It may be the first time a math problem has gone viral on the Internet.

A frustrated father posted a subtraction problem from his second-grade son’s math quiz on Facebook this week with a note to the teacher calling it ridiculous. Conservative pundits, including Glenn Beck, seized on it as evidence that the new standards are nonsensical and “stupid,” adding more fuel to the backlash against the Common Core as it rolls out in schools across the country.

The problem asks how Jack, a fictional student, miscalculated when he used a number line to find the answer to the subtraction problem 427 – 316. Students are then asked to write a letter to Jack explaining what he did right and what he did wrong.

Critics say the problem takes a simple one-step subtraction problem and turns it into a complex endeavor with a series of unnecessary steps, including counting by 10s and 100s. The father, Jeff Severt, who has a bachelor’s in engineering, told Beck the problem was particularly difficult for his son, who has autism and attention disorders and trouble with language arts. He said that after spending two frustrating hours going over the earlier pages of his son’s math quiz, he was stumped by the problem himself.

So why is the problem so difficult? *The Hechinger Report* asked a couple of the lead writers of the Common Core math standards, Jason Zimba and William McCallum.

Their response? Don’t blame Common Core. Blame a poorly written curriculum.

“That question would not be in a textbook if I wrote it,” Zimba said.

McCallum, math department chair at the University of Arizona, had some of the same concerns about the problem as the conservative critics.

“It’s a complete reversal of the truth to call this a Common Core problem,” he said. What Common Core actually requires, McCallum argues, is fluency in the simple skills of adding and subtracting that critics are calling for. “Complaining that this is a Common Core method, when the Common Core doesn’t require this method, but does require the method he wants, it’s just a lie,” he added.

The question appears to be aiming for several of the main Common Core math standards for second grade:

1) A requirement that students understand place value, for instance, that “100 can be thought of as a bundle of ten tens — called a ‘hundred.’”

### Common Core

We’ve been covering the controversy and facts behind the Common Core for years. Check out our special section for more or read some of the highlights below.

2) That students be able to “add and subtract within 1000, using concrete models or drawings and strategies based on place value … and relate the strategy to a written method.” Also that they “understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.”

3) That they can “explain why addition and subtraction strategies work, using place value and the properties of operations.”

4) And that they can “represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram.”

In general, being able to explain how you arrived at an answer – not just memorizing a formula – is also one of the standards’ key goals for students.

In the math problem encountered by Severt’s son, “What the kid did is kept subtracting 10. So they didn’t go down to the smaller unit. And whoever is looking at the problem is supposed to see that the student was confused about place value,” said McCallum. “A discussion in the classroom is supposed to talk about how 10 is 10 times bigger than one, and 100 is 10 times bigger than 10.”

But mashing together the different standards for place value and the number line is potentially confusing. “The number line is not an appropriate model for place value,” Zimba said.

The writing component is also problematic. “The standards don’t require essay writing in mathematics,” Zimba said.

The problem the question highlights is not an issue with the Common Core itself, McCallum said, but rather one of curriculum. Textbook publishers, smaller startups, school districts and teachers are all grappling with how best to incorporate the standards into the lesson plans, classroom activities, homework and quizzes that students encounter on a daily basis.

So far, there has been little quality control. Some of the new curricula labeled Common Core include high quality materials that match well with the standards, but many don’t, supporters of the standards say.

“Like it or not, the standards allow a lot of freedom. People think the Common Core is a curriculum, and it’s not. The curriculum authors are going to interpret the standards in different ways,” Zimba said.

“There will be a lot of variety, and it doesn’t make sense to me to pick one thing and say that’s the Common Core,” he added. “Particularly something that doesn’t get at the mathematics that’s being emphasized in the Common Core.

*This post has been updated.*

## Comments & Trackbacks (69) | Post a Comment

at 4:15 pm

1) A requirement that students understand place value, for instance, that “100 can be thought of as a bundle of ten tens — called a ‘hundred.’”

An obviously essential skill to realize the value of place in a number system of ANY base. Easy.

2) That students be able to “add and subtract within 1000, using concrete models or drawings and strategies based on place value … and relate the strategy to a written method.” Also that they “understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.”

Other than borrowing or carrying a value, and realizing the very easy to understand significance of that, what additional real value is gained by anything more?

3) That they can “explain why addition and subtraction strategies work, using place value and the properties of operations.”

Can be understood very simply by explaining the borrowing and carrying.

4) And that they can “represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram.”

Why? No need to cover this at all until they progress into x-y graphing.

I suspect the horrendous examples of Common Core Math problems are the result of problem designers who don’t understand what is to be gained by the core requirements who therefore design very strange problems because they don’t know the reason behind the requiremnt.

You’re going to need to explain to me precisely and with documented data and proven results exactly what is to be gained by teaching 2nd grade math any diferently from how I learned it.

at 6:02 pm

No, the system is really badly written.

I have twin boys that are currently using this Common Core stuff in the state of NJ.

They turn a simple:

43+12= 55

into 40+10=50 3+2=5 50+5= 55

other examples show them always saying to add the 10′s then the 1′s forcing them to add once again if the one’s happen to go over 9 causing the addition of another 10.

Looking further ahead they have the EXACT data displays in the book as is shown the work sheet in the article. They need to kill this fast. I showed my kids how to do it the way i was taught and they can now add in their had triple numbers with little to no problems. Before that double numbers was killing them specially with a carry over from the one’s.

at 7:49 pm

A lot of people are misreading the diagram. The large jumps are 100s, but the small jumps are 1s, not 10s. This is an easy mistake to make because the diagram is not drawn to scale. The difficulty is compounded by the fact that the author wrote his own numbers on the diagram, and he was counting down by 10s. The correct answer for this task is that Jack forgot to subtract 10, but he correctly subtracted 306.

