Math used to be taught with more drill style. Now with common core every single problem is an epic quest of 10 frames and double pluses. It seems so ridiculous. I'd rather them crush a worksheet of 20 problems that practices a single skill then 2 problems that try to include everything from reading to drawing just for a simple subtraction problem.
The problem with these 20 problems of basically the same identical challenge is that it's actually less effective than intermixing of different kind of problems, at least according to learning science.
You and I may prefer 20 problems that practice straight subtraction, but that's not what the science says is actually the most effective learning strategy.
You want different kind of problems in a problem set. It shouldn't be straight subtraction, but also additions, word problems, and so forth. This creates a level of desirable difficulty, which embeds knowledge more deeply than something that is very easy to do by rote.
In reality the problem is more complicated and the issue is that the current media of teaching via worksheets and teachers is lacking and insufficient, which renders this debate obsolete. What you have is different parts, learning new stuff, practicing it, but also spaced repetition. Those need to be in balance with each other but also rely on cognitive overload, tiredness and motivation (among others) of the learner. So what you really need for a solution is software that replaces those work sheets and does a good job (as opposed to many of the current cheap learning apps) of giving you the right task at the right time. Eg. it knows that you have been drilling stuff and gotten good at it and so now its time for some more mixed stuff that could be paired with srs (stuff that needs refreshment). I think apps like kahn academy are good but could be improved and personally tried to build my own language learning flashcards app[0] after becoming frustrated with duolingo where I have a 2000 day streak.
0 - https://ling-academy.com/
It's a bit of a mess. I found that its pretty hard to build a language app.
Cool idea, my first impression is that there should be some kind of mini-arcs or long phrases that make the content more digestible.
What I mean is that now the speaker goes on and on, and the subtitles are abruptly changed to another set of words.
As a learner, I would like to have better sense when the words will disappear.
I noticed it's arbitrary Youtube content so it's hard..
A simple testable solution for arbitrary content: option to _automatically_ pause/slow down the video just a for second before changing to the next set of text.
Another simple and stupid idea would be to show previous words below the the current context.
In the long run usage of a particular user, maybe the app should not highlight words that it knows you have encountered in previous videos many times or if the system knows you have mastered that word -- in case the system is testing user, did not notice if it does.
Btw. Not sure what is the difference between green and black colored words. (Don't know Spanish so hard to guess.)
Also there's some typos at the landing page, at least these: "Activley", "wont be"
Seems like a great concept, good luck :) (I don't find Duolingo that effective either.)
Appreciate the feedback! My biggest challenge is to polish features. I have taken out a few features from the app because they where buggy and would break. I always had some ideas and prototyped them in the app but then after trying it out and getting a feel for it, I would jump to another idea instead of polishing the prototype. I'm definitely gonna improve the youtube feature, especially the ui. Also, showing the previous subtitles in smaller font somewhere is a great idea! Thanks for that.
This ling-academy looks promising and I like your philosophy. After playing with it for a few minutes, I looked for a way to create an account to save my progress -- is that not implemented yet?
Along the same lines, Alfred North Whitehead had a very similar approach to education and learning as a whole saying it is cyclic with one important stage being precision analogous to the idea of practice with a later stage of generalization analogous to the idea of performance.
> Whitehead conceives of the student’s educational process of self-development as an organic and cyclic process in which each cycle consists of three stages: first the stage of romance, then the stage of precision, and finally, the stage of generalization. The first stage is all about “free exploration, initiated by wonder”, the second about the disciplined “acquirement of technique and detailed knowledge”, and the third about “the free application of what has been learned” [0]
You are combining too many things. Focusing on 20 simple with increasing difficult problems builds visual memory, pattern matching which is lacking with a few compounds problems.
The science must be missing some inputs because the current theory is lacking.
The current theory isn't particularly lacking, the average teacher (let alone layperson's) understanding of it is lacking. Plus there's dozens of rubbish theories that are sorely lacking so you have to find the researchers that actually do solid research.
IIRC (see the above, it applies to random comments on the internet) drill work is more effective (but feels less effective to both teachers and students) if it's mixed up with different topics or question types, kind of like how doing a kata is better than doing exactly the same punch 10x (obviously katas are not ideal either, at least not as the only tool).
