Calling all math teachers: Should simple subtraction problem require full page of work?

A Forsyth parent sent me a copy of a note she sent to Superintendent Jeff Bearden with questions about why her young son’s math was so much more complicated than it needed to be. The mom is an engineer by training.

Any math teachers willing to tackle this question?

Here is the mom’s letter and the worksheet:

Dear Dr. Bearden

I know you have a very busy job and the last thing you need is one more parent complaining. However, I am very concerned about some of the methods of teaching happening in our county.

I was reviewing my second grader’s math worksheets and came across a subtraction and addition problem. My son is doing well in math, so this isn’t a parent concerned about his struggles. I like the fact the students are being taught different methods to learn. However, it appears there are strong focuses in certain areas that I have a concern.

Please see the adjacent math problem. You will notice it takes an entire page to come up with the same answer I did in a very short time. When I have my son attempt the problem the simple straightforward way, he gets mathnoteconcerned he is not doing it the right way. Can you please help me understand why the district is continuing to do the base hundred/ten/one method and not the straightforward method?

I have an engineering degree, which required tons of math. Often, it would take an entire sheet of paper to work just one problem. Yet, it involved many different formulas, rules, and variables (calculus, differential equations, algebra, etc).  I’m concerned about how our students are being taught the simple math when later they will be attempting the harder, more complicated math.

I assume there is data that backs up why this method of teaching math has improved results. Is there a place I can go to that shows this information?

There are many frustrated parents who share the same concerns. I believe we are ready to see and hear how we plan to move forward in the future based on data-driven results (not just trying and seeing if it is going to work out).

If there is any way I can assist in any way to help make a difference in our county, please don’t hesitate to ask.

 

Reader Comments 1

83 comments
Betsy Ross1776
Betsy Ross1776

It looks to me like the full page is simply explaining how to do "mom's math."
If we lined up the ones, tens and hundreds in the math problem as "mom's math" shows we can get the answer -- but do the children understand what they are doing?
I'm all for explaining the math in different ways and additional ways so that our children will be good at math as this mother is. 

We need MORE engineers just like this smart mom and LESS fry cooks at McDonalds.
If explaining the math in several different ways makes the children learn better, by God, let's do it!

OldPhysicsTeacher
OldPhysicsTeacher

Whole Language vs Phonics..... Now this...when will people learn that not everybody is "gifted?"  Sure, the upper 10 percent can understand HOW and WHY math works at an early age and will thrive.  The 90% that's left will struggle with this and hate math even more.  If you want to separate out the top 10% (like schools, and most parents, are really competent to do this?), fine, but don't try this on everyone.  Kids mature at different rates.  How about this:  we don't use any teaching technique that has not been put in place in Scandinavia, Germany, or China FIRST, AND SHOWS POSITIVE EFFECTS?


We don't do this in medicine.  If an MD came to you and said, "We have no evidence this will really work, but we believe in our heart it will, can we experiment on your children?", would you do it?


Sigh, in 5-10 years different researchers will show that there is no overall effect of this new math working any better, and essentially it'll take another 10 years to get it stopped (colleges of education will continue to graduate 21 year-old math teachers who bought into this), and we will have lost an entire generation.  In French there is a phrase, "The more things change, the more they remain the same."  It applies here.

liberal4life
liberal4life

@OldPhysicsTeacher 

You are giving colleges of education way too much credit.  The biggest factor in teacher preparation is the cooperating teachers during the student teaching.

Quidocetdiscit
Quidocetdiscit

@OldPhysicsTeacher


From my experience, I am seeing just the opposite.  My students, overall, seem to enjoy math much more using these hands on, constructivist based math techniques. That includes my lower level and upper level students.  They have fun exploring math concepts as we "play with numbers".  That being said, the teachers I work with are all "veterans" so we know how to best "tweak" whatever "new and improved" program is handed down from above - so we differentiate.  Those that are ready to move on to more traditional algorithms and approaches (having demonstrated they know the underlying concepts) are allowed to do so, as they are often more efficient.  Those that cannot deal with multi-step problems (very low ability) move from concrete to more traditional approaches that reply more on memorization of discrete steps and less on understanding of the underlying concepts.   Good teachers do this naturally - we also balanced whole language and phonics - determining what worked best for each individual student. That is what comes with being in the classroom for several years and "learning" what works with children.  However, it seems the tide is turning against veteran teachers, as folks suggest teachers need to be young and fresh (and cheap) in order to be any good at what they do, and that older teachers are 'out of touch and too expensive."  A good faculty needs BOTH as veterans and newbies both have strengths too offer.

