If you’re like us, you’ve studied the mathematician [Euler], but all you really remember is that you pronounce his name like “oiler” and not much else. [Welch Labs], on the other hand, not only remembers what he learned about logarithms and imaginary numbers but also has a beautiful video with helpful 3D graphics to explain the concepts.
This post, however, isn’t about that video. If you are interested in math, definitely watch it. It’s great. But it also got us thinking. What would it be like to be a high school math student today? In our day, we were lucky to have some simple 2D graph to explain concepts. Then it hit us: it probably is exactly the same.
Changing the Subject
Well, maybe not exactly, but the problem is, we are guessing that your math teacher — no offense to him or her — wasn’t the same kind of person [Welch Labs] is. To be fair, we couldn’t have produced that video either. So, the way we see it, you have a few choices.
First, maybe you get lucky and you happen to get a teacher (about math or any other subject) who is just awesome. We are lucky enough to know a few of these people, but you have to admit world-class teachers are rare, and even rarer outside of colleges and universities.
Second, maybe you have a teacher who is greatly engaged and goes out and finds material like this to share. We suspect that goes on a lot, but maybe not as much as it could. There is a whole industry, too, set up to provide teachers with materials for profit, but it often isn’t at the same quality level as something like this. That’s unsurprising. If you are a movie studio, not every movie wins the Oscar.
Third, if a student is motivated, you have an extraordinary research library at your fingertips. Individuals create amazing articles, videos, and even courses. Major universities have their course material online for anyone to use, in many cases. You just have to find it.
A Mixed Bag
This, too, is a mixed bag. While you have access to more information, you have to critically evaluate if it is correct or not. You could presume anything you found in a traditional library was probably not patently false. Not that everything in a library is true, but, statistically, the way books used to be produced and library collections created, it was far less likely than finding false information on the Internet. On the other hand, how motivated were you as a kid to do things like that? Well, being a Hackaday reader, you probably were. Maybe a better question is how many of your classmates were in the library while you were reading about computers?
In a way, it is like tech support. Sure, AI might not be the best of all possible tech support. But it might be better than what you probably will get. Realistically, every teacher can’t be the greatest, and even if they were, they probably don’t have the time to produce huge amounts of high-quality material for their classes.
The Answer? (Or, at Least, the Question)
So what’s the answer? That’s where you come in. How could we make sure that all students get access to high quality resources from everywhere? I frequently hear of kids using Khan Academy, for example, to explain things they aren’t getting from their teachers. But that’s just one resource. Are there curated lists of resources for each subject out there somewhere? If not, why not? What other ways could we get the serious educational material produced on the Web every day into the classroom? I’m sure there are lists, but we’re thinking about something with the go-to recognition of, say Wikipedia. Not just a random blog posting. Let us know what you think and what’s already out there.
Maybe the best scenario is when great teachers share their materials with the world. We just need to get the word out. Another good scenario is when great teachers let their students take the lead. If you want to see how not to produce educational videos, have a look at this series of parodies of 1970-era science videos.
Since this is “Ask Hackaday”, does every comment have to include a question?
And will we get an answer?
Nope… YOU are Hackaday!
I was deep into the technology of education awhile back, thinking it would be the wave of the future, coming up with innovative ways to make education easier. The problem is that no one wants to actually do that.
The answers to this are fairly straightforward, there are several elephants in the room that serve as barriers to education that we could remove instantly.
The problem is that no one wants to remove those elephants.
For example, edX wants to simply put college lectures online (and then charge people for testing and accreditation for having taken the course). I had a meeting with the president of edX and pointed out that a) some of their course descriptions had no information about what the course was about, and b) the lectures made by their CEO (MIT professor teaching electronics) were perhaps not the best and perhaps that specific course material would be better served not by drawing on a blackboard, but by computer graphics.
I was told that a) the courses in question came from associate colleges and universities, and that edX had no control over their content (or quality) and so he could do nothing about it, and b) the CEO flatly refused to do anything except lecture from a blackboard, it had always worked in the past, so he figured it would work online.
With the exception of Sal Kahn I don’t think anyone is making any progress in actually modernizing how education is taught. With Kahn academy you can always go back and redo a video to make it better, so it’s got a pathway for improvement. He’s also trying new things such as flipping the classroom structure, where the students view lectures at home and do homework in school (where the teracher can step in and help if needed), that sort of thing. He’s also taking comprehensive measurements so he knows which methods are working.
One of the star trek movies showed a Vulcan academy where the student stood in a pit surrounded by screens and the computer would manage the education material. This got me thinking about how the curriculum could be managed by a computer, going slower over bits that the student has trouble with, reviewing parts to be sure the student got it right, switching to a different topic when the student got bored, and so on.
We know a lot more about the mechanisms of learning, but we never seem to implement any of it in our school system.
We still teach geometry to children because our curriculum is based on “the classics”. Perhaps skepticism or personal financial management would be of better use to students.
So I lecture at a UK University, and we’re encouraged to try to modernise things and take into account some of the more recent literature on better ways to learn. The problem is that implementing these things can take a boatload of effort, may not always pay off, and there’s no actual recognition for trying new things, so we spend so much time trying to improve teaching, sometimes succeed, and end up putting ourselves under time pressure, and get no consideration for that when it comes to other duties.
