I teach both middle school "technology" (think shop class mixed with Computer Science) and I later teach the same students in geometry and calculus in high school. This means when I first work with students there are no grades, just an opportunity to be creative and learn how to use tools and programming to make things.
This creates an amazing foundation for our work in academics later.
I wonder if it could be a model for improving math education we could expand?
When I only work with students in a context where I'm giving a grade, and that grade is "high stakes" because colleges care about math grades the students are less likely to bring their full creative potential to the subject of math. Grade grubbing happens.
But when they know me from working on a project first, where the feedback is narrative, where they help set the goals they are just more open to really learning the material, not just "getting through it"
This is so well said. I work in a school with a middle school that most definitely covers the basics, but the emphasis is on experiential learning. There are no grades, all feedback is narrative. Classes are mixed ages, 6th-8th grade. Lots of work is project-based and thus hands-on. Math, science, humanities, art -- they're all integrated with each other. Students set goals for themselves, dive into personal interests under an umbrella topic, understand the inter-relatedness of various fields of study.
These students go on to flourish in high school.
But every year, *every* *single* *year*, we have at least one family that takes their kid out of the program, because the adults in the family don't think our academics are "rigorous" enough. Because what we do doesn't look like the rote learning they themselves endured.
It is heartbreaking, and no matter how well we communicate what we are doing and *why* -- it still happens. I wish I could just whip out your quote for these folks to read, every time they start getting nervous. But it probably wouldn't matter. We say all the things you say, in our own way, and it so often falls on deaf ears.
What would you like to know? 🙂
schools should be preparing kids for real life and teaching critical thinking skills. things like math & science will be a necessary part but so are "soft" and vocational skills. that means art, music, shop too. if we expect 18 yr olds to be mostly like adults, they'll need all of this.
@futurebird I went to a lot of different schools, with different budgets for extras. I always hated gym, got absolutely nothing out of it, so dropped it as soon as it was optional. Shop class was for boys. It was mandatory for 1 year, with home-ec for the girls, and I opted out as soon as I could.
But I always had an art class in younger grades, and really appreciated my grade 7 school, in which teachers thought music so important, we had music class with sticks and triangles.
@futurebird That's actually really cool!
Most of my education experience was from teaching math at the college level while a graduate student. (I taught a smattering of courses from remedial algebra to multi-variable calculus.) By then, most students have either succeeded at or learned to hate math. I'm not going to say "failed" because I honestly don't think it's their failure a lot of the time.
The thing I observed the most there was that most students success came down far more to them feeling like they could, rather than any poorly defined definition of how smart they were or their aptitude. And a lot of that came down to having a teacher or an environment in the past that a) took time to help them understand and b) encouraged them for getting it, not just for grades. Even one good math teacher in highshool was often enough to make the difference.
So many of the students I saw who struggled at the college level just didn't believe they could do math. They might have confidence and bravado in other areas of life but someone had convinced them that they were dumb at math and it was so hard to break through that barrier once it's set in stone like that.
So anything we (or you) can do to help provide them with an environment where they can believe in themselves a bit and learn is amazing.
@futurebird I worked at a private international school doing a similar curriculum, but not long enough to get to see the younger kids come through to my calc/ physics classes.
Now I do IB, and I have lots of good to say about it when speaking about THE STUDENTS IT WORKS FOR
and not as much good to say for those it doesn't work for.
Obviously, school just isn't for making educated/ capable/ thinking/ empathetic individuals, and as educators we have to secretly do that part on the side.
What doesn't work as well for students?
@cpkimber @futurebird grades, tests, and pressure didn't work well for me, I did well in tests up until my mid teens when actual study was necessary instead of just "read everything because you're bored", then I started underperforming.
What did work was a completely off hand comment by a teacher, intending to make sure I didn't piss off new classmates by being too cocky, saying something to the effect of "there's a lot of smart people in that room, don't go in there and act like you're the bee's knees"
It's odd what motivates people!
It is odd, and if I stay a teacher for much longer, I will spend a good portion of that time figuring out how to motivate different learners.
My strategy the past few years is to just deliver the syllabus, give them enough practice and feedback, but actually try to get them to like it. If I can get them to like math, then teaching and the grades are all secondary.
@futurebird I have been wondering about this - I am a middle grades art teacher, so I see kids year after year and there are grades but they're way less high stakes. We tinker and create an environment where failure and risk taking can happen, and they get to show a teacher what they care about. By the end of a quarter we have a great rapport.
And then our poor math and even ELA teachers are stuck on a curriculum with coaches overseeing it and data collection like crazy and no room to tinker
@futurebird meanwhile, math teachers and ELA teachers get harped on all day to "build relationships" - many of my kids do not try without a relationship with the teacher.
But that relationship-building can happen naturally in a class like the one you're talking about! And then they can look forward to seeing you later for academics and trust you.
