kitchen table math, the sequel: Another reason to distrust the spiral

Tuesday, November 15, 2011

Another reason to distrust the spiral

We've discussed often how Everyday Math doesn't build to mastery, but spirals through the same topics year after year at a shallow level so students never get enough practice. Teachers and parents are told to "trust the spiral"--if the student doesn't learn the concept this time, they'll learn it next time.

But no one tells the students that.

I hear stories now of children in tears of frustration in first and second grade because they are being asked to "learn" concepts without enough background. These children aren't able to blithely say "oh well". They are crushed at their obvious failure. They feel stupid. They feel miserable. They are learning to hate math and their inability to do it. The assignments aren't meant to be mastered yet, according to the adults. But the spiral won't stop their students' feelings of awfulness.

We can't teach children that math is coherent, reasonable, and learnable with effort this way. Students need to be given concepts of slowly-increasing difficulty, designed so hard work leads to success. It's not just we've robbed them by giving too little chance to build up to complexity. Giving "tastes" of concepts they aren't ready for undermines the "effort is good" message and reinforces you're math-smart or math-dumb, and there's nothing you can do about it.


SteveH said...

Why isn't this obvious to K-6 teachers? Is it because the educational system sorts the teachers with the worst math skills into the lowest grades? Are their skills so bad that they have no basis for understanding what's going on?

What is the liklihood that K-6 schools will ever have math classes taught by certified teachers (whatever that means). I know that we got rid of CMP in 7th and 8th grades once our state stated to require that those teachers had to be certified in the subjects they taught.

In our schools, the fundamental philosophy is full inclusion. They like EM because it allows them to track kids by age. However, they have no way of figuring out whether kids are struggling because they are not ready for the material or whether the material is not being taught properly. Besides, if kids are really not ready for the material (however that's defined), how would giving them repeated half-lessons going to help? It's worse that drill and kill.

You can't discuss these issues because you would be telling them that their basic assumptions are wrong.

ChemProf said...

In my mother's school, there is a small revolution going on. They've discovered Saxon math, and are using it on the QT without district approval (but with their principal's ok). I know this isn't Singapore math, and that the new Saxon isn't quite the old one, but trust me it was a big improvement over what they used before. This was driven by two things -- low test scores that they need to bring up (which isn't surprising in a school that is over half English language learners) and by my mother who isn't afraid of math.

Interestingly, Mom insists that Saxon IS a spiral curriculum, since it keeps building on itself. In explaining to her the problems with her old curriculum, I've borrowed from KTM and told her it was a "trust the spiral" curriculum that didn't ever expect mastery.

A lot of K-6 teachers are simply scared of math. If the district says "this is the best curriculum for our students", they'll accept that and try to teach it. Often, they will figure that students aren't learning the math because they aren't teaching it well, but they don't understand enough to blame the curriculum. This is especially true of young teachers (and most of the teachers in Mom's school have been there fewer than five years).

Actually, one thing Mom loved about the Saxon math package they are using is that it prioritizes activities, so that it gives "arty" math projects, but it says clearly "do this first, do this second, these are if you have time." This avoids the old "Russian doll" problem and helps keep art from crowding out math. It is also set up nicely physically, as a binder filled with folders so the teacher can easily bring home just the unit she are working on (just a note for those at KTM who are helping to develop materials!)

Grace said...

I've witnessed the frustration first-hand, where new concepts and skills are introduced to students who cannot fully understand and appreciate them because they never mastered last year's lessons. It's awful, and one teacher told me directly that the spiral is a "death knell" for students who need lots of practice to achieve mastery. They never get the practice in school, and they continue to fall behind.

Another aspect of this is while a school will insist that tracking students by proficiency level will "break their spirits", they have actually created a hidden tracking system that is very inefficient. Then the teacher in this situation must attempt to differentiate instruction in her class to address students at several different levels of proficiency. The differentiation lessons I've seen are laughable. The teacher instructs the whole class at the lowest common level, then breaks ups the class into groups for differentiation. It makes no sense to me. Bad for students at all points on the learning spectrum.

Grace said...

"Interestingly, Mom insists that Saxon IS a spiral curriculum, since it keeps building on itself."

The Saxon I've used required mastery at every level before a student can move up.

CassyT said...

SteveH asked:
Why isn't this obvious to K-6 teachers? ...Are their skills so bad that they have no basis for understanding what's going on?

Working with hundreds of teachers this year, I can tell you that most don't see the light until their eyes are opened for them. Many teachers have no backup from admin, which says, "use this curriculum, it's what we think is best". I've been to schools where every classroom at a grade level has to be on exactly the same lesson, the same day. Sometimes teachers are provided no content-based pd. How can we expect them to know the difference between crappy and quality materials if they've never seen something to compare EM with?

And, sad to say, yes, there are a few teachers that think that what they do is "good enough". I'm working with a large group of teachers this week. Yesterday was second grade. We looked at the Common Core and discussed teaching strategies. When we were talking place value & how to use base-10 blocks & a place value chart, one teacher asked:

"For my students that struggle and just don't get it, can't I just teach them the algorithm so at least they can memorize that?"

