Teaching fractions and decimals simultaneously

Well, I’d see how he does with it but I wouldn’t be surprised if it’s overwhelming. My college students find it so — but, they do learn the “change a decimal to a fraction” and “change a fraction to a decimal” pretty much together. They tend to learn them as separate sets of procedures (which is why it’s overwhelming) and it’s silly math education theorists that don’t realize that an awful lot of these students simply aren’t up on their theories and (of all the nerve!) their brains refuse to magically absorb all the concepts and therefore see the nifty connections between teh decimal and fraction worlds that they see.
I’d pick one to have him *really* learn, which ever one he seems closest to getting first.
Going through everything, fast, every year means students learn they’re stupid in math, every year, instead of learnig the math. Which is stupid because they aren’t stupid and *could* learn the math if it weren’t waved at ‘em like a flag and they were somehow supposed to remember it all when the flag’s put away.

Actually, teaching the fraction and decimal at the same makes sense as they are just 2 different ways of writing a part of something. If base 10 blocks are used to represent them, why not write 3/10 of something as a fraction and a decimal? All my students did it quite easily, but we used manipulatives (base 10 blocks and then 10x10 grids on paper) for several days.

“just”

what a word!

Yes, they are “just” two different ways, but they *are* different, and just enough similar to invite confusion for many of my students. Were the base ten blocks your main manipulative? HOw challenging did you get with the problems? (IMO keeping them simple is the way to go until the concept and procedures are solid, unless you’ve got somebody who *thinks* they’ve got the procedure and needs to be challenged to think — my guys are usually *just* beginning to connect, say, 3/10 to .3 when they get to problem 7 … and of course they only do the odd ones… and it’s 22/131 or something on that line.)

Just so. :) 22/131 = .16794 rounded up.

I don’t see how common fractions can be taught without teaching decimal fractions at the same time.

For instance, when teaching the meaning and practical usage of, say, 3/4…how in the world do you avoid showing that 3 divided by 4 equals .75? Or in the case of 1/2 that 1 divided by 2 equals .5, and so forth.

Doing it separately is as silly as teaching basic addition first and then basic subtraction later. For instance, since 6 + 3 = 9, why not show them that 9 -3 = 6?

Why not show them that 1/4 is pronounced “one quarter” and that there are 4 quarters in a dollar and 4 quarters in a football game? They need to see the practical applications if they ever to develop any interest in numbers. Otherwise it’s just (there’s that word again) a futile abstract exercise destined to evolve into torture.

No wonder we do vocational evaluations and sit and wonder what happened along the way in school to some of these folks. The amazing thing is that the vast majority of individuals I’ve worked with in the past 29 years can sit in my office and make amazing progress on their math skills in a very short period of time - an hour say. Maybe it’s just my love of numbers…or maybe I was taught the commonsense approach to arithmetic and mathematics in the late 1950s before ‘they’ invented that new math foolishness. The clients pick up this stuff up so fast that I’m convinced they’ve never seen it before. Who knows? As it stands their high school diplomas are pretty worthless to an employer who needs employees with the basic 3 Rs.

Sorry if I’ve stepped on any toes, but learning the basics isn’t that difficult given the right approach and enough time. (No, I don’t expect an overworked teacher with a large class to be successful in every case given the constraints.) Heck, we have an L.D. specialist on board, a public school teacher running 2x a week GED classes on site, and two O.T.s and a computer engineer doing computer accommodation evaluations.

John

Gosh, it’s just wonderful that you can do that arithmetic. Can you possibly understand, though, how threatening that problem looks to the neophyte? Please try to consider it, please.

There are separate procedures for going from fractions to decimals nad vice versa. When you’ve got the concepts nailed down, then they don’t seem separate— but I have the fun and glee of watching my students buffetted by the waves of complexity, bounced back and forth and turned over as they’re supposed to be able to step back and see the big picture and work with it, but they simply don’t have that “big picture” view. They just get steps confused and concepts utterly muddled because, in fact, the procedures for getting from one to the other are rather different.
Not everybody learns best with things taught simultaneously. There are many students who need to grasp one thing before they can learn the next thing — and often they need additional time and instruction and practice to incorporate all the ideas. They *can* learn about fractions (but often need something beyond pies — you have to teach them what in the world the pie slices have to do with 3.256).
This is a bad thing if it’s because they’re just learning procedures, and they need the practice because it’s of course much more taxing on memory to learn a procedure you don’t understand. However, what many math teachers don’t understand is that this isn’t always the case — and the solution isn’t to teach everything so that you can’t do it unless you understand the concepts. The end result of that approach is that you get a bunch of students who can’t do it — there’s no magic motivation that makes the concepts happen.

Many of my students can figure one direction of that relationship conceptually — but not both at the same time. Taking the time to master one — conceptually and procedurally — and then building the other concept from the first is often successful.

So… basically you think that something that is successful for students is silly. I’m hoping this is because you actually accommodate the part-whole learners in your simultaneous teaching, perhaps without realizing it. If your studetns are successful, that’s what matters (assuming, of course that you have students and aren’t just speaking theoretically, which is also fine :))

Simply said, all decimals are fractions but not all fractions are decimals.

Fractions and decimals both represent parts of a whole but to teach them at the same time to young children is likely not going to work well. I’d teach fractions first and then teach decimals - I see a logical progression there. When fractions are understood, it then becomes easier to understand decimals which are a kind of fraction.

Fads in math instruction come and go often. My own school changes books every 3-4 years and each time touts the new textbook as the best they’ve ever seen and oh so exciting. Yet without fail, 3-4 years down the pike, they’re spending thousands of dollars to buy new math textbooks as I guess the excitement has worn off…

Yet all we’re doing is jumping on the bandwagon of the latest popular textbook. We always end up buying whatever’s ‘hot’ and Everyday Math is ‘hot’ right now.