There's a bit in "The Real Computer Revolution Hasn’t Happened Yet" https://tinlizzie.org/VPRIPapers/m2007007a_revolution.pdf in the section titled "Children Discover, Measure, and Mathematically Model Galilean Gravity" that might be interesting.
https://en.wikipedia.org/wiki/Seymour_Papert
https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_education)
(edit: updated the link to the paper with the current URL.)
Best math teacher I ever had was when he prefaced each lesson with a historical background on what real world problem math was designed to solve.
These parables and stories still stick with me now.
The "narrative & solution" combo is a really effective technique.
Oddly enough, it's also why Republican propaganda is so pernicious.
They'll stick a lie or a false narrative in front of a concluding "Fascism is the Solution!" and it becomes "sticky" in people's minds.
There are several examples:
1. Trans rights.
The GOP promotes nonsense about sports & trans athletes, then advocates for "inspections" & foments fake moral panics.
The goal is the eradication of privacy as a civil right.
False narrative:
https://glaad.org/fact-sheet-for-reporters-sex-testing-in-sports/
Fascist conclusion:
No democracy can survive the loss of privacy as a civil right.
https://www.wired.com/story/republicans-differential-privacy-census-overhaul/
https://prismreports.org/2025/07/10/surveillance-state-in-u-s-is-far-worse-than-you-imagined/
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2. Women's rights
Republicans fund narratives about "male loneliness" on manosphere web sites & blogs.
They decry falling birthrates & fake stories about infanticide.
False narrative:
https://laist.com/brief/news/kpcc-archive/how-to-la/men-are-lonely-we-explore-some-reasons-why-and-what-can-be-done-about-it
https://internationalviewpoint.org/Loneliness-suicide-misogyny-capitalism
https://www.buzzfeed.com/hannahdobro/shocking-things-men-said-on-first-dates
https://19thnews.org/2024/09/trump-doubles-down-abortion-execution-babies-debate/
Fascist conclusion: male supremacy
Repeal the 19th amendment & impose a de facto poll tax on married women to vote.
https://thedispatch.com/article/women-vote-empathy-19th-amendment-repeal/
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3. Immigration, POC, & crime
Republicans promote a sick ideology that cleaves immigrants and POC to crime rates.
False narrative:
Immigrants are less likely to be involved in criminal conduct, not more. There's no such thing as voter fraud in POC communities.
https://www.reuters.com/world/us/trump-focuses-migrants-crime-here-is-what-research-shows-2024-04-11/
https://truthout.org/articles/data-disproves-right-wing-talking-points-about-migrant-crime/
Fascist conclusion:
Felony disenfranchisement & mass deportation programs
https://www.democracydocket.com/news-alerts/new-gop-anti-voting-bill-may-be-the-most-dangerous-attack-on-voting-rights-ever/
Donald Trump is blaming migrants in the U.S. illegally for fueling violent crime as part of his campaign to win back the White House, repeating rhetoric used during his previous run for the presidency. But studies show immigrants are not more likely to engage in criminality.
I liked the history of Pythagoras, Archimedes, Leibnitz, Newton, Einstein, and how Catholic & Islamic mathematicians saved copies of Greek maths etc.
https://www.popsci.com/science/lost-greek-manuscript-discovered-france/
https://en.wikipedia.org/wiki/Al-Khwarizmi
https://en.wikipedia.org/wiki/Archimedes_Palimpsest
When Hawking's On the Shoulders of Giants came out, I bought the book immediately
It's amazing that Babylonian base 60 math for time is still in use today
https://en.wikipedia.org/wiki/History_of_mathematics
David M. Burton's book is great!
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One of my favorite documentaries
https://www.bbc.co.uk/programmes/b00dxjls
https://en.wikipedia.org/wiki/The_Story_of_Maths
Euclidean geometry and Fermat's theorem -- the concept of how mathematical proofs are developed is an excellent story. (Well anyways, I find it cool. Can't promise every high school student would agree with me )
https://en.wikipedia.org/wiki/List_of_mathematical_proofs
https://en.wikipedia.org/wiki/Mathematical_proof
The documentary on Andrew Wiles & Fermat's Last Theorem I've watched several times.
https://www.maths.cam.ac.uk/features/fermats-last-theorem-history-new-mathematics
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https://www.quantamagazine.org/the-core-of-fermats-last-theorem-just-got-superpowered-20250602/
https://www.pbs.org/wgbh/nova/article/andrew-wiles-fermat/
Well deserved
https://www.npr.org/sections/thetwo-way/2016/03/17/470786922/professor-who-solved-fermat-s-last-theorem-wins-math-s-abel-prize
https://en.wikipedia.org/wiki/Wiles%27s_proof_of_Fermat%27s_Last_Theorem
@futurebird One of my 6th grade geometry lesson series involved creating 3D paper shapes (cubes, etc.) using basic drawing tools. It was actually fun, and I still remember how to do it.
Interestingly enough, medieval architects used the same, simple tools to design the great cathedrals.
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