### Everyday Math + Investigations = ?!?!

Why do I have to learn algebra that I'll never use? Ah, the universal question posed by many of my friends when I was a kid. Only this time, it came from my nephew -- the next generation. And sister-in-law's comeback was great! "Yes, you will. When you have to teach it to your kid."

Clearly, math is one of those subjects that gets parents riled up. Just look back at the comments last month in "Do You Kumon?"

From Arlington:

I'd love to see a study on the correlation of a Kumon's center revenue and the local public school's use of Everyday Math, Investigations, or other new-math-crap that fails to teach foundations. Kumon's popularity has risen in response to a failure of the public schools to teach math properly.

and justlurking:

I put my kids in Kumon when they were still counting on their fingers in fourth grade. Thanks, Everyday Math. They're not too thrilled with it, but I got worried when my daughter started telling me that she 'just wasn't any good at math.' Now she wants to be an engineer. Seems like a good investment to me.

Pair that with parents in Prince William County who are battling against the math curriculum called "Investigations in Number, Data, and Space." Clearly, plenty of parents don't think these newfangled math approaches are working.

Everyday Math is used by 2.8 million students, according to the curriculum's Web site. It strives to apply math to real world situations, has many ways to review information already learned and encourages students to explain how they have derived their answers. Investigations, meanwhile, directs students toward understanding blocks of numbers by tens or hundreds, for example. Rather than memorization, students are encouraged to find answers creatively through drawing pictures or playing games.

Recently, I borrowed a concept from Everyday Math without much thought and tried to get 6-year-old to explain to me how he knew a simple computation answer. His response: A blank stare. "It's just 2, Mommy" was his answer. Hmmm. Maybe I need to approach these questions a different way or stop digging.

How are your kids doing with these math curriculums? What works and what doesn't? Do we like memorization better than these methods because that's how we learned?

By Stacey Garfinkle |
February 28, 2008; 7:00 AM ET
| Category:
Elementary Schoolers

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### Comments

Posted by: FashionistaMom | February 28, 2008 7:56 AM
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My initial guess why math is such a problem in schools is because the people developing and teaching the curriculum really don't understand math themselves. I am not talking about arithmethic here. My guess is they do understand additions, subtraction, multiplication, and division. But they have no higher understanding of mathematics. They think it is just computation. Therefore they can't develop or teach math correctly. I would have to say one approach (which is probably feasible for an entire classroom) will always leave some kids behind. I agree with the first poster about learning different approaches. How you implement several approaches to 25 kids seems like a challege to me. But at least they would have different tools to work with. The problem with straight memorization is you forget the material easily and quickly. Then your left with nothing. Also to really do math, you need a lot of foundational material before you can do the fun stuff. I say let kids learn the way they want to learn. Life is a much better teacher then anything.

Posted by: foamgnome | February 28, 2008 8:12 AM
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Everyday math is, in my opinion, a disaster. It insists, among other things, in having students master several different ways of solving mathematical problems. This is peddled as providing choice and perspective, but in fact that is an illusion, because all of the various methods must be mastered by every child, and each is tested against. As a result, a ton of time is spent learning various methods, instead of focusing on one method and moving forward through concepts faster. This is a disastrous mistake.

As for memorization, I tend to agree that focusing on rote memorization for arithmetic may not be a great use of time, but I think that the situation changes when it comes to multiplication and division. There are multiplication facts that are simply very, very useful to have on the tip of ones tongue, but, again, instead of giving the students the opportunity to plug these facts into their super-absorbent brains at a young age, the curriculum fills that space with nonsense like "partial sum multiplication".

As a result of this mess, we're simply supplementing our son's math education on the side at home using the well-known Singapore Math curriculum. Fairfax county's approach to this is almost completely useless.

Posted by: Brendan | February 28, 2008 8:13 AM
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Counting on your fingers is NOT inherently bad. It is just another method of calculating, and it is more effective at showing on had learned concepts over memorization. My undergrad degree is in math education (secondary) and my masters is in engineering (I wasn't cut out to be a teacher). I still count on my fingers sometimes. And frankly, I never totally memorized my multiplication tables (I still get jumbled in the upper 7s, 8s, and 9s.

