kitchen table math, the sequel: math wars

## Saturday, February 20, 2010

### math wars

comment left on Numbers Wars: School Battles Heat Up Again in the Traditional versus Reform-Math Debate in the March issue of Scientific American:
Sad but true. I was at a fast food drive thru when the computers were down. They had to make change the old fashioned way. But the girl could not figure out how much change to give me. She seemed lost as she tried to calculate the difference between what I gave her and what the food cost. She had to call in the manger, who took way to long to compute the change (eventually she found a hand-held calculator).

Apparently even simple arithmetic is no longer well taught, learned and/or retained. Reliance on machines to "teach math" is only good if one has a machine when it is needed. My daughter had these classes where the calculator was required. The problem was that after smacking the keyboard a few times, she could come up with an obviously nonsensical answer. She would just write it down and move on. I asked her one time how she could multiple two numbers that each were less than one and come up with an answer that was greater than ten. The blank stare said it all (fyi - she failed to enter the decimal points correctly).

Want to terrify a teen-ager? Ask them to multiply 12 times 12. Is the answer immediate or not? Forget adding simple fractions. And we expect these kids to learn algebra and higher mathematics?

Are kids today less proficient even in arithmetic than in the past? Surely we can tell if these newer teaching methods are getting better results or not. As for me, I think my daughter did better in arithmetic in elementary school. After middle and high school, she seems to have "lost" the ability to easily do the arithmetic she learned earlier in life. I blame the calculator.
Twenty years of reform math.

That's a long time.

ChrisA said...

Having tested Algebra students a few years back on their multiplication facts, I'm fairly optimistic that many can do 12 x 12. It's just one of those multiplications that "sticks in the mind" That said, I agree that many don't know their multiplication tables.

I had the job of pulling kids out of class and going through multiplication cards with them. Skip counting was prevalent. Taking the 12x as an example, many students could do 1, 2, 3 and 4 x 12. When you got to 5x and the "carry" it was a curve ball. For a great percentage I would ask them (for 6 * 12 for example):

1. Do you know what 6 * 10 is? yes, 60

2. do you know what 6*2 is? Yes, 12

3. And 60 + 12 is? They would say '72' and their eyes would light up.

What a tool the distributive law of multiplcation is. Why didn't they know it?

My theory is they have been exposed to so many different ways to work problems that they were way past confused.

P.S. The use of calcuators needs to be scaled way way back.

Mrs. H said...

As an algebra teacher, I can attest to the fact that calculator use needs to be scaled back. But just to play the devil's advocate, have any of you ever tried to teach algebra I to students who are currently working on a 5th and 6th grade math level? That is what I am required to do. In Texas every single student, even special ed, must take algebra I to graduate. Without the calculator my job would be impossible.

rocky said...

It is unfair to be shocked that kids can't make change when they don't know how. It wasn't just the smart ones who could do it before calculating cash registers were invented. They would all be taught to count from the sales price, starting with pennies, up to the dollar bill that the customer gave them.

It's a lost art.

lgm said...

I'm in a district that doesn't use reform math. The problem is that the material isn't covered in the classroom or as homework. The curriculum map over the grade level may say it was, but guaranteed that 'time ran out', especially if the district is running full inclusion with whole class math instruction in the elementary. It is not fair to blame the calculator use or the student. The responsibility is with the adults.

concernedCTparent said...

My very first job was at The Gap when I was in high school. The cash register was automatic but the manager didn't allow us to use the automatic function. He said it would make us lazy (we were all teenagers). So we had to count back change the old-fashioned way. Low so many years later I realize he did it because he cared. Limiting/restricting calculator use in the classroom would certainly be the students' own good even if they have trouble realizing it now.

farmwifetwo said...

My niece is 12 and both of her parents are primary Teacher's. She HATES to play games that involve a bank or addition with my son who's 10... the one with the NLD...

WHY??

B/c he can add and sub and make change in all kinds of combinations - in his head - and she can't. She's never certain if he's right or not.
Yet her parents think this is OK... just like her 8yr old bro who refuses to write properly and only in phonics.. that's ok to.

Not in my house....

Dawn said...

Ha! I ran into a kid at a music store who couldn't even use a calculator. He had to figure out how to take 30% off a book I was purchasing. Couldn't do it in his head or with the calculator. Eventually the owner came to help. Although my daughter, 11, likely could have given him a hand as well.

Anonymous said...

Reading older justifications for reform math from the early 1990s before it was notorious makes it clear that the original goal was not which method worked best-explicit with examples or a discovery approach.

If you read Richard Lesh or Lauren Resnick from that time it is clear that they believe that traditional math creates different outcomes in skill and knowledge levels and that different outcomes on such important skills is somehow undemocratic.

To obtain equity and something closer to equal outcomes, these professors with NSF funding decided to reimagine the very nature of math.

Unfortunately for this nation's long term economic well being, India, China, and other rising powers apparently are not impressed with this bogus new math scholarship.

Anonymous said...

The scariest aspect of the Common Core Standards Initiative being foisted on the states is the \$350 million going to develop new types of national assessments for this common curriculum.

The people who brought us reform math have been complaining about SATs, ACTs. ITBS, and other standardized tests since the beginning of standards reform more than 20 years ago. What these tests measure was not what reformers wanted the modern classroom to be about. As long as these tests are in use though, reformers recognized that parents and taxpayers would be outraged anytime these tests showed poor results.

Now they finally get to change the nature of what is being measured to "the knowledge and capabilities we want to teach". These new tests will no longer "favor aptitude over effort in our thinking about the possibilities for children".

If you look at the list of Gates Foundation recipients last week to help design the assessment and other instructional materials for CCCSI, it's many of the same NSF funded Centers for Learning and Teaching that developed and pushed these reform math textbooks.

That cannot be a coincidence. It looks like we are about to get that "radically different kind of measurement" reformers have dreamed and written about for 20 years.

And it will be national in scope and international in its detrimental consequences.

Catherine Johnson said...

They would all be taught to count from the sales price, starting with pennies, up to the dollar bill that the customer gave them.

I learned how to do that when I checked groceries in high school.

Catherine Johnson said...

It looks like we are about to get that "radically different kind of measurement" reformers have dreamed and written about for 20 years.

My district just bought the Fountas & Pinnell 'assessments.'

ChrisA said...

Mrs. H,

I hear you and am sympathetic to your cause. You have a full schedule on your plate to teach Algebra I, not do the remedial work that some of your students require.

It seems that the earlier grades aren't taking their job seriously or perhaps they are and their job doesn't entail making sure their students can + - * and /. The principal at our Middle School pushed back on the elementary feeder schools to make sure they were teaching the basics. Believe it or not it worked (I think). I realize that may not be an option at your school district.

Anonymous said...

Fountas & Pinnell = Whole Language or Look/Say

or Guided Reading = Balanced Literacy. The idea is that reading somehow happens with proximity to books.

Between math instruction and reading, too many ed schools are pushing the equivalent of bloodletting and leeches.

SteveH said...

"...have any of you ever tried to teach algebra I to students who are currently working on a 5th and 6th grade math level? That is what I am required to do."

What are you doing to make sure that kids come into your class prepared? As ChrisA says, someone has to push back, and it has to be pushed back to Kindergarten. This is not your job? Make it your job.

This is also not about the calculator. It's a philosophy. Schools want to push kids along and hope that the spiral will take care of things. It doesn't and they know it doesn't. They like to point to the kids who do well, but they know that many of these kids are tutored or helped at home.

What they are doing is educational child abuse. Talk of balance and mastery fails any level of litmus test.

Anonymous said...

"What they are doing is educational child abuse."

Yes, this is how I felt.

And this is how I lost my job.

Anonymous said...