I am surprised that a flawed assignment would generate such a strong reaction. Teachers are only human, and they make mistakes. Instead of spending two hours struggling with this problem, the parent should have simply said: “I don’t know. Why don’t you ask your teacher tomorrow?”

at 2:20 am

This common core is the most rediculous way of teaching I ever had the displeasure of dealing with ever.

at 7:07 am

Jack forgot to subtract ten and then counted the ones as tens. Therefore, he got the question wrong. That took me five second to figure out.

at 8:58 am

We need to graduate a generation of problem solvers. Did the dad here bother to get the instructions first. He uses Facebook then he should have been able to do a search for common core math number lines. A brief read and the information falls into place. He should then be able to walk his son through what he should be looking for in Jack’s mistake. Using a number line to solve simple math problems is like counting on your fingers and just as easy.

at 9:30 am

No, this type of problem is PRECISELY what common core math is all about. Overcomplicating what should be very simple. As a special education teacher I tell you that this will be a disaster for students with learning disabilities. There is no way this common core is going to fly.

at 10:06 am

The small jumps are 10s not 1s. Jack skipped 117 when counting back on the number line arriving at 121 rather than the correct answer of 111.

at 1:40 pm

“The small jumps are 10s not 1s. Jack skipped 117 when counting back on the number line arriving at 121 rather than the correct answer of 111.”

Nope. Small jumps are 1s. He forgot to subtract by 10. It’s okay though, it’s a stupid question.

Dad’s right, math should be used to make things easier, more efficient and the subject has a certain elegance to it. What’s the next ridiculous requirement? Coding in binary?

at 1:54 pm

When I was in Jr. High School (the ’60′s), they introduced the ‘New Math’ curricula, which turned out to be such a total disaster that it was eventually abandoned for the ‘old math’ which dates back a long way and has always worked. Now they come up with some new and apparently ridiculous method of dealing with simple arithmetic. Why? Is the human race now getting stupider over time? Or aren’t there enough decent teachers to teach basic skills?

at 3:58 pm

A lot of engineers are very bright, but some of them are anything but. Jeff Severt looks like a candidate for the latter group. Look at his notations, especially his “57 67 77 87 97 107.” What could he possibly have been thinking?

at 3:59 pm

I like the problem for several reasons, but it gets in deep trouble by implying that Jack is considering this an efficient algorithm for subtraction. (I know engineer dad’s differential equations class was full of efficient algorithms for solving over-simplified, non-real-world equations. How useful is that?)

How about “Jadyn was goofing around with a number line, trying to compute 427-316. He was surprised not to get 111 (which he was able to instantly get from Google Speak). Explain to Jadyn how to fix his number line game.”

at 4:25 pm

Before passing judgment, read the real backstory. Context is everything. Wow, much ado about nothing.

https://www.facebook.com/jeff.severt1/posts/10201895304210800

at 5:26 pm

Can we at least agree that the father handled this in a very unprofessional and unproductive manner? By undermining the legitimacy and authority of the teacher (by completing his son’s work in such a snarky manner) and by obviously having a personal/political axe to grind (by posting it on Facebook) he got his son no closer to an understanding of what the professional educator was trying to convey, which only hurts his son. I find that alone appalling.

Beyond that, as an educator myself I see CC as addressing precisely this need — we have memorized formulas and practiced computational skills by rote, but have had absolutely no deeper understanding of the mathematical underpinnings of problem-solving. We know “It works” but have no idea why or how it works. Sure, this is a roundabout and more complex way of solving a problem. But in that process, it conveys deeper mathematical understanding that once internalized will help solve outside-the-box problems which do not easily fit into the formulaic computational method. We have created good calculators but poor mathematicians, and that is why CC — like any practice routine — complicates things initially so that you truly grasp their eventual simplicity.

at 5:33 pm

I have a BS in electrical and a BS in manufacturing engineering. If Jeff Severt can’t handle evaluating subtraction using place values and be able to clearly communicate the root cause of Jack’s failed attempt, then I would question his ability as an engineer. Bragging about the ability to solve differential equations is irrelevant. In the real world, especially engineering, the problems that must be solved do not provide an equation. The ability to problem solve to derive and equation is where our children are falling short.

As to all of the people complaining about making the standards to meet the needs of children with learning disabilities, perhaps they should realize we tried to model the curriculum to achieve this goal with “no child gets ahead”, err “no child left behind.” The only thing accomplished there was the “dumbing down” of all children to ensure the feelings of the learning disabled and their parents were not negatively effected. Thank you political correctness.

Common core is a working model to try to help our children CATCH UP to other developed countries globally. Plan, Do, Check, Act is a method to solve any problem. If the methods in common core do not yield successful results, then find out why and modify the curriculum. There is no plan that can be guaranteed to have 100% success without implementation for testing.

It is important to accept that the methods used for decades are antiquated. The reason we are losing jobs and products to other nations is due to the fact that we are falling behind in education. If anyone has a better plan to heal “no child left behind” issues, please step forward and dazzle everyone with your brilliance. If not, then let ANY method be tested. If it fails, then use the information about the failure to ensure we don’t duplicate the failures in the future.

at 8:19 pm

The fact that people who seem to understand common core can’t even agree on the correct answer to this riddle really proves that this approach is making simple concepts difficult.

at 10:46 am

Actually, if you understand the number line, this problem is not at all difficult to solve. The parent in this post misunderstood the problem to be a simple subtraction problem. However, it is an assessment of students’ abilities to analyze others’ work and find the mistakes. It takes solid understanding of the number line to be able to do this. Good analytical skills are essential in all kinds of problem solving. It seems that the parent that wrote this letter is lacking some of those skills.

at 9:26 pm

Being from Texas we don’t have common core. However, just to test the theory…I gave the problem to my 1st grader to solve. He had it solved in two minutes ’cause it “wasn’t that hard “. He did question why he had to do English in Math. It’s just missing 10s spot. No different then the cubes we use with the added bonus of being able to read a number line.

at 9:25 am

James, when you stack 43 over 12 and add them together, you are doing precisely what the broken out 40+10, etc. does. You are grouping 1s (in a vertical column), adding them, grouping 10s (in a vertical column), adding them and then adding those two groups together by virtue of place at the bottom. By explicitly breaking them out, it shows the CONCEPT of what is going on, rather than a rote process. I agree that not spelling out all the steps is faster in most cases and is what most people will do even when knowing what is really going on. But knowing why that process works is valuable. I use the grouping concepts all the time to do arithmetic in my head and it certainly helps with estimation.