Good luck. If you can’t stand your school’s math program and/or textbook, be patient. This too shall pass.

Thanks, everyone, for your replies.

We had our “Everyday Math” meeting yesterday where the 3rd, 4th and 5th Grade teachers presented all the benefits of the program. My son is in 4th, and the other thing that needs mentioning here, I think, is that he is in a private school. I can see lots of benefits as this program really seems to get the kids thinking (manipulating numbers lots of ways, etc.). I left the meeting feeling pretty good about the program but no less concerned about the fact that this switch is in 4th Grade and many parents are realizing that instruction in foundational skills has been lacking. For example, fractions (among other things) were not covered at all in 3rd Grade. 3rd Grade math consisted exclusively of addition, subtration, multiplication and division. So, in other words, they are teaching the conversion of fractions to decimals when the kids don’t really, truly understand fractions.

The meeting gave me an idea of what the 3rd Grade Everyday Math program covered in fractions. The 3rd Graders will be learning about mixed numbers (taking 7 1/2’s and turning it into 3 1/2), and they will also be learning about equivalent fractions. Our kids haven’t learned this yet. The 4h grade teacher is covering the concepts now, at the same time as all of this, with some neat cooking exercises…but no real practice reinforcement, etc.

I found out last night from my son, now equipped with this little bit of knowledge, that he doesn’t know what a numerator or denominator is, nor did he know what I meant when I asked him what the whole number is in 3 1/2. The vocabulary wasn’t there. He simply knows that a fraction is less than 1 of something, and he can identify that 2/7 of the jelly beans are green…simple stuff like that…that’s all they’ve learned prior to this.

My son hasn’t had difficulty with math concepts before…he’s always been the ultimate “get the hard stuff right and make a mistake on a simple addition fact” (he has organizational, attention, motor issues). He isn’t getting this at all!! I’m not particularly upset about that because it takes time, but I’m primarily concerned about learning this all superficiously (sp?) without a depth of understanding and then trying to build higher level math concepts on a weak foundation.

It seems to me that it makes much more sense to get solid on fractions then relate them to decimals. But I’m not a teacher so I really don’t know.

I’m seriously considering taking him out of this school, but feel he needs at least tutoring or homeschooling for a few months to get him caught up and solid in his foundational skills. I don’t think he could handle tutoring after a full day of school and my husband is against taking him out of school and hiring a tutor for a couple of hours a day. So we’re at odds. It’s a shame, because the school is a relatively new school (he started in 1st Grade the first year the school opened. It seems they’ve fixed the problems for the younger grades but our grade has missed out on valuable instruction and it’s catching up with them.

Any feedback would be appreciated!

Lori

“Gosh, it’s just wonderful that you can do that arithmetic.”

Gosh, ain’t it. :) Wouldn’t it be nice if each and every student were afforded the same opportunity? I think so. Are they? I don’t think so. Have I stated a blanket condemnation of the teaching profession? I don’t think so - I had some excellent teachers both in Baltimore City in the ’50s and then in Montgomery County Maryland in the ’60s. Want to hear my rant about school boards and central offices? ;)

After 29 years of full-time work (as a rehabilitation counselor and vocational evaluator) with individuals with disabilities (some high school students, but mostly recent grads and adults) I see day in and day out what they’ve missed and listened to their stories about how they missed it - in other words what was taught, what was not taught and how it was presented. Planning for the future, or even an immediate job placement, takes a careful review of the person’s skills, knowledge, etc. and is best done face to face - two people sitting and working together to form a plan of action. Employers don’t hire a diploma or certificate - they want skills because they have work that needs to be done and we need to figure out the best match for the person seeking our assistance.

Yes, I understand that many things that are said need to be taken with a grain of salt, so I’m not offended by your attitude. The four evaluators we’ve had in this office for the past ten years or so have been dealing with many of these issues for decade upon decade - we have a combined total of 104 years of experience. If you’d like to count my boss we can add another 20. Unfortunately, some of the more experienced folks retired. Seriously. I’m only 53 so I figure (thanks to a teacher I can figure) I’ll need to work at least another 10 years or so before I can afford to retire.

We’re dedicated, educated and experienced, and I believe we’ve earned the right to express our opinions in public and be taken seriously.

Hey, is it possible that it’s just the school systems here that have problems?

John

Well, the one thing that bugged me most about your post was that you thought it was silly to teach any way but one. I don’t care if it’s silly, if it works — but it doesn’t sound like you’re teaching math (tho’ years of experience, as I”m sure you’re aware, don’t really add up to effectiveness in these fields). But yes, we’re on the same team.
I”m constantly referring to the wisdom imparted upon me by my seventh grade math teacher (in PG county). One thing I have gleaned is that I could, easily, have been a “good at words but just don’t understand math” person if I hadn’t had the right teachers, or if I’d had programs yanked back & forth.
My sister wasn’t as fortunate and she had to relearn fractions on her own in eighth or ninth grade, because her fifth grade teacher avoided math and failed to teach it. However, she hadn’t acquired the anxieties about it that really inhibits many of my students’ learning (which is another reason that there’s an advantage to presenting the stuff differently, simply for the sake of it being different and not triggering automatic cold sweats). I wouldn’t pull somebody out of a school based on *only* the math program — there’s no reason to believe another school would do it better, for one thing, and there’s more to school than math, and just as with reading, you *can* learn it on your own, despite the schools.

Unfortunately, math isn’t the only area of contention. I only highlighted that because it referenced my specific question about fractions, etc.
Many of the children are behind in writing composition skills also.

