> But drill isn’t popular. It’s widely seen as boring. Worse, there’s a body of opinion, especially in education, that considers it an ineffective way to practice. That’s a shame, because it’s the most effective way to build your skills. This resonated with me as I watch my kids go through school. Math used to be taught with more drill style. Now with common core every single problem is an epic quest of 10 frames and…
Math teaching has never been successful. Nobody knows why we do it. The parents all learned it the old way, meaning that they got good test scores but did not retain any useful facility with math beyond their obligatory high school and college courses. A few people who managed to carry math to the level of being an art, like painting, probably can't tell you how or why that happened. My kids did lots and lots of dril…
How to get better at painting without painting anything (2015)
161–170 of 170 posts
Re: How to get better at painting without painting anything (2015)
#162Earlier quoted context omitted.
Math teaching has never been successful. Nobody knows why we do it. The parents all learned it the old way, meaning that they got good test scores but did not retain any useful facility with math beyond their obligatory high school and college courses. A few people who managed to carry math to the level of being an art, like painting, probably can't tell you how or why that happened. My kids did lots and lots of dril…
A Mathematician's Lament (A Mathematician’s Lament): https://www.maa.org/external_archive/devlin/LockhartsLament.... is an outstanding article on the topic.
Even the useful side of math -- the stuff supposedly taught in service to the science and engineering courses -- is taught with a computer nowhere in sight. Yet people who use math in those fields, including myself, always do it with the assistance of a computer, whether it's to help avoid dumb mistakes or to automate tasks involving large amounts of numbers. And the physics problems that can really be solved with purely symbolic math are few and far between, and rather contrived. It actually leads students to believe that the formulas are false when applied in the real world.
I don't think teaching computation would harm the handful of students who develop an interest in math as a liberal art. If they want to explore, they will, either on their own or with guidance. There's no reason why they can't be introduced to abstract math, and proofs, along the way.
Re: How to get better at painting without painting anything (2015)
#163Earlier quoted context omitted.
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 cha…
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…
Re: How to get better at painting without painting anything (2015)
#164Earlier quoted context omitted.
> The person who drills 90% of the time and spars 10% will pretty much always beat the reverse person IMO this is true for beginners, then more and more the other way around. > Sparring is for practicing skills under real conditions. If you don't have those skills, there's nothing to practice I agree, and wrote "sparring becomes more and more determinant as technical flaws become more rare".
Kind of true, but for pros, sparring is also a drill. Normally a sparring session focuses on a specific thing they'd like to work on, because they've mastered everything they can outside of the ring. They aren't doing a full "performance" during sparring.
Re: How to get better at painting without painting anything (2015)
#165Earlier quoted context omitted.
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 cha…
> 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…
It's not about whether it's boring or not when it comes to intermixing versus blocked practice.
It's that intermixing require more thought and thinking rather than just following steps by rote.
Re: How to get better at painting without painting anything (2015)
#166Earlier quoted context omitted.
I don't personally do katas, but I would recommend them. As a disclaimer, I've written a research paper on the use of typing exercises to help learn CS [1]. For typing exercises, I consider it akin to building muscle memory at getting comfortable with code syntax with a variety of examples. I look at katas in a simple fashion, small scale problems designed to get you comfortable with building mental models in your he…
Interesting! There's a SaaS that let's you do this https://typing.io/
Re: How to get better at painting without painting anything (2015)
#167Earlier quoted context omitted.
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 cha…
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 ep…
Re: How to get better at painting without painting anything (2015)
#168> But drill isn’t popular. It’s widely seen as boring. Worse, there’s a body of opinion, especially in education, that considers it an ineffective way to practice. That’s a shame, because it’s the most effective way to build your skills. This resonated with me as I watch my kids go through school. Math used to be taught with more drill style. Now with common core every single problem is an epic quest of 10 frames and…
This comment has engendered a lot of responses. Some arguing a position on personal experience and others arguing the supposed science of learning. A different and perhaps useful way to look at this is to consider how outcomes differ between large groups of schools around the world following different strategies for teaching math.
The Program for International Student Assessment does world wide testing of 15 year olds in mathematics (and other subjects as well). The evidence suggests that whatever the US is doing isn't working. The USA ranks 25th in 15 year olds' mathematical ability with overall scores far lower that many other countries.
Unfortunately, I can't read Mandarine, Japanese, Korean or Estonian so most of the effective text books (based on the PISA student scores) are inscrutable to me. However, Singapore's students have always scored near the top in math (second place in the most recent tests) and their text books are in available in English.
I used Singapore math books to help my daughter improve her math after her school switched to Everyday Mathematics, a typical US math program developed at the University of Chicago. It wasn't terrible, but it wasn't good.
The Singapore Math books are quite small and printed in black in white. They introduce the concepts with diagrams, etc. and have a set of easy introductory exercises to make sure the students understand the concepts. The books then have harder problems using the concepts and include word problems. The focus is on learning and practicing the techniques of mathematics. In Singapore Math, there is rote learning going on; in Everyday Math there is a kind of impressionistic emphasis where alternative approaches are encouraged, unusual methods of computation are introduced, inefficient solutions are treated as just as valuable as better approaches, and calculators replace fluency with basic operations.
I've read the research paper the Everyday Math web site uses to justify the principles underlying the program. It's garbage and not any sort of science of learning. It even cites Knuth's Art of Computer Programming: Searching and Sorting as justification for introducing multiple non-standard ways to perform subtraction, multiplication, and division to elementary school children. This is completely ridiculous.
Re: How to get better at painting without painting anything (2015)
#169Earlier quoted context omitted.
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 cha…
> 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…
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.
Re: How to get better at painting without painting anything (2015)
#170Imho he did not be became better at "painting" but he made better designs for paintings . He trained one important aspect of the whole piece of art, the design. The aspect of applying paint was not trained, so that probably has not improved.
A skilled painter isn't just someone who is good at applying paint the way he wants, similarly as how a skilled writer isn't just someone who writes the words he intends to write. The skill includes all aspects required to make great pieces.