I think I just had one of those dawning moments of recognition re: all the worksheets I did in first grade circling groups of coins in 5, 10 and 25 increments.
It’s also quite laborious to move 40 lbs. of gravel with a child’s beach bucket and shovel.
For what it’s worth, the New Math method in the Tom Lehrer song makes complete sense to me and the old way he mentions at the beginning may as well be witchcraft for all I understand it.
Exactly.
Most people who complain about the Common Core have never read it. In fact, I’d be surprised if more than a couple of people on this thread have even read it. I’m pretty sure the self-righteous bitchers on Facebook haven’t read it.
I’m going to assume for the sake of illustration that this exercise (in the OP) is from the 5th grade. Here is the actual, 5th grade, Common Core standard regarding the kind of math which I believe is represented by the exercise in the OP:
[QUOTE=Common Core on 5th grade math]
Understand the place value system.
Recognize that in a multi-digit number, a digit in one place represents
10 times as much as it represents in the place to its right and 1/10 of
what it represents in the place to its left.
Explain patterns in the number of zeros of the product when
multiplying a number by powers of 10, and explain patterns in the
placement of the decimal point when a decimal is multiplied or
divided by a power of 10. Use whole-number exponents to denote
powers of 10.
Read, write, and compare decimals to thousandths.
a. Read and write decimals to thousandths using base-ten numerals,
number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 ×
10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
b. Compare two decimals to thousandths based on meanings of the
digits in each place, using >, =, and < symbols to record the results
of comparisons.
Use place value understanding to round decimals to any place.
Perform operations with multi-digit whole numbers and with
decimals to hundredths.
Fluently multiply multi-digit whole numbers using the standard
algorithm.
Find whole-number quotients of whole numbers with up to four-digit
dividends and two-digit divisors, using strategies based on place
value, the properties of operations, and/or the relationship between
multiplication and division. Illustrate and explain the calculation by
using equations, rectangular arrays, and/or area models.
Add, subtract, multiply, and divide decimals to hundredths, using
concrete models or drawings and strategies based on place value,
properties of operations, and/or the relationship between addition and
subtraction; relate the strategy to a written method and explain the
reasoning used.
[/quote]
That’s it. That’s the Common Core.
There are some others for geometry, etc., but they’re similar in character. Most decent school programs were probably already teaching these things before Common Core anyway. Common Core is more like a checklist for states to use–on a voluntary basis–so that there is consistency between them.
It doesn’t mandate any specific problems, or tell teachers how to design them. It doesn’t say anything that would force a teacher to give an exercise like in the OP. If that exercise is a problem, the problem is not with the Common Core, but with a lack of teacher training at whatever district came up with it.
There are clearly some problems–in some states–with the way Common Core has been implemented, and as Jragon says, the textbook industry has often exploited the situation with bad results. Also, an argument can be made that having such standards will inevitably lead to unhealthy administration. Okay, that may be.
But the problems have nothing to do with the standards in Common Common themselves.
Looking a bit ahead into the higher grades: Last year, I tried helping a 10th-grade kid with his Algebra I. That was a total fail: The kid was a dunce and had zero interest or aptitude at it, and was living in a dysfunctional family.
But what caught my interest was the abomination of a textbook: As far as I could tell, it was hardly better than a Schaum’s Outline in its presentation of the material, and had very limited problem sets – and it was all explicitly designed to “Teach to the Test” – the Common Core Test, apparently.
The organization was awful. A normal Algebra I text would certainly teach special products and factoring before teaching quadratic equations – since you use factoring to solve quadratics and also to develop the Quadratic Formula. But no, this book taught quadratics first, showing the Quadratic Formula (by rote, just memorize this, we’ll get to the theory later). The chapter on special products and factoring was later, near the end of the book. :smack: I thought the workers at the bindery must have dropped some chapters on the floor, and then reassembled them in the wrong order.
And who wrote this monstrosity of a book? Why, none other than Roland Larson et al, who have been writing math textbooks (and excellent ones, too) since forever. I learned Calculus I from Larson, 2e, way back in 1984, and it was an excellent text. I was disappointed to see that he had prostituted himself to write this trashy Common Core algebra text. I couldn’t have learned algebra very well from it.
I understand the argument, but it seems a bit inefficient compared to a mechanical procedure that’s the same for every situation. I’m not a teacher, but I sometimes think the “old” new math as taught in the middle of last centuy might have been better for me as an elementary school pupil. We did have a very diluted helping of that era’s New Math, but I never saw any meaningful visual aids like the proportionately sized number rods which could be used to concretely illustrate how basic algebraic expressions can be factored and evaluated. Some years ago, I picked up a copy of the old Time Life book Mathematics which includes an appendix discussing New Math; and it seemed like everyone was raving about it. ES pupils were protesting loudly if the teacher tried to skip the day’s math lesson. College instructors were quoted to the effect that arriving freshmen were much better prepared in math than formerly; I was surprised to learn that New Math had been going on long enough at that time for college students to have benefited from it. As one who struggled with math all through school, I wonder where that whole New Math thingy went pear shaped.
What do you mean by “just adding the numbers together”? What are you actually doing when you do that?
I suspect it’s as UDS said: you mean “using the method I learned.” But they’re both methods, and just because you’ve already gotten used to one of them doesn’t automatically make it better or more natural.