Happy Hippie
Happy Hippie

My son is learning this math this year in accelerated first grade and he has had a lot of fun (really - fun!  With math!  Go figure.) learning that he can reach the same answer using different maths. It looks weird to us because we aren't used to seeing it presented this way - but to the kids, this is a great foundation.  I didn't really get it at first, but now that I understand why it is being taught this way, I think the new math is incredibly useful because it teaches the foundation of how to add and subtract large numbers in your head very quickly. My son is in first grade and he can add and subtract in the thousands in his head because he has learned to do it using the big number blocks first rather than the ones first, which is how I learned. What you are seeing on the page in the story is just the most basic foundation. The kids quickly move on to other methods. For some kids, this method is what will stick. For others, who use their brains in a different way, they will reach the answer another way that they will be taught as well. By showing their work in detail, they are showing the teacher that either they fully understand the material, or exactly where they are having difficulty.

BurroughstonBroch
BurroughstonBroch

Nothing new in this - it's yet another educational repackaging of what was called "New Math" in the 1960s. Tom Lehrer hit it spot on in his song "New Math", "the important thing is to understand what you're doing rather than to get the right answer."

If we want every child to be a potential university math major then this is the method they should be taught. But don't expect them to quickly solve simple problems in their head or without pencil and paper to graphically depict the solution. If we don't expect every child to be a university math major, then they should be taught the traditional method that will quickly produce the correct answer.

Of course, today's students depend on a handheld calculator as a crutch and are often clueless when asked to solve a trivial problem without a calculator. Ever watched a millennial try to make change at a cash register when the register is on the blink?

ateacherfirst
ateacherfirst

As the poster below noted, this is the same method. The graphic representations show students how 3-2=1 nor just that 3-2 =1. Showing them how the process works teaches students to think mathematically rather than just to know the answer. As a teacher, I've encountered many students who will say "but how do you know that 3+5=8?" When students see it, they get it. This is a paper version on using manipulatives like marbles or something to demonstrate the process. 


This way of presenting problems and other techniques (such as showing students that if 3+5=8  then in 3+? = 8 the ?=5 allow students to experience the ideas of using known quantities to find unknowns before they hit pre-Algebra or Algebra. 


In short - this approach teaches mathematical reasoning and problem solving skills.


My brother and sister in law had the same concerns about my niece's math until I explained why it is approached that way.

KeepinItSimple
KeepinItSimple

Wow.  All that writing and she didn't even realize that this method is the EXACT same method she used.  The only difference was it had a graphic to go with to help show it visually.  They subtracted the ones, but there weren't enough so they took one from the tens and added ten to the ones and then proceeded.  SAME THING she did, just without visuals.


I am sure this is just the entry point to learning the method and eventually the graphical depiction will be dropped.  Showing the steps is critical when learning arithmetic and math based sciences and will continue through advanced degrees in math and math-based sciences.

OriginalProf
OriginalProf

@KeepinItSimple 

I think this letter shows that knowing the subject-matter is not the same as knowing how to teach it! Pedagogy is a skill.

redweather
redweather

@OriginalProf @KeepinItSimple  You all are having a lot of fun dismissing those of us who question this lesson.  When I look at the instructions and the graphics, it appears to be anything but simple and obvious.  Graphic illustrations were being used when I was in the second grade--I seem to remember adding and subtracting blue birds and colored balls--so that part of this lesson shouldn't raise any eyebrows.  Rather, it's the way the instructions are delivered that I find less than crystal clear.  There are surely better ways to present this concept using graphics.  I can think of a quite a few that would make this a whole lot more understandable.


Okay, now you can go back to laughing at the rest of us.  Whatever floats your boats.

popacorn
popacorn

Educator, educate thyself. 

liberal4life
liberal4life

@KeepinItSimple 

Isn't it amazing.  I think you are one of a few posters who understood the methods shown on the worksheet is exactly the same as the traditional algorithm.  I think it is an evidence of how little people truly understand mathematics - even elementary school mathematics.

Drexel-Gal
Drexel-Gal

@KeepinItSimple I noticed the same thing.  It seems as though everyone wants their fifteen seconds of fame (no longer fifteen minutes, given today's attention spans).


Must be another slow news day.