I’m not saying CC is good or bad, or whether particular applications of it is good or bad. I’m just saying that for that problem, your kids are being taught the concept of what is going on, not how they should solve that problem once they have the concept down.

at 11:10 pm

The discussion about whether common core standards will have a positive or negative impact on student learning is a waste of time because ALL teachers who will be judged on the TEST scores will teach directly to the test! They are already looking closely at the Pilot questions that the students are currently doing online and districts are already designing parallel tests to give ALL students every quarter or at the end of each unit! The TESTS will determine what is actually taught and the idea teachers will have time and/ or freedom to have long discussions to talk about aspects of a real problem or math teachers assigning written explanations of why a student answered a certain way or explain what they were thinking will not happen! They do not have time now to grade all assignments and create excellent lessons. They have 180+ students each day and have many other duties to perform like after school supervision of a sporting event or a school play or a school dance or a meeting to hear about new state requirements for doing x, y, or z. I hope you are starting to get the idea.

at 9:26 am

This look like that horrendous TERC math curriculum. It takes the simple and makes it complicated. Fortunately, we moved to another district and then spent 1.5 years to catch my kids back up in math.

We need to remember that Common Core is a set of standards and not a curriculum.

at 1:33 pm

In general, Common Core’s big sin is recycling all the worst ideas from the last 50+ years: sight-words, constructivism, and reform math, which comes in a dozen varieties.

No one can make sense of all this nonsense unless you start with the historical reality that John Dewey and all his pals were socialists, and they intended to use the public schools to create a socialist America. Their project continues.

(Here is a pretty good explanation of the whole shenanigan, “Common Core: Anatomy of a Failure,” on American Thinker, easy to find.)

at 4:43 pm

“In the real world, especially engineering, the problems that must be solved do not provide an equation”

Absolutely not true. I would certainly doubt whether anyone who says this is an engineer. There are many ways to solve a problem: analytically, empirically, and numerically. Two of which typically require equations. Even aerospace problems which are typically unsolvable are solved using equations. Navier Stokes equation is typically worked to the point of a simple(r) system — and then compared against real life.

Many engineering problems today involve computation based on equations, that is numerical problems solved using an analytical (equation) as a framework. The engineering is in the efficiency of the system — like calculation of Eigenvalues of the next time delta for the system of equations you are attacking.

To say equations are not used in engineering is odd.

at 6:35 am

I honestly feel bad for our “Frustrated Parent” because it is clear that his B.S. in Electrical Engineering left him ill equipped to recognize the algorithm the number line approach is proposing and how it might relate to the algorithm he employs.

Writing:

427

- 316

——

111

is a nice way of organizing the information, but what Frustrated Parent fails to recognize is the underlying algorithm that we all employ in order to arrive at 111. Namely, we start by subtracting the 1′s, then the 10′s, then the 100′s. In doing so, we recognize that:

427 = 400 + 20 + 7

326 = 300 + 10 + 6

and by the associativity and commutativity of addition

427 – 326 = (400 + 20 + 7) – (300 + 10 + 6)

= (400 – 300) + (20 – 10) + (7 – 6)

When we perform subtraction by the method proposed by Frustrated Parent, we start on the right with 7-6, then move left, but we run into a problem when the number we are subtracting is larger. Recall, this is when you “borrow a 10″ from the next number to the left (cross it out and write that number less 1) and then add the one to the top digit. Jeez, that can be confusing, what are we doing?

The number line approach simply proposes attacking the problem “from left to right” as I wrote it above:

(400 – 300) + (20 – 10) + (7 – 6)

That is, start by taking off chunks of 100 until we have exhausted all the 100′s in 316. Then take off the 10′s, followed by the 1′s.

Hence, our friend “Jack” skipped the 10′s. He removed three 100′s, then he removed six 1′s, and failed to remove the one 10 in the middle.

This isn’t rocket science, Frustrated Parent, it’s just an algorithm much like the one you propose. I know engineering gave you a lot of tools, ones that you’ve probably internalized without remembering the details of their justifications, without remembering the underlying algorithms and why they work, but that doesn’t mean this homework is too confusing. It just means that you are unaware of the origins of your knowledge. You are a machine unaware of your software.

Lastly, this isn’t Common Core, it is a specific curriculum used to try and meet the Common Core requirements. It is not the fault of Common Core, but the fault of the local education board members that chose this particular curriculum.

at 9:54 am

Let’s flip the question: Does anyone know of a good CC curriculum?

Any teachers out there using something that you are happy with?

at 1:29 pm

Hmm, well I think that several people on this thread are very correct, and that interesting points about philosophy of education are being considered. I also think that the father, although his snarky attitude is unhealthy for his child’s education, has a point. The graphical presentation of the concept is confusing because it is not drawn to scale. The underlying problem is that the subtraction of hundreds, tens and ones are most naturally considered on a logarithmic scale, but the math quiz shows it on a nebulous number line which is not to scale, causing Frustrated Parent to mistake Jack’s subtractions of ones for tens, and transforming the problem into a head-scratcher for him. Of course, we don’t typically teach kids about log scales until they are significantly older, so the best way to illustrate this type of problem graphically for children is not straightforward.