Um, no, sorry, you can't cheat your struggling learners anymore.

By the way, dear 2nd grade teacher, have you considered the message you're sending? "You kids don't have to understand how to add or subtract, just do what I tell you and you'll pass"... the unit, the test, on to the next grade, ...confused.

ChemProf said...

Right, Grace, and the teachers at Mom's school see that is why it is better, but they've been told so often that spiral curricula are superior that they think Saxon must be one, since you do keep coming back to topics to build on the material that you've already mastered (as opposed to everyday math which is really more of a circle, where you never move up, than a spiral).

SteveH said...

Thanks for your comments Cassy.

Would K-6 teachers say no to math specialists teaching math? Would they think that their jobs are at risk? How about requiring specialists in K-6 for all core subjects? Are these issues being discussed anywhere? I thought I read about math specialists in the lower grades somewhere.

Allison said...

re: Saxon: what word would you use to describe this sequence of DAILY lessons? (From Saxon Intermediate 4)

21: Triangles, Rectangles, Squares
22: Naming Fractions and Counting Money
23: Lines, Segments, Rays, Angles
24: Inverse Operations
25: Subtracting Word Problems
26: Drawing Pictures of Fractions

I sure wouldn't call it linear.

Allison said...

(Here in MN, there are a bunch of varieties of ed credentials in this range, most of which don't specialties in content. They include a pre-grade 2 early ed cred, a k-8 elementary ed cred, a 5-8 middle school cred with a math specialty, and others.)

There's talk here in MN about the big districts moving to specialists for grade 4 and up, but there simply aren't enough credentialed folks to do it for those low grades.

The teachers I've been working with most are in grades 4-8. Their general view is that K-5 teachers are generalists, and that's for a philosophical reason about what kind of classroom model is best equipped to handle pre-adolescent children. The generalists are trying to meet all the social needs of young kids, the organizational/executive function needs, "learning styles", etc. To some extent, they view elementary ed as without boundaries with respect to the disciplines too--or at least as fluid across them. How would a specialist relate to the youngsters? What would their education be in terms of classroom management? So they want to see specialists, but they don't really see that there's a big group of people ready to handle kindergarteners and 3rd graders who have enough math knowledge. For them, a better model is still high quality professional development for the elementary ed teachers first.

And don't forget, other than Wu's class, there are no *math courses in elementary ed* at the undergrad level in our nation at this time, and merely a handful of pedagogical math methods courses in education depts that have any math content for k-6 at all.

SteveH said...

I can understand why schools might not want math specialists in K-4, but how can one explain or demonstrate the problems of spiral curricula and low mastery? On one hand, they talk about balance, but on the other hand, they are not willing to define what that is. In our school, they finally (!) try to get all kids to learn the adds and subtracts to 20 in third grade.

With full inclusion, they have no way to tell the difference between not being able to handle the material and bad teaching. They don't have to becuase the curriculum tells them that the spiral will take care of it.

My son's fifth grade teacher knew that kids in her class were bright enough to be far ahead of where they were. There is a fundamental flaw here but nobody wants to say that the king has no clothes. They don't want to see that their fundamental assumptions are wrong.

As Grace says: "The differentiation lessons I've seen are laughable."

The ones I've see are laughable too. It started in Kindergarten when the teacher tried to explain how an entire class reading lesson could be differentiated by the kids. I think one teacher referred to it as Differentiated Learning. I remember thinking that they are pushing the onus onto the kids. I think that's the idea behind Everyday Math. It's not differentiated instruction; it's differentiated learning just by cycling through the material. All they need to do is point to the kids who are successful, even though they might not know why.

This seems like a really tough nut to crack.

kcab said...

My son's elementary school uses math and reading specialists. In the past, there has been a separate reading specialist just for 4-6, with an additional literacy specialist who covers all grades. I don't know a lot about the reading side, just what I've learned from open house and randomly picked up. However, the math specialist was instrumental in getting my son more appropriate instruction. That was back in 2nd grade and may have been unusual, but it seems that the specialists here are flexible about grade level and achievement level.

kcab said...

Oh, and I want to say that I am *very* thankful to the math specialist!

Anonymous said...

I quit a math teacher job not because I was afraid of math -- but because I was required to follow what's described above. I was told what to teach each day, what activity to do first (before they'd had the lesson, they had to "figure it out), which problems to give, what questions to ask.

My kids didn't have the basics, from years of EM (this was an oddly thrown together hybrid of EM and another program which was better, but no great shakes).

It was insanity. Couldn't do it. Wouldn't be given tenure if I didn't. Was responsible for test scores, but had to follow their guidelines, pacing, order of concepts delivered. Had to give their tests (which were often oddly tricky, in that they would word things in very strange ways -- *I* knew what they meant, but some 5th graders (and their parents) would not.

I now use the phrase "teach to mastery" in cover letters, if I can't tell what curriculum a school is using. That seems to scare off the ones that don't.