The problem with new math is that it was created by mathematicians--that is, people for whom thinking mathematically is as easy as breathing. They didn't value memorization because they never had to work to memorize anything--they just "saw" the answers. They wanted the delight of mathematics--and the creativity of it and the formality of it, too. Which worked great for other mathy kids. My 7-year-old is using the CSMP's Elements of Mathematics books and is thriving. They're made for the top 1-2% of 6th graders through 12th graders and do stuff like teach linear algebra, topology, and Diff Eq to kids. Without excellent teachers and gifted kids, though, kids floundered. And so reform math tried to be everything that new math was, but for average kids by getting them to "discover" all this cool stuff. The cold, hard truth is that not all kids are able to handle Everyday Mathematics, even when the teachers are excellent, and MOST kids can't handle EM when the teacher isn't excellent, which she rarely is, not understanding, herself, what she's trying to teach. Instead, explicit, systematic instruction in proper mathematical manipulation is SO important! That's what the Asian math programs do so well--and ours fails at miserably.

Linda Seebach said...

I think Anon@12:31 is conflating two different waves of math reform. The earlier one went by the name "New Math" -- Tom Lehrer sang about it -- and when I was teaching college math, around 1965-70, we were just getting freshmen who had been through the New Math curriculum, SMSG (for School Mathematics Study Group). What Anon says is true about this program; it was designed by mathematicians, it was terrific for students with the smarts to be mathematicians if they had a teacher who understood the material. For most everybody else, and in this regard pretty nearly everybody was "else," it was a disaster.

The current wave is called, with a similar level of snark, the New-New Math. It dates, roughly, from the National Council of Teachers of Mathematics around 1989, but had been percolating through the '80s (see "An Agenda for Action," http://www.nctm.org/standards/ ). The awful curricula we have today are based on those NCTM standards, as developed by professors of math education with massive support from the federal Department of Education. NCTM primarily serves math teachers, math educators and administrators; you will notice that mathematicians are not prominently involved. For a summary of the sometimes troubled history of NCTM and the Mathematical Association of America, see here: http://www.maa.org/past/maa_nctm.html

Very few mathematicians were involved with the development of these "inquiry"and "spiral" curricula ( and there are always a few bad apples in the most selective barrel). They're terrible for even very good students, but worse for everybody who isn't naturally talented in math, which is most everybody else.

These bad ideas about teaching math developed alongside broader philosophical trends in teaching; heterogeneous classrooms, group learning, project-based learning, antipathy to teacher-directed learning, and a general disregard for knowledge. Math is too hard for most children to discover it; joy in discovering they can do it is usually motivation enough. Despair at not being able to do it, because they haven't been taught how, kills interest in all but the very best, or those with the most support outside of school.

SteveH said...

"And this is how I lost my job."

What's your point, that you went about it poorly, or that it was time to move on? Welcome to the real world.

SteveH said...

Good summary, Linda.

EM fails because you cannot just "trust the spiral". Even the best students need help at home. EM is not even good in some sort of idealistic sense. It's just bad.

lgm said...

>>Math is too hard for most children to discover it

It's hard because the pre-requisite skills aren't there. If we're going to stick with full inclusion, then back the curriculum up three years and have the nursery school skills be the K curriculum. Or offer free all day nursery, preschool, and preK to pull in those whose parents/sitters won't or can't teach the pre-requisite skills.
It will be less expensive in the long run than prison and poverty.

Sara R said...

They would all be taught to count from the sales price, starting with pennies, up to the dollar bill that the customer gave them.

I learned how to do that when I checked groceries in high school.

FYI, Rod and Staff Mathematics teaches this skill still, starting in their 4th grade book. Rod and Staff is a Mennonite curriculum popular with homeschoolers, similar to typical math books of the 1960s.

Anonymous said...

Not conflating!

New-new math was an attempt to make the vision of new math--that all children will be mathematical thinkers--work in a different way, since the first way was a failure. Everyday Math actually DOES work when gifted kids AND gifted teachers occur together, but it's actually far ***less*** kid- and teacher-friendly than old new math, with even less work on the fundamentals. It was created out of the belief that discovery learning will make all the connections that were lacking in old-new math. Unfortunately, it just doesn't work that way. Most kids have no idea what it is they're supposed to be discovering, the actions becoming perfectly meaningless, and most teachers have no better idea. Math becomes LESS accessible and LESS explicable.

(Another example of old-new math still in existence and quite successful is Stanford's computer program for gifted kids.)

Linda Seebach said...

@lgm, who said math is hard because the pre-requisite skills aren't there. True, the lack of pre-requisite skills makes math impossible, not merely hard. But even with them, discovery is too hard for most people. How would you discover long division or the quadratic formula?

Anonymous said...

>Very few mathematicians were involved with the development of these "inquiry"and "spiral" curricula ( and there are always a few bad apples in the most selective barrel). They're terrible for even very good students, but worse for everybody who isn't naturally talented in math, which is most everybody else.

>These bad ideas about teaching math developed alongside broader philosophical trends in teaching; heterogeneous classrooms, group learning, project-based learning, antipathy to teacher-directed learning, and a general disregard for knowledge. Math is too hard for most children to discover it; joy in discovering they can do it is usually motivation enough. Despair at not being able to do it, because they haven't been taught how, kills interest in all but the very best, or those with the most support outside of school.

To clarify further, the "fix" for new math was to make it align more with educational theory. Mathematicians weren't involved, as a group, with that step--educators who thought they were solving all of new math's problems by making it align with educational theory were. Unfortunately, they didn't.

I don't think we're disagreeing--just coming from different directions.

lgm said...

I have a mathy kid. Long division on his own was easy...same process as the child used in kindy to divide cookies among the tablemates with the bonus that he and his mathy friends had fun deciding how to keep long to keep splitting the crumbs. It is not fair to average kids to say they are 'bad at math' when they've not been given the opportunity to develop the pre-requisite skills. Those skills are assumed to have developed before compulsory school starts - but they obviously haven't.

I do agree that Alg. and up will take so long to discover from the average child's environment that guided teaching is beneficial. However, should we decide to give cannons to kids and let them figure it out, it might spark a great interest in Alg I. Same with two trains on the track...

SteveH said...

"Everyday Math actually DOES work when gifted kids AND gifted teachers occur together, "

One of the authors of EM said years ago that EM was not for "elite" students. I'm sensitive to anything that might suggest that EM is best for any student at any level. It doesn't even do discovery properly.

My son took EM from 2nd through 5th grade. The spiral is not designed for the best kids who will master the material the first time through the loop. Each pass through the spiral is not used to build on top of previously mastered skills and knowledge. It's used to make an additional attempt at the same old material. If you had a class with top level students, EM would drive them crazy.

Everyday Math tells schools what they want to hear; that they can have it both ways. They can have very mixed ability, full inclusion classes and somehow provide a better math education than before. All you have to do is "trust the spiral".

It's all so perfect. If you assume that the spiral works by definition, then all you have to do is blame the poor math students (which many do with 7th and 8th graders) and point to those who manage to do well. It helps if you think of math as some sort of scary and difficult thinking and discovery process.

Betty said...

Our district adopted EM and we are implementing it for the first time this year. We've had a number of "training seminars", and every one begins the same way: several minutes of the presenter spouting disclaimers attempting to reassure all of us to "trust the spiral", and other such nonsense pleading with us to suspend our disbelief. The first time I heard this, I thought that if this program is so great, why are they going on with all these apologetics? Talk about a red flag...

I've been teaching K-3 for over 20 years, and I think EM sucks big time. Thank God I have tons of supplemental stuff to impart the basics.

SteveH said...

"trust the spiral"

Each lesson gives just one litle view of a topic. I remember many homework assignments consisting of less than 10 questions. I got angry with my son once because after 5 minutes, I realized he was not doing his math homework. He had it done already! It was not that he had mastered the material with just 8 questions.

I think what happens in class is that the jumping around frustrates many kids and teachers spend more time on the material. If you follow the spiral to get everything done, then math becomes a frustrating sequence of repeated partial learning. The assumption is that if you do this enough, mastery will automatically occur and it will effectively deal with full inclusion.

It doesn't.

After a few years, all students are on a different page of learning and it's impossible for teachers to diagnose and fix problems. EM assumes that the spiral will take care of everything.

In my son's old school, the fifth grade teacher realized that something had to be done. Too many kids were getting stuck on things like adding 7+8. These were bright kids. Obviously, the spiral wasn't working. She set up an after school "club" and slowed the process down. That's why she didn't get to 35% of the material. Teachers are in a no-win situation. Then again, the kids just get passed on and the problems go away. I wonder what 6th grade teachers think when there are no more grades to trust the spiral.

