# What Common Core math technique was that check mocking? **URL:** \ **Category:** Factual Questions\ **Created:** [September 21, 2015, 11:28pm UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162 "2015-09-21T23:28:16Z")\ **Posts on this page:** 20\ **Page:** 4
**Author:** ![griffin1977](https://avatars.discourse-cdn.com/v4/letter/g/977dab/32.png) [@griffin1977](https://boards.straightdope.com/u/griffin1977)\ **Post date:** [September 22, 2015, 11:10pm UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/61 "2015-09-22T23:10:27Z")
> [@Frylock](#): > > [Here](http://www.patheos.com/blogs/friendlyatheist/2015/09/21/the-dad-who-wrote-a-check-using-common-core-math-doesnt-know-what-hes-talking-about/) is a nice blog post explaining why the dad who wrote that check doesn’t know what he’s talking about. That link just came up on my Facebook feed and is the first article from the dozens I have seen discussing this that ACTUALLY talks about the technique he is meant to be criticizing (and answers my OP): > [@](#): > > Herrmann, in particular, was frustrated with something called “ten-frames.” What are those? They’re a handy way to think about numbers in groups of ten. . > [@](#): > > Those are ten-frames. They’re really neat. And they’re a nice way to show little kids how to count in different ways. . > [@](#): > > So let’s go back to Herrmann’s “Common Core” check and see if we can make sense of it. > > Nope. Still really dumb. > > That place on the right, where you’re supposed to write the check amount? He uses a ten-frame with only eight boxes. But technically, I guess it says $8.43. ($8 from the eight boxes, 40 cents from the four circles, and 3 cents from the three x’s.) At least that’s what I’m assuming since the circles and x’s are his own creations. > > That line where you’re supposed to write in the amount? There’s a properly filled-in ten-frame, followed by four circles, and three x’s. So I guess that’s $10.43. > > It’s a good thing he didn’t submit the check since he couldn’t even write out matching amounts. ---
**Author:** ![Joey\_P](https://avatars.discourse-cdn.com/v4/letter/j/919ad9/32.png) [@Joey\_P](https://boards.straightdope.com/u/Joey_P)\ **Post date:** [September 22, 2015, 11:28pm UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/62 "2015-09-22T23:28:51Z")
> [@Frylock](#): > > **JoeyP** , you _majored in math in college_. Your reaction to not understanding what you’re seeing should be _embarrassment_ > \ > Honestly? It’s not that hard. If you don’t understand it after a little poking around to find out what’s up, the simple fact is, you don’t know how to do math. You know how to run some algorithms, but you don’t understand numbers. Majored-in-math or no. Yup, you’re right. I’m an embarrassment and I don’t know how to do math. Derp, what’s 2 x 4 xxxx xxxx it’s 8 right? Nope, sorry, that’s incorrect, the correct answer is xx xx xx xx = 8. BTW, maybe it’s possible, just possible that as someone who spent years studying math in college I actually do know what I’m talking about. Don’t get me wrong, this is grade school arithmetic, I think most of us know what we’re talking about, but criticizing me like that was kind of an asshole move. Gee golly, don’t know how I ever made it though mulitvariable calculus or non-euclidean geometry or differential equations. BTW, you’ll note that near the beginning of this thread I even mentioned that the way the check was written it was probably gibberish anyways, just to make it look needlessly complex. I never sided with him and even said he was hurting his cause. Frylock, I’ll ask you the same thing I asked the others. Do you have young kids? Are you a parent to someone going though this right now? It’s not about ‘well I would just google it’, I can do that, I have done that, but if you google it and do a little differently than the teacher wants/expects, it’s still wrong. But thanks for playing (maybe next time try not to tell me what I do and don’t know). ---
**Author:** ![slash2k](https://avatars.discourse-cdn.com/v4/letter/s/439d5e/32.png) [@slash2k](https://boards.straightdope.com/u/slash2k)\ **Post date:** [September 22, 2015, 11:34pm UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/63 "2015-09-22T23:34:57Z")
> [@Joey\_P](#): > > It’s not about ‘well I would just google it’, I can do that, I have done that, but if you google it and do a little differently than the teacher wants/expects, it’s still wrong. But thanks for playing (maybe next time try not to tell me what I do and don’t know). THAT, however, means your kid has a teacher who is a dolt (or, possibly more likely, a curriculum supervisor who is a dolt). That’s got nothing to do with Common Core, because a dolt is going to be a dolt no matter what pedagogy they follow or what curriculum they’re handed. ---
