I disagree. Memorization, brute force memorization, is how they teach math in places like Korea, Japan and Taiwan. They get to 2297=3007-7 much faster and earlier than American students growing up through the common core system. The memorization method is like language immersion. They are exposed to numbers to the point they start to become fluent in them.
I have heard those exact words “deep understanding” from my kid’s teacher as they tell me that 3 rows of 7 is wrong and 7 rows of 3 is right.
FWIW, the Russian School of Mathematics, a popular after-school program which started in Massachusetts and has now branched out, maintains that, “Memorization is temporary, understanding is forever.” Award Winning Approach to Math Education | RSM This site claims: [INDENT]Yet data from the 13 million students who took PISA tests showed that the lowest achieving students worldwide were those who used a memorization strategy – those who thought of math as a set of methods to remember and who approached math by trying to memorize steps. The highest achieving students were those who thought of math as a set of connected, big ideas.
I’ve already provided a cite for the brute force memorization techniques used in places like korea/taiwan/japan in the singapore article. I also know from personal experience. By 2nd grade you can sing the multiplication tables from 2 to 9 as easily as you sing the alphabet. By 3rd grade you have a reasonably good understanding of what you are singing.
I don’t think there is a study that shows that particular equation being solved by American kids vs Korean/Japanese/Taiwanese kids but it is almost universally agreed that they are better at math. I would bet a lot of money that the average east asian kid will perform better on almost any math test than the average american kid.
A recent study shows that Korean third graders outperformed the U.S. students in creating multiplication word problems, constructing a number sentence to represent a word problem, and identifying real life situations in which they utilize multiplication skills.
U.S. students gave better definitions of multiplication, yet they were not able to apply this knowledge to creating a multiplication word problem and a number sentence that corresponded with the problem.
I am NOT saying that the East Asian method is the best possible method. I think that with a sufficient number of good, teachers a combination of concept and memory would be best. But if I was looking for a method of teaching multiplication that almost any idiot could teach, it would be the Korean/Taiwanese/Japanese method. I don’t know how you could fuck that up.
You keep injecting these statements that imply that I’m just making shit up. Why would I be making shit up? Have you ever seen me bitch about this topic before? I would love for common core to be a universally good thing. In practice, from what I have seen, it seems to be geared towards teaching to the lowest common denominator. It seems to instill a contempt for memorization in the teachers and administrators and “not real teaching” or “not real learning”
There is a Russian School here in Reston and I’m pretty sure they rely on multiplication tables (or "math facts). What it doesn’t do is emphasize memorization of mathematical algorithms. For example, it doesn’t just have kids memorize how to solve quadratic equations, it shows kids why the algorithms for solving quadratic equations works and then kids can apply the algorithm in unorthodox situations. But memorization of the multiplication table does seem to be part of the curriculum.
“Practice multiplication tables! Create a routine: for the first 2 minutes (and no more!) of every trip you take, review the table. Make sure to start with small numbers. In two minutes, you can ask 15 questions! If all answers are delivered within 5 seconds, your child wins!”
The PISA report DOES NOT undermine the notion of memorizing the multiplication tables in favor of gaining some “deeper understanding” of multiplication. It is criticizing the memorization of algorithms. You can teach a kid the 4 steps to solving a quadratic equation but that kid isn’t learning math, they are learning an algorithm.
Your claim is that “brute force memorization is how they teach math in” various countries. If you want to revise you claim to “is one part of how they teach math,” it’s not longer a weird claim.
Actually, there’s some evidence that the United States brings different demographics to the tests–that some countries (China at least) game the system by only offering tests in large cities where the educational infrastructure is stronger.
In any case, Common Core is a response to the perceived superiority of the Singapore/Japanese model, not a cause of the difference. Complaints about how US schools are failing in teaching math go back to at least the days of Sputnik, and the complaints from the 1980s spurred US educational scientists to study what was happening overseas; Common Core is to a large extent the result of their research.
As for your study: did you see that the US students were using a curriculum published in 2001? Do you see the implications for using this study to trash Common Core?
I don’t think you’re deliberately making shit up, but I also don’t think you’re making much effort to give us a rounded and fair account of events. You seem pretty ignorant about what you’re talking about (and this is my wheelhouse, I’ve taught third grade math for 8 years and have been to countless hours of training on Common Core methods and can name-drop theorists in the field and can speak intelligently about different packaged curricula), and more importantly you don’t let your ignorance stop you from opining.
Your latest statement about how it teaches toward the lowest common denominator is a great example. Talk to any teacher about how it goes down: the time when we drop our common core ideology is when we’re dealing with kids who just can’t wrap their brains around math, and as a stopgap measure we’ll teach them the old, easier way, where they just memorize a method instead of building that conceptual understanding. It’s better than nothing, but we’re never satisfied with that as a solution. Common Core’s demands are far, FAR more demanding than the methods traditionally used in US math education.
Hopefully it’s OK to take a tangent, since we’re a long way into the topic.
In the late 60’s, early 70’s I attended a small Catholic grade school in a Minnesota farming community. We learned the times table from 1-9.
The kids in public school (also small), learned 1-12. This struck me as odd at the time (and still does) - if you can do 1-9 and understand how to apply it to calculate 11*12 - what was the point in learning 11 and 12 (10 being simple enough in any case)? Why not go all the all to 20 or some other arbitrary number?
Ok, we’ve established that memorizing times tables is unsurprisingly part of Common Core. Question: are you aware of any school district that believes that memorizing times tables is unimportant?
(I learned my 10x10 times tables in 4th grade. I’m pretty sure multiplication was introduced before I tackled that though. At some point someone nudged me up to 12x12. I’m currently unaware of 13x13. Ok, I just did it in my head. Still.)
Well 10s and 11s are pretty easy. Basically you only have to memorize 11x11=121, and you’ve mastered 2 rows/columns.
How else are you going to know how much are in one gross?
Seriously, I have no idea why they went up to 12. IIRC we were only required to memorize up to 10 but all the printed material we had listed them up to 12.
Even in the dark days of 1980s elementary school, we weren’t expected to memorize them by rote, but to do thousands of practice problems over the course of the school year and memorize them by immersion. Which we did, for the most part.
The common core standards are not new. We were doing the same kind of conceptual stuff back then to learn how arithmetic really works, it just wasn’t as formalized.