Really you need a bit of diversity, and IMO two of the big traps to fall into are overly homogenous drill work (which doesn't retain as well as mixed drills, but looks effective because anyone who doesn't eat their crayons can do it without thinking too hard) and one-off problems (do an assignment where you solve a heavily obfuscated problem once, then pretend that it's now something that students actually understand, when they've literally just answered one single question assuming they even did it themselves).
In first grade we were given a workbook for learning how to write the letters. There was one whole page of A, one page of B, etc. You had to write maybe 100 As in a row. The kids quickly figured out that the fastest way to do it was to first write the left slant 100 times, then the right slant 100 times and finally all the 100 crossbars. So yes, you do need a little variety to defeat such shortcuts.
According to the article this is actually a really good way for kids to learn and improve. The point being that just practicing the lines is hugely important.
Exactly. That page full of A's, whether they "cheat" it or not, will teach the kids how to draw all lines that make an A. Repeat that with other letters, and then throw combination of different letters into the mix, which will force kids to draw one letter at a time, after they've already mastered all the component movements in isolation.
I'm not seeing any research linked. It will have to be pretty convincingly done too because we've seen a metric ship load of issues in psych research of late.
I don't have an opinion on the issue at hand. "Because the science says" With nothing in support makes me really suspicious. It really starts looking like "Because $authority says so you may not question" Which is the opposite of what scientific inquiry is meant to be.
They are not the only one, I see the same. Kids without math drills have problems in storing crucial bits of information in long-term memory and consequently fare worse at solving simple arithmetic problems than myself when I was much younger. I'm not talking about complex things but basic arithmetic, like multiplying digits, adding fractions or, more importantly, dealing with ratios. Drills give you a considerable advantage here.
I have another peice of anecdata with my parents/grandparents. They grew up in the USSR and went through school there, drilling (according to them) was extremely common.
They can still remember some peoms verbatim over 70 years later (in my grandfathers case). And they still remember/understand pretty much all the math they were taught. When I was doing my Advanced Highers (final exams in Scotland) I was asking my parents for help and they could answer all the questions without looking things up.
I looked up the exam paper[0] I sat, I'm pretty sure there's no way I'd get an A again if I sat it right now without studying for it. But I'm pretty sure my parents still woudl.
I had a bit of schooling in that kind of educational system (Asia) before continuing schooling in North America. I'd say that you there is no free lunch. You're always giving up something for something else.
I had a job 10 years ago doing in-person training at a company trying to digitize their paper-based office for the first time. They were in a commodity distribution business, so while the math isn't hard, there is a lot of day-to-day arithmetic (conversion between unit of measure and price/unit vs total price) for all the employees from the warehouse guy to the sales staff.
The system introduced a change in their workflow. Before in their old manual paper system, people just kind of put things on a truck and figure out later how much got shipped and how much to invoice a customer. The whole can be very hand-wavy. There was no live inventory system either.
Digitization meant that sales have to write sales orders that had precise units to be sold. Based on inventory, they know how much they will actually ship and they know that down to the dollar. Everybody suddenly had to start being aware of the math involved in their work.
It was kind of funny to see a bunch of blue-collar, ex-con, high school dropouts learning faster than all the college-education office workers. The college-educated guys were too drill-orientated and approached the work like the math worksheets that everybody is talking about. The ex-cons had a working relationship with the numbers on the screen and the things that are hanging off their forklifts. Many of the white-collar clerks had been getting by memorizing formulas. They had no idea what any of those formulas mean.
Sure, you can drill them. I am just saying you should intermix them with other problems.
I am not telling you to do multiplying digit only 1 times. That would be silly. I would be telling you should mix up multiplying digits with other previously learned concepts, say 10 addition and 10 subtraction questions, and the rest can be 80 multiplying digit problems. I don't know the optimal intermixing ratio here, but it shouldn't be a straight 100 multiplying digit problems which all use the same algorithm to solve it.
Drilling and repetition is good, but there's the danger of having illusory mastery because it's already there in short term memory. Your goal is to encode those skills into long term memory.
> You and I may prefer 20 problems that practice straight subtraction, but that's not what the science says is actually the most effective learning strategy.