Basically, what I think we have here is a situation where the school was new (although a great deal of experience in the team that started the school); Grade 1 (first year) was decent; Grade 2 was a wash (teacher let go); Grade 3 did some catch up from Grade 2, but teacher was very literature (but not alot of writing, oddly) and at home project driven (not a math person); and now Grade 4 we have a class that’s behind in basic skills primarily in the areas of math and writing. They really haven’t learned how to compose written pieces in any kind of structured way.

And it’s one of those things where when you start realizing there’s a problem and you start asking around, you start seeing more and more that your kid isn’t doing/learning that others are (both public and private!) For example, in Grade 4 our kids have yet to have vocabulary as a subject (no vocabulary lists, tests, etc.). When I asked, I was told they learn the vocabulary through the “integrated curiculum” such as science and social studies vocab. But I mean regular words…not spelling words (too easy) and not science words like photosynthesis. They also have only had a handful of reading comprehension tests (I can only think of 3 or 4 the past 2 years). Add this to the writing and the math and the result is very unhappy parents who have paid dearly for 4 years of private tuition thinking that academically (not socially) your kid might have been better in public school!

We’ve got other issues to consider, however, because our son needs motor therapy and needs motor activities like karate…they are really important for him and that leaves little time or energy for tutoring after school to solidify his schools before he gets further behind.

So, we’ve got to figure out what’s best. I think taking him out makes sense for a few months only so the stress is relieved vs. exacerbated giving us more time for the physical as well as academic stuff. My husband is really against pulling him out of school and says he will only accept this as a recommendation from a psychologist!

Lori

Several issues:

JohnBT — you are comparing apples and pomegranates, and as an apparently intelligent adult you should be ashamed of yourself. You are working with adults; the parents here are talking about quite young children. You are dealing with people who have been through the school system, and no matter how bad that system is — and I lived in PG county for the decade of the 90’s and could share horror stories all night — nonetheless they have been exposed to this material for twelve years or more; the parents here are talking about neophytes who have never seen such an idea in their lives. You are working with people who come from the general population and presumably have the normal range of learning skills, however the schools have failed them; the parents here are talking about children who have serious learning problems before they even start. You are dealing with adults who are highly motivated to learn (or re-learn) skills in order to get a job; the parents here are dealing with children who have a number of problems and who are likely not very motivated to learn math that they see no purpose for in their lives (true they will need it later, but these are kids and they are not exactly big on planning ahead.) You simply cannot make blanket statements about teaching and learning based on your clientele and expect that this is the answer for everyone.

And specifically your point relating fractions to division, like 3/4 equals 3 divide by 4 equals .75 — absolutely true, correct, definitely something to make clear to adults — we are talking about a *child* in Grade 4 here, and they don’t know how to divide yet!!! Very basic integer division like 15/3 = 5 has barely been introduced; long division as 3/4 = 3.00/4 will come in Grade 6, later. You can’t build Rome in a day, John, and you cannot teach the whole system of mathematics all at once; something has to come first (counting, base 10, addition, then subtraction, then integer multiplication, then integer division, then intro fractions, which is how far we’ve gotten) and some other things will have to wait until later.

General pedagogy: (A) Teach one new idea at a time. Teaching two or more brand-new ideas simultaneously is the guaranteed road to failure. This is more and more true the younger your students are. AFTER students have some knowledge and experience, you can *review* and *reteach* using compare-and-contrast-and-relate techniques, but first you need the two basic facts to compare. Yes, you do teach only addition at first. You spend several months getting addition down. Then you spend a few weeks teaching only subtraction. Then you show the relation between the two. Yep, takes time. But confusing people so they don’t know which is which sets them up for a lifetime of failure, so taking the time is a positive investment, not in any way a waste. I am sure Sue and other experienced teachers here will back me up on the fact that one of the disasters in the present system is that our students in college add or multiply pretty much at random, so you can’t teach algebra because the students haven’t a clue which operation is going on.
(B) Take the time and do it right. Many people here have commented about the fact that their kids have “done” all sorts of math topics, but don’t *know* any of them. To know something means being able to do it independently, to retain it permanently, and to transfer it to other situations. Just because someone fills out the “right” answer on today’s test or sheet doesn’t mean they actually have a skill they can use. Adults can often make connections for themselves and retain because they see connections; younger kids need help and review and drill. Get it right and then go on and build on a strong foundation. Poorly understood recipes will shed off the brain like water off a duck’s back and are a waste of time.
(C) Math is *supposed* to be logical. Teach it as a logically connected subject! Decimals *are* fractions — fractions with denominators of 10, 100, 1000, and so on. If you know what a fraction is and how fractions work, then you can do decimals. I defy anyone out there to explain logically how to work with decimals without a strong base in fractions first (A recipe of “do it this way” is NOT a logical explanation). You must understand fractions to know why .5 = .50 (why? 5 is not equal to 50!) and why .25 is less than .5 (why? 25 is not less than 5) and why .25 + .5 is NOT .30, and why .1 x .1 is .01, and so on. You simply must know fractions first, decimals after, no way around it if you are going to do real math and not magical mystery tour.

Lori — your problem of the Great Curriculum Gap is a common one. It happens in many schools. If your school changed from one math program to another, it is absolutely necessary to do some adjustments to fit the new curriculum. (and would apparently be a good idea in other subjects too). You need to make some noise and insist that the material missed from the Grade 3 program be explicitly taught. The teacher can get the materials from the Grade 3 teacher, photocopy the fraction introduction materials, and take a few weeks teaching them. Again, this is time *invested* in actual learning, not “wasted”. If the teacher is adamant, you need to get some good tutoring whether or not it suts into after-school time. If you get this done right away this year, your child has a good chance of getting ahead academically. If the teacher insists on teaching Grade 4 on top of a gaping hole in Grade 3, your child will carry the weakness for years and it will come out in algebra failure.