CassyT said...


In my experience, most teachers would welcome a Math Specialist, especially above third grade. This week, I'm in NY working with teachers from a large area on how to teach the common core. Yesterday, with just 4th grade teachers was quite interesting. Of 50+ teachers, NOT ONE raised their hand when I asked if they knew what the area model of multiplication was and how to use it to get to the algorithm. Not even the specialists.

I met with a Math Interventionist yesterday afternoon, who comes from a literacy background, but is open & excited to learn more about math. Her school is struggling with MIF. (<- more on that school's experience later. It isn't pretty.)

I think a lot of Math Specialists/Coaches come from someone at the school who is good at math. Of course, these can also be the first positions cut in a school, so they can be risky to take. So even if a school has one, it doesn't guarantee they know what they are doing. At least at the start. While they don't have a specific background, I find most teachers that take these jobs work so darn hard and are so passionate, they end up discovering a new love for math & become quite good at it. But it takes some time.

momof4 said...

Schools do not want to know why some kids "get" whatever; they simply point to them as proof that the schools are doing the right things. They don't want to know that parents are teaching the kids at home, or hiring tutors, or sending the kids to Kumon - and it starts in kindergarten in a highly-educated, affluent school system. It was the same when my kids were in school. Some of it - probably a significant fraction - is trying to get ahead of the Joneses, but a lot of kids need help the schools aren't providing. I've also heard too many ES teachers say they're not good at math, don't like math, or went into ES because they wouldn't have to take any math classes to have much faith that they really have the ability to teach it well.

Anonymous said...

It's my understanding that the spiral, conceptual approach was a knee jerk reaction to the old fashioned drill and practice. Educators back in the 70’s dubbed the repetitive drill set "drill and kill" and not only did away with drill sets, but also minimized phonics instruction in favor of "whole language." We're just now recuperating from the lack of systematic phonics instruction in grades K-3. Phonics returned in the late 90's with NCLB funding for new text books. Many schools bought the new Math Their Way or Everyday Math text books during that era when the federal government provided funding for NCLB. It's a shame more schools did not purchase Saxon Math or Singapore Math. One reason they may not have chosen either of those because Saxon and Singapore math text books are about a year to two years ahead of our classes here in the good ol' USA.

SteveH said...

I guess I'm not talking about math specialists. I'm talking about taking away math from the regular K-6 teachers. Math would be taught by teachers who had specific training in math. The downside might be that they would just have specialized training in Everyday Math.

Anonymous said...

In most schools in my kids' district (and I'm the teacher who quit due in part to the crazy and bad curriculum) by 4th grade kids are taught by someone who teaches all the math for that grade (or for both 4th and 5th grade). So, technically, they are or could be "specialists."

But if you have a strictly enforced curriculum, that's what you teach (and then you assign what they tell you for homework and for the "project" day every other week, you do the exact project they tell you...even if it's totally stupid).

@CassyT Very odd about the area/multiplication thing. I'd guess that most 4th graders in my district could tell you about it and definitely all of the 5th graders.

However, they don't know their math facts and would have to actually laboriously draw out a grid or pattern of crossing lines to check their answer. They wouldn't even know if they were close or not in many cases.

lgm said...

ime most teachers ARE aware of the dismal math education in their districts. Many live in the best districts and commute to their job in the poorer districts & some send their children to private school in order to be in classroom situations that aren't so fully included. The commonality around here is that they all utilize a tutor for their unclassified K-6 aged children in order to get in to 8th grade Algebra and Earth Science.

Math Specialists here are sped teachers. They are proficient in techniques such as turning the paper sideways to use columns to line up numbers and using different colored markers for the tens place & ones place. Actual The people that have that understanding are the ex-gifted teachers who haven't been allowed to have a gifted program in over 20 years (yes they are being forced to retire and soon will be gone) and those from a culture that historically values scholarship. What elementary principals are doing now is partnering up teachers..the one that does know the math will teach two classes while the other will teach SS to both.

What they can't get around is full inclusion. Without sufficient proficiency in reading, writing, and remembering, it's hard to teach a K-2 child to a proficient level. Then extend the ban on written work to all students, decrease the amount of material taught and you have an impossible situation. It's been good for teacher employment though ...lot of extra teacher hired for rTi in the lower grades and double period math in the upper while the sped teachers are now embedded in the classroom.

SteveH said...

"What they can't get around is full inclusion."

That's a fundamental stumbling block, but it's not just a matter of getting rid of it.

I see two different things going on. The first is the question of academic standards in K-8 and whether one emphasizes content and skills or whether one emphasizes other fuzzy learning goals. Our town emphasizes the latter. Years ago, I sent a letter to members of our school committee telling them that they needed to send out Hirsch's Core Knowledge Series of books "What your first (..second, third..) grader needs to know" to parents and tell them that that is NOT the education their kids will receive. I got no reply.