HS_Math_Teacher
HS_Math_Teacher

(200 - 100) + (70 - 40) + (3 - 6) = 100 + 30 + (-3) = 127


Truncating numbers (100's & 10's), and adding the differences seems like a better alternate way of teaching this; however, I don't know if kids learn or know anything about "integers", or dealing with negative numbers at the target grade/level here.  I don't know much about teaching elementary kids; however, I do know one thing - never confuse students, and try not to bore them, or you'll lose them.  Sometimes the convoluted, concrete-visual approach can backfire.  

HS_Math_Teacher
HS_Math_Teacher

@liberal4life @HS_Math_Teacher


I see.  I can appreciate the aim of the worksheet - manipulatives and visual aids can effective tools for teaching algebra (polynomial arithmetic and solving equations).  Like another poster mentioned, I am sure the traditional method would be introduced and used once kids have a foundation set. 

liberal4life
liberal4life

@HS_Math_Teacher 

Integers are first introduced in Grade 6 - no calculation with integers.  So, 2nd graders will definitely not have integers as their reasoning tool.

popcornular
popcornular

If only we could invent a math that required no work whatsoever to master.

EdumacateThat
EdumacateThat

I was "one of those mothers" that asked the teacher, school and county administrators, etc., about this crappy New New Math.  I hear what everyone is saying and I totally understand that kids learn differently and at a different pace, BUT... my issues was the LACK of differentiation that they purported to be providing elementary students.  Please don't insult my intelligence by telling me differentiation is working well, and then turn around and mark wrong a student's work that used the simpler, traditional method just because you wanted them to draw out a friggin' lattice.  This actually happened to my kids.  Thankfully, they are beyond this now.

True story:  I still remember a New New Math guru telling me that if didn't matter whether a student got the right answer in math.  What mattered more was that they were talking about math, doing hands-on math, and could explain their process of how they arrived at their answer even if it was wrong.  Whoa!  Math is a language that demands accuracy.  What a dweeb.

Another true story:  I have spoken at several county school board meetings about the math insanity.  Three years ago, a HS principal stopped me and asked me why a good chunk of HS kids had trouble doing multiplication, division, fractions, etc.  Simple math, really.  I gathered up some worksheets from several parents of ES kids (all different grades) and asked her if she thought anything had been mastered... considering the numerous processes taught.  Sometimes, too many pathways just muddies the ground.

Wascatlady
Wascatlady

The mother's question would have been answered by the teacher, if it had been asked.


An important reason to "show your work" is so the teacher can figure out WHERE you are confused, so s/he can help you.  And, when I was teaching this, I taught my students that it was helpful to have more than one tool in their toolbox.  Not only to help you check your answer, but in case you get stumped.  For example, if you know how to do partial products for two digit multiplication, you can check your work, or if you come out with an answer that does not make sense, you can use pp or the lattice method to figure out what is wrong.  Of course, that requires patience and an unwillingness to just slap down any answer.


What I saw with fourth graders, particularly, is that their parents called these alternate strategies "stupid" and reinforced the rush through method of putting down answers without showing HOW you got there (each step), so that when they missed a problem they did not understand why.  Getting them ingrained to do it step by step and show their work would help them when they got to truly hard math, and save lots of frustration.  You'll never get to Diff Eq unless you do!  (little math joke)


As a former teacher, I know I was able to help students get past repeated mistakes once they started showing their work so that we could analyze where the glitch was.  That is why, for many, the "full page of work" is useful.



grumpster
grumpster

@Wascatlady 


This semester is Linear Algebra for me.  All the way through my math courses, it was "show your work, show your work".  Sometimes I got frustrated with that - after all, I can do this in my head.  I didn't realize that everybody is not just like me. 


Now that I'm back in school and doing "higher" math, I see the value in showing your work.  Not only does it force me to think the problem through step by step, it does, as you said, allow the professor to spot where I went off track and give me some constructive feedback to help straighten out my thinking.


And I firmly believe that one good problem can take a page or more to solve and it can teach me more than a page full of simpler problems would.


Now if I could only remember how to do long division... This CRS syndrome is killing me.

BKendall
BKendall

@ Maureen... After reading the comments I can honestly say, "I am thankful I do not have your job." 



RichardKPE
RichardKPE

Looking at the problem in question, the parent missed the point that her method and the one being taught are EXACTLY the same.  The one in the homework was simply shown in a visual manner.


I don't have an issue here unless the student never advances past this level.