And EVERYONE uses algebra in life, they might just not realize it. I have a good friend who is an editor. She helps me with grammer, and everytime she gets a new job, she sends me the numbers and has me figure out what percentage increase she is looking at. For example, she if is making $40k and has an offer for $44k, she wants to know what the percent increase is. Thats algebra folks. And one of those dreaded word problems, too.

Calculus? Thats another story. For as much as I loved it (my love for calc is the reason I majored in math), I couldn't differentiate or integrate today if my life depended on it. Although the logic skills learned in advance calculus and proofs are still used.

Posted by: RT | February 28, 2008 8:15 AM
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Different people do indeed learn math different ways, but I strongly believe that some "memorization" is required before moving on to some of the more advanced concepts. And that includes addition and subtraction, as well as multiplication and division.

The problem is that the math curriculum tends to swing wildly between the two ends of the spectrum ("memorize everything" and "understand math theory and then prove that 1+1 = 2"), and when the pendulum is too far one way or the other, you're not helping the kids. A good balance is necessary.

(This is not too different from the battle between "phonics" and "whole language" in English classes.)

When I was teach college classes, I used to only give open book exams, because real engineers don't memorize things, they understand how to solve problems. On the other hand it really helps to have a lot of the facts memorized. It really bothered me when I was teaching "Statistics for Liberal Arts Majors" (Math 141 at the time) and somebody would stop me to ask how I knew that the square root of 49 was 7, or how I could be sure that one-half was equal to 50%. Yes, I could have proven those facts but it would have been a waste of time.

My youngest is now in sixth grade so we're largely avoiding the Everyday Math stuff, but to me it's a good idea that suffers from the problem that the kids don't have a basic knowledge of math facts BEFORE they start it.

(And re: FashionistaMom's comment about mathematicians spending a lifetime on a problem. When I was a grad student at Purdue I had the office across the hall from Louis deBranges when he was working on his Bieberbach proof. Talk about a fanatical, devoted guy!)

Posted by: ArmyBrat | February 28, 2008 8:32 AM
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ArmyBrat is so in tune with my feelings about Everyday Math its amazing. When my daughter started kindergarten, they introduced it at our school and I thought it was great, it really seemed to take math and match it up to the ways I had always done it in my head anyway. It's interesting that they try to find a way to do these things functions in different ways so that a kid can find a way that they are most comfortable with and truly understand what they are doing. The problem is, that the kids have no strong foundation in math. My daughter is now in fifth grade and still struggles with basic addition and subtraction. She knows 7 ways to do long division, and is terrible at all of them. We've taken to doing about 30 minutes of flash cards of basic multiplication so that it only takes her 1 hour to do 3 problems as opposed to 2. They just go through so quickly through all of these concepts that the kids don't get enough practice to really grasp them. Nice idea, just extremely poor execution.

Posted by: Chris | February 28, 2008 9:35 AM
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The thing about addition, subtraction, multiplication and division is not IF your child can get the answer correct, it's how FAST you child can get the answer correct. When my son was in 3rd grade, I got sick of fighting with him to do worksheet after worksheet of the basic multiplication problems for homework. Most of my effort was expended by getting him to sit still for the 20 or so minutes to concentrate and write down the answers. I couldn't understand why he couldn't just burn through the worksheet in a minute or 2 and get it over with.

So I went to my computer and wrote a program to teach him his multiplication tables. Then I made a deal with him, either do the worksheets or learn the tables on the computer. He chose the computer, about 20 minutes a night.

Two weeks after he learned his mathfacts on the computer, he burned through those silly worksheets in a minute or 2. Cool!

Since then, I've improved the program and included addition and subtraction. Right now, my kindergartener is using it to learn addition.

Anyway, if you have a k through 5 kid that needs to learn or could use a little practice with the basic facts, you can download this program using the link at the bottom of this post.

