# Is this an actual New Math problem? **URL:** \ **Category:** Factual Questions\ **Created:** [August 7, 2017, 10:57pm UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042 "2017-08-07T22:57:05Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![Slash1972](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/slash1972/32/6461_2.png) [@Slash1972](https://boards.straightdope.com/u/Slash1972)\ **Post date:** [August 8, 2017, 1:04am UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/21 "2017-08-08T01:04:18Z")
That seems subjective. I don’t think they are easier. ---
**Author:** ![Isilder](https://avatars.discourse-cdn.com/v4/letter/i/cc9497/32.png) [@Isilder](https://boards.straightdope.com/u/Isilder)\ **Post date:** [August 8, 2017, 1:06am UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/22 "2017-08-08T01:06:39Z")
The first step is listed as 12 -3 , but it should of course be 12 +3 . Whether that was changed on purpose or accidentally, is unknown. It is an example of how someone might use their knowledge of the multiples of 5 to use addition to step through the problem. Any normal person might try to do it that way. They might think, well what do I need to add to 12 ? . If they forget was 20 - 12 is, then they might just see 12+3 = 15. So add 3. then the next step, add 5, and and remember that 3+5 is 8… so then add a few 10’s … Its actually how lots of people might solve the problem, rather than doing it as direct subtraction. But of course, the smarter way is to get close with the 10’s column (hey, add 20 !) and THEN look to see a smart way to solve the ones column… thats 0. There’s nothing wrong with getting kids to practice doing maths this way, because its just an excercise in using the numbers and maintaining accuracy in mathematics… thinking of multiple things at once. While it might appear to be teachig how to do what is obviously to most a simple question a long way, the idea is that you might do it for "76 - 29 " ? 29 is one short of 30… add 40 to get to 70, add 6… so 1 + 40 + 6 = 47. So the picture is not wrong, its a valid way for any intelligent person to do subtraction. Apart from the error with the + being written as a - at the first step. The current trend is for teachers to advise to get toward 10’s and 5’s. But you can do it as “toward 10” only. toward 5’s is the first step because its easier to mentally count a group , and subsets of, five. (eg 2 +3 = 5.) But one would think that rote learning could easily get one to know all the sums to get to 10… 2+3, 3+7, 4+6… Why bother with 5’s ? Thats all the argument is about… whether to rote learn the "add to make 10’s , or do it by counting toward 5’s. And then whether to rote learn the times tables, or just pick it up by usage. ---
**Author:** ![Slash1972](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/slash1972/32/6461_2.png) [@Slash1972](https://boards.straightdope.com/u/Slash1972)\ **Post date:** [August 8, 2017, 1:10am UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/23 "2017-08-08T01:10:46Z")
And you think that is easier than just “Subtract the ones column, then subtract the tens column”? ---
**Author:** ![Malphustes](https://avatars.discourse-cdn.com/v4/letter/m/e9c0ed/32.png) [@Malphustes](https://boards.straightdope.com/u/Malphustes)\ **Post date:** [August 8, 2017, 1:45am UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/24 "2017-08-08T01:45:41Z")
> [@Slash1972](#): > > And you think that is easier than just “Subtract the ones column, then subtract the tens column”? When giving a problem to a student in a math class, the goal of the teacher is not to get the answer. The teacher already knows that 32-12 is 20, and they have no need of using the students as an efficient calculating device. The goal is to teach the students a variety of methods and concepts that they may reapply later when they are needed. Therefore, your method being easier isn’t important in the moment. They’ll be taught your way too. For a metaphor, imagine if the only roads in the US were the interstates. ---
**Author:** ![Slash1972](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/slash1972/32/6461_2.png) [@Slash1972](https://boards.straightdope.com/u/Slash1972)\ **Post date:** [August 8, 2017, 1:56am UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/25 "2017-08-08T01:56:50Z")
See, I think the goal is to teach the easiest method to subtract numbers. For a metaphor, I use Google maps to find the easiest way to a destination, not to explore all the alternate routes. ---
**Author:** ![dropzone](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dropzone/32/7515_2.png) [@dropzone](https://boards.straightdope.com/u/dropzone)\ **Post date:** [August 8, 2017, 2:25am UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/26 "2017-08-08T02:25:31Z")
> [@AlsoNamedBort](#): > > And yes, it should be plus 3, not minus 3. It looks like whoever made this image didn’t realize that the vertical line on the plus sign was covered up by the box. No, because the box is nowhere near the -. What’s missing is another - in front of the 3: 12 - [-3]=15 (brackets represent the box) ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [August 8, 2017, 2:42am UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/27 "2017-08-08T02:42:50Z")