Victoria,
I was hoping you would weigh in on this one. Great response. Thanks for perservering in keeping us all on the straight and narrow path to teaching math.
Mariedc

We teach fractions in 5th grade in our school and the structured paragraph. I don’t think it’s written in stone that such things are taught in the 3rd grade. We don’t do vocabularly lists such as you’re speaking of until 6th and I prefer the integrated curriculum approach to vocabularly. Most children forget the words they memorize for the test shortly after it.

If you would pull your son out to catch him up, that will be a great deal of work on someone’s part. It will take great discipline to get a child alone to put their shoulder to the wheel when there’s not a roomful of other children doing the same. But there’s no doubt with that structured discipline, a lot of ground can be covered so long as the child isn’t angry or resentful and fully understands that it will be less fun - not more - to be schooled at home.

Good luck.

John B, not everyone had mathematical ability even way back when. It has nothign to do with educational fads (though they existed back when too), I was around when the cutting edge of reading techniques was “look say”.
And I was in what was a wonderful school district as far as that goes, with very high college enrollment etc. But I have about a 5th grade math level— comprehension being rather higher. I remediated myself somewhat as an adult when I became a special ed teacher.

What you describe might be fine for a mathematically gifted person, but the kids discussed in this forum are not. Go over to yahoo and I am sure you can find some forums on mathematically gifted kids. We are talking about normally intelligent children who have processing difficulties that make math esp hard. Throwing that out all at once sounds nice from the mathematically gifted adult standpoint. But for myself, I know that I could not have learned that way. I had enough trouble that they didn’t spend enough time using manipulatives and getting me to really see and feel what we were doing. Get out the pies one day and the next day you have it on paper wasn’t good enough for me. And it isn’t good enough for the kids discussed in this forum.

But the goal of math instruction is to get everyone to be capable and hopefully the programs for kids who are so gifted can concentrate on developing creativity and go beyond the extra skills. More complexity and so on won’t do that. It will only further confuse the kids we discuss here.
And don’t forget all those regular non-ld adults who hate math, would lose them too.

>Gosh, ain’t it. :) Wouldn’t it be nice if each and every student were afforded the same opportunity? I think so. Are they? I don’t think so. Have I stated a blanket condemnation of the teaching profession? I don’t think so - I had some excellent teachers both in Baltimore City in the ’50s and then in Montgomery County Maryland in the ’60s. Want to hear my rant about school boards and central offices? ;)

The school system did NOT make you gifted in math!! Your brain did that. I am sure there are any number of kids that you graduated with who had no clue what was going on. At least we now have the interest to look at all learners, not just the more able ones. Not that I think it is happening now, but at least I feel we are more on track than when I was in school.
The big plus back then was size. I think my hs school was large at about 1000 or 800 kids, that school is prolly now double or triple that size.

I am roughly your age, John, yet I recall distinctly about kids who we would now describe as ld, dyslexic, or ADD described as wierdos, slow (they had a “special ed” class a mixed bag of mentally retarded, severe ld, etc), lazy, etc. Perhaps your brain has conveniently enabled you to forget these painful things or you never saw them. I didn’t have the luxury, as I was one of them.

>Hey, is it possible that it’s just the school systems here that have problems?

It isn’t true though. Kids in other countries have learning disabilities. I believe that this is pretty well recognized in European schools. I don’t know how the Asian schools deal with it. Perhaps the kids get shuffled automatically to completely lower levels of expectation and these kids would never go to college as I did.

In the third world they are working in sweatshops at 12.

John[/quote]

—des

It’s of course not as simple as being gifted in math or not, either.

You were remediated by becoming a teacher — when I got into teaching I realized that under *most* of the teaching kids were getting, I would never have developed into the “gifted in math” person that people call me. (I am always surprised when SAT/GRE type tests get me higher math scores, though logically it makes sense since there are a set number of ideas and procedures you ahve to know, while there are a few zillion words and verbal ideas that could be presented).

But the bottom line is that how it’s taught is important, and that if the person isn’t learning, then you aren’t teaching, even if it’s the “best” way to teach it.

>It’s of course not as simple as being gifted in math or not, either.

Perhaps not. I felt it was highly UNLIKELY that he really learned math the way he described. I have never heard of teaching substraction at the same time as addition even though the two are connected. Even back in whenever, I believe I was taught addition first. I felt his memory for how he learned in the first place was possibly not correct. He was longing for the good old days and my main point of the post was to remind him that not everybody DID learn back then either. He was perhaps unaware of that and thought this is some type of recent development. (or that was my reading of it). I actually think, though there have been some wierd sort of fads, that math instructional techniques are prolly *better* as a whole. Maybe Virginia would be more qualified to say yea or nay on that. However, at least they have the idea down that you do need to have manipulatives. Whether they are used well or whatever, now that’s another story.

>You were remediated by becoming a teacher — when I got into teaching I realized that under *most* of the teaching kids were getting, I would never have developed into the “gifted in math” person that people call me.

Yes, I actually had to go back and do some of the manipulative exercises and found out (I think I said out loud “Oh that’s what you do when you divide”.) I had no clue. I was going over a rote set of techniques that had been taught to me but I didn’t really understand it until I saw it. Since I now LIKE math, and like to teach it, it leads me to believe that had I had better teaching I might be better at it, even *good* or gifted at it. I’m not sure if I am so much dyscalculic as someone that does not learn well from auditory techniques. In school it was pretty much go over the idea a couple times, then talk the kids thru it, and then do it.

Though I do feel there are people who survive bad instruction better than others. Perhaps they also would be better at it if they had much better instruction as well.

>But the bottom line is that how it’s taught is important, and that if the person isn’t learning, then you aren’t teaching, even if it’s the “best” way to teach it.