**Author:** ![Joey\_P](https://avatars.discourse-cdn.com/v4/letter/j/919ad9/32.png) [@Joey\_P](https://boards.straightdope.com/u/Joey_P)\ **Post date:** [September 22, 2015, 11:51pm UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/64 "2015-09-22T23:51:19Z")
Know what, I’m bowing out. My kid’s teacher’s have been insulted. My kid’s school/district/board have been insulted. But most of all, the crack about me not knowing math had jackshit to do with this thread. Clearly I’m the only person that doesn’t like whatever it is that’s going on and I can’t argue my side all by myself against everyone else who thinks the system is in perfect working order. Many (most?) of you who don’t have current first hand knowledge of it. As I said before, I encourage you to go talk to parents of young kids and see how they feel. Talk to teachers and see what they have to say. In fact one teacher chimed in and blamed the mess on CC. I’ve swayed and given in to the possibility that this might not be 100% the result of CC, but I don’t know yet. The teachers I know complain more about CC than about anything else. Anyways, I can’t do it anymore. Whatever the problem is, whoever is to blame, I’m not changing it on my own, all I can do is help my kid get through it as best as I can (gonna be tough though, since I don’t know how to do math. Hopefully I remember how to read). ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 22, 2015, 11:58pm UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/65 "2015-09-22T23:58:32Z")
> [@Joey\_P](#): > > Know what, I’m bowing out. > > My kid’s teacher’s have been insulted. > My kid’s school/district/board have been insulted. Aren’t you the one arguing the teachers/school are being unduly obstinate about things like “2 x 4 must be counted via 4 rows and 2 columns rather than 2 rows and 4 columns”? That other posters agreed with you that this was foolish seems an odd reason for you to get upset. ---
**Author:** ![slash2k](https://avatars.discourse-cdn.com/v4/letter/s/439d5e/32.png) [@slash2k](https://boards.straightdope.com/u/slash2k)\ **Post date:** [September 23, 2015, 12:03am UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/66 "2015-09-23T00:03:54Z")
> [@Joey\_P](#): > > Know what, I’m bowing out. > > My kid’s teacher’s have been insulted. > My kid’s school/district/board have been insulted. > > But most of all, the crack about me not knowing math had jackshit to do with this thread. > > Clearly I’m the only person that doesn’t like whatever it is that’s going on and I can’t argue my side all by myself against everyone else who thinks the system is in perfect working order. Many (most?) of you who don’t have current first hand knowledge of it. As I said before, I encourage you to go talk to parents of young kids and see how they feel. Talk to teachers and see what they have to say. In fact one teacher chimed in and blamed the mess on CC. I’ve swayed and given in to the possibility that this might not be 100% the result of CC, but I don’t know yet. The teachers I know complain more about CC than about anything else. > > Anyways, I can’t do it anymore. Whatever the problem is, whoever is to blame, I’m not changing it on my own, all I can do is help my kid get through it as best as I can (gonna be tough though, since I don’t know how to do math. Hopefully I remember how to read). No, you’re not the only person who doesn’t like what’s going on. There is a problem here that needs addressing. The system is not remotely in perfect working order. However, in order to address the problem, you need to understand what the problem is. Blaming CC for something that has basically nothing to do with CC does not in any way address the problem. Talk to those teachers again. Ask them if the problem is Common Core or [commoncore.org](http://commoncore.org) (which are not even close to the same thing). Ask them why they are placing emphasis on form (doing it just like the teacher wants) rather than comprehension. Ask them who picked out those particular worksheets and why. Ask them how much emphasis their administration puts on test scores. Ask them to what extent they dislike the standards versus their administration’s implementation of the standards. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [September 23, 2015, 12:23am UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/67 "2015-09-23T00:23:13Z")