This fuzzy idea of K-8 learning allowed them to implement full inclusion. In gerneral, how can one increase the range of abilities in the classroom, track kids by age, and not expect to take a big hit on academic expectations and performance? You do that with easy state tests and spiral curricula like Everyday Math that say that if you follow the spiral, kids will learn at their own natural pace. Perfect! It all fits and the onus is placed on the kids. Enough kids will do well (and they don't know why) so that they have plausible denial at the top end. All the school has to worry about are the low state standards. Those are easy for non-urban schools. Because of that, our schools have no pressure to eliminate full inclusion. They just fuss over new differentiated learning techniques. They still don't know what it takes to prepare kids well in math.

Some teachers might complain about the problems of differentiation, but that doesn't mean that they support an emphasis on content and skills. Before our town dove into full inclusion, they used the MathLand curriculum. Clearly, full inclusion didn't create bad math curricula. It just brought us the spiral and claims that less is somehow more.

Most teachers might be "aware of the dismal math education in their district", but they surely don't know the depth of the problem or how to solve it. I haven't met a single one who did. We might be on the same wavelength, but they wanted their own solution. They didn't ask my advice on what the solution should be. It's a turf thing. I never, ever got the idea that there was some sort of inner group of teachers who held the same expectations of education that I did. I never thought that if parents could only find and support these teachers, then everything would be fine.

lgm said...

Low state standards are not easy for non-urban schools when full inclusion is used. True, full inclusion didn't create bad curricula, but it certainly brought the use of inappropriate, time-consuming 'instructional' techniques to nonbraindamaged students as well as the denial of appropriate instructional placement. A turf thing? No, it's a forced mixing of very poor people in with the middle class, designed so that middle class children do not acheive as much as their parents did. It is a jobs program too.

momof4 said...

lgm is spot on: Montgomery County, MD never misses an opportunity to pat itself on the back for its decades-old socioeconomic integration policy that requires developers to include a certain percentage of low-income units; all in pursuit of diversity. Never mind the problems that come with it; fights hadn't existed in my kids' MS until the newcomers arrived - and they were primarily fights among themselves. It was particularly problematic for the middle-class black and Hispanic kids who were targeted as oreos etc. I've known black families who have had to send their kids to private schools to escape the toxic pressure and they sure weren't happy about it, since they'd paid for houses in good school districts.

Allison said...

The problem isn't limited to public schools which must take students with a wide variance in preparedness. Private schools, which would seem to have less reason to have such disparity in their full inclusion classrooms do, nonetheless have similar problems.

In a basic sense, the spiral leaves the teaching of students up to the students themselves. Even a dedicated teacher who has high standards can't do much in an environment that fails to recognize how little the students know, and fails to adapt to their needs in order to make them know.

Building to mastery is hard work. Understanding why and how partial product multiplication or long division work is hard work. It is made easier when students have been given the right tools to handle the job. Without that, most will just be confused, and many will give up.

I've been saying that 4th grade is the make-or-break. By 4th grade, a student behind in reading or math can't catch up in a typical school environment (a school like Morningside Academy being an outlier where they can; individual child tutoring is also an outlier.)

But I'm beginning to think that the answer is really 2nd grade.

My son's kindergarten using Orton-Gillingham to teach every child to read by the end of K, no matter where they started. The teachers understand the details of that method/curriculum, the reasons for it, and where students go wrong. Right now, there's no program with that level of teacher knowledge equivalent for K-2 for math anywhere in the country.

Glen said...

Yesterday was our first real talk with my son's teacher. I had talked to her for about three minutes on the first day of school and had requested that she excuse my son from Everyday Math and let me provide his curriculum. I would teach his lessons at home, and she would let him use his math time at school to do my homework. I had expected a fight but, to my amazement, she had instantly agreed, and it had been working smoothly ever since.

Yesterday, I found out why it had been so easy. She had just come to California from a teaching job in Illinois. In Illinois, she had gotten in some trouble, because she had taught math a little too well. She had significantly beefed up the third-grade curriculum with more substantial outside materials, which was so successful that the fourth- and fifth-grade teachers were complaining that, essentially, their incoming kids were prepared too well, which put an unfair burden on them to teach more than they thought they should have to. Some parents whose kids were in a different class complained that their kids were being left behind, which was unfair. Then some *parents of kids in HER class* complained, too, saying that by doing this, she had made fourth and fifth grade math classes boring for their kids. The administration told her to dial it back.

Then she had come to California and was immediately informed that we don't put up with such nonsense here. She would stick closely to Everyday math, period. I think she was given more flexibility with the slower kids, but for the kids who could handle more than EM, meaning most kids in her class, she felt that her hands were tied.

So when I had made my proposal, she had seen a way around her restrictions and immediately agreed.

My own take on it: In our district, there is no penalty for teaching "advantaged" students too little. I wasn't asking her to teach him more, I was asking her to go teach the disadvantaged kids and leave him to fend for himself. That was something she felt free to do, and since she was obviously more committed to my son's success than to defending her own turf, she went along with it without hesitation. Bless her.

Anonymous said...