I agree that in theory the idea behind this problem is nice. Not only is the child being asked to understand the subtraction problem correctly–he or she is also being asked to follow the logic used by another student and understand where the other student went wrong. My opinion is that kids need to learn both things. They need to learn the efficient algorithm for doing simple arithmetic (lining up the columns and subtracting, as dad showed), and they also need to learn the skill of following someone else’s approach and finding the fallacies, because it may help them understand why their method works. I think if children are not being taught the efficient algorithms for doing simple math and are instead being taught that drawing a weird not-to-scale number line is the best way to subtract numbers, then that is a failing of the curriculum, and that is the point that Confused Parent is trying to make. On the other hand, if kids are first taught the efficient algorithm and are then asked to broaden their understanding with critical thinking exercises that force them to consider different ways of visualizing the problem, I think that is an excellent approach to learning/teaching–although poorly executed by the author of this particular problem.

at 1:21 pm

The whole reason behind having students complete a subtraction/addition problem using these new strategies is to simply expand their understanding. Students are not required to continue to use these methods to solve problems, it is just important to show them that there are different ways to solve a problem. Different strategies work for different students. Using the tape diagram shows students that you can make a problem easier by turning the numbers into friendly numbers. Though I doubt anyone will take the time to draw the diagrams on an exam, it is a helpful tool that teaches students to strengthen their mental math. Students learn to take a complicated subtraction problem (ex. for a 2nd grader) like 83-28 which they would have a hard time doing quickly in their heads, and turn it into 85-30 which they can solve in their heads. These strategies are just meant to show students different ways and deepen their understanding of place value, and how addition/subtraction work.

at 2:33 pm

I am not a fan of common core. That being said, Why does everyone find this so difficult. He subtracted the Hundreds, He subtracted the ones (What he did right) He didn’t subtract the ten (what he did wrong) My second grader was able to see it. I can see it If the engineer cant see it, he shouldn’t hold that degree. BTW my son is an average student. Maybe we should focus on the excessive testing, one size fits all , and the data mining of our children.

at 10:30 am

I am a computer scientist… went to school before standardized testing became a thing.

i figured out common core math and its not that hard..

the method you used is just a trick to get you the right numbers because log base 10 math allows us to do that.

but you don’t get the numbers

i actually don’t see anything wrong with common core so far except that parent’s are used to the tricks to solve math problems instead of knowing the numbers and what they mean in base 10 math.

at 10:32 pm

Funny thing is that it actually is very similar to the way I and others I know add and subtract in my head. If you asked me to subtract 316 from 427, I think 427 – 300 = 127, then 127 – 16 = 111, and this same methodology works well for bigger numbers or other types of problems like percentages for example. The problem is much more related to how the question was written and shown. It is confusing.

at 6:20 pm

People are upset because they think the goal of teaching math is to solve problems as quickly as possible. This Jeff guy is just a typical American trying to be better than the test instead of reading the problem and answering the question. Math, like this problem, is to teach people how to think conceptually. This problem adds an extra skill to it: writing out the answer. There are two central elements to answering this problem: 1) find the mistake. 2) explain what was correct AND what was incorrect about Jack’s diagram (which is kind of nice to require, so as to find not only errors, but positive aspects). This is not a hard problem, folks, if you just remember the goal: fundamentals, not efficiency. I would have expected my students to write this answer:

“The mistake Jack made was that he only subtracted 306, not 316. I would tell Jack that he did a good job subtracting 3-hundreds from the hundreds place and 6-ones from the ones place. I would tell Jack that he made a mistake by not subtracting 1-ten from the tens place. His number line had three big gaps to subtract the hundreds, and six small gaps to subtract the ones, but he needed one medium gap to subtract the ten. I would also tell Jack to not respond to letters from strange, old men who say they just want to help you with your homework. You aren’t an engineer yet, Jack, you are in 2nd grade, and using number lines helps you understand the fundamentals of addition and subtraction. Only AFTER you get the fundamental concept should you begin to use short cuts like stacking numbers on top of each other and computing, because when you don’t have a piece of paper or calculator with you in a real-life situation, you will using the mental math concept of chunking to arrive at the answer.”

at 6:37 pm

I am really surprised that this problem was seen as difficult by a man with a degree in Electrical Engineering. I’m not going to say that this problem would be easy for a young student. However I think it’s important that not every homework or quiz problem is easy. If every student was getting every problem right every time, we would have a huge issue. Part of learning is struggling initially because the purpose is to fully understand a foreign concept and that usually doesn’t come easily the first time. Yes, as a parent you can teach your kid the “easier” way of learning how to add and subtract, and completely remove the opportunity for them to struggle and eventually achieve a conceptual understanding. However they will reach a point in their education and later in their careers where memorization and easy tricks aren’t going to cut it. They are at some point in their lives going to need to utilize critical thinking and tackle problems that require an initial period of struggling, whether in mathematics or something entirely different. I can see where this problem might be difficult at first for some students and cause some amount of frustration but I think that’s why the essay portion is built into it. It’s meant for the student to really think about the concept behind addition and subtraction and it allows them a work space to hash out their thoughts in writing-sometimes writing about a math problem is a lot less scary because students are generally more comfortable at that level with writing than computation. If we continue to simplify our childrens education and teach them to take the easy way out I really feel like we are doing them a huge disservice by failing to nurture problem solving skills in favor of memorization.

at 9:14 pm

The bottom line is that implementation

of common core is causing far more harm than

good in the education of children and it should

be abandoned before more children are hopelessly

confused by it and forever turned off by

mathematics.

The overly cumbersome approach I see in my

Daughter’s homework has effectively tossed the baby with

the bath water .

baby with the bath water. The children and I suspect

, most of their teachers, don’t understand what

these lessons are trying to teach.

at 2:45 pm

I have an M.S.E.E., and had no problem figuring it out. I guess the extra 18 months in college paid off.

The answer is, “he forgot to put in a hop for the 10′s place”.