I have no problem with that statement. The statements I had a problem with were the implications that these are dumb kids cause can’t you see this is just so logical. Of course, Victoria did an excellent job of ‘splaining why he was off on this.

—des

To Des and others — I do happen to be one of those mathematically talented people. Nonetheless, I HAVE failed a few math classes in my time, and I dropped out of my math grad school program because I found myself in a program that stressed all of my weaknesses, and by now I’m smart enough to see trouble coming (should have left a year earlier in fact, but let “good advice” sway me).

Even as a math person, I DO get confused when too many new ideas are thrown out simultaneously.

I also DO get lost when the presentation is entirely verbal — although I’m quite good verbally, I do my math concretely/modelling. (The grad school I dropped was far too verbal, and the tendency was worst in the new young staff)
Anecdote: One day in a grad school math class the professor/head of department gave us a challenge problem to work on. The next class he asked who had come up with a proof. Three of the six students raised hands, and he invited us to present our work on the board. The first one went into some tremendously high-flown algebra and invented a new operation and his own symbols to deal with it. The second did a terribly logically complex proof referring to eight other proofs in both our text and two others. I got up and drew boxes. :D Not only was the math professor *pleased* to see my simple and direct approach, he even asked me to do my thesis with him, and it’s unfortunate that the rest of the program was so unsuitable to me that I couldn’t stay. He also complimented me another time on my tendency to wrestle a problem to the ground and strangle it with my bare hands.

My point here is that concrete work, visualization, and step-by-step presentation are NOT repeat NOT the second-rate approach for those poor things who can’t do it the supposedly “normal” way; exactly the opposite!! REAL mathematicians, i.e. senior tenured Ivy League professors/department heads/published authors/large research grant holders, do their own work this way and look for students who do. Verbal arguments are sometimes necessary but are *not* the center of action in the subject.

As far as JohnBT and his memories — well it has been pointed out that many people have far too good a forgettery. It’s easy to remember our own successes and not to notice or remember anyone else’s difficulties. It’s also easy to edit the past.
I happen to collect old textbooks, and I have found the books we used in elementary school back in the dark ages. Specifically for me the dark ages were 50’s and 60’s, but these texts and relations were used from the 30’s until the disaster of New Math in the late 60’s. (Back then, my schools couldn’t afford to throw books out; many texts especially in languages were used for decades) I’ve also collected other series from the same era With the actual *evidence* in front of me, the *facts* are:
(A) Yes, one thing is presented at a time. First addition, then subtraction, and later the relations between them. First multiplication, then division, and later the relations between them. Good pedagogy has not changed.
(B) Fractions are definitely presented before decimals.
(C) Order and speed of presentation may vary slightly, but the general plot is that very elementary fractions — recognizing 1/2, 14, 1/3, 3/4, 2/3 — recognition *only* — is done in Grades 3 and 4; arithmetic of fractions is just barely introduced in Grade 4, then makes a large part of Grades 5 and 6. Decimals are used only for money up to Grade 4, presented only in introduction in Grade 5, and really worked on in Grades 6 and 7. Division is presented very slightly in Grades 3 and 4 - evenly divided integers only, as undoing multiplication, and is then worked on somewahat in Grade 5 and heavily in Grade 6.
(D) Problem-solving is the central and most time-consuming focus of the program.
(E) Although the operations are presented later than in “new” curricula, each operation is taught to mastery and so doesn’t have to be re-taught from scratch every year; by Grade 7 these programs are far in advance of most newer math programs, and by Grade 9 algebra and formal geometry were the standard program and yes, 90% did well.
(F) **ALL** the new ideas are presented concretely, with pictures and diagrams and suggestions for drawing and measuring activities etc. Fractions are not only pies but also bars and parts of the class and measurements, multiplication is area and money problems and measurements, and so on.

We had at the time what is now called a criterion-referenced curriculum; you had to pass an end-of year test covering a fixed set of skills. With a well-planned curriculum that was actually taught, and with standards that were reasonably attainable for the average student, most did quite well; the failure rate was below 5% (one or two kids out of a class of 35)
There were indeed a certain number of kids who didn’t make it — in fact my school had two students out of seventy starting Grade 9 at age seventeen. We didn’t even note those at sixteen. (It is to be noted that they were welcomed and encouraged to keep learning and trying) Yes, lots of kids left school at sixteen — it was considered a perfectly respectable and responsible option if you wanted to work and not go to college. And yes, there were a certain number of kids, including our neighbour, simply warehoused for mental retardation. We did have a very effective academic program, but unlike John’s rosy memories, it was a little less than perfect.

Virginia, that was an awesome post. A couple comments. I didn’t mean to suggest that for good students that good teaching is not important, perhaps what I meant was it was not quite as devasting to have poor teaching. I went thru the look/say fad of reading instruction in the 50s. However, since I had pretty much taught myself to read it was not so critical. I’m sure it was much worse for the more average reader. And my sister, who was a good reader, was effected by becoming a poor speller. I’m sure that math, which is not quite as ubiquitious as reading, would be harder to grasp without decent instruction.

As for the comments you made on the manipulatives in the 50s, I wonder. I just don’t have the memory that they used them so much. However, perhaps they are still not used quite as much as they should. I was going thru carrying with one of my student (who has now decided she really really likes math!?) with OCN and Math U See (unifix and then ones, tens and hundreds blocks). I kept making her do it with the manipulatives and said, “I know you’ve done this before but I think maybe you only had 3 days or so of this.” And she commented back, “In some cases only one”. I’m quite certain this isn’t the recommended version— so maybe I didn’t get the recommended thing either. There’s certainly more to chose from, but it isn’t all great. The visual aspect of OCN in very nice for carrying but using unifix is pretty inefficient for such things.

Anyway thanks for your comments.