I don’t think the listed authors of gradeschool textbooks are usually the actual authors. There was an author who wrote the first (or first few) editions, but subsequent editions are basically revisions (or complete rewrites) done by someone else (or more likely a bunch of people working together). Kind of like “Webster’s” Dictionary.
Moreover, it is really doubtful that Johnny LA or anyone else does what he describes as “just adding the numbers together” when faced with the prospect of, for example, adding 2 to 998. In fact, he probably uses exactly the method depicted in the image in the OP when putting together numbers like those.
Old method of adding numbers like 36263 + 72639 would be [3+7 = 10][2+6 = 8][6+2 = 8][6+3 = 9][3+9 = 12] (to me) and then I’d just move any extras over, so [10][8][8][10][2] and then [10][8][9][0][2] which gives me 108902, which is correct. This new method seems really very complicated when numbers get larger. The old method requires you to add single digits for each decimal place and then at most carry over the same number of times. The new math seems to require you to figure out how to break the numbers down first which is just silly.
The really funny part is that a lot of the conservatives who are complaining about the New Math, and want things taught the old-fashioned way they learned it… For a lot of them, the old-fashioned way they learned it is the New Math, and they just don’t remember it. For instance:
If you’re in your late 40s, then you were born some time after 1965, and started school some time after 1970, by which time the New Math was in full swing.
That’s one of the ways that I learned how to multiply in elementary school the early 1980s, and we had old textbooks. So if “new fangled” means “at least 30-40 years old,” then yes, yes I have. I liked it because I liked drawing rectangles. It also gave me a better understanding of how the numbers fit together.
But to the problem in the OP, I wouldn’t add those particular numbers in my head using that method - but there are other problems that I would do that. It’s a good skill to have. I once astounded grown, college educated adults by adding a column of numbers using the associative and commutative properties of addition. Hopefully, a kid who learns this method will learn that 37+53=30+50+3+7=37+3+50 =53+7+30 = 60+30-7+7 = any number of combinations, understand why that’s true, and will be able to get to the answer using whichever method is easiest for them.
87 + 93.
93 + 7 = 100, + 80 = 180.
Why bring subtraction into it? And:
225 + 331
25 + 31 = 56, + 200 + 300 = 556
I see what they’re doing in the new method, but I don’t see the point in all of the tens. You can see that 25 + 31 is 56 just by looking at it. Why go to the trouble of breaking 31 into 10 + 10 + 10 + 1?
I’m short on time at the moment, so I’ll watch the video and read the other responses later.
I added bolding to the particular part I’m responding to. I watched a video on open-area, too. And it seemed very cumbersome to me. But my cousin’s child, who is learning it, loved open area. My cousin, who is a teacher, said she teaches the kids five different ways to multiply, but the majority of them prefer the open-area method. Just an anecdote to contribute.
I really do think many of us (the general population) get stuck on the idea that the way we learned is best (at least if we succeeded in learning it). We were taught that way, and it was reinforced with years of schooling, so that way becomes the default and seems “intuitive” to us, even if it’s really more that it’s just familiar. Like the start menu on Windows.
However, my understanding is that common core is more about what children should learn (how to multiply two-digit numbers by grade X) instead of how they should learn it.
As an aside, I loathed word problems in school, but as an adult I think they are the best way I can think of to make sure students understand how to apply the math/science (momentum, acceleration, etc.) that they are learning to real-world situations.
For what it’s worth, the OP’s example seems to me more in line with the Common Core standard regarding Grade 1 for Numbers & Operations in Base Ten, this part of the standard being as follows:
Perhaps also it goes beyond the grade 1 standard of “Add within 100… using concrete models or drawings”, to the grade 2 standard of “Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.”.
I think you were agreeing with Indistinguishable here. He was advocating for the importance of being able to manipulate numbers in your head, and asking why we should stress only the old-fashioned way of doing addition.
Interesting article. Although it does not answer the ‘how to’ question in the OP (which has been answered) it’s nice to know that Common Core defines what kids should know and not how they come to know it.
I learned my arithmetic in the 60s - and 53+30+7 is how we did it then. What is “new” about it?
Isaac Asimov wrote “Quick and Easy Math” in 1964. It contains many of the same tips being described in this thread. They aren’t new ideas. They weren’t even back then.
53 + 37 is
53 + 40 = 93 then
93 - 3 = 90.
That’s the way I was taught to do this stuff back in the 40s when calculators were slide rules.
Same idea really - break the sum down into manageable chunks to make it easy.
I don’t know why, but if I have a long multiplication on paper, I start from the right:
356 x 45 on paper would mean multiplying by 5 and then by 40 and adding the results. To do it in my head, I multiply 356 by 4 and add a zero, then add 4 x 45.
My kids learned the Distributive Property (and related concepts, like the Associative Property and Identity Property) in 4th grade - which by my recollection is at least several years before I was taught them. My fifth grader was doing homework last night which was basic algebra, which I wasn’t introduced to until 7th grade. It seems to me that the new methods of teaching have allowed my kids to learn the advanced concepts faster than I did 35 years ago.
FWIW, Morgenstern’s method is exactly how I do it in my head. I’d add 100 and subtract 7. That’s by far the quickest and least prone to error for me. Others may find other methods easier.