Doing it this way allows you to eventually do these problems in your head without having to borrow. Ask an adult what 702 – 598 is, and they’ll struggle to visualize borrowing 100 and 10 in their head. But it’s 702-500=202-90=112-8=104.

at 6:28 pm

It’s because after subtracting 100, he subtracted 6, not 16. This may not be the best method for teaching subtraction, but it gives you the strong number theory intuition which is much more powerful than knowing an arbitrary subtraction algorithm. If it was really about the speed of finding a solution, just plug it into a calculator. You don’t even need your brain! But the point of teaching math is not teaching computing, it’s teaching concepts. Surprisingly(!), the same thing that distinguishes a good engineer from a mediocre one. All this shows is that engineers aren’t good mathematicians, which everybody already knew.

The reason mathematical methods are cumbersome is because you get back quite a bit more than you put in. Hence, the extreme power of generality. A subtraction algorithm only works for certain sets of numbers, and has to be adjusted for each base system. The general method allows you to do it to anything: base 10 numbers, “clock counting”, metrical patterns, and much more.

at 6:43 pm

Oops, 300!

at 3:05 am

“Any intelligent fool can make things bigger, more complex and more violent. It takes a touch of genius–and a lot of courage– to move the opposite direction.” -Albert Einstein

at 3:47 pm

I haven’t read thru every comment, but that some of the discussion turned to an argument of a simple subtraction shows the ridiculousness of CC.

at 10:08 am

I think the whole idea of using a number line defeats the purpose. The idea is convey what is being done with addition and subtraction. Why not start with money? You have a pennies dimes dollars. You add the pennies together, changing ten in for a dime which you put in with dimes. You then add the dimes, change 10 for a dollar if needed and so forth.

You can then as an exercise got to inches and feet, in which you use base 12. Hopping around on a number line is an already abstract way to represent and abstract concept. Kids already know about money and by showing the idea of how numbers can be grouped the concept behind addition and subtraction can be taught.

at 12:40 pm

I don’t see the problem with this assignment. It is merely asking one to subtract by counting up from the lesser figure. This is the same way one makes change. Easy. Intuitive. The engineer who complained about this assignment should have instantly perceived this.

at 7:12 am

To everyone who says that Common Core is meant to be about understanding concepts rather than rote routines – that’s all well and good, but clearly it isn’t working. Virtually every single I’ve learned in my life – swimming, foreign languages, music, computer programming, martial arts, and cooking – all required a great deal of time invested in repetitive practice before getting into abstraction and reasoning. You wouldn’t teach Spanish by starting with the morphology of the subjunctive mood before practicing greetings and basic sentences, why would you teach math that way?

at 9:38 pm

All those whose comments support CC or criticize the engineer should have read the back story, as was suggested in one comment. The new math of the sixties (based on set theory) was a complete disaster and is partly to blame for our current lagging in math. I had figured out the so called “place value” concept by the third grade. A student will really understand a number line when he studies vector algebra. I present two numbers, 4897 and 7493. They have a common multiplier. Find it in 2 minutes without using a calculator. If you can’t, look up Euclid’s Algorithm. How much do you really know about math?

at 1:50 pm

I don’t have any children. I’m very far removed from this, but have read a few articles on the matter. Math was never really anything that made much sense to me and this would only confuse things more. What I’m getting out of this article though, is that there’s aren’t any standardizations on how to bring this information to children. Aside from this being somewhat obnoxious and extra steps and complicated explanations for simple problems, it seems like the teachers don’t even understand how to teach this to students the way it’s supposed to be taught. They say it’s not a curriculum, then what is it? A suggestion on how to potentially teach math to children who may have a hard time understanding math? To me, I would look at this and say “why are you doing this extra stuff? where are these numbers coming from and why are you doing that?” When I was kid, I learned math easiest, when I could see it – if I had 30 of something and I took 10 away, I could then count 20 – which helped me understand why 30 – 10 = 20. I needed a visual component to quantify what was happening so I understood how 20 came to be. Personally, the biggest problem with math is lazy teachers – I had several teachers in school telling me to “ask a friend” or “read the book” when I said I didn’t understand something (after reading the book and asking friends) – which just shows the teacher doesn’t even understand what they’re teaching, if they can’t explain it in multiple ways. If we’re trying to improve education for our youth, I think we need to look at how we get teachers ready to teach them (not all, there are fabulous teachers out there).

at 2:41 pm

I do not usually respond but I had to. To all those that have criticized the frustrated parent, Please read his actual post https://www.facebook.com/jeff.severt1/posts/10201895304210800. It states first and foremost that he did not post it on Facebook his wife did. This was actually just something that was stated to the teacher To all those how have made snarky and not relevant comments about the parent, should realize a few things:

1) The frustrated parent is a parent of an ASD child and not a “normal” child.

2) The 2 hours was on the whole assignment and not this problem. The other thing is at least he is spending time to help him on his child’s homework and not just leaving it up to the teacher to do all the teaching. It does not work that way.

3) The child new the correct answer and was not having trouble with the actual math of the problem but the context. This child has problems with the subject of grammar. Word problems are always going to be a problem for this child.

4) What everyone also has to understand this child was in the process of a breakdown and made things worse on parent.

I also do not understand why this and many other things online become a bashing on the parent or the math itself. I understand that this problem is a little difficult for a younger student to understand and at first was confused by what it was asking. This problem is not asking for the correct answer to 427 minus 316 but to find the mistake in the reasoning of the previous person.

The I do not understand is the bashing of the memorization because you need to memorize everything to be able to subtract the smaller numbers. You then make this problem a multi-step problem by having to do each step separate and then put them together. I do not know if this helps or hurts children in the learning process. I have no opinion on it without further research.

I do know that our children seem to be learning less and people tend to give up if things get a little hard. The thing is if something is hard and they do not get help then they just quit. We need to help our children learn and not just leave it to the school.