> [@Slash1972](#): > > See, I think the goal is to teach the easiest method to subtract numbers. “Easy” is relative. For this particular problem, yes, I think the usual method is easiest. But once you get to stuff like 35-17, all bets are off for me. I like doing it the way I was taught, which was with borrowing tens and all that, but the “counting up” method must be easier for the majority of people, given how almost everybody who works in retail and handles money seems to “count up” when giving change. Honestly, I never understood it myself, since when I was handling money, I would just subtract the “normal” way and not bother with the counting up stuff, but a lot of people seemed to find that easier. That’s perfectly fine with me, as long as they get to the right answer. ---
**Author:** ![Some\_Call\_Me.Tim](https://avatars.discourse-cdn.com/v4/letter/s/439d5e/32.png) [@Some\_Call\_Me.Tim](https://boards.straightdope.com/u/Some_Call_Me.Tim)\ **Post date:** [August 8, 2017, 2:43am UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/28 "2017-08-08T02:43:06Z")
> [@Chronos](#): > > How old are you two? Because if you’re under about 50, then you are familiar with New Math, because it’s what you were taught in school. New Math is a bit older than that. Tom Lehrer was [satirizing it](https://www.youtube.com/watch?v=samZhaDravI) in 1964, and Peanuts did [a strip](http://www.gocomics.com/peanuts/2012/10/02) on it in 1965. So, if you were born after 1960 or so it’s likely what you saw in school, so the age border is more like 57 or so. ---
**Author:** ![Slash1972](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/slash1972/32/6461_2.png) [@Slash1972](https://boards.straightdope.com/u/Slash1972)\ **Post date:** [August 8, 2017, 2:46am UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/29 "2017-08-08T02:46:48Z")
> [@pulykamell](#): > > “Easy” is relative. For this particular problem, yes, I think the usual method is easiest. But once you get to stuff like 35-17, all bets are off for me. I like doing it the way I was taught, which was with borrowing tens and all that, but the “counting up” method must be easier for the majority of people, given how almost everybody who works in retail and handles money seems to “count up” when giving change. Honestly, I never understood it myself, since when I was handling money, I would just subtract the “normal” way and not bother with the counting up stuff, but a lot of people seemed to find that easier. That’s perfectly fine with me, as long as they get to the right answer. I haven’t seen anybody in retail not use what the register says to count change. Have you seen many people using their brain to calculate change? ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [August 8, 2017, 2:57am UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/30 "2017-08-08T02:57:28Z")
> [@DPRK](#): > > (btw if you hate subtraction, just complement the number: 32-12 becomes 32+88, 92-5 becomes 92+95, is my advice) That’s kinda what I was thinking in the OP, the [complements](https://en.wikipedia.org/wiki/Method_of_complements) method. Or the way my old Commodore 64 treated 256 as -254 in some instances. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [August 8, 2017, 3:00am UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/31 "2017-08-08T03:00:41Z")
> [@Some\_Call\_Me.Tim](#): > > New Math is a bit older than that. Tom Lehrer was [satirizing it](https://www.youtube.com/watch?v=samZhaDravI) in 1964, and Peanuts did [a strip](http://www.gocomics.com/peanuts/2012/10/02) on it in 1965. > > So, if you were born after 1960 or so it’s likely what you saw in school, so the age border is more like 57 or so. Born 1961, about all I remember is base 8 and some Venn diagrams. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [August 8, 2017, 3:50am UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/32 "2017-08-08T03:50:34Z")
> [@Slash1972](#): > > I haven’t seen anybody in retail not use what the register says to count change. Have you seen many people using their brain to calculate change? Yes. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [August 8, 2017, 4:05am UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/33 "2017-08-08T04:05:47Z")
> [@Slash1972](#): > > See, I think the goal is to teach the easiest method to subtract numbers. > > For a metaphor, I use Google maps to find the easiest way to a destination, not to explore all the alternate routes. Define “easiest”. It may be easiest for you but what if someone else finds another method easier? For a metaphor, I use Google Maps to find _a_ route to a destination, then I use my own knowledge and experience to modify it so that it suits me. Personally, I would almost always subtract using the old fashioned method, but I recognise that other methods are valid and may be easier to “grok” for some kids. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [August 8, 2017, 4:07am UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/34 "2017-08-08T04:07:04Z")