> [@Indistinguishable](#): > > The only difference is that in the New Math part of the song, there is some explanation as to why this borrowing is conceptually appropriate, as well as a second verse in which the example is worked out in base eight (illustrating that there’s nothing special about ten for the concepts)\*\*. I learned basic grade-school arithmetic the Old Math way in the early 1960’s, and we certainly DID learn about why carrying and borrowing works. We learned about place values. We learned that a 1 in the ten’s place becomes a 10 in the one’s place (borrowing). It was actually taught and explained as part of the practical process. The problem with New Math, in all its editions and versions and incarnations, lays in how overly abstract it’s made. In another thread about New Math a while back (maybe I will search it up and link), I pointed out how “negative numbers” were taught in my New-Math-ish Algebra I class, complete with an abstract incomprehensible definition of “additive inverses”, given without any motivation (that’s why it’s abstract) that looked like something a lawyer would have written. I wrote about the importance of learning the Five Fundamental Laws of Arithmetic, only to hear that other posters – some of the same mathematically-savvy posters who are in this thread – didn’t even know that phrase. ETA: Here it is. [http://boards.straightdope.com/sdmb/showthread.php?p=18638477](http://boards.straightdope.com/sdmb/showthread.php?p=18638477) Check it out. The present thread, in large part, overlaps with that thread. ---
**Author:** ![Measure\_for\_Measure](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/measure_for_measure/32/557_2.png) [@Measure\_for\_Measure](https://boards.straightdope.com/u/Measure_for_Measure)\ **Post date:** [September 23, 2015, 1:17am UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/68 "2015-09-23T01:17:25Z")
> [@Joey\_P](#): > > Know what, I’m bowing out. > > My kid’s teacher’s have been insulted. > My kid’s school/district/board have been insulted. > > But most of all, the crack about me not knowing math had jackshit to do with this thread. Woah. I got your point about 5x2 vs 2x5 arrays. But ISTM that your school’s teachers and board are deflecting blame for their own poor curriculum. Common core doesn’t set curriculums. It’s basically a freaking standardized test given at the end of the year. If your school is teaching to the test, you might reflect upon where the problem lies. ---
**Author:** ![Fair\_Rarity](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/fair_rarity/32/153_2.png) [@Fair\_Rarity](https://boards.straightdope.com/u/Fair_Rarity)\ **Post date:** [September 23, 2015, 2:20am UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/69 "2015-09-23T02:20:53Z")
My kid couldn’t subtract 6 from 10 the other day (2nd grade) without filling out the ten frame. Rote memorization is boring and not for everyone, but like… I think that level of problem should be just rolling off the tongue for your average 2nd grader, not something that has to be calculated with dots. Maybe rote memorization and doing it over and over isn’t always a fail for every kid. I mean, yeah sure, it’s great to be able to figure out how to answer a problem without knowing the answer from memory, but sometimes you just have to be faster. Maybe that comes in 3rd grade. And I know it’s not Common Core that’s necessarily the problem and the books we use at our school, but ugh. I was not a math major, but I was always in the highest level math class and I can’t figure this stuff out when it comes home. The sheets we get are so wordy. Plus there is a lot of gender bias in the math (lots of trucks and “boy” toys in the convoluted word problems which just alienates some girls. Can’t put in flowers and princesses, apparently, because it’s worse to alienate boys). I helped with my niece’s geometry last year. I was the only adult who could even understand the problem. I pulled out theorems out of dusty corners of my brain that I forgot even existed. I sweated blood and tears over that thing. I got the right answer. It was marked wrong. She turned it in with all the right numbers for lengths and areas, but we solved it “wrong”, even though she showed her work. Like… a right answer is a right answer, ok? (I did not do the HW for my niece. I pored over the problem to figure out the answer myself, then I asked her questions to guide her through it, like “if this angle is 90, what does that tell you about that side?” kind of things and checked her math when she was done). ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [September 23, 2015, 2:25am UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/70 "2015-09-23T02:25:11Z")
> [@Fair\_Rarity](#): > > My kid couldn’t subtract 6 from 10 the other day (2nd grade) without filling out the ten frame. Rote memorization is boring and not for everyone, but like… I think that level of problem should be just rolling off the tongue for your average 2nd grader, not something that has to be calculated with dots. Maybe rote memorization and doing it over and over isn’t always a fail for every kid. I mean, yeah sure, it’s great to be able to figure out how to answer a problem without knowing the answer from memory, but sometimes you just have to be faster. Maybe that comes in 3rd grade. You think that’s bad, I do research level mathematics and on the odd occasion I still use my fingers! 😛 ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 23, 2015, 2:36am UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/71 "2015-09-23T02:36:25Z")