By the way, it's completely free (I have no intention of making money off it), there is absolutely no advertising, and it installs in seconds. It's also fun for adults too. Of course, if you happen to use it, tell me what you think when you get a chance. Have fun!

Posted by: DandyLion | February 28, 2008 9:37 AM
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I agree with everything ArmyBrat said, including the phonics/whole language issue.

And I also agree that elementary school teachers are often not comfortable enough with mathematics to 'get it' themselves.

With an algorithm based curriculum at least these weaker teachers can step through the agreed-on algorithm. With a spiralling, broad-reaching curriculum like Everyday Math I think it can become a disaster.

I do think it is great to give kids alternate algorithms and theory, but often I think kids need to feel grounded with a few standard facts and algorithms before they go on to experiment.

This was a compelling video about it, if biased:

http://www.youtube.com/watch?v=Tr1qee-bTZI

Posted by: Shandra | February 28, 2008 9:56 AM
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I agree with everything ArmyBrat said, including the phonics/whole language issue.

And I also agree that elementary school teachers are often not comfortable enough with mathematics to 'get it' themselves.

With an algorithm based curriculum at least these weaker teachers can step through the agreed-on algorithm. With a spiralling, broad-reaching curriculum like Everyday Math I think it can become a disaster.

I do think it is great to give kids alternate algorithms and theory, but often I think kids need to feel grounded with a few standard facts and algorithms before they go on to experiment.

This was a compelling video about it, if biased:

http://www.youtube.com/watch?v=Tr1qee-bTZI

Posted by: Shandra | February 28, 2008 10:05 AM
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Math is abstract and abstraction as well as formality. The old school is to build up the formal rules brick by brick. For many children this works and for many others it is tedious. Tedium makes for poor learning. So, other approaches to get concepts across that engage children and help them learn are more valid in their case than the formal approach. My son once got a "0" on the solution (not the result, but the solving) to a problem and then that was scratched out and he got full points for the problem. The (enlightened) teacher realized that his approach, while wildly different, solved the problem in a perfectly good and analytical fashion. Now he is 17, in college and is a reluctant math and physics whiz. (I gather that being a nerd does not fit in well with ripping the hills on his snowboard).

Learning by rote (eg: multiplication tables) is not for everyone. And if it's not for someone, it should not be forced as long as the kid learns how to solve the problem. Concepts first, real life math next, formal math last is a valid approach for many students.

And better that they get there, by whatever path, than not get there at all.

Posted by: Alan Browne | February 28, 2008 10:06 AM
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I like the theory behind Everyday Math but in practice it has not served either of my kids well. In theory, it's nice for kids to get exposed to different ways to solve the same problem if they can then pick which method works best for them and become expert at that! Or if teachers could see what works best in their particular classroom and focus on that.

But that's not what happens. The teachers march through the curriculum page by page. For my older daughter it was slow and kept coming back to concepts she had a firm grip on. When I inquired about enrichment activities for her, the teachers were totally flumoxed. No one seemed to have anything. She had homework each night that bored her to tears and left her hating math though I made every effort to find supplemental materials/puzzles to keep her from turning off totally.

Meanwhile my younger daughter can't deal with the constant shifting between material. It's as if she was just expected to come in one day knowing all her multiplication tables and apply them. The work never focused on one task for long enough for memorization to take place for her. (though my older one has a locktrap memory and got her multiplication tables down with no practice whatsoever.)

So I'd say it's time to review the curriculum. I don't see it working for kids on either end of the ability spectrum though it might if teachers were given greater flexibility to use it in a way that works for their own classes.

Posted by: anne.saunders | February 28, 2008 10:24 AM
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Can someone please explain Every day math vs Investigations? As a parent of an infant, it's been a long time since I've had to deal with the learning of math skills, but as it is something on the horizon. I'd like to understand the situation before we get there. I guess I am confused as to which is the Math (if either) that we learned in school, and how they differ from each other. Thanks!