Glen, I did something very similar with my son in K–3, sending Singapore workbooks to school and grading them myself. None of the teachers had any trouble with that—it was certainly easier than teaching him a grade or two up from the rest of the class. When he went to private school for 4th grade, they gave all students a math placement test at the beginning of the year and placed them in the best-fitting math group (my son went into the 7th grade group). By sixth grade, when he had exhausted their curriculum, we again sent in our own books (Art of Problem Solving Geometry) and he continued to teach himself math, with occasional assistance from teachers or parents.

Glen said...

@gas, that's interesting that you got away with it for so long. I tried getting the same deal for my 2nd grade son that I got for my 5th grader, from the same school, but no dice. His teacher insisted that it would be better for both him and his classmates if he stayed and taught them what he knows instead of working on his own math. So he sits and listens, then she asks, "Does anybody know...?" and he raises his hand and waits and waits, the only hand raised, as she ignores him ("I have to give everybody a chance, not just him") until his arm gets tired, then he starts staring out the window, at which point she'll call on him to punish him for not paying attention....

Yeah, that's so much better for everyone than just letting him work independently on his Sing Math workbook.

SteveH said...

So how much do schools really lie about their agenda? Is it really that blatant? Do they believe in full inclusion or do they think it's just good PR? I've always wanted to be a fly on the wall in their meetings. When I was once part of a teacher-parent school improvement team, teachers were sometimes hushed by their peers when they ventured into contract or inside topics.

So what to schools and teachers think about more able kids? Do they know them when they see them? My general impression at my son's schools was that many were just going through the motions. We got preemptive strikes that made it clear that parents needed to keep their distance.

Even at the private school my son went to for a few years, the headmaster deliberately did not tell parents that their kids qualified to take the Johns Hopkins CTY test. I specifically asked him why. His answer was, in effect, that they did not want to have to deal with kids and parents asking for something different or extra. We returned to our public schools in 6th grade.

Based on full inclusion, parents should be able to ask what a school will do for their more able kids. The principal of our town's K-8 schools at least claimed to care. Our son did qualify for CTY so we didn't argue over that point. But the question is what could they do? The answer was that they had no real plan or model. All in-class differentiation is a joke. They can't handle acceleration. How can one have true differentiation without acceleration. I've heard some really stupid answers to this question. Basically, they redefine what acceleration means. It's their motto. If you don't like something, redefine it.

When my son came back to our sincere full-inclusion public school in 6th grade, I did manage to allow him to skip a grade in math, but he had to take the 6th grade EM test before doing so. It was odd to work on 6th grade EM at home with my son during the summer. It was still jumping around and I saw no way that kids who had followed the spiral (circle) could catch up. They pump kids along and then blame them when they fail. They just need to take responsibility for their own learning. How do they expect to become life-long learners? By this time, it's so easy to blame the kids, parents, peers, society, and poverty.

So, my 6th grade son was put into the 7th grade math class. This really screwed up his schedule, and eventually, some teachers got pissed off at his special schedule needs. The principal tried to smooth over the issues, but we could tell. Also, the math teacher tried hard to show that my son was not really that smart. Some seventh graders referred to him as the "baby" in the class. By 7th grade, it was clear that the class scheduling needs were a big problem. The only solution was an online course. The school would pay for it. They all stunk. I told them that I would teach him at home and he could take the class math tests at school. This was better, but I did the work, not the school. They talked differentiation, but they had no workable plan. I continued to teach him Geometry at home for 8th grade, but I had to do all of the work to make sure that the high school would accept this course and his grades. I had to make sure that he took the regular high school geometry tests.

So, how bad is the lying in K-8? Are their ideas of education so fuzzy that anything they do is reasonable? I've heard excuses like "Public schools have to teach
ALL kids." Yes, but not necessarily in the same classroom.

Glen said...

@GSWP, what did you end up doing for middle school math? My son will be starting AoPS Geometry in 6th grade, too, and I'm just trying to figure things out as I go along. What options did the school give you? Independent study? Online courses?

Steve, your middle school story gives me the shivers, because I'm afraid that's what I'm walking into when my oldest starts 6th next year.

I don't (yet?) have the sense that anyone is lying. They claim to be trying to close the achievement gap, and I think that's what Everyday Math is designed to do. If each kid got an individually-paced Singapore Math program, all kids would do better, but it would amplify the achievement gap, with the slower kids doing better and the quicker kids doing MUCH better. That degree of fan out would create even bigger logistical problems for the schools. EM spirals around them, keeping the herd together.

Parents who pull their kids out of the herd create herd management problems, and my schools are telling me frankly that those will be MY problems to solve.

SteveH said...

It wasn't so bad, but the only reason it worked was that I was able to teach him at home. What about the parents who can only rely on the school?

My story tells you that some teachers, and in my case the principal, really believe in differentiated instruction and knew that it should be applied to even the most able kids. (The private school my son came from wouldn't consider that sort of thing because all of their kids are smart, right?) However, that doesn't mean the school knows how to do the differentiation. It may turn out to be putting the kids into an empty room and allowing them to work on their own or to access an online course. The only one that our school offered (would pay for) was by I didn't like the courses and how they worked.