MaureenDowney
MaureenDowney moderator

The mom sent me an update that Forsyth County responded to her and explained the rationale. Her is her short summary of that conversation:

From the parent:

I now understand why they are taking this approach. We discussed that yes some people get math very easily, such as my son and me. However, others don't and this approach helps give them a foundation to be successful now and later on. In addition, it prepares the students earlier for algebraic scenarios before they would normally first see it in middle school, in which those that may struggle with math might have a very hard time grasping.  He said my straightforward subtraction method is introduced more in 3rd and 4th grade for all. I understood what he was saying.  

Dr. Bearden would be a good person for you to talk with on this subject. This method of teaching our younger kids is not how we were taught and hence the parent's frustration.

Mirva
Mirva

What people outside of education don't understand is that there is a big difference in doing something and teaching that thing. Just because you don't understand why something is being taught this way, doesn't mean that is automatically stupid and worthless. Everyone is the expert on teaching but the teacher. This parent starts a letter trying not to be "that" parent, but going to the superintendent with a question about a second grade math problem is that parent.  Why not have a meeting with the teacher? Or the Assistant Principal in charge of curriculum or the math specialist? Forsyth county schools turn out some of the best and brightest and most accomplished students this state has, so there must be a method to their madness.  

BKendall
BKendall

@Mirva What we don't know about this situation is more than we know.  One should not assume the parent did not talk to the teacher, the math specialist, the assistant principal in charge of instruction, or the principal before seeking an answer from the Super.  

hssped
hssped

My experience with this type math is that the avg and above avg IQ kids get it.  They see the patterns sometimes before they are even introduced.  It's not a big deal for them.  They don't like drawing the models though (they don't like showing any work).  But, the below avg IQ kids just get confused and can't remember how to draw the models.


On another note...Bearden sure does hop around!!   He screwed FC out of a whole year's pay and then took off for Rome. Now he is in Forsyth??  They have my sympathy. 

BKendall
BKendall

@hssped average and above average IQ is not a guaranteed determinate in the ability to learn mathematics. 

Wascatlady
Wascatlady

There is a lot of emphasis now on teaching the why, and on using various strategies to come up with the correct answer, unlike in the 1950s when you just accepted that "these are the rules, this is how it works, follow the procedure and you will get the right answer.  I was always good at math; I never worried about understanding it.  I just followed the rules and made 100.  It was not until I got into college and learned HOW to teach math that I actually understood WHY these rules produce the correct answer!


I like the idea of teaching the kids multiple strategies to get to the answer.  What is a problem, however, is when they get the different strategies mixed up.  I saw this a lot in remedial sections of 3rd and 4th grade math.


Let me also mention I worked in adult literacy for a while.  Without exception, the students could not remember how to do subtraction with regrouping and anything related to fractions.  They had no strategies that allowed them to come up with the correct answer.  That was sad.  I spent a great deal of time showing them, in second, third, and fourth grade terms, WHAT they were doing so they could choose a way to find a solution.


I do think the parent should have talked to the teacher.  That teacher could have saved the parent a lot of angst and embarrassment instead of bringing it as a complaint to the superintendent.  However, in this day and age, EVERYONE knows better than the teacher, and EVERYONE wants to start at the top to get information.  It is a symptom of the times.

DawgnIT
DawgnIT

There are many problems with schools today but this specific case is a non-issue.  

The title including "Should simple subtraction problem require full page of work?" is misleading mainly due to the parent's assessment being misguided.  By reading this title along with the parent's letter, the suggestion is that the student had to do something requiring a full page of work to solve a subtraction problem.  The example presented shows that this is NOT the case.

The example worksheet is nothing more than a fully articulated and visually supported lesson on how to do subtraction.  I don't know why this parent is categorizing "straightforward" vs "base hundred/ten/one".  What does "straightforward" mean, not using fingers, a calculator, or not showing work?  Well the parent showed her work and it supports exactly what the lesson intends to teach.

Mom's math shows that you cannot subtract 6 from 3 so she scratched out the 7 in the tens place (70) and reduced it to 6 (60).  Then she added the 1 taken from the tens position and placed it with the 3 in the ones position making it 13.  Isn't that pretty much what Step 1 descibes in words and visualization?

The mom then solves the ones place for 7, the tens place for 2 (20), and the hundreds place for 1 (100) giving an answer of 127.  Isn't that exactly what Step 2 shows in words and visualization?

Kids aren't born knowing how to do this stuff but some learn the concepts faster than others.  It's no secret that many in our societ dread math and continue struggling with it as adults simply because math concepts can be intimidating when taught so many students never master those concepts.  What's wrong with giving both articulated and visualized examples with the lesson instead of "teaching" it by just doing it "straightforward" and telling those students who don't get it to just trust the process and figure it out?