Posted by: jp | February 28, 2008 11:20 AM
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It is absolutely pathetic that there are only 12 comments on this. Parental involvement - heck, anything but parental indifference - is what makes kids want to strive and achieve. It's no secret that our kids are falling behind in math and science. Yet try to get a conversation going on a blog with caring, educated parents -- and you only get 12 comments! And 3 of them are duplicate posts by Shandra! That is parental indifference at its worst.

But when start gabbing about picky eaters or disciplining other people's kids - watch out! 10 times as many comments.

No wonder our kids are falling behind. It's not the math textbook's fault - it's OUR fault for not caring enough to even want to discuss it.

Posted by: Pathetic | February 28, 2008 11:46 AM
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2* of them are duplicate posts.

Posted by: Anonymous | February 28, 2008 11:47 AM
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Ok, here's a thought...why don't schools group students into classes based on learning styles? In the 80's it was all about dividing classrooms by ability, we decided that we didn't want to hurt anyone's self-esteem. Now most districts place students of all abilities in one room where some kids are bored and some aren't getting enough attention. There are at least 8 documented learning styles, some of which work well together. Doesn't it just make sense that if we put the kids who learn similarly in one room with a teacher who can adapt to one or two particular syles of learning that they will get more out of their classroom experience? It even makes a teachers job easier...

Posted by: Momof5 | February 28, 2008 12:01 PM
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I think every math curriculum has it's own issues. My daughter's school uses the Saxon program so there is A LOT of review even while new concepts are introduced. So much reviewe, in fact, that our daughter refuses to acknowledge that she has learned anything new and thinks Math is too easy and boring. Interestingly, she loves Math as a subject and does workbooks etc. during breaks from school.

Our problem with Saxon is that, like other curriculums, does not allow for individualization.

Posted by: 21117 | February 28, 2008 12:04 PM
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My daughter used Every Day math until this year (6th Grade). They are using another Math Book in 6th grade much to some parent's relief. She hasn't had any trouble with math except for the multiplication tables memorization. She HATES any type of memorization, and I really don't blame her. I didn't pay much attention to the Math techniques being used. She understood what was going on. As for me, I had no clue what method she was using. She'd get frustrated with me when on those rare occasions, she had questions.

When I was in school in the 60's we had "new math", whatever the heck that was. I remember my parents scratching their head and, even though they were college-educated, they had a hard time helping me. Does anybody remember "new math"?

Posted by: Anonymous | February 28, 2008 12:11 PM
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I think when it comes to secondary schools, it's best to shove as much basic skills in them as possible to prep them for whatever they choose to leap into after that.

I did have a love/hate relationship with math because it was honestly the only subject that did not come naturally to me and the only one I had to struggle through and achieve good answers with. I loved our AP Calc class because the teacher only graded on tests. Homeworks and classworks (mostly reviewing homework and then adding a new step) were always about the PROCESS of getting the answer and understanding how the system worked.

I didn't love the multiplication memorization either, but it really does just help constantly with basic stuff all the time.

As always, it's important to try and work at it from the perspective the child will understand and learn through so they can take the next step.

Posted by: Liz D | February 28, 2008 12:20 PM
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I agree with foamgnome. Basically, many people who go into early childhood education love kids - but hate math. So those people are who are teaching the kids math. It hasn't worked for zillions of years (hey! why do I know this? Cause we keep changing the curriculum every few years).

Momof5: that's what we did when I went to school - we were all put into different classes so we could learn according to our abilities. The whole idea that everyone should be together all the time doesn't always work. We were split up very early - by fourth grade, I think. It works better, in my opinion.

Then you could actually have MATH teachers teaching, rather than people who may not even know enough to teach (i.e., you need to know and understand more than you are teaching in order to teach it, typically).

Posted by: atlmom1234 | February 28, 2008 12:28 PM
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And you can tell people that they use math/algebra ALL THE TIME. To figure out how much is going into their 401k (using percentages) and their company match - and what their raise is going to be wrt being given a percentage - and figuring out their retirement savings and if it's enough.