The other issue was coordinating and making sure that the high school was on-board for this process when he got to geometry in 8th grade. I had to do most of the coordination and making sure that my son got the correct book (and edition) and that he knew exactly what the high school covered. He had to take the same mid-term and final tests. I got to test and grade him other times. The principal accepted my grades and combined them with the test grades from the high school. The regular math teacher was pissed off for some reason about this process and when it came to selecting the math award recipient at the end of 8th grade, my son was skipped because he was taught somewhere else.

The middle school principal also offered to let my son skip 6th grade entirely, but my wife and I rejected that. He has always been mature, but the kids at that age can be really weird. We also didn't think there was a need to put him on a track that led to high school graduation one year earlier. The worst problem was math and boredom was not too big an issue for the other classes.

I would have, however, liked him to skip 8th grade science and 9th grade Earth Science (required by the state!!!). So now he is a sophomore and can't get to any more than two science AP classes. What with the modern separation of honors science and AP science, high school science is a real big problem. There are not enough course slots unless you double up and skip your elective (like orchestra - that isn't going to happen). It would have been much better to skip the silly 8th grade science and take the state-mandated Earth Science then. We could accelerate math, but there was no way to do that for science. (I would have checked on that given what I know now.)

The other issue is that even though a high school shows an AP class in the catalog, it doesn't mean that the course will be taught. I just found out that AP Chemistry hasn't been taught for years! That changes all of our planning. This is also a problem if you are concerned about your weighted GPA/class rank. While others are taking their 5 top weighted AP classes in their senior year, like psychology and art, you are stuck taking a lower weighted honors chemistry course. This may not matter too much for college admission, but class rank is not meaningless.

So, my advice for parents trying to accelerate their kids is to look at the whole process through high school and ask a lot of questions.

kathyiggy said...

Our middle school just changed its math program this year. Previously, everyone was in EM for 6th grade and then split into either Pre-Algebra or "Math 7" for 7th grade, followed by Algebra or Pre-Algebra in 8th. Now, the kids take a MAP test at the end of 5th grade and are put into either Prentice-Hall Middle School Math Course 1, Middle School Math Course 2, or Pre-Algebra in 6th grade. The top track does Honors Geometry at the high school in 8th grade. My daughter does Course 2 in 6th grade. The teacher admitted at conferences they were glad to get rid of EM in 6th. She tells the kids it's time to do "real" math in junior high. I'd guess maybe 60% of kids are in course 1, maybe 30% in course 2, and the top 10% in pre-algebra (mostly the kids of HB1 workers from India)

Catherine Johnson said...

kathy - hi!!!!

Great to see you!

I was thinking about you the other day -- I was thinking: Remember when kathyiggy used to write comments?

ESP is real, apparently.

Catherine Johnson said...

I have to repeat that.

In just the past few days, I was specifically thinking: "I wish kathyiggy was still writing comments."

Catherine Johnson said...

I haven't read the thread or the posts (OR MY STUDENTS' PAPERS) Things are REALLY bad out there. I was trawling the internet, looking for help on paragraphs & how to teach them (yes, my students have purchased a $170 developmental writing texbook, and, yes, I have read it...).

Anyway, I was trawling the internet searching for materials & enlightenment when I came across a bunch of stuff on WHOLE LANGUAGE in ESL classes ----- !

kathyiggy said...

I'm still lurking here! Seems like a lot of the conversation here has been SAT-related which I can't relate to (yet). It's almost all ACT around here and my focus lately has been looking at post-secondary programs for my oldest with ASD...U. of Iowa has one, and Edgewood College in Madison too, as well as Minnesota Life College. Back on the spiral/EM oldest is taking Algebra 1 as a 10th grader. It's the first time she has been in regular ed Math since 4th grade EM. Math is now her best subject as there is none of that inferential thinking involved! I credit the SpEd Math teachers (along with ALEXS).

SteveH said...

"Our middle school just changed its math program this year."

Is there some hope or is this an outlier?

Anonymous said...

Glen asked "@GSWP, what did you end up doing for middle school math? My son will be starting AoPS Geometry in 6th grade, too, and I'm just trying to figure things out as I go along. What options did the school give you? Independent study? Online courses?"

For 7th and 8th grade, we were in a different private school, one that did grades 6–12. They gave him a placement test and made him retake geometry. This turned out to be rather slow for him, but he liked the teacher. The style of geometry was different from the AoPS presentation, and the greater formality of the proofs was probably good for him. Lots of parents complained that year that their 7th graders had been placed in too-low math courses, but this complaining happened in January, as everyone had expected the pace to pick up.

For 8th grade, he was placed into Honors Algebra 2, with the same math teacher that he liked. Again the class was a little slow for him, but he got good at using his graphing calculator, and the teacher used a fairly rigorous approach (Foerster's book). The teacher had a PhD in chemistry and was a retired electrical engineer, so took a more engineering approach to the math.