> [@dropzone](#): > > No, because the box is nowhere near the -. What’s missing is another - in front of the 3: 12 - [-3]=15 (brackets represent the box) No, in the [original](http://www.patheos.com/blogs/friendlyatheist/2014/03/07/about-that-common-core-math-problem-making-the-rounds-on-facebook/) the box is obscuring the +. ---
**Author:** ![suranyi](https://avatars.discourse-cdn.com/v4/letter/s/e36b37/32.png) [@suranyi](https://boards.straightdope.com/u/suranyi)\ **Post date:** [August 8, 2017, 4:22am UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/35 "2017-08-08T04:22:02Z")
> [@Slash1972](#): > > See, I think the goal is to teach the easiest method to subtract numbers. > > For a metaphor, I use Google maps to find the easiest way to a destination, not to explore all the alternate routes. My wife is an elementary school teacher, and she has learned from experience what people in this thread have been saying: What seems obviously the easiest method for you is not always the easiest method for every kid. ETA: How do you think Google maps works? I used to work on mapping software very similar to Google maps, and I can tell you it did explore alternate routes. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [August 8, 2017, 4:31am UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/36 "2017-08-08T04:31:11Z")
Next we’ll be arguing what method to teach the kids to use for extracting square and cube roots… ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [August 8, 2017, 4:41am UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/37 "2017-08-08T04:41:35Z")
(Cf. Feynman vs The Abacus: ) > [@](#): > > I realized something: he doesn’t _know_ numbers. With the abacus, you don’t have to memorize a lot of arithmetic combinations; all you have to do is to learn to push the little beads up and down. You don’t have to memorize 9+7=16; you just know that when you add 9, you push a ten’s bead up and pull a one’s bead down. So we’re slower at basic arithmetic, but we know numbers. ---
**Author:** ![bob\_2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bob_2/32/3341_2.png) [@bob\_2](https://boards.straightdope.com/u/bob_2)\ **Post date:** [August 8, 2017, 12:11pm UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/38 "2017-08-08T12:11:14Z")
> [@pulykamell](#): > > “Easy” is relative. For this particular problem, yes, I think the usual method is easiest. But once you get to stuff like 35-17, all bets are off for me. To illustrate the way that different people solve problems; When I looked at that, I immediately saw that 35 is twice 17 plus one, so the answer must be 18. When I was at school (in ye olden days) we learned tables (up to 12 times) by rote and I still remember them. We also had to learn the squares up to 12 squared and memorise the prime numbers up to 100. If you are wondering why “12”; it was because at that time there were 12 pennies to a shilling and 20 shillings to a Pound. Forty years later, my daughter never learned tables. She calculated them in her head by simple addition - not quite as fast as remembering, but nearly. Of course by that time we had 100 new pennies to the pound. ---
**Author:** ![Slash1972](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/slash1972/32/6461_2.png) [@Slash1972](https://boards.straightdope.com/u/Slash1972)\ **Post date:** [August 8, 2017, 12:29pm UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/39 "2017-08-08T12:29:21Z")
> [@suranyi](#): > > My wife is an elementary school teacher, and she has learned from experience what people in this thread have been saying: What seems obviously the easiest method for you is not always the easiest method for every kid Fair enough I guess. Hard to answer MY kids though when they ask me “Why do we have to do this stupid way of subtracting?” > [@](#): > > ETA: How do you think Google maps works? Some form of magic? ---
**Author:** ![naita](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/naita/32/5862_2.png) [@naita](https://boards.straightdope.com/u/naita)\ **Post date:** [August 8, 2017, 1:20pm UTC](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042/40 "2017-08-08T13:20:09Z")
> [@Slash1972](#): > > That may be. But they are not teaching kids to convert to binary or octal and then adding. Aren’t they ways to solve problems? Why this way? Just seems like a lot more work for little gain. This way is really good for some problems, such as what is 111-98. And learning both this and subtracting in columns with borrowing increases the number of kids who walk out of class understanding how and why 111-98 is 13, which is important. At every stage of the way you run the risk of some kids walking out with only the ability to do the ascribed math problems with a rote learned algorithm, and those kids are on a path to innumeracy. [Previous page](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042.md?page=1) [Next page](https://boards.straightdope.com/t/is-this-an-actual-new-math-problem/793042.md?page=3)