I am going to leave one last note to this post. Please do not criticize before you know all the facts. I understand the frustration from the father but also understand that we do need to do something to help our children learn. And Spencer I cannot get over your comment. Did you actually read his post that was posted just above your opinion? He said he did not post it to Facebook and this was only meant to go to his child’s teacher. He also explains what was behind his writing. He even states this “On a lighter note: Our beloved & dedicated 2nd grade teacher thought it was great, and even agreed with my basic point in the letter.” so I have no idea how you can say in your own words, he was undermining the legitimacy and authority of the teacher. The professional educator understood what the frustrated parent was trying to convey with his ASD child. To say that he had a political/personal ax to grind is just annoying. If you want to say anyone had an issue it would be the wife for posting it. But I leave you with this question: If this was not an issue in our children’s education why would this have had such a big response?

Thank you all for reading my opinion and yes this is my opinion if you agree or disagree that is your prerogative.

at 5:18 pm

I believe Common Core is very unnecessary and stressing , my child (who will not be named) has come to me angry and confused with his homework , and I don’t blame the teachers either, the teachers are confused also. Currently I am a teacher of the 5th grade and the math is confusing. I am just saying if it’s to hard for an adult then it’s way to hard for a child.

at 9:30 am

‘The small jumps are ones/tens’? In the line graph, two sizes of “small jumps” are shown. The medium jump is where the budding math whiz was “supposed” to have subtracted ten for a subtotal subtraction of 310, and THEN continued onward toward academic stardom by subtracting six more ones in mini-jumps. The future math professor (?) thus left out one mini-jump, which could be argued in court as having the value of ten or one, depending on whether the pint-sized mathematician is accused of becoming confused with the problem before or after drawing the medium jump.

at 1:10 pm

The thing that bothers me about some common core supporters is that, to them, it is a doctrine. If you don’t do it our way you are not up to our standards, or you may even be wrong. If they are so rigid about simple subtraction what will they be like when we get to multiplication, division, roots and powers?

To me addition and subtraction were natural extensions of counting. I learned to count by ones, twos, tens, hundreds, etc. This quickly lead to an understanding of place value and powers of ten. The old way of subtraction by columns was straight forward. The terms carrying and borrowing are not ideal but one can quickly get used to it. This process can be easily adapted to other bases, say, base eight, or hexadecimal if you are doing primitive programming on a digital computer.

This understanding also made sense in multiplying. I quickly noticed that you could start at either end in long multiplication if you kept your columns straight and also you could carry on a long division if your guess for the next digit was to large or small by working with the current remainder.

Later on I learned there are other methods for multiplying such as Pool’s method or the old party trick of doubling and halving the two elements in the multiplication, casting out evil (even) numbers then adding the remainder. This “system” is particularly easy in binary arithmetic and works pretty efficiently on a computer.

Conclusion: If any teacher, at any time, insists that, a student who gets the right answer but didn’t use their preferred system, is wrong, he is a detriment to education. The student may be smarter than he, and he is hiding his incompetence behind forced conformity.

at 2:20 pm

@Dan R

I had never heard of that before man is it neat. I was able to come up with answer eventually but is great exercise.

As to the common core, the do learn to do things the standard way first. This kind of problem comes at the end of subtraction not the beginning. I am glad that they teach many different ways to do the same thing. If you have paper, then up and down right to left is the best but when you don’t then going the other way is better.

at 3:40 pm

Not sure if you have heard about this, but one of the lead writers of the Common Core Math Standards, Jason Zimba, founded the company, Student Achievement Partners in 2007. What does SAP do? It is a nonprofit organization dedicated to *drum roll please* helping states and districts implement the standards. Maybe I’m off base here, but doesn’t that seem like a conflict of interest??? Source: http://educationnext.org/straight-up-conversation-common-core-guru-jason-zimba/

Straight Up Conversation: Common Core Guru Jason Zimba – Education Nexteducationnext.org

So the guy writes the standards that are so perplexing college professors are stumped, that way states and schools can hire his company to come in and explain how to implement the standards he wrote. SAP is a major player in Common Core implementation, especially with the aid of $18 million in support from the GE Foundation. Now you know why these standards are so hard and make no common sense! So the company the writer co-founded can pay his salary through is non-profit company and receive millions in grant money!

at 8:29 pm

Forget Common Core what the children in school need to learn is how to count TRILLIONS….. since this debt will be like an albatross

around their necks teach them how to add to a trillion and what that looks like coming out of their paychecks every week…now you have some worthwhile math!

at 9:37 pm

Because David Radcliffe, the teachers tell them to do it at home when they ask for help. They don’t ‘Teach” anymore. It’s maddening and the damage being done be very difficult or impossible to undo.

at 9:38 pm

This common core math problem is like going to the doctor because your throat hurts. He says you have tonsillitis and they need to be removed, Only I have to go in through your rectum because we are using a common core surgical method.

Lets see how well that works too.

at 8:45 am

So, not only do our kids have to do the math, they have to dissect the math, embrace the math, be the math, and know it’s motives,and understand the psychology of the math? Just knowing that 2 + 2 = 4 isn’t enough? I suffered through that stupid “New Math”, 6th grade level inflicted on a 2nd grader,as a kid.Can’t we just turn out kids who know the math needed to do a budget,make change, balance a budget or checkbook? I have seen 12th graders grab an calculator to make change for 10 cents from a dollar,and they were in algebra! We need the basics, to crap with all this over difficult and under helpful systems

at 2:22 pm

It’s not that hard think of it as counting money back , I did this in my head in like 3 seconds 427 – 316 Add 10 to get to 326 plus 1 to 327 is 11 plus 100 to 427 Answer 111 done if cashiers didn’t have working registers do you think there going to use standard math to figure your change back , ie hang on sir let me get a paper and pencil and write is down

at 1:07 pm

As a software engineer this is THE BEST problem I can imagine to give kids higher level skills.