The teacher was laid off after my son's 8th grade class because enrollment was dropping at the school with the recession and he was not popular with the parents (he graded too strictly for their taste—most thought that their kids deserved easy As). My son and I liked him, because he knew what he was doing and didn't water stuff down too much.

For 9th grade, we were back in public school, and the "trig and analytic geometry" class turned out to be heavy drill review of algebra, so my son dropped it in favor of AoPS Precalculus online (see and He did not get credit for this through the school since AoPS is not accredited (they should be by next year). He did get an 800 on the SAT 2 math 2 test.

This year we are homeschooling, so most of his classes are unaccredited. We decided that the content and quality of the education was more important than the seal of official approval.

Catherine Johnson said...

Kathy - Glad you're dealing with the ACT, not the SAT. I started out as an SAT enthusiast, and I enjoyed the test prep, but the Midwest focus on ACT makes MUCH more sense.

I'd love to hear about the ASD programs if you have time.

Catherine Johnson said...

gasstation wrote:

This year we are homeschooling, so most of his classes are unaccredited. We decided that the content and quality of the education was more important than the seal of official approval.

Boy, I'm with you there.

I tried to pull C out of math here & homeschool him just for that subject, but it's illegal in NY.

He had to stay in fantastically bad & fantastically difficult math class in his middle school, which meant I spent all my time doing emergency reteaching and overseeing "cramming to mastery."

Looking back, I now think I should have taken him out of the accelerated track and taught him math here at home.

That wouldn't have been a sure thing, however, because the many kids who were dropping out of the accelerated course were doing badly in the 'regular' track course, too.

I could have been doing the same emergency reteaching for the regular course.

Catherine Johnson said...

They are learning to hate math and their inability to do it.

That's exactly what my cousin said about her daughter's experience with Everyday Math. It was a miserable experience: miserable and deeply disheartening.

Glen said...

Steve and GSWP, thanks for taking the time to provide those details. It's very helpful to have advanced warning of the road conditions ahead.

Steve, thanks for the warning about HS science. I've been trying to put together a long-term plan (thru MS and HS) that was based on the schools' websites and their course descriptions. I've found the science prerequisite tree baffling, and that was with my (unthinking) assumption that all of the classes actually existed and could be taken when wanted (no scheduling conflicts.) It's apparently worse than I thought.

GSWP, it's interesting that the better the education you provide your son, the less official credit you get for it until you're driven to full-scale homeschooling.

I've been pondering the question of what an ideal K-16 curriculum would look like if there were no state requirements, SATs, elite universities and their admissions game, and so on, to target, and all you had to do was optimize (as best you could) for real adult life in the 21st century. I wonder if a school with such a curriculum would even be legal, much less accredited.

ChemProf said...

The issue of scheduling is huge, especially if students also are in drama or music classes. At my local high school, with 2700 students, there are three sections of AP English, two of AP Chem, 1 of AP government, etc. If you are taking things out of order, you need to really plan it out, and the high schools generally don't make it easy to figure out how to do that. It is easier to just make everyone move in lock step.

SteveH said...

"I've been pondering the question of what an ideal K-16 curriculum would look like if there were no state requirements, ..."

I see two issues. In K-8, I just hoped for basics that would lead to algebra in 8th grade - better, if we could have what kathyiggy talked about (minus the EM in the early grades).

Beyond that, my son takes private music lessons from a music professor. Many kids do sports outside of school. Last year, I thought it would be nice to have my son take private chemistry and physics lessons. I never followed up. We have to play the high school/GPA/SAT game. I also know that somewhere in our state is an open club for kids who want to prepare for the FIRST Lego League competition.

The question is how can you increase these opportunities and get them to fit in with the schools. I think kids would find a lot of support from the community. The one thing that really strikes me about the rise of the internet is how much people are willing to give of themselves for free.

Is there anything happening in college towns for academics? Our university has a preparatory program in music for the community. Some colleges must provide true acceleration options for kids.

Our high school is looking into allowing students to take college courses, but the problem is scheduling. The other problem is providing an academic path to get there, but I think they will leave that up to the students and their families to figure out.

Many kids would be so much further along in lots of subjects if they were given the chance. (I just had to look up when to use further versus farther.)

Niki Hayes said...

Allison: You quote some Saxon lessons to show how "unlinear" they are. What you don't explain to those who have never used Saxon is those topics are "introduced," with 5 problems out of 30 on that particular topic found in their written practice/homework. The other 25 problems in that written practice are review--or are a "spiraling"--of all the previous lessons before that assignment.

THAT is the difference between Saxon's spiraling--a constant repetition of pieces of a concept so that it is mastered by the end of one year--and the fuzzies' spiraling which is based on repeating lessons on one concept for two or three years.

Saxon's method has been justified by researchers who label it now as "shuffling" different topics so students do get the incremental development and continual review (practice) that John designed.

Saxon Math cannot be used episodically by teachers to shore up a student's particular weakness because it is designed to be the whole cake, not one ingredient. For that reason, John hated chapters, which he called "hunk" learning that required students to swallow a big hunk prior to moving to a new chapter. That's why his daily lessons are written in a manner that has constant repetition and APPEAR not to be linear by those individuals used to working with chapter formats.