What bothered me the most was that while each unit introduced or went over a small amount of material, EM also gave Math Boxes that reviewed old material. Given the spiral nature, this was material that may not have been mastered. These boxes did not review and explain one particular topic. They covered many different types of problems. If you had not mastered the material before, there was no way you were going to magically do it by just seeing one more problem.

If I had to give some advice to EM teachers who are forced to keep up the pace and trust the spiral, it would be to ignore the Math Boxes. Do not interrupt each unit with random old problems. Use that time to ensure that as many kids as possible have mastered the current material. Try to keep everyone on the same page and your efforts will be more beneficial. As soon as you get into an individual diagnose and fix regimen, you've lost.

By fourth grade, teachers are in an untenable position if they really know what math their kids need. EM might say there are points where they expect kids to have mastered particular material, but there is no feasible way to diagnose and fix those problems.

When it comes down to a choice between kids and the EM spiral, the kids lose. As long as enough kids (who get help at home or with tutoring) do well, then schools will continue in their dreamworld and trust the spiral. Then, once the kids get to 7th and 8th grade, it becomes blame the kids, and parents, and society, etal.

Anonymous said...

Same Anon again...

>One of the authors of EM said years ago that EM was not for "elite" students. I'm sensitive to anything that might suggest that EM is best for any student at any level. It doesn't even do discovery properly.

Oh, I agree that's it's not at all best for ANYONE! It's better than your standard US primary fare for very strong students--that's how it raised test scores to begin with in the initial trials. This got misconstrued as evidence that it was a "better" program, period, when it didn't begin to establish the fundamentals of basic numericity for those who don't just "get" it.

If a truly gifted kid gets a choice between EM and whatever more standard edition their school uses, he'll likely take EM because it's more interesting and because the gifted kid would ALREADY be way beyond what's supposed to be taught in the grade. But Stanford's EPGY would be MUCH better, as would Singapore's PM with Intensive Practice on an accelerated schedule or a grossly accelerated RightStart Math.

And Singapore's PM and RightStart are both much better for average AND below average students than any normal US math program!

Additionally, RightStart, particularly, is excellent for ever relatively poor teachers, as it teaches the teacher as it teaches the student and has the option of using a script.

Now, my gifted DS would have crashed and burned with a good EM teacher--he has an auditory processing disorder, and EM is too poorly set up to make the idea/words/brain bridge so clearly that works become extraneous. RightStart was heaven-sent for us, with Singapore just as strong once the first link was made. So it's not even like it'd work well even for all gifted kids.

Barry Garelick said...

If a truly gifted kid gets a choice between EM and whatever more standard edition their school uses, he'll likely take EM because it's more interesting and because the gifted kid would ALREADY be way beyond what's supposed to be taught in the grade. But Stanford's EPGY would be MUCH better, as would Singapore's PM with Intensive Practice on an accelerated schedule or a grossly accelerated RightStart Math.

I do not feel this is any kind of endorsement for EM. If EM is appropriate only for students, gifted or otherwise, who are already beyond what is supposed to be taught, then EM is not a good choice. I found when tutoring my daugher and friend with Singapore math, that as long as we stayed ahead of the EM train wreck, the EM lessons were good supplements to what they were learning at home. I also disagree that it is better than standard US primary fare for very strong students. Perhaps some of the problems are better, but the alternative algorithms and their avoidance of long division and converting fractions to decimals is a very big strike against the program.

Cranberry said...

EM was not right for my gifted kids. One kid, on deciding to change schools in 3rd grade, said, "well, I have lots of friends at (EM school), but the curriculum was driving me nuts."

It may be harder to discern the damage done to bright kids by teaching math in the slowest, most disorganized manner possible, but the damage does exist.

Allison said...

someone said re: EM: "it's better than the standard US primary fare..."

can you tell me what the "standard fare" is, if not EM?

Here in MN, the St. Paul district uses Everyday Math, the Mpls district uses Everyday Math, and three suburbs that I know of use Everyday Math. I know of know public school districts here that use anything else. In CA, I only know of districts that use Everyday Math.

What, pray tell, is the current standard, if Everyday Math isn't it? What math content, methodology, or treatment characterizes the so called standard fare so as to distinguish it from EM?

Anonymous said...

I never said it was an endorsement! It's an "it's not entirely awful program and can work better than others in certain circumstances."

Gifted (top 2% and above) is different from bright (top 10%). A truly GIFTED kid isn't taught hardly anything about math at the elementary level--he or she *does* figure it out on his/her own, either before being introduced to the concepts or within moments of an introduction to it. There is little gained by a traditional curriculum beyond automaticity--which is important, but which most parents make sure their kids get, anyway. If a child is being *taught* at grade/age level, he or she is not likely to be gifted.

It's better for gifted kids simply because is isn't as tedious. That's it. In an oppressive environment where children aren't allowed to be accelerated to their appropriate academic level, a curriculum that's really better for a supplement is better than a curriculum that's only teaching things a child already knows.

Now, you're thinking, wouldn't a much better solution be to have gifted kids in classes suited to their level and give everyone a decent math program? Why, yes, it would, but most schools wouldn't let my next door neighbor's kid skip a mere two grades for his proper placement into 2nd (and then let him skip at least one more time later...), much less let mine skip 7 grades for math and 4 grades for English, not even in an in-class acceleration option.

They'll feel bad because they're shorter than the other kids in their grade, see. Because school is about socialization, see. And equity. Because it's fair to put a kid in a class in which they already know all the material so that other students don't feel bad about themselves. Right? Right???

By "standard fare," I mean the more commonly used post-new-math American programs--whether Holt or Harcourt or whatever. EM/TERC/etc. are NOT the norm in most places--and with any luck won't be.

SteveH said...

"A truly GIFTED kid isn't taught hardly anything about math at the elementary level--he or she *does* figure it out on his/her own"

My son has been tested to be in the top 1% nationally in math, but this doesn't mean that he can create knowledge out of thin air or that he can magically understand something the instant he sees it. I had to work with him at home.

Second, EM was extremely frustrating for him, perhaps not the first time through the spiral, but all of the 'n' times after that. EM spirals all around the material and never dives right in.

But what, exactly, are we comparing it to? EM at my son's school replaced MathLand. Anything would have been better than MathLand.

lgm said...

Allison, could you explain how your district operates?

Here (NY) the district supposedly is teaching the math objectives supplied by the state. The person in charge of curriculum does not dictate which particular text the teachers use, but does dictate objective order and a pace. Teachers are free to use any text or resource they wish to accomplish the objective. Most just explain the 'how' of the daily objective and hand out a sheet of exercises. The sped teachers will present finger tricks. Occasionally some exercises from a text will be used. The problem solving is all out of one text (Houghton Mifflin), but that is because the other texts are soooo old that they don't have problems that meet the current state objectives.

So, it isn't possible to say what curriculum is used in elementary here as the teachers are held to teaching objectives, rather than completing a curriculum package.

Are you saying that elementary teachers in your district actually follow a packaged curriculum, and go through it page by page, with no teacher allowed to drift off the script?

--------------------------------
Anon, the gain to a gifted child in going through the grade level mat'l is in learning the nomenclature & honing the problem solving ability. Compaction is a good idea.

lgm said...

>>If a child is being *taught* at grade/age level, he or she is not likely to be gifted.

This is one of the myths regarding giftedness...see resources such as http://www.nagc.org/commonmyths.aspx for more.

There are circumstances that mean it is appropriate for a gifted child to be working on grade level material. Note grade level written notation needs to be mastered, even if the child has worked out the concepts for himself.

VickyS said...

In my experience (with my own kids and the gifted pullout I used to run at their school), Everyday Math was disasterous for gifted kids. Either they get frustrated with moving away from newly introduced subjects before they are mastered, or they are bored because they already know the material. Additional frustrations occur because of the constant demand to describe in words what they do in their heads. The kids bristle at the insistence on concretizing that which they have already internalized in an abstract fashion.

The real casualty is the number of gifted kids who get so frustrated with this curriculum that they lose their interest in math altogether.

VickyS said...