Congratulations that your child has mastered subtraction.  But the real story here seems to be a mother who cannot manage the child's budding self-esteem/self-doubt issue.  

"When I have my son attempt the problem the simple straightforward way, he gets concerned he is not doing it the right way."

As an engineer, why can't this mother probe for the source of her son's concern and provide a solution that doesn't require writing a letter to a public official?

I'm only guessing but I assume this child is conditioned to watch his teacher's example and mimic it exactly to gain approval.  I wonder where he learned that behavior.  As an engineer, why can't this mother explain that there are many potential methods for solving a problem with some being more efficient than others?  Why can't this mother also explain that as long as the child is producing the correct answer, he's fine since these varying methods are all really encapsulating the same fundamental principles which is why the correct answer is the correct answer no matter how you reach it?

UGAGuy
UGAGuy

@redweather I'm not a teacher and wouldn't want to be with the way they are currently treated.  With that said, your son's work SHOULD have been marked wrong if he failed to follow the instructions.  Imagine if your science teacher gave your son the following short answer test:  Explain why the sky is blue.   Your son answers, "The sky is blue because that is the color we see."   Is he technically correct?  Yes.  However, he didn't explain why that is the color we see.  Therefore, his answer is WRONG.  


If he didn't answer the question as instructed, he was wrong.  If you want to be successful in life, you have to learn the "why" component.  You also don't have the luxury of going through life and always doing it "your way" and never answering to anyone else's expectations or instructions.  

redweather
redweather

@UGAGuy @redweather And what does the "why" component amount to in the graphically illustrated page accompanying this blog article?  Explain it to me, but go slow because my brain is only that of a functioning second grader.

DawgnIT
DawgnIT

@redweather @DawgnIT I did consider that but I didn't read anything in the parent's letter stating that the teacher would mark answers wrong for not obtaining the correct answer.  If that's the case, then a new letter should be written.  As such, I'm sticking with addressing exactly what the parent wrote as a concern.  In any case, I remember my child going through this many years ago and it wasn't the end of the world.

redweather
redweather

@DawgnIT @redweather  It may not be the end of the world, but the way math is taught these days seems unnecessarily confusing.  There may be sound pedagogical reasons for doing this, but they were never abundantly clear to me, and I was good in math way back when.  Still am, for that matter.

DawgnIT
DawgnIT

@redweather @DawgnIT Okay, so what's wrong with my post?  I pointed out how the mom's work was exactly the same process that the lesson illustrated.  They are in fact teaching the exact same thing with words and pictures.

redweather
redweather

@DawgnIT  I think you've misread the son's concern.  I can remember my daughter telling me that she and the other students in her math class "had to find the answer in a certain way or it's going to be marked wrong." And this was for fairly elementary stuff.  They weren't doing geometric proofs.  That may by why this young man is concerned.  Maybe his teacher will only accept his answers as correct if he crosses through the illustrations correctly.  As I used to complain to my wife, why can't these children be allowed to arrive at the answer in more than one way?

JustThinking07
JustThinking07

The parent in this case was taught to subtract using  traditional algorithms. Yes it allows the user to get the correct answer quickly but does the student actually understand what is happening? Students should not learn short cuts or "tricks" until they discover for themselves or understand why that method works. Terms like "borrowing" are really incorrect. In Math we don't actually borrow- we regroup. Children that don't have an understanding of the Base 10 system will think they are magically turning numbers into 9s or 14s. You can say that you have concerns about students not being taught using traditional algorithms but the United States currently ranks 30th in world in Mathematics. Most of our students do not understand or like math.

You might want to investigate Math in Singapore. http://www.echohorizon.org/cms/lib/CA01001232/Centricity/Domain/16/Singapore_Math_Intro.pdf

The math curriculum in Singapore has been recognized worldwide for its excellence in producing students highly skilled in mathematics. Students in Singapore are typically one grade level ahead of students in the United States.

Lexi3
Lexi3

Westerners have known the best way to teach math since before Archimedes and his Sand Reckoner. Seems as though education reformers in the last century have a need to do something important, to "contribute," and they have-- to math illiteracy. Then too, few learn American history, world history, literature, writing or anything else useful in the progressive era of decline.

Enoch19
Enoch19

So based on the 25 comments here there is no evidence that most children learn better with such methods?