This exact problem scenerio happens to me every day. Jr level engineer picks a really stupid algorithm to do a calculation. It breaks somthing and you have to debug the software to figure out what went wrong. Then you have to tell this person nicely (in the best case scenerio), why they did this wrong so they can learn not to do it again. Proving you are smarter and can solve it in an easier way does nothing to advance your team other then making you a complete jerk that no one wants to work with. Those bad apples bring down whole teams. The engineers who can explain things to others, they make okay teams great.

2 hours spent on the actual problem between father and son, would have been an invaluable lesson. Knowing his father did not know the method the kid used, learning to look it up, or have his son explain how it should work, the figuring out the error and coming up with a great explanation together, that would have been a learning moment. Instead the kid learned that you get a ton of likes on Facebook by being a myopic jerk. Good job dad.

at 12:36 am

Are you kidding me about this Common Core Math!!! I tired to help my granddaughter do her math home work tonight. Oh my gosh – the poor thing had a “Mental Breakdown” – it was so stressful for her. I’ve read most of the statements and I cannot believe how we are teaching our kids to do Math.

427

-316

=111

Whatever happened to 7 – 6 =1 (If you have 7 apples and take 6 away, you have 1)

2 – 1 =1 (if you have 2 apples and you take away 1, you have 1)

4 – 3 = 1 (if you have 4 apples and you take away 3, you have 1)

thus your answer is 111. This is the way I was taught math, jeez this is the way most people do their checkbooks!!! I don’t think you are going to sit there and draw a bunch of lines in your check book engineer or not. What ever happened to memorizing the “tables”. I work in retail, what a disaster with some of our young adults if the something happens and the register/computer does not tell them how much change to give back. Does Common Core mean in the future we will have customers waiting in line while the clerk draws lines with 10′s and 100′s to figure it out? Common Core is going to cause a lot of problems, it’s not teaching children to use their memory and memorizing things. Memorizing things is a super way of retaining the things we learn. If I was a parent in these time I would opt to “Home School” my children, unfortunately most families have to have both parents or the single parent has to work.

at 1:53 am

Diane @ 5.17.14 1:07pm. As a fellow software developer you are absolutely right. My thoughts exactly. Problem is myopia. I learned math in the 50′s. Then I learned stuff like set theory, the number line, Venn diagrams, etc. A core value of conservatives is change is bad. Common Core is change. Erog it’s bad. It’s also easy to forget how tough it was to learn simple math in the old days. Now that that math skills is second nature to some adults they seem to think that the way they learned is the way everyone should learn.

at 8:09 pm

Just to be clear…these are not new or revolutionary math teaching concepts. Students all over the world in countries that score far, far better on international tests than US children are learning multiple approaches to computation. I am really surprised that this parent has a Bachelor of Science in Electrical Engineering. An old-fashioned cashier would be able to understand this problem quickly.

If you think that the way we learned math is just fine, ask an adult to mentally subtract 32 – 19. If you see them using their fingers to write in the air because they are trying to ‘solve it in their head by borrowing’, feel sadness . They should be mentally calculating 32 – 20 + 1 or thinking 19 + 1 + 12 = 32 to know instantly the answer is 13. If you cannot see this, then you should be especially appreciative of the Common Core.

I am a math person so I made up these little tricks on my own growing up and did it the teacher’s way when I needed to show work. When I started working abroad and reviewing math curricula from the UK and Singapore, both countries that outscore the US on international exams, I realized that other countries teach these tricks to their students.

The Common Core does not prohibit memorization. It is critical for students to know many math facts by heart (4 + 5 = 9). It is also critical for them to be able to deftly manipulate numbers quickly to do mental calculations (24 + 9 = 33). There are several ways this can be done instantly: 20 + 13, 24 + 10 – 1, 24 + 6 + 3. Mentally, these are very simple to solve (although hard to explain). We try to push students to practice these methods because, as they get older and their problems have more steps and reasoning required, they will need to be able to quickly solve computations in their head without much thought. Mentally, the traditional method: 4 + 9 = 13, write down the 3 and carry the 1, 1 + 2 = 3, there is a 3 in the tens place and the ones place….is really cumbersome.

It is true that sometimes the questions that assess whether the child understands the underlying concepts are really awkward. It can be really difficult to assess whether students understand what they are doing. Since we are obsessed with ‘accountability’ in the US, we end up requiring that students show that they can solve it in this way. In a homework assignment, that is fine. It gets them thinking about it. In a formal assessment, it should be sufficient to give students a rapid series of computation problems that they must solve mentally (without writing the problem down). If the child is able to quickly find the answers, then they are definitely using these tricks and not the traditional methods.

Go online and try to learn about thee methods. You will actually find that they are much, much simpler than what we do.

at 12:50 am

Common core is the beginning of the end for the American coin known as the Quarter. It has no place in mathematics based on 5 and ten. I envision one day when I receive five dimes and a nickel for 0.55 change, because it’s faster for the clerk than using one of those weird 25 cent pieces.

at 11:45 am

Heaven forbid the cashiers at McD , B King or just about any store, have to use a cash register that doesn’t tell them how much change to return. The associates can’t count change now in most places.

at 12:05 pm

I saw this problem posted on Facebook and I still believe this is entirely bogus. Having a degree in Mathematics, myself and having read all articles as well as the Common core individual standards on line, nothing even close comes to this as an example. Once must remember that Common Core, was devised by State Educators with the backing of Governor’s , not the Federal Government, and most disturbing by a publishing company…Pearson to be exact. Pearson Publishing (Prentice Hall, Scott Foresman, Addison Wesley, etc) was the real driving force behind this. The real vested interest lies with this British and publishing company and not the states.

The real issue why kids can not do basic arithmetic let alone algebra in my opinion is twofold. First, Teachers “teach to the test”. No true learning or thought process is involved. Second, Teacher’s are not trained as they were when I taught and the textbooks used (no matter who the publisher) are a total disaster. I have numerous texts which I have collected since the 60s, most teacher’s editions, and as you progress through the decades the books become more “watered down”, more psychotic in thought process and just not engaging to students.