And let's not forget the ELL kids. My school district (St Paul MN) has 44% ELL. Language-intensive math curricula like EM are killer for them. So sad, when math could so easily be a success story for them right from the beginning.

VickyS said...

lgm: the nomenclature taught in Everyday Math is one of the problems. Do you know what a friendly number is? How about a number sentence? EM replaces standard nomenclature that would be recognized by high school and college teachers with an alternative lexicon. Another way (like their convoluted algorithms) EM is trying to leave its mark on the world, I guess.

Also, because of the spiral, EM is impossible to compact. That's another one of its problems for the gifted population.

I can answer your question to Allison about St Paul since that's where I live too. In our metropolitan area, textbooks (not objectives) are adopted by the superindendent and the school boards. Some committee that recommends the textbooks is supposed to have compared them to the state standards and done some mapping. All schools in the district have to teach the same curriculum, i.e., use the same textbooks. This allows them to buy in bulk and have district-wide professional education.

We have math coaches (for the teachers, not the kids), but they area really math police. They arrive in classrooms and make sure the teachers are not deviating from the prescribed curriculum. Supplementation is not allowed (officially) although good teachers still try to do it.

There is a movement, which is beginning in middle schools, last I heard, to have daily lesson plans prescribed by the district, so that each teacher, at each school, will be teaching the same lesson plan on the same day.

Sounds like a real fun time to be a teacher.

Bostonian said...

Anonymous wrote
"EM/TERC/etc. are NOT the norm in most places--and with any luck won't be."

I live in a town near Boston where the district uses Everyday Math, and most nearby towns also use it. Here is a story from 2008 about its adoption in Plymouth, MA.

Cranberry said...

A grave fault in EM for gifted kids is the lack of logical organization and the lack of a textbook. Some students are able to teach themselves math, from a textbook. Without a textbook, it's impossible to read ahead.

EM also hops around so much, it's difficult for students who do think deeply about a topic to think of further ramifications of a concept. There are no "further challenge" sections.

SteveH said...

"Either they get frustrated with moving away from newly introduced subjects before they are mastered, or they are bored because they already know the material"

Exactly my experience.

They introduce material in their own quirky way ("What is the one?") not because it's better, but because it's different. The lattice method does not provide more understanding. They teach it because it's different. Any attempt they make at discovery or understanding is on a very superficial level. It never translates to the abstract understanding needed for algebra.

I really don't want to be a pain in the butt about this, but I will argue against any view that says that EM would be good "only if". I consider EM to be fundamentally flawed. You cannot trust the spiral. That's a huge cop-out and disastrous for any student.

I don't know the details of what went on in my son's classrooms, but there was a limit to how much a teacher could or could not vary from the script, so to speak. This could be good or it could be bad. Unfortunately, this line of argument often leads to the idea that all you need are good teachers; that the curriculum doesn't matter so much. Usually, those promoting this idea have no plan to achieve that goal other than looking for more EM teacher training.

lgm said...

>>Sounds like a real fun time to be a teacher.

Sounds like a lot of desperate measures to combat incompetent teaching and student mobility. Perhaps it would be more effective just to stream a video, then have the teachers and aide go around to help everyone individually.

Number sentences are used here. Alternative names for the proprties are used too, but they are aligned with the state req'ts so that the children will be able to understand the questions on the state grade level math tests. Friendly numbers...no- when we went to full inclusion, all topics that weren't in the state objectives were dropped. In the name of equity, nothing extra can be included per local politics. Estimation (both back and front-end) and compatible numbers are the most difficult concepts remaining in K-5. Fraction operations are introduced in 5, but left for the middle school teachers to develop competency.

Our K-5 objectives do spiral to the point that G kids just view math class as handwriting and mental math practice, unless they are assigned to of the ex-G teachers that know how to teach math well and develop their students' problem solving abilities. There are only 2 new units per year.

>>Additional frustrations occur because of the constant demand to describe in words what they do in their heads.

It is a necessary evil. In the real world, one does have to learn to communicate with colleagues in words as well as symbols.

The frustration I found was more with the insistence on breaking apart concepts mastered while the child was much younger...the child really didn't have the words back then in his vocab to describe his thought process. I doubt my mathy child ever used some of the techniques that the concrete included 'basic' level learner uses (and are only taught in pullout for that group) yet the state test asks for them to be completely described.

SteveH said...

"because of the spiral, EM is impossible to compact"

You would have to separate those kids into a separate area or room. There would then be no need for the small tidbits of partially mastered material. You would need a different spiral. However, mixed-ability learning environments are the basic premise of EM.

"Compact" is an interesting term. It seems to be used as a replacement for acceleration. I'm not sure what happens during the rest of the year when those students have finished the grade-level material. Schools don't like this because they can't pretend that all kids are equal.

However, EM is anti-compacting. It's expanding. There is no such thing as grade-level material. Rather than continue a topic/skill to achieve mastery, they spread it out over multiple years. A friend of mine once complained that she had three kids in three different years and they were all covering the same place value ideas. To compact EM would be totally absurd.

Our public schools used to have a detailed chart of ITRE for all topics. Introduce (I) was the year in which the topic was introduced. Teach (T) was the year in which they actually taught the material. Review (R) was the year(s) that the material was reviewed, and expect (E) was the year in which they expected the material to be learned. These were all different years!!! I never saw anything about how they diagnosed all of the individual student problems and fixed them. They just probably trusted the ITRE. There are no feedback loops here.

So, EM claims it works in a full inclusion environment, allows for differentiated instruction (I NEVER saw that), AND it provides for proper mastery, better problem solving and critical thinking skills - all done automatically! Wow!

Trust the spiral ==> blame the kids.

SteveH said...

"EM/TERC/etc. are NOT the norm in most places"

I must live very far away from most places. It's all EM/TERC around here.

lgm said...

EveryDay Math's website claims nearly 3 million students worldwide use their materials. Quick search showed the US Census stating there were 33 million elementary students in 2003. http://www.census.gov/Press-Release/www/releases/archives/education/005157.html

If a child is being *taught* at grade/age level, he or she is not likely to be gifted.

Wrong, wrong, wrong.

It is another common "myth" to equate giftedness with high academic achievement. Data from my district shows that almost all teacher referrals for "gifted" classification are of high achieving students. These are almost always bright kids -- 75th %ile or better -- who are industrious and "teacher pleasers." Few are gifted. To qualify for a gifted classification, a student must be at the 99th percentile or higher on *both* the subscales of the WISC.

Truly gifted children -- sometimes nicknamed "severely gifted," with tongue in cheek -- are more likely to be serious underachievers than the average student. (I'm not talking gifted/LD students here). A substantial number are disengaged from school, may be culturally alienated from the academic emphasis, are characteristically asynchronous in development and so may fit in much better with older peers or adults than with their same-age classmates, have intense and consuming interests that diverge from school expectations, and so on.

I'm a little proud of myself for nominating for "gifted" classification several students who were perceived as weird, stupid, slow but nice, and otherwise absolutely NOT gifted because they did not have average or better academic achievement. In one case, the psychologist told me this student was the highest-scoring student she had ever tested in 28 years. Another student (I write about her in an earlier KTM post) was also in about the top .05 %ile. Neither was "above grade level" in any area.

Like Steve's son, one child needed explicit teaching to excel. Another was simply engrossed in his own world and was writing a book on some kind of cosmological theory based on various physicists (Hawking and others, plus the many-worlds hypothesis guys) he studied on his own. None of his teachers considered him particularly bright.

Gifted students are disproportionately represented in the dropout statistics. It is hard for many to find their niche and their gifts are often not recognized by teachers. That's one reason my district had a formal screening program for a long time, because teacher referrals were a poor source of appropriate candidates.

ChemProf said...

I think the "spiral" language is part of the problem in fighting EM, actually. I was talking to my mother, a 47 year veteran of the elementary school classroom who is currently waging a guerilla action using Saxon instead of the district approved math (which is Harcourt, not EM, but which is very EM-like). When I commented that the problem with EM is the spiral curriculum, she countered that Saxon was a spiral, which was great. By spiral, she meant that it moved cleanly from topic to topic, building on itself, as opposed to the Harcourt which jumped around from topic to topic.

I think spiral sounds better than it is.

Anonymous said...