I read a few comments defending the system and some attacking how this math is being taught.  What seems to be missing is a meaningful, data driven conclusion.


Has common sense gone on sabbatical in our schools?




RealLurker
RealLurker

What grade level is this worksheet for?


I too have an engineering degree.  The mom's solution also uses the ones/tens/hundreds method, but leaves out all explanation.  IF this is for a very early grade in which they are teaching the method, I have no problem with it.  If it is for third or fourth grade, in which the students should already understand the method, then it is an issue.

HollyJones
HollyJones

@RealLurker The mom states in her letter to the superintendent that this is her son's 2nd grade math.  


RealLurker
RealLurker

@HollyJones @RealLurker I missed that when I read through it.  


Reading the statement from the mom after discussing with the district, it appears that they use this in first-second grade to teach kids the concepts and then abandon this method in third and fourth grade.  It makes perfect sense to me to teach this way.


Lee_CPA2
Lee_CPA2

Seems to me if a child could read and comprehend those instructions, they should be able to work a simple math problem in columnar form. And if they need visuals such as this in order to work this problem, then you need to go back to square one.

Tell you what, go find a textbook from the 60's and figure out how they taught it back then - then use that method.

redweather
redweather

@Lee_CPA2  "Seems to me if a child could read and comprehend those instructions, they should be able to work a simple math problem in columnar form."


Go to the head of the class.

DawgnIT
DawgnIT

@Lee_CPA2 That's the rub here.  Many Americans are deathly afraid of math including those who were in school in the 60s.  That includes many people who can read and comprehend at a high level but aren't great at math.  Some people "get it" while many don't and fear math the rest of their lives to the point that they can't make change, can't budget, can't invest wisely, and don't work STEM jobs while other markets continue to dive in the toilet.

For those students who master concepts quickly, this is a non-issue.  It's the many students who just get by without mastering basic math who suffer in the long run and I think that's what this lesson intends to target.  For students who are naturally weak in math but strong in reading comprehension, it seems like this method would help them greatly.

The idea is to stop having to go back to square one in later grades.  A lot of time is wasted on refresher courses teaching topics that should have been learned in previous grades.  I mean refresher courses are great at the college level for adult learners who have been away from school and working with a specific skill for a long time but should grade school kids really need entire refresher courses as part of their curriculum?  Passing by definition suggests that the student should have learned it the first time.

Lexi3
Lexi3

@HollyJones @DawgnIT @Lee_CPA2 


The proof of the pudding is in the eating. Education at the primary and secondary levels is blessed with "something new" every several years, yet none of them work well. Is this the right iteration, like the newest diet-this time it's real?


I tutored math at the college level. Most of the kids I worked with had gaping holes in their mastery of the fundamentals. And, to make matters worse, most were cursed by well-meaning, misguided individuals who told these kids that "some people are just not good at math." That advice becomes a self-fulfilling prophesy and an excuse for the kids not to try. Why bother, when you're destined to be "bad"? Most folks smart enough for a solid college are smart enough to master college level math, once they overcome the self-doubt, associated anxiety and missing basics. I'm not convinced the newest new methods are going to make meaningful improvements over the ancient methods. I suspect they'll make things worse.

HollyJones
HollyJones

@DawgnIT @Lee_CPA2 I was exactly the student you describe- I am able to do a number of things very well, but math was never one of them.  I could only work a problem if it was exactly like the example because I didn't understand the how and why.  As I see my children's math work, I keep thinking, "That makes so much sense.  Why couldn't my math teachers have explained it like this?"  My kids are taught multiple ways to arrive at the answer, any of which are accepted by the teacher.  But they are also given some drill exercises for the fundamentals  They have had addition, subtraction, and multiplication timed tests.  My daughter had a math teacher who had a daily problem where they had to go from fraction to decimal to percentage- skills I still can't do without a calculator.  


I find it fascinating that the outcry over new teaching methods focuses so much on math.  This is my guess- because so many of us aren't good at math, probably only know the one way we were taught to do problems, we can't wrap our heads around a different approach (I include myself in this group).  Conversely, those who "got it" easily can't understand why there is a need to change something that, to their mind, works just fine (this would be my Georgia Tech grad husband who rocks at math). 


The problem is that what works for one student will not necessarily work for another.    Teachers are required to differentiate instructional methods to reach all the many learning styles and levels in a class.  That is why we're seeing all these varying approaches- but it's not a bad thing.  It's not "dumbing down" and it's not ruining math for everyone.  It's just new.