debit or credit has nothing to do with math or even numbers. On other hand,adapting a recipe meant for a 8 inch round pan to be used in an 9 inch round pan requires actual math- by which I mean not the actual arithmetic operations , but knowing which operations to use and which measurements you need. It might appear that the pans are close in size*, but the first step in adapting the recipes is knowing the volumes of the two pans . Change that - the first step is knowing that you *need *to know the volume of the two pans.
*The 9 inch pan is about 25% larger by volume.