We’ve integrated things like simulations of lab experiments that students have to complete before coming in to the physical labs to do the same experiments, as it means they’ve already “done” the experiment and can focus a bit more on the experiential learning rather than trying to understand what is going on. They can then repeat the sims at any time through the year, and we see a spike in this near big assessments. We’ve only been able to do this because companies (usually textbook companies) have put these sims together, and we can just pay for the textbook + sims and then link the students to the bits we want them to do.
Would I love to do more? Yes. Do we get the time or resources to do it? No, not to mention the fact that I do not have the skills to design sims myself. I saw a talk at a conference from someone who had implemented course-specific VR lab simulations and educational resources, and the first question asked was “How the hell did you get the funding and time to do this and buy the kit?”, and the answer was “a really specific education grant which only runs at our institution”.
Modernising education is a great idea, but it isn’t trivial, and it needs serious buy-in in terms of support and recognition from the institution, which I think most places don’t get. Look at pedagogic research: it is often sporadic, with low sample numbers and short timescales, and so even the research itself can be very bare-bones because there’s not a lot of push to do it I think.
There are currently a number of awesome resources for standard track math, to and through calculus, including Geogebra and Desmos, to full blown tools like Wolfram (Alpha for cheap or free, Mathmatica for actual money), Maple, and a slew of others. The barrier is low for these tools, and they are not really conceptually new- The earliest go back to the 1980’s, with packages like Geometric Supposer, Derive (bought and killed by TI), and a numebr of others- but they are Much better.
Khan academy is another tool. It is a low barrier tool that works well for use on its own or to support traditional education. But students need to put forth effort to use it effectively. A disinterested student can’t be led through concepts with Khan acad like with, say, Desmos.
Which brings me to Geometry. “We still teach geometry to children because our curriculum is based on “the classics”.” This statement is maybe true to a point, but is not meaningful. A nice application of the Red Herring fallacy. How does this mean we should not teach geometry? I can easily argue that the foundation is necessary, both for college bound students (not just STEM. Art, Fashion, design, and the like, and even finance, where the relative concreteness can bring understanding to a some of the math) and for non-college bound students (Many trades need a solid foundation, for example). Does this mean ALL students NEED Geometry later in life? No. But many will, and, in my opinion, an education should expose students to a broader range of ideas than a job training program does, including topics that the student may not hold interest in.
I could even argue that the classics are key, because these are the subjects that our societies are founded upon. Geometry (Euclidean) is not the Only Geometry (capitalization intended), as evidenced by traditional construction in Japan, for example. THere are other presentations and structures. But saying in essence that we only teach it because we always have is not useful.
As a side: Every time someone tells me school was a waste of their time because they only ever use 5 percent of what they learned, I ask if they knew which 5 percent it would be when they were in school, and if it is the same 5 percent twenty years after school as it was ten years or when they left school.
I’m not suggesting that geometry isn’t valuable, it most certainly is.
My point is that we teach the topics we do because of tradition, and perhaps we should step back and consider whether a different set of topics would be more useful to the average student.
Basically, I’m saying that we should apply the scientific principle to learning. We have all these traditional ways of doing things, maybe we should have A/B testing with different methods to see what works best.
And as an example, learning about skepticism and various fallacies that will be presented to an adult in our society might be more valuable, on average, than calculus. Another example would be personal finance, and I might also add “how to raise a family” as extremely useful.
(And for the record, I aced geometry in HS (literally) and have a college degree in math, including geometry courses, so I don’t say this out of any sort of hatred or frustration with geometry.)
Ok, so we do an experiment (on children). We teach a third of them geometry, a third of them no geometry at all, and a third of them can sit around on beanbags reading Facebook (that’s the control group).
After twenty years we see which group was more successful in life…
Great idea.
This is a ridiculous comment.
None of the above commenters are suggesting that you run experiments that could be actively detrimental to people later in life. There is plenty of data available on what may or may not be useful, and there are plenty of options for how to present those topics to varying degrees.
The commenters are suggesting we re-evaluate how we choose the topics and where the focuses might lie. Is a curriculum designed in the 1980’s still the best option in 2024? Probably not.
Teachers teaching skepticism only teach their own POV. The problem is the population we have as teachers in America. They just don’t get ‘critical thinking’, instead indoctrinate. Can’t teach what you don’t know. Another downside to sending worst students to education schools (where they get 4.0s).
Calc is far more valuable, is not average though.
The Average kid gets to Algebra 2, passes, but understands and retains nothing. Average HS grad can’t actually add fractions.
You want HS teachers to teach ‘how to raise a family’…Seriously? You must be joking.
Want to start a war between parent factions?
Dirty hippies vs holy rollers.
Headbangers passing ammo to both sides and instigating…’That thumper said he was glad Jerry Garcia was dead!’ I digress.
Also: Geometry was the only HS math class I did that included ‘proofs’. (I did AP calc in HS.) The rest of the track was problem solving. I’m not a math major type, but proofs deserve a HS introduction.