> [@Fair\_Rarity](#): > > My kid couldn’t subtract 6 from 10 the other day (2nd grade) without filling out the ten frame. Rote memorization is boring and not for everyone, but like… I think that level of problem should be just rolling off the tongue for your average 2nd grader, not something that has to be calculated with dots. What’s involved in “doing” the subtraction for you? It’s just the fact that you’ve already memorized it to be 4, isn’t it? Well, hey, maybe if your kid comes across this fact frequently enough, they’ll come to remember it’s 4 too. And one way they might come across it is by actually figuring out what the answer is on various occasions as they organically arise (possibly via the ten-frame, or other methods). If it turns out that in your kid’s life this particular calculation doesn’t come up frequently enough for it to stick in their mind… well, then, maybe it’s not that important that they memorize it anyway. They’ll still be able to figure it out on those occasions when they need it. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 23, 2015, 2:43am UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/72 "2015-09-23T02:43:12Z")
As for speed: I can’t think of a non-contrived situation that the average human needs blinding manual arithmetic speed for. Like, taking the time to figure out 10 - 6 by, say, counting up “7, 8, 9, 10, ok that’s four steps” is actually perfectly sufficient for many purposes, and for others, ubiquitous access to electronic calculators works way better than manual arithmetic. If some specialty comes up that does require honing one’s arithmetic speed, though, we can train the kid for it then. ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [September 23, 2015, 2:56am UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/73 "2015-09-23T02:56:25Z")
> [@Indistinguishable](#): > > As for speed: I can’t think of a non-contrived situation that the average human needs blinding manual arithmetic speed for. Like, taking the time to figure out 10 - 6 by, say, counting up “7, 8, 9, 10, ok that’s four steps” is actually perfectly sufficient for many purposes, and for others, ubiquitous access to electronic calculators works way better than manual arithmetic. If some specialty comes up that does require honing one’s arithmetic speed, though, we can train the kid for it then. An EMP has knocked out all electronic devices, the adults are dead, and a group of scrappy, wise-cracking grade schoolers must calculate where the Soviet’s nuke is going to land before it’s too late. (In theaters this fall) ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [September 23, 2015, 3:00am UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/74 "2015-09-23T03:00:46Z")
> [@Joey\_P](#): > > BTW, maybe it’s possible, just possible that as someone who spent years studying math in college I actually do know what I’m talking about. Don’t get me wrong, this is grade school arithmetic, I think most of us know what we’re talking about, but criticizing me like that was kind of an asshole move. Gee golly, don’t know how I ever made it though mulitvariable calculus or non-euclidean geometry or differential equations. You stated outright that you couldn’t understand your daughter’s math homework, and that you refused to educate yourself about it in order to help her. I’m amazed that you couldn’t understand it, and I’m amazed that you refused to learn it, given that you majored in math in college. > [@](#): > > Frylock, I’ll ask you the same thing I asked the others. Do you have young kids? Are you a parent to someone going though this right now? Yes. Two of 'em. (And two more coming up.) Again, like I said–it’s not hard. If you understand math, the weirder looking stuff should nonetheless make sense to you after some brief investigation. Or if necessary, taking a “remedial class” at your local library. > [@](#): > > It’s not about ‘well I would just google it’, I can do that, I have done that, but if you google it and do a little differently than the teacher wants/expects, it’s still wrong. That’s a separate problem from your avowed inability to understand your daughter’s homework. The teacher is clearly either missing the point or _really_ doesn’t understand math. > [@](#): > > But thanks for playing (maybe next time try not to tell me what I do and don’t know). I repeated back to you what _you said_ you did and did not know (and refused to learn). ---
**Author:** ![svd678](https://avatars.discourse-cdn.com/v4/letter/s/53a042/32.png) [@svd678](https://boards.straightdope.com/u/svd678)\ **Post date:** [September 23, 2015, 6:11am UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/75 "2015-09-23T06:11:14Z")
My son was in grade school in the early 60s, and I couldn’t help him with arithmetic. “In my day” equations were supposed to balance. Then they invented points that mean one is greater than the other - which means the equation is wrong., - no? ---