And figuring out how much they've made on their house and if they can afford a new one. Or figuring out how long it will take to save for that vacation/wii/whatever they want. All the time.

Posted by: atlmom1234 | February 28, 2008 12:31 PM
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My eldest is only in Kindergarten but I've already become concerned that the schools do not seem to provide individualized attention in math. They'll have reading groups that are grouped by ability, but everyone in the class is still learning how to write their numbers, or learning basic concepts like under/over. I'd like to see addition or subtraction introduced to those who are ready for it (we like playing number and simple math games in the car, and even our 3 and a half year old has figured out simple single digit addition & subtraction).

I'm open in theory to the idea of everyday math, etc., but I intend to supplement at home by helping my kids memorize the basic tables when they are old enough. It's just so much easier to think about the bigger picture if you have the basic tools at hand.

I also think that having good math teachers is key. I've always been a liberal arts type, but I still remember my awesome calculus teacher in high school (and really excellent teachers that taught the classes leading up to it) who not only taught us how to do the problems, but explained why & what we were doing. She must have done something right because everyone in the class who took the AP test got 4s or 5s.

Posted by: sfl | February 28, 2008 12:59 PM
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To anon @ 12:11: "Does anybody remember "new math"?"

Yep, sure do. Going to dependent schools (Fort Knox and Germany) we got all that stuff.

Here's Wikipedia's opening summary:

"New Math emphasized mathematical structure through abstract concepts like set theory and number bases other than 10. Beginning in the early 1960s the new educational doctrine was installed, not only in the USA, but all over the western hemisphere.

Much of the publicity centered on the focus of this program on set theory (influenced ultimately by the Nicolas Bourbaki group and their work), functions, and diagram drawings. It was stressed that these subjects should be introduced early. Some of this focus was seen as exaggerated, even dogmatic. For example, in some cases pupils were taught axiomatic set theory at an early age. The idea behind this was that if the axiomatic foundations of mathematics were introduced to children, they could "easily" cope with the theorems of the mathematical system later."

Similar to what's happening now. There's a view among some people that you have to teach kids the theory behind why 5 times (7 + 3) equals (5 * 7) + (5 * 3), so kids spent a lot of time learning the distributive property (plus the associative property and the commutative property). The problem was that too many people weren't being taught how to really solve the problem and get 50 as the answer. They were being taught the theory and asked to prove/explain their steps. Wrong order, in my book. (Disclaimer: I was mostly taught "New Math" in elementary school but started taking college algebra in 6th grade and wound up with a graduate degree in Computer Science & Statistics, so it didn't hurt me too badly. :-)

Posted by: ArmyBrat | February 28, 2008 1:09 PM
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jp - Find the video link posted above. It explains everything pretty well.

As a teacher, I'm disgusted by what little math reformation my students DO bring into the classroom (they use a fairly standard curriculum, but it integrates HORRIFIC new math concepts once in a while, like the cluster reasoning and like stem-and-leaf tables). Moreover, my 6th grade students are NOT encouraged to lay out their work on the paper, and they were making mistakes that we couldn't find because their only work was a jumble on scratch paper. I kept pushing the kids to lay out their work neatly, but they resisted until their math teachers told them to do it.

I absolutely believe that students should be grouped by ability. It's apalling to slow down kids who HAVE the concepts so everyone can catch up. These kids are not actualizing their potential and they KNOW it. Its frustrating for the students. Moreover, kids who are slower at grasping the concepts should have a teacher who is dedicated to going over the same problem three or four times until everyone gets it.

The idea that separating kids hurts self-esteem is ugly and mostly perpertuated by ambitious parents ("Why aren't YOU in that class?!") and teachers/administration who don't work enough to make sure the slower classes still feel valued.

When I was a kid, I was totally the one who could just solve algebra problems by looking at them, and I got knocked down on my grade CONSTANTLY because I didn't show my work the way the teacher wanted it. Finally, my parents went in and asked her why I got a C in the class if I was getting all the answers correct, and knew the math.

And yes, everyone uses algebra.