Sure doesn’t matter for 80% of the kids, but those 80% themselves don’t matter.
World needs ditch diggers.
It’s all about the brain.
https://www.amazon.com/gp/product/B08M5Y7PV5/
A few days ago I read a story about solidifying memories while sleeping.
https://singularityhub.com/2024/08/19/newly-discovered-brain-wave-helps-lock-in-memories-while-we-sleep/
It sounds pretty much like science fiction, but Musk is also tinkering with direct brain to computer interface and the first test subject can now move a mouse cursor faster and more accurate over a monitor then human arms can.
Overall, we’re now on a pivotal moment in history. Somewhere in the coming 50 to 100 years we either find a way to create a decent and durable society, or we use up most of the important resources and then it’s back to the stone age.
Technology and teaching materials are fine, but they won’t solve the problem of bad teachers. Good, motivated teachers who are interested in their students’ understanding and success can do with surprisingly few materials, whereas tons of materials don’t make teaching any better if the teacher isn’t involved or competent.
Of course, the trend towards teaching “practically relevant” topics in favour of teaching the fundamental concepts necessitates more and more intricate teaching materials, but will just lead us to a point where people are enamoured with fancy materials devoid of actual content and not realise it. That being said, technology can absolutely help with teaching, but it shouldn’t be the focus. For example, modern smartphones are packed full with sensors and high-speed cameras that can really help with physics and chemistry experiments. Having lectures and notes available online or accessible from wherever is a great boon.
“Technology and teaching materials are fine, but they won’t solve the problem of bad teachers”
No, but breaking up Teacher Unions or implementing school vouchers can fix that.
You missed the /s on your comment.
“It don’t have what it ain’t got!”
School vouchers are a pox. Designed to move public money, earmarked for education, into private pockets.
Unions are a double-edged sword, but if billionaires can exist it shows that there is enough money sloshing around in the system that we can afford to pay people properly.
You have no idea what you speak of.
Just DERPing.
Vouchers are an escape from failing schools. But you are in favor of failing schools.
Teachers unions are a pox.
All public employee unions are. They should have to pick, strike of politic. Not both. Are we France now?
Also two unions for critical function public unions (airline pilot, train driver etc). Banned from striking at same time. Like Germany. Assigned union a/b by lottery.
The problem of bad teachers is deeper though. Sure the education is easy AF (4 year blackout drunk/4.0).
Putting the worst students in teacher college was just a bad idea.
Nothing to do about it now except doze the schools, hand the profs shovels (for new job: ditch digging) and start over.
Vouchers are simply a way for rich people to take public money. That’s it.
You don’t think they then use the money to pay private teachers well, do you?
@Andrew
“Vouchers are simply a way for rich people to take public money. That’s it.
Maybe you should tell that to the single-parent minority mother who just used school vouchers to get her child out of a dangerous, underperforming school. why so racist?
Nuf said…
Replying to Somehuman.
Citation needed. Do you have a link to the story?
Has anyone tried learning a language with Duolingo? It essentially gamifies learning, and adds other addictive elements that social media uses. It practically stalks you, if you don’t do a short lesson for a day, not only does it ruin your streak, but it messages and emails you as reminders. I recommend it!
False information isn’t the boogeyman everyone thinks it is, specifically because it is false. If you try to use it, it won’t work. If it does work, then it’s either true or a close enough approximation of truth for the task at hand. If we’re in a situation where false information is being successfully propagated, all that means is that the information is never actually being used, or was never useful to begin with. Consider someone learning the pythagorean theorem incorrectly, then trying to build something using it. They’d quickly find out that they’ve made a mistake. People complaining about “false information” are usually just trying to advance their own (useless) ideology. Useful truths enforce themselves.
Teachers and schools don’t matter as much as people believe, their contributions count for about 10% of academic performance with the personality of the student being the most significant contribution. There is more to it than just IQ, and even that is interconnected with genetics but the influence of genes grows over time with family environment dominating early on. So what is the takeaway from all that recent research? You need to fine tune the educational program and environment to match the individual students, and technology such as AI is going to make a huge difference in that area.
My four remaining students are mostly offline but each run ollama for local AI and have kiwix plus a very large offline library for reference. They can also combine the two in Firefox using Page Assist to allow for a dialogue with the texts via the AI. This gives them the equivalent of access to the library and tutors in a small university, particularly in the STEM subjects we prioritise. I’m not exaggerating, the instruct versions of some of the latest open source LLMs make all but the best tutors and lecturers redundant in many subjects.
I’m sure Jerry Garcia would rather have someone other than Karen Carpenter leading the band in which he now plays.
B^)
Satan himself, will always play lead in that band.
I remember seeing a small reel of film in muddle school nearly 60 years ago in which I learned more than weeks of that awful pecking and scratching of chalk from the math teacher could do. I wished then they could do this always.
Bring on computers and animation to teach math and any symbolic study, nothing human here. Realtime interactive even gamify, better.
Replace teachers with AI !
Khan Academy has been experimenting with an LLM based tutor called “Khanmigo” and it’s remarkably good for what it is.
better pencil sharpeners, until 18 years of course.