—des

When I read up on using manipulatives (did a paper on it for grad school) I found that for themost part, manipulatives were used to introduce a concept — and then boing! instant transition to the numbers, often assuming (incorrectly, as the research generally indicated) that the student would connect Tuesday’s “fun activity” with Wednesday’s Math Problems. (Another classic Matthew Effect deal — the bright kiddo who for some reason made those connections was going to get smarter, while the equally bright kiddo who didn’t mention it at the dinner table and have somebody show her the same thing with the peas and how it really was math would *not*… and would now not be as smart because other connectins wouldn’t be made… just knowing to try to make connections like that is a huge part of Growing Up A Smart Kid.)
Also (more the theme of the paper) manipulatives were pretty much relegated to elementary school, when in fact they’re awfully useful later, too. (I got to take a class in using them in Middle & High School math and that was fun :-))
I think the toll on learning of things like look-say and constantly shifting programs in math means that folks who could be really good at it stop short of that (It’s those look-say taught people that never learned the difference between affect and effect <grin>)

>When I read up on using manipulatives (did a paper on it for grad school) I found that for themost part, manipulatives were used to introduce a concept — and then boing! instant transition to the numbers, often

Oh yes, get em out of the manipulatives and into “real math” whatever that might be. However, I tend to think the road from concrete to abstract is a bit more gradual. Maybe it comes from my speech/language pathologist interest, but you go from concrete (sorry about the terminology as I don’t think it is the real terminology) to semi-concrete (which would be blocks, say) to pix to pix of blocks say. (Though I wouldn’t normally do the “real things” (ie apples, pencils, etc.) except with real young kids. There is the Algebra project, however, and I think they used the el trains in Chicago to introduce algebra.

>not*… and would now not be as smart because other connectins wouldn’t be made… just knowing to try to make connections like that is a huge part of Growing Up A Smart Kid.)

Making the connections for oneself is part of intelligence. But the process of connection making is how intelligence is made (or part of it thereof).

>elegated to elementary school, when in fact they’re awfully useful later, too. (I got to take a class in using them in Middle & High School math and that was fun :-))

I’d think it would be rather important to know what the what algebra is all about. I have to say, i never had much of a clue. We were told stuff.

>stop short of that (It’s those look-say taught people that never learned the difference between affect and effect <grin>)

Well quite possibly to take your statement seriously here. But I think that what really confused me was psychology. You know all that affective disorders and affective state. So wouldn’t how you felt or how something impacted on you how it affected you? I have never gotten this straight since. :-)

—des

Not math, but maybe this answers a question

In the most common uses:

affect = *verb* meaning *to change* to some degree
The -30 weather we are now having AFFECTS the electric distribution system.

effect = **noun** meaning the **result** of something
The long-term EFFECT of this high demand on electricity will be power shortages and even outages.

If you learn the above usages correctly, you will be correct in almost all ordinary writing.

*****************************************************

In grad school and business school jargon:

affect: used as a noun to mean expression of emotions
Depressed people often have a very low *affect*.

effect: used as a verb to mean to cause, most commonly combined with the word change
The radio anti-smoking campaign was unable to *effect* any change in teenagers’ behaviours.

These are jargony and would not be needed unless you are writing a school paper, in which case you copy the usages in your texts and instructors’ notes …

***************************

Now, does anyone want to know how to use “lay” and “lie”, and “Mary and I” versus “Mary and me”?

>Now, does anyone want to know how to use “lay” and “lie”, and “Mary and I” versus “Mary and me”?[/quote]

Hmm, don’t have a jr high or hs kid conjugate the verb “to lie”. The effects may be unpleasant and may have cause an unpleasant affect on your affect.

Don’t know about Mary and I or Mary and me. We were never very close.
:-)

—des

I remember the affect/effect stuff by *not* thinking about it too much, and thinking “cause and effect” to prevent the affect from sneaking into the wrong places, and “I want to effect a CHANGE” as my example for effect as a verb. Affective means “oh, all that stupid feeling stuff” and “effective” — that’s stuff that works.

At least one of my English teachers rather strongly suggested we limit “impact” to being a noun (even though the dictionary has given in on that one, I think) and left only wisdom teeth to be impacted :-) I hope she never watches the weather channel. It would effect a deleterious impact on her affect, I suspect. \

Enuf already!!! :roll: :roll: :roll:

Thanks everyone (and especially Victoria for going as far as looking back at a bunch of old textbooks!)

Haven’t seen any math homework since my last post..until tonight. Now they’re adding and subtracting decimals…and mixing tenths and hundreths at that requiring the adding of 0’s to do so. My son was confused, and actually I was too, at first (it’s been a while!). They can’t possibly expect anyone but the most talented/most math-enriched kid to really understand this when they haven’t taught fractions yet, can they? As I see it, the kids can be taught how to do this rotely, but they can’t understand why they are doing this (why is it that you add a 0 to 3.4 when you subtract 1.47 from it *if* you don’t really understand fractions?)

My son didn’t remember this from class. He even got confused about lining up the decimals when one number was a tenth and the other was a hundredth. I have been in a mode of “let it go so the teacher knows he doesn’t get it”, but I really wanted to understand what he tried to do (he did it on his own, but quite a few answers were wrong). Once we got past the temporary frustration and anger which he directs at me when he’s upset and anxious, he got it rather quickly at face value. I don’t know if he’ll remember it because, primarily, he doesn’t fully understand why the procedure is done.

I hate being in this position. I am not able, nor do I want, to teach this. He unleashes impatience and frustration on me that he wouldn’t do near as quickly on others.