I really grew to dislike Saxon math when I used the 4th grade book for my homeschooled kids, largely because of the spiral. The feeling is like this: today learn the terms mean, median, mode; next day add 4-digit numbers, or whatever; next day find right triangles, ... randomly bouncing around. It seems to make a lot more sense to introduce the topic, learn it, move on to something new, and continue reviewing, cumulatively, what has been learned all year. Saxon does a decent job with that with its cumulative problem sets. I "hated" spiraling.

SteveH said...

It's difficult to have any sort of discussion when it's not clear if everyone is on the same page. You end up talking page each other.

With EM, it's a spiral to achieve mastery over a period of years. They never introduce a topic with the idea that even most kids will "learn it". (whatever that means) Their use of the spiral is not to build upon previously-mastered skills and understandings. The purpose of their spiral is to allow the slow kids to move along with the fast kids and give the look and feel of some sort of parity. There is no way to tell the difference between poor teaching and slow students. Since the mantra is "trust the spiral", the assumption is that they will never know the answer to that question. Of course, my son's fifth grade teacher knew that her students should have learned how to add 7+8 quickly long ago. This was her evaluation. The spiral did not give her that information. It told her to keep going.

I don't know the details about Saxon, but I assume that each pass through the spiral requires much more mastery than EM. When you get back to the material again, it should be more like a spiral than a circle. Many more kids are on the same page and the teaching/learning process should be more effective.

There is also the issue of how one topic leads to another. That is a separate issue from spiraling. All curricula have to deal with this. You can have a "bouncing around" feeling if you barely understand a topic before you move on, or you could have a bouncing around feeling because consecutive topics have little to do with each other.

Everyday Math creates problems by allowing all kids to go with the flow of the spiral. There are no checks or balances along the way. After a couple of years, all kids have different levels of mastery and understanding with no way to fix them.

Anonymous said...

Spiraling, to me, means touching on a topic and if you don't master it, you'll probably get it next time around.

Saxon shoots for mastery of the topic at hand by doing a chapter practice first. Usually several chapters hang around the same topic, so the knowledge learned from the one chapter is needed for the next ones. From there, practice examples of that topic show up in the distributive practice after nearly every chapter in the book, which is a good way to assess your child's mastery of a topic should he/she keep missing a particular problem.

In fact, in the homeschool workbooks every problem has the source chapter written down next to it so that the teacher/parent can go back to the corresponding chapter if the child misses the problem.

If we mean spiral in that we revisit a subject, then yes, I suppose Saxon spirals. But I'm thinking of the more recent definition of spiral used by reform textbook authors meaning, "Don't worry if you don't get it, we'll do it again NEXT year when you're older."

The problem with Saxon is in dealing with gifted kids and what to skip. The review is much too long for mathy kids. But the topics covered need to be taught, they can't be discovered.

SusanS

Anonymous said...

We just removed our children from the Seattle School District because we felt the inquiry-based math materials were actually doing them harm.

The sequence is Everyday Math for elementary, CMP2 for middle school, and Discovering for high school.

Like SteveH, we learned early on that we needed to supplement (actually, supplant) the math curriculum at home. We used Singapore Math and other workbooks with a traditional, sequential, computation based focus.

This worked for a few years in the elementary grades, but once our older child started the CMP2 books, we surrendered. It just didn't work. Our daughter absolutely.hated.math. The actual math was quite simplistic, but it was presented in such a tedious convoluted way. Lots of time was spent deciphering the problems, but very little math was being learned or mastered.

They are now at a private school using more traditional texts. The difference is astounding. Homework can now be done independently and they are tested for mastery before moving on to the next chapter. It is expected that they know their math facts. They are spending less time on math, yet learning more.

What we have seen in Seattle public schools is that the texbooks are dictating the math curriculum. The adopted textbooks do not fully meet the state standards, yet parents have little recourse. Many families use Kumon or supplement at home.

As an aside, Washington State is a local control state, meaning that the state can set educational guidelines and standards, but has no authority to enforce them. The authority rests on the school boards of each district. So if the school board is not enforcing state standards, a parent's final recourse is through the courts.

SteveH said...

"The sequence is Everyday Math for elementary, CMP2 for middle school, and Discovering for high school."

Ugh! That is so awful!

"...but once our older child started the CMP2 books, we surrendered. It just didn't work."

We could make fixing EM at home work for my son, but we were heading towards CMP. Fortunately, when my son got to 6th grade, they switched to a proper pre-algebra and algebra sequence. Unfortunately, many kids were not prepared for the transition.

"(actually, supplant)"

Yes, supplement was not appropriate for us. In fifth grade, the teacher tried to get everyone up to the same page and didn't get to 35% of the material. In the summer, I got him through the rest of the material and through all of 6th grade EM (because that's what they were testing him on) to get him into a proper pre-algebra class in 6th grade.

Anonymous said...

Saxon: I tried their Calculus and I'm not crazy about it at all. It jumps around and there is no mastery before going on to the next topic. I've also found the content to be pretty shallow.

ari-free

CassyT said...

Just have to share an exchange with an elementary school principal here in Fort Collins today. I had just come from the G & T teacher's room. I had heard she was using Singapore Math with her students and I wanted to inquire how it was going. My info was wrong, she'd never heard of the curriculum. (-but was interested after I shared some information.)

As I was walking out, I ran into the principal and chatted with him for a minute. He told me that his 4th graders had finished their math program by spring break last year and had worked with the 5th grade Singapore math books. "We're pretty advanced at this school."

It was all I could do to keep a straight face. Their regular math program that they finished by spring break? Everyday Math.

Anonymous said...

"He told me that his 4th graders had finished their math program by spring break last year and had worked with the 5th grade Singapore math books. "We're pretty advanced at this school."

It was all I could do to keep a straight face. Their regular math program that they finished by spring break? Everyday Math."

So they went from 4th grade EM to 5th grade Singapore Math? If the 4th graders could do this and keep up with Singapore Math, doesn't this imply that EM is doing fine (or did fine for that class)?

-Mark Roulo

J.D. Salinger said...

So they went from 4th grade EM to 5th grade Singapore Math? If the 4th graders could do this and keep up with Singapore Math, doesn't this imply that EM is doing fine (or did fine for that class)?

It means the principal thought they were using Singapore Math, but they were using EM.

Allison said...

--ChemProf said...
I think the "spiral" language is part of the problem in fighting EM, actually.

I do, too, but for reasons other than what you gave here. The classical curriculum is a 4 year spiral. Undergrad is a 1-2 year spiral. These spirals may leave things to be desired, but they have nothing to do with daily subject changing.

-- I was talking to my mother, a 47 year veteran of the elementary school classroom who is currently waging a guerilla action using Saxon instead of the district approved math (which is Harcourt, not EM, but which is very EM-like). When I commented that the problem with EM is the spiral curriculum, she countered that Saxon was a spiral, which was great. By spiral, she meant that it moved cleanly from topic to topic, building on itself, as opposed to the Harcourt which jumped around from topic to topic.

The problem with EM is not the spiral per se. It's the lack of focus, lack of coherence, and lack of mastery. A spiral where you master before revisiting, where you have a direction you're going is one thing. EM appears to lack that.

re: saxon: it depends on the Saxon edition, I think. I've just viewed the latest, and it's utterly fragmented. I could not see anywhere that anyone could build to mastery, because there weren't enough problems in anything before moving on.

By that I mean that in a given chapter, the daily lessons were: count by twos, multiplication, division with fractions whose denominator is a multiple of 2, perimeter, more multiplication, then estimate.

There was no mastery, because there were maybe 20 problems per lesson, but 4 were "use the number line to multiply", the next four were "use a grid to multiply", the next were "use the standard algorithm", then some "multiply". The individual lessons' material was largely reasonable, except you were expected to do the "same" thing 5 different ways, all in one daily lesson, and then the next day, move on to something else.

Yes, I could work very hard to see how these ideas above all "built on each other" but then again, so does all math, if you're sophisticated enough about it. How that helps elementary students, though, is a different point entirely.

Anonymous said...

"It means the principal thought they were using Singapore Math, but they were using EM."