Posted by: Kat | February 28, 2008 1:31 PM
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I loved math. Even had a math teacher sign one of my high school yearbooks. She wrote something about me not needing a math teacher, but how much she needed a student like me in her class.

DH is math-phobic. But he didn't really go to school much after 4th grade (long Dickensian story of his childhood omitted here), and never got a chance to learn.

Once our kids got to fifth grade they were on their own for their math homework. Fortunately, they both seem to have my attitude and aptitude, so they aren't struggling.

To whoever was having a fit about the lack of posts today - maybe people like me don't post on this topic because we don't have anything we feel is useful to bring to the discussion.

I certainly don't feel that what I wrote has added anything meaningful to the discussion, but at least you'll have a higher number of posts.

Posted by: Sue | February 28, 2008 1:59 PM
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My daughter is in Kindergarten and uses Everyday Math. It seems okay for now.

She loves arithmetic, and I work with her myself. I do *love* the graphing her class does. She's been doing bar graphs since pre-K and they seem to do a bar graph a day (e.g. how may brought lunch vs. are buying, how many letters are in your first name, how many siblings do you have). Is that part of the Everyday math curriculum or extra?

I have no idea how the curriculum will go in the future. But, I teach math and physics, so I can teach her myself.

Thanks, Dandylion, for the program. It's amusing and looks useful.

Posted by: inBoston | February 28, 2008 4:08 PM
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It's not a "fit." It's an *observation* that the loving, caring parents here seem to care more about what's-4-dinner-lolz than about their child's math curriculum. And then we wonder why we have to import so many engineers and doctors ....

Posted by: To Sue | February 28, 2008 10:06 PM
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I did the distributive, associative, and commutative properties. I guess that was new math? I loved it. I felt like all I had to do was remember the properties and everything would flow from there. It made it very easy for me. I remember being taught the multiplication algorithm and being confused but I worked it out because I understood the concept of multiplication. It would have been good if the teacher had explained it instead of just making us memorize the algorithm. I think this issue is what everyday math is trying to get at, but I don't think doing away with the algorithm or the times tables is the answer.

I've looked at the textbooks for Fairfax's 3rd grade curriculum and I found them dreadfully confusing. I can't even begin to describe all the things that were wrong with them. They made even addition seem utterly daunting. It was quite sad really.

Memorization is a tool you use so your brain doesn't have to worry about the arithmetic and is free to think about more fun aspects of math.

I think the solution is not to force every child to learn every possible way of doing a math problem; it just becomes a tower of Babel. Rather it is to reduce class sizes so that the teachers can interact with each kid individually. My teachers used to teach the concept, give exercises, then walk around and individually help those who were confused. Also, I think it's important for kids to get feedback by having their homework corrected.

Posted by: middle70 | February 29, 2008 9:12 AM
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The comments to this entry are closed.

I think different approaches work for different children. Everyone can do math, but if a teacher does not use an approach that resonates with a child, the child will not "get it" and feel inadequate and it can become a problem in the long run. This is especially true for girls. I think teachers should be allowed the freedom to become familiar with many approaches and teach whatever works for the specific classroom that year.

As for counting with fingers, my daughter's VERY incompetent second grade teacher said that my daughter wasn't doing well in math because she still used her fingers to count. Well, I told her, I'm an engineer and I use my fingers to count! Most of us have ten and that comes in very handy (pun intended!) I ignored the teacher, the child ended up in the GT program, and now she's at TJ. So there. Using fingers is NOT a good indicator that someone doesn't understand math. US Society puts too much emphasis on memorizing addition facts (multiplication can be a different story). In reality, mathematicians sometimes spend a lifetime, A LIFETIME, folks, trying to solve ONE PROBLEM. Counting with fingers is the least of their concerns!

I think the focus on mathematical concepts and the practical uses of numbers are much more important for our children to understand than how they reach the conclusion that 21+13=34.

Memorizing math facts led to generations of folks who "hate math". Think about that... Scientists know more about how the brain processes information and this is leading to better curricula. I think the new approaches are worth a shot.