Hi, I'm an pedagogue and a licensed teacher. Another way to phrase that, is that humans tend to find repetitive tasks overwhelming and boring. Got a load of dishes you have to do? I bet most people feel right at home in that gnawing urge to postpone that mundane and monotonous task. I mean how many times haven't you sat there with a really dull chore and started daydreaming until someone snapped you out of it?
The fact is, humans need variety, but more importantly we need a sense of agency. You kinda lose that when you're forced to do something repetitive over and over, and so naturally it's not a very effective way to learn or teach.
If you're faced with repeating something 20 times, even with slight variations; first off it's overwhelming, and second if you feel that it's forced on you, then you lose agency. In other words, you're no longer the owner of the task. In turn that means you're no longer in control, so why would you slave away for that "evil" tutor over there? This is why repetition isn't very effective pedagogically speaking, because worst case it can even create antipathy towards you or the task you're trying to teach.
On the other hand, it's exactly repeating something over and over that makes you master it, though... But how can you master a thing when it's too bloody boring to learn in the first place? Enter motivational strategies! And tactics to heighten morale.
This is explains why you may prefer solving 20 problems that practice straight subtraction, because you're already motivated for it, and then it's easy. But when you're dealing with an entire class of pupils, you have to make sure as many of them as possible feel the same way about those tasks, or they'll fall behind. And so, at the most basic level, teachers need to vary their approach to a topic in order to effectively teach it. This means finding new ways, new angles, to look at a problem, and make sure you get some variety in between, so the thing doesn't become boring. Meanwhile, if you already know that your pupils are very motivated, you can get away with more straight repetition.
> But when you're dealing with an entire class of pupils, you have to make sure as many of them as possible feel the same way about those tasks, or they'll fall behind.
One reason this topic is hard to talk about, I think, is that, "what is best for my kid" and "what is the best strategy for a roomful kids from various backgrounds" are often not the same thing; in fact, they can be in direct opposition to one another. Educators think about the latter, naturally, but parents think primarily about the former.
I am of course not an empirical scientist in that area but I tutored math middle school students when in High School. [Note: This was in Germany and not in the US so it wasn't 'common core']
You see, the students who failed at the interleaved problems initially, were rocking it when I had them work through like 3 of these 20-similar problems worksheets before moving on to the 'pedagogically designed' problems.
And epistemically I think it makes a lot of sense to train basics and build upon that.
I think Math education could benefit a lot if we split the subject in two courses, 3h per week on drill (Arithmetics), 2h per week on the beautiful math (can also expose the student to axioms there, functions, mappings, etc, more complex problems and solving that with math, potentially with CAS support). Best separated with different teachers.
Fact is, most high school graduates will find it challenging in their lives to apply the 'rule of three'. During the covid pandemic we have seen that members of the executive branch have no understanding of exponential growth (bad during the pandemic, but I wonder how the fiscal policy is affected by that??).
Maybe we need to rethink mathematical education once again.
I don't know this was how I was taught. Mind numbingly boring rote style in 1-6, them a mix of stuff like reading problems and assignments along with practice assignments, by high school it was fairly even mix of progressively harder problems mixed with "reading problems" and projects (geometry, trig, calculus, diffeq)
Do yourself a big favor and read the book "Why Don't Students Like School?" by Prof. Daniel T. Willingham. He's a prof of psych at the University of Virginia specializing in the application of cog sci and neuro sci to K-12 education.
I don't know who chose the title, but it doesn't describe the book, which is really a collection of articles about the results of experiments comparing various learning & teaching techniques. Only one chapter is about why children, who like learning some things, don't like school.
Willingham publishes in academic journals and in journals for educators, so you can find other writings online. He tries to persuade teachers that so much of what the elite grad schools of education teach is intellectual fashion out of touch with actual cog sci findings, but all he cares about are the science experiments.
The problem with these 20 problems of basically the same identical challenge is that it's actually less effective than intermixing of different kind of problems, at least according to learning science.
You and I may prefer 20 problems that practice straight subtraction, but that's not what the science says is actually the most effective learning strategy.
You want different kind of problems in a problem set. It shouldn't be straight subtraction, but also additions, word problems, and so forth. This creates a level of desirable difficulty, which embeds knowledge more deeply than something that is very easy to do by rote.