Oh :-(

Reminds me of a story told about Jack Warner. When leaving the animation studio one day, he is reported to have said, "Take good care of Mickey." Mickey Mouse being, of course, a Disney character ...

Thanks.

-Mark Roulo

CassyT said...

The principal had no idea what they were using.

Isn't EM based on a daily, 90 minute lesson? How could they have possibly been done with the 4th grade curriculum by Spring Break?

Anonymous said...

>EM at my son's school replaced MathLand. Anything would have been better than MathLand.

TERC? ;-) I think TERC is decidedly worse than EM. Haven't even heard of MathLand. That may be a good thing....

There's a big difference between giftedness and being tested at X grade level or at X percentile in achievement. There will likely be a mere handful of kids in the NATION who are doing what my DS will be doing at age nine--meaning, maybe 10--and while he's more than highly gifted, he's not THAT smart. If I didn't make him do every problem in the book (for maturity reasons), he would already be on NEM 3. It doesn't make him smarter than some poor schmuck of a kid who's still stuck on first grade and has never seen a linear equation--or dumber than he would have been if I didn't have the requirements to progress that I have! I stand by my statement that it takes very little for a truly gifted child to master the concepts, if not the fluency, of arithmetic. My mother's mathematics professor led me through the sum total of school arithmetic at the age of four in approximately 15 minutes through a series of well placed questions that led me to intuit multiplication and division of fractions and fraction equivalents. (I still remember this distinctly, so it is not merely a mother's tall tale.) There just isn't that much to master. Terminology and formal presentation would have taken me a couple of weeks, perhaps, at that age, and the only thing left was automaticity. (This takes the longest--probably would have taken me a year, as there's a strong temptation just to derive everything on the fly.)

>Anon, the gain to a gifted child in going through the grade level mat'l is in learning the nomenclature & honing the problem solving ability. Compaction is a good idea.

Well, it took my son 1.5 years to complete the ENTIRE RightStart program, Singapore 1A-5B (and it would have taken less because he fought me like crazy for the last 6 months until I agreed to let him do NEM 1 and Elements of Mathematics on alternate days with Singapore), and all of Singapore IP 1-3 (will skip 4 and 5 and will do 6 instead--too repetitious). He's starting Singapore 6A tomorrow--since striking our deal, he's completed all of Singapore 5 in 15 school days of 40 min each.

I'm not saying this to say how smart he is. He's not the smartest thing ever. He was doing at 6 what I did at 4, and *I'm* far from the smartest thing ever. There are WAY more kids in school who are perfectly able to do this--in WAY less than 90 minutes a day(!!!!)--who are not being served. EM stinks for them, but it stinks less than many programs because it's less likely to make them hate math with quite the passion that more routine things do.

>If a child is being *taught* at grade/age level, he or she is not likely to be gifted.

BWAHAHAHA!!!! My SAT and GRE are exactly what you'd think from my description of my early achievements (and so was my GPA in high school), and guess what? I was taught at grade level. I was excluded from even the pullout TAG program because my poor handwriting meant I was clearly stupid. (I was reading at a 12th grade level at age 8, not having begun to read for pleasure until six months before. So it's not like I was merely good in math and mediocre in other subjects.) The teachers' attempt at rectifying my handwriting by having me write more pages with no further explanation somehow failed to help, but oddly, when the "honors" separate-track program began in 5th grade, somehow I was the strongest student among the 1021 fifth graders at the (5th grade only) school. Funny, that.

--SameAnon (who now has a name?)

Anonymous said...

Oh, and by that time, I'd LONG since learned to loathe math. I have something like 30 credit hours of math at the calc III level and beyond (multivar), and I hated every moment of it except Calc BC (teacher made math kind of fun again) and my harder Dif Eq class (the one that wasn't for engineers), which was pretty fun.

It was actually partly because of me and one other student, then a third one four grade levels behind, that our school district's system of dealing with gifted kids changed--for the better. They began allowing radical acceleration, single-subject acceleration, etc. The school district is very much in the minority, however, among a wave of district moving in the opposite direction--removing the piddly so-called "gifted" programs that are already in place (which target 10-15% of student body). More gifted students in K-5 have minimal to no differentiation than have true acceleration.

>There are circumstances that mean it is appropriate for a gifted child to be working on grade level material. Note grade level written notation needs to be mastered, even if the child has worked out the concepts for himself.

It is NEVER appropriate for a gifted child to be assigned on-grade-level material. Written notation takes moments to master, and as long as the kid builds up the stamina to be able to do the written work, algebra and above is completely appropriate.

Bright kids can be given enrichment and later tracked into honors courses, and that's all well and good. But gifted programs are almost never appropriate for gifted children.

>Spiraling, to me, means touching on a topic and if you don't master it, you'll probably get it next time around.

Saxon spirals. Period.

Saxon does less harm to brighter kids than to those who are happy just stepping through the algorithms, but it is a stake in the heart of any gifted mathy kid in terms of its dryness, the lack of variety and challenge within a lesson, and the sheer, mind-numbing repetition. Singapore's practice problems are THOUGHTFUL. Saxon's are ROTE.

I'd daresay, though, that for truly gifted kids, EM is better than Saxon for keeping them from hating math. For bright kids, Saxon can be fine. For regular kids....well, at least they can step through the procedures, even if they don't understand them. Better than EM, where they can't do anything at all!

>The classical curriculum is a 4 year spiral.

Depends on whose "classical."

--SameAnon

Anonymous said...

Less than 10% of the country, at most, is a small minority. It seems to be concentrated in the NE, CA, and the Chicago area, but just because there are pockets where it's the norm doesn't mean it's the norm everywhere. I don't understand why citing a figure that is less than 10% is evidence for its overwhelming prevalence when EM is the most popular math program of the new-new math type.

Then again, I don't see why d*mning with faint praise is seen as defending it, either! My stance is this: It stinks, but it stinks less than some other things in certain circumstances. Hardly a resounding statement of support!

--SameAnon

Anonymous said...

Another fundamental problem with Saxon: while there's lots of review for topics in the beginning of the book, there's hardly anything for those closer (and more advanced) to the end.

Rightstart: What is that? Is it one of those mental abacus programs that are popular in Asia?

ari-free

Lisa said...

Back to the original comment about not making change. My very average 3rd grader can make change and multiply 12 by 12. Kids can do this, no one is teaching them. That lands squarely in the laps of schools. I began home schooling because it was obvious that for an average student basic just weren't being addressed. Two other things. I have 2 other kids who are gifted. Our school system has no program for these kids, thus school is just a place where they get lots of reading done. Rightstart does use and abacus and 'Asian' ideas but it's written by an American PhD , Dr. Joan Cotter. I use it along with Singapore 3B for my 8yo. Who again is not a gifted kid. Just teach the kids for crying out loud!

Anonymous said...

ari-free,

I'm only familiar with grade school and middle school Saxon, plus around 20 chapters of the algebra 1 book. I've never heard much about the upper levels and that might be why. I also agree about the length and amount of review. But, it was perfect for my math struggler. I think it might be too much for even a regular math kid.

SameAnon,

I stand by my post. Saxon does not spiral. Period.
If you go by what is meant by spiraling today, it is totally different. Saxon seeks mastery so that when the topic is broached the next year, it is a true review. Not so with EM and other reform curriculums.

Saxon has rote exercises for speed and fluency. Sorry, but I'm not against that as long as it isn't overused and children can skip.

Yes, Singapore has more thoughtful problems, but that is a problem with most American math texts, not just Saxon.

I can only speak for IL, but EM is all over the Chicago suburbs and downstate. Gradually, however, districts are dropping it, but often for for just another version with a different name.

SusanS

SteveH said...

"Haven't even heard of MathLand. That may be a good thing...."

It's a very good thing. Actually, it was so bad that any (good) mention of it has disappeared off of the web. Nobody admits to owning it, but there is a reason why our schools switched to EM.

"Then again, I don't see why d*mning with faint praise is seen as defending it, either!"

I'm sorry, but it doesn't even deserve faint praise. It's not appropriate for any student at any level. I would agree that it's better than TERC, but they would take that as a recommendation! It's amazing what they do with the What Works Clearinghouse comments.