The fact that college students CAN NOT compute what 20% of 100 is in their head is astonishing. This is not calculus, it is third grade arithmetic and they simply can not do it without a calculator or smart phone in hand.

I applaud what Common Core is trying to accomplish, which is primarily one standard across the board for 50 states, as opposed to 50 individual state standards. I mean x+y=z and you do not need 50 individual standards to teach that. However, until math teachers are prepared how to be teacher’s once again and not to test but to students; and until the textbooks become a tool a student can use and learn from, the “conservatives” will win this argument.

at 3:23 pm

One last thing to my previous post. The other issue facing today’s mathematics teaching is that it is ALL emphasizing real world application. Look at any text, be it first grad, sixth grade, algebra or geometry. 95% of the text involves “real world” application … meaning all word problems.

There is almost no explaining or emphasizing mathematical theory. There aren’t any exercises to learn theory and the basic fundamentals. It is completely swept aside for application. Without being taught and understanding theory and proof, the “real world” applications become meaningless and pointless and no true concept of the subject matter is understood.

at 10:16 am

Even the university dept chair in the article identified the mistake incorrectly. “What the kid did is kept subtracting 10. So they didn’t go down to the smaller unit. And whoever is looking at the problem is supposed to see that the student was confused about place value.” That’s what the father did, as that’s his handwriting on the paper. What the “student” in the problem did is count subtract three hundreds, then subtract six ones to go from 127 to 121, and then the kid stopped without subtracting one ten. So he forgot to subtract the number in the tens place. Not a brainbuster.

Agreed, there are several things wrong with the question and it’s not good for a second grader, but it shouldn’t be that hard for an adult to figure out. I’m more scared that the kid’s dad couldn’t do it.

at 2:55 pm

In response to V. HERRST HMC…HOW RIGHT YOU ARE. I was recently in a small bakery, in a college town. The associates working in the store were all college students. I purchased an item and it was $2.72. I hated the cashier $3.02, so she could give me back $.30. She stared, and stared and stared. I looked at her and said “problem?” Her reply was “my register is not working, so I do not know how much to give you back.” Things like this make me hit the ceiling. I looked at her and said, “you are a college student and you can not give change if your register is not working?” She replied again, her register was not working. I then loudly said “30 cents. This is not difficult honey, this is third grade mathematics, not higher mathematics, and you’re in college.” she then called me an “asshole” and I called her something I can not type.

Your point is well taken and this problem of “basic math skills” existed long before and will continue even after common core. Basic are being pushed aside, learning theorems and postulates is passe, memorization is akin to killing your first born male child, and for what…so that all students can feel good about mathematics. Well, the reality of it is that some students will always do well in math and some will not. except, now we are making it so that even those children whom might have done well, are being hindered for the sake of a few.

at 8:18 pm

Almost all of this discussion is done from an adult point of view, not a second-grader’s. It doesn’t matter one bit if the commenters above can see why this process works; it matters tremendously if the student does.

If she doesn’t, then a teacher should have many other ways of explaining the concept. The question faced by teachers in school systems that have adopted a rigid CCSS curriculum is: “Will I be allowed to show my students other ways of thinking about this?” If the school system is worried that problems like this one will appear on *the test*, then the powers-that-be will probably say “No.” That’s inherently unfair to the students who don’t understand this one particular approach, but might be just fine with another way of looking at it.

at 11:28 pm

I’m so glad I opted to homeschool my sons, using math texts they could actually read and learn from! Despite my being a certified math teacher, I never really had to teach them math after they learned how to read. Now I tutor students who, 1) never think to look at the text to see examples, 2) are tied to their calculators like umbilical cords, and 3) have trouble keeping away from their smart phones while their parents are paying me to tutor them! I am also teaching in a classroom again after many years and find students who’ve never learned concepts I would have expected they needed to, like fractions or the slope-intercept formula. And the textbooks are less student-friendly, as the harder problems rarely have examples. The teachers who write the texts must be trying to ensure that some teacher (with a solutions manual) will always be necessary – it’s called job security for the mediocre! All this makes me even more glad I homeschooled and that my sons all plan to do the same. I just don’t trust Common Core to solve the problem of this generation’s math-ineptitude.

at 9:44 pm

The fact that the most Universities courses that have the most sections are remedial math is proof enough that we are failing our children.

This CC nonsense is going to make things worse.

HS seniors who want to continue on to college need to be prepared for freshman mathematics, which is Calculus and Linear Algebra. If students can not graduate high school and step into one of these classes, he or her HS has failed.

Posters should also note, that the problem being over-complicated is arithmetic, which is a tiny subset of mathematics.

As a CS graduate student, I am struggling to remember the last time I had a mathematical problem that I needed to solve as part of a larger computation system that had any numbers in it at all.

at 8:13 am

Dude should put his B.S. in Electrical Engineering in an envelope and mail it back to wherever it came from.

The answer is pretty easy. Jack counted the 6 ones as 10′s – and he forgot to count the one 10.

I have been dumbfounded by all the examples of people claiming to have advanced degrees who can’t figure out these simple problems.

BTW, counting backwards from the minuend to the subtrahend is actually the way experienced cashiers in the “real world” count out change. Much of common core math involved getting kids to think about math in a way that makes it easier to do IN THEIR HEAD. Counting backwards from the minuend is a far simpler way of doing math in your head than lining up digitis and keeping track of borrows and carries.

at 1:58 am

To get the correct answer you have to have to know the answer already. To get the right answer you have to jump 3 “100′s” groups, one “10′s” and the rest are “1′s” you have to know the answer to answer the question. I could see using this to shorten a graphic depiction, but not as a solid way to solve the problem. It basic creates a group of people who have to count backwards in thier head for every subtraction problem.