Lori

Adding one-place to two-place decimals at this stage of his learning is point-blank ridiculous. Yes, you can temporarily teach him by rote, and he will then in a week forget half of it and do it all wrong and swear “but that’s what the teacher/you told me to do!”.
Most kids taught this way luckily let it run off them like water off a duck’s back, so it’s just a waste of time that could be spent more productively. I personally feel that Chinese poetry or anything else would be a better use of the time, but that’s another story.
If someone makes a big fuss over it — you, the teacher, a helpful aide, or an older kid who forgets his own struggles and says this is so easy — then this can be a very good approach to teaching your kid to hate and fear math for the rest of his life. He is “supposed” to know this stuff, “everybody else” knows it (they don’t, they just do dog training rote imitation), and so he is “stupid, lazy, lousy at math”. Don’t make a fuss over it, tell him honestly that he will see this same junk again and again every year until Grade 8 and above so he’ll have plenty of time to get it, and you honestly think it’s a badly-organized program, and really try hard to work with your teacher and school to get the necessary foundation work in place. The rest of the class is not finding this easy either, no matter what the teacher says.

…and I will heed it. Hopefully, I can undo some of the damage I may have done last night. I didn’t make a big deal of it, really, but I think he perceives it that way which is what counts. I just wanted to know how he tried to get the answers because I didn’t see any back-up work (he tried to do them in his head!) Then he got mad/frustrated. Then I showed him the wrong way (I’m rusty…it’s been a while), etc., etc. so it was all dragged out and counterproductive. My biggest mistake to this regard was bringing it up at bedtime. I only got 2 words out of my mouth when he blew a gasket (not a good sign, huh).

It’s his perception (right or wrong) that he’s having the toughest time with this in his class. I didn’t help him with his homework last week so the teacher would know he didn’t get it. I don’t want him to get behind, however, so I think I should help him and then let the teacher know what he needed help with. Any feedback on this?

Thanks, again.

Lori

Perhaps the teacher does not have much to do with it. She didn’t have much choice chosing the texts! OTOH I feel her attitude may be fairly damaging. Apparently SHE doesn’t remember (or know) that it shouldn’t be taught that way.

I think somewhere Sue or maybe Victoria listed some common math series that do a better job at teaching math and perhaps you can work with the school on this (and perhaps not).

Meanwhile I think you can say that you were wrong and go about undoing the damage as Victoria suggests and not beat yourself up too much in the process. It might start with something like:
“You know I just learned something new today about math.” And then you could go on and tell him that you learned he really needs to know fractions first. etc etc. ”

Yes I agree with Virginia it’s a waste of time what he is doing.

—des

It probably is a case of the teacher not really knowing in that she is a first year teacher just out of school. I know that has its negatives and its positives. I think she is trying her best and is very talented but she doesn’t have experience on her side yet.

There isn’t any talking to her about the downside of all this because her father is an elementary principal elsewhere in the country and his school has used this program with great success (supposedly!).

Lori

New teacher — OK, she has almost certainly forgotten her own struggles learning this. She just puts this number here and that number there and moves this around and the answer pops out, and of course it’s so easy so why are some kids and parents making such a fuss over it? Over time, if she really is good, she will learn that kids who have never seen this don’t find it automatic and easy. Meanwhile you just have to help your child the best you can.

Following the textbook — well, you said you’re using Everyday Math and unless they have gone back on everything the program was supposed to be (always possible, see “whole language”) then this is a no-textbook program, isn’t it?
Teachers are supposed to have extensive training before using this program — did she get the training?
It sounds to me like she is a typical teacher who was herself taught in a rote drill system and she probably doesn’t understand what EM is getting at. In this very common situation, the teacher unfortunately misses out on all the parts of a new creative program that are valuable, and stresses all the parts that are the worst.
The strengths of EM are supposed to be a focus on solving real problems, discussion in class on the why as well as the how of math, class and group learning through discussion and experiment as opposed to constant drill, and flexibility with no text. The weaknesses of EM are said to be lack of focus on any one topic, unevenness of presentation, complicated and confusing materials organization, and high dependence on the teacher and therefore very uneven results. Does sound like she’s hitting all the weaknesses and none of the strengths.
Some discussion with both the teacher and the prioncipal about how the program is supposed to work may possibly help.

In some cases I get kids who are completely lost by the school’s presentation of a subject — lately I’m getting this a lot in French Immersion — and I tutor them following a good developmental program without any special reference to school assignments except in test emergencies. A good math tutor for a year or two can make a real difference if you go this route.

Yea, we got this huge grant to help with underprepared studnets, and one of my regular visitors saw that there are 20 study sessions a week (for the various developmental levels) and I told her about the grant and that math classes had a fairly horrendous failure/drop rate and she said “really??? It’s not just me??” (she was serious) — I told her if she checked journals she’d find it was nationwide.
I was just taking a guy through the ol’ “commutative” and “associative” deals… commuting is going back and forth and associating is who you hang with, right? … but did duly inform him that he needed to know this for the first test, the final… and never in his life would somebody stop him on the street; but that he *should* look for examples of this stuff and just not worry about getting the right name.

Don’t know why the kids really have to learn the terms. OCN does not teach them although I wouldn’t consider OCN exactly a complete program. But really, how many times in live are you called on to say “this is the associative principle”. EEKS. Still the application of the principle is important. I recall when my current student “got it”. BTW, she actually did remember the term, just didn’t know what to do with it, which was what really matters.

—des

Learning the words for “commutative” and “associative”: This is one of those “New Math” gems, a holdover from a whole bunch of failed programs that were based on the false idea that learning to talk *about* math was the same thing as learning to *do* math. In the dark ages we had oodles of exercises and problems where we used these principles, but we were never asked the names; I learned the names when I first hit a New Math text in Grade 12, and five or six vocabulary words are literally the only thing I learned from that text — my old math was literally two years ahead of it as far as actually doing things instead of yakking about them — I went from Grade 10/11 old first to 12 “new” and then jumped to 13 “new”.
If it happens that you literally the one person in a few hundred who studies linear algebra and abstract algebra and vector analysis in university, then you do need to know these concepts and you need the names in order to talk about them. But you can learn the names in the course where you need them, and they will mean more to you.