As for gifted issues, I think it's more a matter of matching a student with the proper environment and acceleration. This applies to any student. Unfortunately, K-8 schools are going the other way; lumping all kids together and trying to differentiate in class. Then they tell parents that the education is better! Wow! I wonder why they allow high schools to separate kids by ability.

SteveH said...

I agree with SusanS. Spiraling now means spiraling to achieve basic mastery. This is a multi-year cycle for each topic. They should call it circling. When they add new material, it's added more like a new concentric circle. EM may not dominate the market, but this approach to math does.

Allison said...

Susan,

Saxon says it spirals. When was he last time you saw i?

http://saxonpublishers.hmhco.com/HA/correlations/pdf/s/SM_3_NA_TOC.pdf

fractions are presented in lesson 12, 17, 21 and 24, 25, 26, 37, 61 and 73.

The addition facts are equally frenetic in distribution.

Allison said...

http://saxonpublishers.hmhco.com/HA/correlations/pdf/s/SM_3_NA_TOC.pdf

Anonymous said...

Allison,

I'm speaking of spiraling the way EM or Trailblazers speaks of it. Saxon may use a kind of spiraling that is spoken of in classical homeschooling books, but I'm referring to the way reform curriculums throw everyone in the same classroom and say they'll spiral back for the ones that didn't get it that year. That's really different than what Saxon does.

With Saxon there is a lot of repetition throughout the following chapters which is probably too much for smart kids, but helpful with others. I don't think of that as spiraling.

I'll go check out your link. I only taught from it a few years ago, but I used it cover to cover from three of the years and am very familiar with the pre algebra and algebra texts. Catherine worked from most of the same texts, but I believe went through the algebra 2 text.

SusanS

Allison said...

Here's saxon math 4 TOC:
http://saxonpublishers.hmhco.com/HA/correlations/pdf/s/SM_M4_NL_TOC.pdf

much the same material. maybe this spiral is better than EM, but it's definitely spiraling back over the same material.

distributed practice doesn't require this level of context switching.

Anonymous said...

Hmm, I'm not sure what you mean by that. I don't recall any context switching and I'm very familiar with a few of the texts.

When I speak of spiraling, I'm not just speaking of returning to the same material, so this might just be a question of semantics. Yes, you are spiraling, but not in the way the EM, Trailblazers and others mean. They mean that in a classroom where there's a few kids 1-2+ years ahead and a few 1-2+ kids behind, and 20-something children in between, don't worry if your child isn't able to understand a topic because we'll spiral around to it next year when they're "developmentally ready" to learn it. That's what they mean by "trust the spiral."

I never saw where Saxon used the word spiral, but upon thinking about it, it wouldn't surprise me if they started to do so. They've been changing the curriculum to be more competitive with the others by adding different chapters on probability and baby stats. They may have started using the word "spiral" meaning the way you mean it, but again, that's not what EM means when they use it.

SusanS

Allison said...

Susan,

Did you look a my links?

By context switching I meant cognitively by analogy to computer science. In CS land, context switching is what a computer must do when it switches execution threads: it must change everything that is in working memory and everything on the stack and heap, so that it can start computing on the new problem, be it the MS Word doc you want to edit now or that logistics time sharing problem you are solving or whatever. It takes time and effort to move between those things. If you rapid fire click to toggle between applications a bunch of times, the computer grinds to a halt, because it is spending time swapping into and out of memory, changing the stack, etc.

Just read the links. I keep hearing you say "not in the same way." But what my links showed was UTTER CHAOS, and no sane human could learn in that environment. The insanity of constantly changing material and lack of difference between the 3rd and 4th grade TOC looks like your defn of spiral to me.

Anonymous said...

Allison,

I did look at your links, but their description isn't how I experienced it firsthand. Now, I say that not knowing the texts before 4/5.

What I found was quite a bit of flow from one chapter to the next building on the skills last used (most of the time). Yes, at times there was a whole new direction, but usually several chapters tied together. Not always, but often. It's one of the reasons Saxon is used for special ed classes a lot.

After each chapter is a practice section for that particular chapter. Right after is a distributive practice that pulls in skills learned from the last few chapters so new skills don't get forgotten because you've moved on. If they do forget something, you can spot it pretty quickly. That practice also throws in what was just learned, as well.

A lot of the complaints about Saxon are how long the reviews go on in the beginning of the next year. But, they do usually add some new variable to the mix with each review chapter, so it isn't just a repeat. However, it is slow and dragged out.

And of course, I have no idea how you would deal with using it with a gifted kid. I wouldn't know what to skip or where to jump to next. That's why I used Singapore with my math kid and I had to accelerate with that, too.

I think we're just disagreeing about definition. To me, the EM people are trying to escape accountability by using the idea of a spiral as they see it. Since your child just isn't ready for these skills based on him being unable to learn them, then it must be that he isn't "ready." (no mention of prerequisite skills unlearned or bad curriculum or anything like that), and so he will learn them when we spiral around next year. It's a kind of, "Don't worry parents, if little Johnny doesn't get it. You don't need to run out and hire a tutor because he'll get it next year."

As Steve has mentioned, they can keep that excuse up for years until the spiral runs out and your kid is facing his math high school track.

And you might be right. Saxon may have changed since I used it. I hope not, but who knows?

SusanS

concernedCTparent said...
This comment has been removed by the author.
concernedCTparent said...

Saxon's approach has been referred to as shuffling and is very different from what a student would experience in EM's spiraling where you wouldn't learn a topic in depth and most likely not revisit it again until the next school year. Saxon is not chaos in the way that EM or TERC are absolutely chaotic.

In the research paper "The shuffling of mathematics problems improves learning," Rohrer and Taylor describe Saxon's shuffling:

"By contrast, a very small number of mathematics textbooks use what we call a shuffled
format (e.g., Saxon, 1997). A textbook with a shuffled format may have lessons identical to
those in the standard format, and moreover, the two formats need not differ in either the number of practice sets within the text or the number of practice problems per practice set. But, with the shuffled format, the practice problems are systematically arranged so that practice problems are both distributed and mixed. For example, after a lesson on the
quadratic formula, the immediately following practice set would include no more than a few quadratic formula problems, with other quadratic formula problems appearing in subsequent practice sets with decreasing frequency. Thus, the practice problems of a given type are systematically spaced throughout the textbook. This spacing intrinsically ensures
that the problems within each practice set include a mixture of different types, as there are
no more than one or two practice problems of each kind within each practice set."

concernedCTparent said...

Saxon is based on the concept of spaced repetition--the spacing effect (which is not even close to EM's spiraling). In a nutshell, it's based on Ebbinghaus' research that indicates that humans learn best when material is studied a few times over a long period of time.

The big problem is that Everyday Math claims to use spaced repetition (which it lovingly calls the 'spiral') while it does nothing of the sort. As is typical in ed-land, they took a relatively good idea and completely messed it up.

SteveH said...

Most of the sections in my son's geometry textbook start with a review of needed skills for that section. We generally ignore those and dive right into the material. Since the old material was mastered the first time, I find that any remembering issues can be resolved on the fly.

He also has the requirement of chapter tests and midterm and final tests. These force him to review the material. My own view is that you have to really learn the material the first time; that you shouldn't depend on some sort of delayed or spaced mastery or even a chapter test cramming process. Most skills will get reinforced over and over naturally as new material is introduced.

I do NOT like the idea that you might start out with only a few quadratic formula problems, with more to follow while you are in the middle of learning something else. This is too pedantic and reminds me of EM's Math Boxes. I prefer the approach in my son's textbook in which each section is prefaced by a review of needed skills, even though I don't often think they are necessary.

We got to a point in his geometry textbook where he had to find the distance from a point to a line given three points, two of which were used to define the line. It just took a few minutes to get him back up to speed on the details. This was not about relearning, but about remembering.

It reminds me of what his piano teacher told him once. If you practice a piece and play it in a performance, you will never have trouble getting it back to that level. If you never quite get to that level in the first place, then the task is much, much harder. You can't just pick up where you left off.

"...it's based on Ebbinghaus' research that indicates that humans learn best when material is studied a few times over a long period of time."

Repeated partial learning or learning and then review or application? The difficult things I have had to learn over the years took place in very short amounts of time. I may forget things over time, but it won't take long to bring them back.

