I'm a math tutor, and I was helping a 6th grader with their personal finance unit recently when this problem came up. There were several other very similar problems that followed. This is not at all how tax brackets work, so I'm already very uncomfortable with trying to teach this to my student, but the worse issue is that this is an extremely pervasive misconception about how they work. This misconception has real, serious personal and political ramifications. This is a misconception that causes people to turn down raises "so they don't get bumped into a higher tax bracket" or what allows people like Sean Hannity lie to their audiences about how unfair it would be to raise the tax rate on higher income brackets.

I emailed the teacher, but I didn't get any response. This is a regular student of mine, so I'm not sure what to do. Do I confuse them by contradicting their teacher and telling them that this isn't actually how tax brackets work? Or do I just go along with it and teach them information that's categorically false and part of a wider damaging societal misconception?

i know this has got to be super common at this point, but make me feel better about math education in the world with AI. or is this what math teaching is now?

When I was in college taking Mathematics Education based courses, our professors had us consume as much Boaler content as possible. I thought it was great; the idea that tracking and Mathematics classes as a whole were racist and inequitable and needed complete restructuring was music to my ears as a young progressive during my college years. However, 5 years later being a Math Teacher for the last 3 years, I have seen the damages overall that have been done by watering down the curriculum and refusing to let "advanced" students move ahead to more intense content. All it has done is create behavior problems across the board by jamming students of every single ability into one class. I am as liberal as it gets, but these "researchers" who haven't taught in a public school classroom in 20 years (or ever for some of them) have no clue that their new approach has caused to stagnation in test scores and increases in behavior related infractions in the classroom. I am curious to hear everyone's thoughts, but if you are just going to call me a MAGA troll I will ignore the lame take.

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When I was a student I was in favor of them, I was never super fast at mental arithmetic, but now I've been tutoring for a while and I noticed they lack the most basic numeracy skill.

A student told me they were unable to divide a number by 2 by hand, all digits were even! I had multiple students who were unable to answer "if I multiply and then divide by the same number, what happens?".

All my students were in high school by the way. They should be taught to engage with the numbers and understand how they behave, not blindly plug them into a machine.

The report https://senate.ucsd.edu/media/740347/sawg-report-on-admissions-review-docs.pdf Between 2020 and 2025, the number of students admitted to UCSD who struggle with middle school maths on their placement test increased by a factor of thirty. The report highlights that many of these students have taken, and passed, higher level maths class. The average high school GPA of their incoming students increased over the period, despite the fact that the actual mathematics skills of the students had declined precipitously, and high school grades had little relation to the actual maths abilities of their students.

To me this is a clear sign that mathematics education is in crisis. Too few students have practiced basic skills enough to reach fluency with them, and rampant grade inflation has been used to hide the collapse in actual student achievement.

Today I wanted to watch back a video on the Fibonacci sequence by Vihart that I had enjoyed, and as I visited their youtube channel, all but one of their videos are gone. There was a remendous amount of interesting and valuable math educational content on there, and it feels quite sudden and without context that it's been privated.

Does anyone happen to know what happened? I wasn't watching the channel regularly, so please enlighten me if I missed out on any context behind this.

It’s so very, painfully obviously C.. And based on that comment section *nobody* learned this. A fractional part of a whole requires the wholes to be the same size -_-

My first thought was to calculate the tip of the pyramid where the lines would cross, then subtract the imaginary pyramid above the ingot from the pyramid from the base of the ingot. However, the lines don't line up like that (believe me, I checked). There's got to be a simple way, but looking it up only shows me trapezoidal prisms. How?

I've heard so many people say that it's hard to come across a good math teacher. I've been studying math for quite some time and I don't think I've had a teacher I really admired. No one who truly builds intuition or makes the subject feel less daunting.
I want to know why math is so hard to teach. Is it the subject itself, or do mathematicians just not have a knack for verbalizing their thoughts?

These “tricks” do not teach conceptual understanding… “Add a line, change the sign” “Keep change flip” or KCF Butterfly method Horse and cowboy fractions

What else?

At my school, it is common practice to make handouts every day to give the kids. The kids follow along the lecture and complete the handouts. Then they complete another handout for homework.

EVEN FOR GRAPHING. Pre-made axes, pre-designated units, etc.

I think this is atrocious. They need to know how to decide for themselves how far apart to make the units on the graph and how to mess up and start over.

These kids have NO IDEA how to decide what's important to write down, either. It's like... sad. I teach high schoolers. Back in my high school days, we got out a notebook and we decided what was important. If we didn't have a notebook, we were SOL. If we didn't pay attention, we were SOL.

I'm not saying SOL is the goal. I'm saying this spoon-feeding is sabotaging the students far more insidiously than a day or two of "SOL."

I'm not mad at the kids, I'm mad at my colleagues who set the kids up for failure with these expectations of hand-holding.

The year so far has been a review of trig and Precalc, a review of linear equation writing, and the build up of a limit by looking at them first numerically and then graphically. We FINALLY got to analytic limits today and it was great! My first time teaching calculus and it's my 17th year of teaching. How exciting!

I get the point and agree, but I would take off points if this was on a test. The symbol "=" doesn't not just mean "my next step". You don't get to write "=" and start throwing in extra factors. I swear, a good 5% of my job is correcting bad habits introduced by teachers without a math degree.

I wanted a new fun way to teach Soh-Cah-Toa. I'm a huge TTRPG/DnD nerd so I created the "Legend of the Great Dragon Soh-Cah-Toa."

It involves the hero of the greeks Pythagoras fighting against the great dragon known as Soh-Cah-Toa. The three-headed dragon had his heads named: Sine, Cosine, and Tangent. Each dragon head had a special breath weapon that made a great sound right before use: Sine - "Oh"; Cosine - "Ah"; and Tangent - "Oa!" In the end, Pythagoras won when he had to combine his swords "A" and "B" to make they hyped C.

When Pythagoras finally won, he felt a shake of the ground and saw black specks rising from the new cracks (had to tie a stranger thing reference) as it signals the coming of the upside Dragon: Cho-Sha-Cao!

Title says it all. Why do my middle school students(I tutor them outside of school) independently and stubbornly(after multiple corrections) think that x * x == 2x ? It feels like they've been trained(not taught) to multiply numbers but they don't understand what multiplication even means conceptually.

I try to explain using these concepts:

• 5*7 can be thought of as a different way of expressing 7+7+7+7+7. Likewise, x*x would be x+x+x+...+x with x many xes

• or that 5*7 can be modeled as having 5 objects that are the same and taking them together as a group. so, x*x would not be 2 objects, but x objects, etc.

but it doesn't seem to click. It's astonishing to me. How can I explain this better?

EDIT: Thank you so much everyone. I'll definitely try all of these.

I’ve read the Wikipedia article on it and it says it’s been deemed one of the biggest educational failures of the 20th century.

Was New Math really doomed to fail because it was too hard for kids to comprehend, or was it more that it was too hard for teachers and parents to come to terms with?