My grandfather used to sit with me for an hour every morning and used to teach me maths.
He would focus on basics first. He would make sure I had the basics drilled in to me. Not just understood them, but mastered them. Then we would move on to the next topic.
It was a bit slow at first. But after a while, once the basics were done, I finished the whole year's math book in 2-3 months.
I have seen this in software engineering too. Once I am good at basics, or once they're drilled in enough, I am faster and quicker.
Drilling basics is basically like having the basics in O(1) look up with very reduced space complexity too. It reduces the amount of overhead your brain utilises. This makes your brain free to think about the actual problem you are solving. Also, I think this is what allows your brain to work in the background, even when you aren't actively thinking about the problem.
Lockdown has really shown up how my 7 year old struggles with his maths work set by school. I've gone back to basics with him and have been drilling him on simple numeracy until he can do it effortlessly using some flash cards I bought and some iPad apps (DoodleMaths, DoodleTables - can't recommend them enough).
Since then he has sailed through all of the new parts we're learning. I really expected it to be much harder than this, but it seems like not fully understanding some basic concepts and having confidence with basic numbers makes all the difference for really understanding the why of all the concepts that are build on top.
In about 6 weeks of me spending around 30 mins to an hour each weekday he has gone from refusing to look at a maths problem to being confident with it.
The entire curriculum is extremely easy when properly explained at correct pace.
I did this for a child recently. He was in the special needs program. I looked at his homework and re-tested his math understanding. It turns out he had no solid understanding of place value and had difficulty with adding two digit numbers mentally. No wonder he was struggling. We fixed that by spending a week 30 minutes per day on just that concept, he caught up to the next roadblock, which was fractions, we fixed that, and so on.
That's expensive if you hire someone to do this, but enabling self-study through ability to backtrack would not require as much teaching skill and be more of a supervisory activity for parents.
There are entire books on how to interpret math word problems, which is really all about converting verbal expressions into mathematical symbols. If you haven't already, buy one or check one out at the library. I am building a parser that implements those books as if they were algorithms.
That's the approach I am working on. No NLP, no ML, nothing fancy like that. It will take a while, but I should be able to pull this off. This is a question about hard problems and I think it qualifies. ;)
That being said, surgery is hard and can be traumatizing if taken on haphazardly. One of the harder problems, in my experience, is if an adolescent has been behind for years, it takes a long time to get to “normal”, and that can be really depressing for both the tutor and the pupil.
Another huge compounding problem is literacy skills. There are people in high school who can barely read, and it dramatically impacts their ability to catch up in every other subject. You can write a perfect explanation, but it might be totally disorienting to these students.
Education is really hard. I wish you the best of luck, it’s inspirational to read your ideas here!
While reading S&W, I had to look up many terms that were assumed knowledge.
Full disclosure: i work at maths pathway.
I totally agree that getting a high quality corpus of information is the hardest part.
I like the idea of explaining “themes/metaphors”, with version-controlled iterative improvements.
I taught a few classes last year on how to program in Scratch to grades 1-5. The 4th and 5th graders really loved it and they went off on their own to learn more. It was not a large sample, but I think presenting the right material in the right way to the right age makes a huge difference.
I have been thinking of ways to improve education. I think there is a huge potential in online video. If it is produced right in the sense of say "Hollywood" verse say Khan Academy, kids will enjoy it a lot more.
You are right though, many parents can’t teach. That’s the problem I am trying to solve - parents shouldn’t have to go to school with their children.
Just wondering as I haven't heard of this at all in my home country. Homework is usually quite clear, and the basics to get through it are made clear in the classroom. We had separate times for learning maths, and doing exercises.
Have you thought maybe your assumption is based on very very old anecdotal data?
The parents I know from my home country are telling me that their kids are often struggling and are overwhelmed by the homework assignments. While this is already recognised also by the board that created the curriculum the changes are slow and half-hearted.
In my opinion, however, that is not even the problem, nor is it the problem that they are trying to solve. We usually forget that teaching is not "transfer" of knowledge. Each person actually recreates the knowledge in their own head and tries to fit it in with the rest of the world they know.
I believe that the best solution to education is to be able to personalize the new content in a way that naturally extends the student's knowledge. As already stated this may mean backtracking a little to be able to put the new knowledge onto a good foundation.
Normally, teachers cannot do that for each student individually so getting a program that could do that customization would be a great win.
Science homework should be able to be done in little more than it takes to copy it from an A student. It should not take hours, which it often does. I am looking through the lens of disadvantaged students.
(no longer remember the series title, but do still remember the penny finally dropping on "x is an unknown")
> Schools are functionally no different from part-time prisons.
A prison by definition cannot be part-time ; ). Plus, it's a totally unfair comparison. Schools are intended for everyone. Prisons are intended for a specific subset of people deemed to have broken a law.
Schools are for children. Prisons are for adults.
And so on.
Sure it can. Check out "weekenders" and "work release" programs, for example.
“X is like prison”.
Work is like prison. Childhood is like prison. Society is like prison.
Is everything like prison?
If we live in The Matrix yes but we don’t?
> Schools are for children. [a specific subset of people]
Bills of attainder[0] may be illegal and unconstitutional, but they're still a thing that happens as long as noone who matters cares.
Schools are functionally no different from part-time prisons. You must attend daily under penalty of law.
Many teachers are plain awful.
They rely on students being additionally taught by their parents. That forces parents to go to school with their children, which perpetuates the vicious cycle. The teacher recalibrates the class to the students who either understood everything the first time or had supplemental education and the rest languish.
Schools assign homework that is not easy to do when the student hasn’t fully grasped the concept. That burns time they could use to get better.
So... I am implementing Math common core in software. The first part is an automatic homework solver for math. Once we solved the student’s homework, we can teach them how to do it with generate problems. Crucially, there will be multiple perspectives and an ontology of topics do the student can backtrack to where they got lost in class weeks ago.
After we are good with math, we’ll do the same with English. It will probably not go too deep, but it will let students obtain the missing foundation of knowledge.