Anonymous said...

RightStart is, indeed, an Asian mental abacus program--but it's actually more. I can say, hands down, that RightStart is superior in every way to Singapore in the first grade level. And that's saying a LOT because Singapore is amazing!

Want to get the worst kid in the class adding two-digit numbers with regrouping in first grade? And adding four-digit numbers on paper with PERFECT understanding? RightStart does it. RightStart takes the very best of Asian mathematics programs and distills it down into it essence. It uses a very few select manipulatives extremely well--as conceptual connectors, not crutches--which echoes the author's original background in Montessori education.

AND it's scripted, so it helps teach the educator even as it teaches the student, even it the educator isn't a naturally mathy person.

If you want your child to score in the 90th percentile, I will guarantee that RightStart can do it with any kid of AVERAGE intelligence. The most that it requires from the instructor is to pay attention to any stumbling place and to further break down and clarify any points of confusion that might arise rather than doing sheer repetition--solve the problem rather than waiting for it to resolve itself by using the approach that YOU'VE learnt from RightStart and apply it to the lesson at hand to chop it into smaller bits.

My son had intuitive mathematical power, but with his language processing problems, communicating anything he couldn't instantly intuit was very, very hard--until I found RightStart. It was amazing. We did the entire series because he needed to make stronger connections between language and concept, and I've never been so impressed with a math program. Ever.

Now, Singapore does have one powerful tool that RS lacks--it has the model method of problem solving, and the word problems are more sophisticated and also much more frequent. RS also weirdly peters out before really giving much work on multiplying and dividing fractions using the standard algorithm, having covered it EXCELLENTLY conceptually but not having practiced it as it does other things.

Anyhow, my very mathy kid is using the sequence RihtStart/Singapore Primary to NEM 1-3/Additional Mathematics/IMACS Elements of Mathematics. His personality is such that getting him to do any practice not on the Flashmaster is WWIII, EVERY. SINGLE. TIME. (which has already added some 6 months to his journey, though daily battles and sheer cussedness...)

My next door neighbor is very, very UN-mathy (failed algebra II), and her kid would be thrilled to step through algorithms without understanding a thing, if he can. After Calvert failed him (letting him get away with zero comprehension), she's now doing RightStart with great results. His sequence will likely be Right Start to Life of Fred/VideoText to either community college or ChalkDust or EPGY for calc.

In short, it works great for very different kids.

--SameAnon

Anonymous said...

Anyhow, read How This Program Was Developed:

--SameAnon

Michelle said...

As an Integrated Algebra, I can attest to the fact that there are many students, even at the high school level, who struggle with basic arithmetic. I try my best to incorporate basic skills into my algebra lessons (spiraling, as is mentioned above), but the bottom line is that I need to teach algebra material to these students within a given time constraint; therefore, I often resort to telling my students to "just use your calculator."

Genevieve said...

Regarding the market share that Everyday Math and TERC have. I wonder if there will be a large increase from a few years ago because of stimulus spending. This district I live in recently used stimulus funds to buy TERC and several suburbs recently bought Everyday Math.
Additionally, does anyone know if it is common for the inner city to get TERC and the suburbs Everyday Math? I suppose in the long run they are both bad so it doesn't matter.

Anonymous said...

Michelle, if they don't know their mult facts cold, they WILL NOT make it in algebra or chem. Drill them daily, if necessary, but don't let them have calcs.

TERC does even worse for minority gaps, doesn't it?

Most school districts are hurting, even with stimulus money, due to overspending during the housing boom giving them bloated budgets.

--SameAnon

lgm said...

School district spending - the budget bubble here was before the housing bubble. It is due to to the increasing percent of the student body that is classified sped/LD & the mandated unfunded services as well as overcompensating the staff. There is no cap on IDEA spending. There is no cap on the salary for a given position. There is no cap on McKinney-Vinto. We have bus routes that are \$100K for a single child. We have people suing b/c the bus can't come down their driveway...and they want the community to upgrade the driveway and add more busses so the route won't take so long. There's a case in this region where the parents want a homebound child to have satellite real-time conferencing capability so that the child can participate in high school classes 'more fully'. Can any community afford these demands in the long term?

Anonymous said...

Sounds like serious over- and misdiagnosis. Why don't they send a taxi or a handicap van? And if they're putting kids who aren't severely MR and/or physically impaired on SPED buses...quit!

Realtime conferencing is cheap. It's called Skype. :-) It's how my kid'll be learning Mandarin next year.

--SameAnon

lgm said...

The price of litigation is enormous. Many times it cost less to give in to the parents' demands than to continue the litigation.

SKYPE - no. The demand is for the replication of the classroom. Think satellite equipped classroom - quality mikes for all participants, computer interface to a whiteboard, hardware for paper i/o, video cams and operators, science lab station & classroom manipulatives. Add in a full time adult at remote student's location to operate the parts of the system that require physical moves. The ulterior motive is for that full time adult. Parent wants to work during that time but doesn't want to provide a caregiver; extended family feels it's a burden to help out. Can't blame 'em, but the current sol'n of homebound tutor is less costly and just as effective in providing the education. They lost the case.

Catherine Johnson said...

This district I live in recently used stimulus funds to buy TERC and several suburbs recently bought Everyday Math.

Can they do that?

I have a memory schools were required to spend stimulus funds on personnel -- ??

Catherine Johnson said...

re: spending

Looks to me like "Response to Intervention" is going to cost a fortune.

Schools are going to stick with balanced literacy, producing 20% (or more) of students requiring "Tier 2" intervention, which I believe must be a smaller class size.

If anyone can fact-check the requirement for much-smaller class size in 'Tier 2' intervention, please do.

Genevieve said...

If I remember correctly, they used Sped and Title 1 stimulus money as well as some district money. I don't know a lot about it because our district tends to quietly adopt curriculum (they chose the reading curriculum over the summer when most people were on vacation) and our local newspaper never investigates. About the only stories we get on curriculum are puff pieces about how everybody loves the new Everyday Math in the community section of the newspaper (lots of pictures of children at "work" very little info on Everyday Math).

lgm said...

Tier 2 reading intervention is done as a pull-out. The student still participates in the daily whole class lesson, but goes to a reading specialist or sped teacher for the intervention with a small group composed of eight or less students who have the same lacking skill that will be the topic of the lesson.

Haven't seen any data yet as to it's effectiveness compared to the old style of leveled reading groups of 6-8 students.

Catherine Johnson said...

lgm - thanks

So that's more staff, right?

Previously, these kids would have been taught inside their regular classroom.

The administration here is certainly saying they're going to be spending more once RTI is here.

lgm said...

Whether it's more staff depends on the population of the district. The existing sped and LD teachers who co-teach in the full inclusion classrooms usually do the pull-out small group reading instruction here. No new expense there. The reading specialists who were responsible for Reading Recovery just shift to be responsible for rTi... no new expense there either. The ESL instructor numbers don't change. The gain in rTi reading specialists would come in the number needed to serve the group that was previously in between the level needed to enter RR and the level needed to stay a grade level behind (or however a district is defining the need and frequency of intervention). I'd guess that # would be directly proportional to poverty levels and teaching competency. There will also be a need for a computer specialist's time to crunch some data too, which is a cost they can allocate to rTi.

I"m interested in knowing if having transitional K or transitional 1st would be a better, cheaper solution. Haven't found any papers though.

There is a facility expense as now rooms must be available for pull-outs. That may mean larger class sizes in the regular classrooms that require an additional aide over the number allocated before.

Are they breaking the expenses down?

Genevieve said...

I would also think this would be cheaper than pullout programs. Especially if the student was in a pullout program throughout elementary school.

Anonymous said...

>SKYPE - no. The demand is for the replication of the classroom. Think satellite equipped classroom - quality mikes for all participants, computer interface to a whiteboard, hardware for paper i/o, video cams and operators, science lab station & classroom manipulatives. Add in a full time adult at remote student's location to operate the parts of the system that require physical moves. ...

Oh, that's totally ridiculous. Around here, it's basically Skype (they have some other service, but it's still voice and video over IP) or tutor.

What's truly ironic is that tutors get you better results!

--SameAnon