Sue — that’s exactly how I teach this stuff too. Commute = drive back and forth, Associate = get together with in groups.

Haven’t they killed that dog yet?

“If it happens that you literally the one person in a few hundred who studies linear algebra and abstract algebra and vector analysis in university, then you do need to know these concepts and you need the names in order to talk about them. But you can learn the names in the course where you need them, and they will mean more to you.”

Amen.

“…the false idea that learning to talk *about* math was the same thing as learning to *do* math.”

Amen. Amen.

Thank you for saving me the trouble of typing something similar.

John

[quote=”victoria”]Not math, but maybe this answers a question

In the most common uses:

affect = *verb* meaning *to change* to some degree
The -30 weather we are now having AFFECTS the electric distribution system.

effect = **noun** meaning the **result** of something
The long-term EFFECT of this high demand on electricity will be power shortages and even outages.

I love:
“The Elements of Style” William Strunk, Jr.

could be read on line at:

http://www.bartleby.com/141/

and for effect/affect:

http://www.bartleby.com/141/strunk3.html

Now, does anyone want to know how to use “lay” and “lie”, and “Mary and I” versus “Mary and me”?[/quote]

for “Mary and me” vs.” Mary and I” I would guess if the question is “who” that would be “Mary and I” (like : Mary and I went shopping. ) if the question is “whom” (e.g. for whom, to whom et.c.) than I would use “Mary and me” (like : The shopping trip was a new advanture for Mary and me.). But I am not a native English speaker, so waiting for comments….

I am homeschooling my 6th grader this year. He struggled mightily with fractions and, after feeling like I was ‘losing it”, I moved on to the next section, saying we would come back to fractions at a later date

The next session involved decimals which he TOTALLY understood. Once we worked through a rather extensive decimal section(this is Singapore BTW) we went back to the fraction section and breezed through

For his logical, step by step mind, decimals with their nice straightforward 10s pattern, were far easier and he was able to take that easily understood information and THEN understand fractions

It makes sense in retrospect. You can fathom that whole/part thing without having to worry about 1/5 and 1/3(remember the word third, not three) and numerators and denominators and simplifying, reducing…….KWIM

Plus decimals are like money-ds was counting money in kindergarten.

Don’t let the decimals scare you

Marycas,
It’s not decimals that scare me, it’s trying to learn both fractions and decimals literally at the same time. I guess they are really expecting these kids to have a vision for this because tonight’s homework included knowing which number was greater .672 or .7 (just 1 example). He had to put fractions in decimal notation and vice versa (up to the hundredths). I tend to think that fractions is easier to learn first (that’s the way I learned it), but everyone is different. It wouldn’t be so bad if they just taught decimals (i.e. money). But they are trying to teach both at the same time without any kind of foundation for either.

I e-mailed the teacher last week when he last had math homework and told her that I planned to help my son if he needed it and then include a note about what I helped him with. At first, I let him go back to school confused for the teacher to help him. I think that was a big mistake because now he is telling me he is the only one who doesn’t understand it and he’s embarrassed to ask his teacher questions about what he doesn’t understand. His teacher didn’t respond to my e-mail, but that is what I am planning to do.

Lori

I understand your point-they are assuming a knowledge base that simply isnt there.

I think ds would have had a difficult time switching back and forth if he hadnt understood decimals in depth first.

I find it hard to believe your child is the only one struggling. Fractions are one of the most frequent topics on homeschooling boards because so many kids struggle, even when they are taught one concept at a time with one on one attention!!

The homeschooling board here is slow, but if you want some ideas to reinforce things at home, try the math homeschooling board at Sonlight.com. There are sites for manipulatives, etc

donnayoung.org

comes to mind. Good luck

To the Guest who commented about “Mary and I” versus “Mary and me” and “who” versus “whom”: well, “whom” is rapidly dropping out of Borth American speech. The vast majority of people, even educated people, don’t use it. And a large majority of people don’t know how to use it. The problem is the question of subject versus object, which most people don’t know. That’s why they use the “and I/and me” incorrectly. So referring to another topic which they also don’t know will not solve the problem, only make it worse. Then we get into the issue of overcorrection — many people correct one error and then also change correct sentences to incorrect, overgeneralizing. People who actually care to improve their speech and writing can learn to distinguish subject from object by using simple model sentences, which is how I explain the problem.

To marycas — from what you say, you didn’t teach decimals without *any* knowledge of fractions. Perhaps the fractions were not totally mastered first, but you had some basis. You mention the pattern of tenths, hundredths, thousandths in decimals — true, correct, and you are using fractions as soon as you mention tenths. If you knew what tenths are and the relation between tenths and hundredths, you have a background. Then you say you went back to fractions and got them on the second go-round, which sounds like a good plan especially if you did it before getting into advanced decimals. The problem here is a student who isn’t really sure what a tenth is yet being asked to deal with comparisons of .7 to .673, a question which stumps many of my adult students and which is just inappropriate at an introductory level.

[quote=”victoria”]To the Guest who commented about “Mary and I” versus “Mary and

People who actually care to improve their speech and writing can learn to distinguish subject from object by using simple model sentences, which is how I explain the problem.[/quote]

this is exactly what I did- I put sentences. :o

just wanted comments whether this is correct… :?

It works ;) WHat solidifed the “mary and I” vs. “Mary and Me” for me was saying the sentence wtihout the “Mary And.” Since I wouldn’t say “Come home with I,” I woulnd’t say “Come home with Mary and I.” (Okay, I might *say* it, but wouldn’t write it…)