**Author:** ![Ignotus](https://avatars.discourse-cdn.com/v4/letter/i/ecc23a/32.png) [@Ignotus](https://boards.straightdope.com/u/Ignotus)\ **Post date:** [September 23, 2015, 2:53pm UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/76 "2015-09-23T14:53:21Z")
> [@svd678](#): > > My son was in grade school in the early 60s, and I couldn’t help him with arithmetic. “In my day” equations were supposed to balance. Then they invented points that mean one is greater than the other - which means the equation is wrong., - no? That sounds like those were really _inequalities_ rather than equations. I’ve never seen the “point notation” myself - I grew up with “\<” and “\>” in school - but that would hardly present an insurmountable problem. Really, it seems somewhat odd to me that parents would have a huge problem understanding their kid’s homework just because of somewhat different notation/algorithms. Did they even try to? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 23, 2015, 3:15pm UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/77 "2015-09-23T15:15:30Z")
The equation isn’t wrong, because there is no equation. 6 \> 4 is an inequality, not an equation. And they were invented long before “in your day”. ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [September 23, 2015, 3:41pm UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/78 "2015-09-23T15:41:34Z")
> [@svd678](#): > > My son was in grade school in the early 60s, and I couldn’t help him with arithmetic. “In my day” equations were supposed to balance. Then they invented points that mean one is greater than the other - which means the equation is wrong., - no? Algebraic inequalities are one of the few bits of the last New Math revolution that stuck around in modern curricula. They’re actually very useful in real-world applied math. And you’re right - equations have to balance. But inequalities are not equations. They’re inequal. It’s right there in the name. I’ve looked at the Common Core math standards and they’re reasonable. I think a lot of the newer techniques that are being tried by curriculum designers are good and useful ways to think about numbers and how to manipulate mathematical objects. A lot of teachers and administrators were blindsided by new curricula (which in some cases were rushed into production with poor editing/oversight) and didn’t have a really strong grasp of what the purpose was. It’s unquestionable that we need to do better at teaching math; the primary deficit is not in pedagogical materials but in teacher training and parental outreach. I don’t know how to solve those problems easily; it will take time. Unfortunately in the time it takes to measure any kind of useful results, they’ll probably change the curriculum again. > [@Fair Rarity](#): > > My kid couldn’t subtract 6 from 10 the other day (2nd grade) without filling out the ten frame. Rote memorization is boring and not for everyone, but like… I think that level of problem should be just rolling off the tongue for your average 2nd grader, not something that has to be calculated with dots. Maybe rote memorization and doing it over and over isn’t always a fail for every kid. I mean, yeah sure, it’s great to be able to figure out how to answer a problem without knowing the answer from memory, but sometimes you just have to be faster. Maybe that comes in 3rd grade. And how did you compute it before you memorized it? On your fingers? Using a number line, perhaps? Do you think that your daughter computing this fact many times might eventually lead to her remembering it? If so, then why does it matter how she does it? ---
**Author:** ![Fair\_Rarity](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/fair_rarity/32/153_2.png) [@Fair\_Rarity](https://boards.straightdope.com/u/Fair_Rarity)\ **Post date:** [September 24, 2015, 1:05am UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/79 "2015-09-24T01:05:30Z")
My kid is super super smart with larger math concepts. She does great on the proto algebra abstract questions. I just think that adding and subtracting digits under ten for results under ten should be able to be done quickly AT SOME POINT. If that’s 4th grade and I’m just worrying early, then that’s ok. It’s only 3 weeks in, so I might just be panicking prematurely. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 24, 2015, 2:17am UTC](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162/80 "2015-09-24T02:17:42Z")
Yes, it should be able to be done quickly. That’s why the schools are teaching these concepts, so the students can learn to do it quickly. I think the biggest part of these parent complaints is that these things look a heck of a lot different while you’re still learning them, as compared to when they’re already learned. It’s been so long since we’ve gone through the process of learning them that most of us have forgotten what it looks like. [Previous page](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162.md?page=3) [Next page](https://boards.straightdope.com/t/what-common-core-math-technique-was-that-check-mocking/732162.md?page=5)