I really do encourage you to read his biography. It's titled John Saxon's Story, a genius of common sense in math education. You might get more insight into a program that more than half of our 1.5 million homeschoolers are using. It's also the one I taught on the Spokane Indian Reservation and brought, as the principal with teacher approval, to an 80% white Seattle elementary school. Great success was experienced in both places, mainly because Saxon is a skills level program, not a grade level one. My 5th grade Seattle kids, for example, were using the 76 book by the end of the year.

Most of all, the kids learned not to be afraid of math--even to love it. The valedictorian on the reservation thanked me during graduation for teaching her algebra, which had allowed her to enroll in college. It wasn't I who taught her, however. It was Saxon Math.

By the way, I am the one who wrote John's biography.

Niki Hayes said...

I was selected to serve on the Texas Education Agency's committee this year to help rewrite our state's math standards. I had asked for grades 3-5 because those are the children with whom I work now as a paid tutor at the local Catholic school (who uses Saxon Math)and am most familiar with the concepts they must learn.

I decided to testify before the State Board of Education last week as they looked at the final draft from our 80-member TEA committee. Strangely, I was the only one from the rewrite committee to be there.

Here's what I told them:
1) Texas may finally step forward from most other states with our mandate that requires the teaching of standard algorithms. This prevents the use of fuzzy methods as the primary source of instruction (Everyday Math's lattice method, for example).

2) We also are prohibiting the use of calculators in K-5 math classrooms. (John Saxon started fighting the NCTM in 1985 and their support of calculator use in early grades. It's only taken 26 years to get that message across.)

3) HOWEVER, I said we have created a document that is a mile wide and an inch deep. It must be pared down. That is, the 4th grade has 43standards. At (realistically) 150 days of seat time instruction out of 185 days, that gives teachers 3.5 days for students to master a concept. And then they must move to the next concept/standard.

4) In addition, in an effort to add "rigor" to instruction, we have pushed harder concepts to lower grades. I explained that is not "rigor." It's just making the lessons "harder."

5) We will therefore see a massive frustration index among our teachers and those training them. Trying to cover too much has been a complaint for years, so I don't think our new standards will improve on that situation. Weak teachers who don't know their math content will become even weaker.

I withstood 30 minutes of questions by the SBOE members, some of whom said we should push adoption of the new standards from 2012 to 2017, when the new textbooks would roll out based on the new standards. I insisted that meant 5 years would be lost in teaching students standard algorithms and how to master mental arithmetic (no calculators).

It will be interesting to see the final decisions made by TEA and our state board.

Brian BTN said...


We here in Greenwich CT are facing a similar issue relating to the timing of a curriculum review and any possible change in text books (if you can call EDM a textbook). Our public schools have their next math curriculum review scheduled for 2014, which means a possible pilot in 2015, and maybe adoption in 2016. Since CT adopted the Common Core States Standards, the Connecticut Mastery Test will become CCSS compliant in 2014.

I have started a push to get a curriculum review moved up to NOW! See my blog at

I highlighted many of the same issues you noted above (calculators, spiral,inch deep/ mile wide, non-standard algorithms) to our board of education when I spoke to them (for the three minute time limit). We shall see if anyone was listening.

I would love to hear more about your work.


Brian BTN (by the numbers)

SteveH said...

Everyday Math and its ilk give spiraling a bad name. I call it repeated partial learning. It doesn't deepen the learning for kids who have mastered the material (probably from their parents), and it doesn't get the job done for those who didn't figure it out in the first place. It's really circling. One parent I knew complained that her three kids (in different years) were covering the same material in pretty much the same way.

"Texas may finally step forward from most other states with our mandate that requires the teaching of standard algorithms. This prevents the use of fuzzy methods as the primary source of instruction (Everyday Math's lattice method, for example)."

The problem really isn't about the standard algorithms versus EM's individually-selected choices, like the lattice method. It's about ensuring the mastery of anything. The major fundamental flaw of Everday Math is that it tells schools and teachers to just go through the motions; to "trust the spiral" without any proof that it works. Teachers don't have to worry if kids don't learn the times table by fifth grade. The "spiral" will take care of it.

The whole goal of Everyday Math is to give schools some sort of pedagogical basis that allows full inclusion. The Holy Grail for many educators is to find some magic way to track kids by age and hope that they all get what they need. They talk about differentiated instruction, but there are no specific goals.

When my son was in fifth grade, the school and parents had a meeting to talk about EM because there were many rumblings. They talked a lot about the "balance" between critical thinking and mastering basic skills. Nobody seemed to be willing or able to define exactly what that meant, even though perfectly capable kids had somehow gotten to fifth grade and were struggling with the times table.

The fifth grade teacher had a choice, to trust the spiral, or to slow down the coverage and spend more time ensuring mastery. She chose the latter, but sent out a letter at the end of the year claiming victory over understanding and critical thinking. My son had a lost year.

They want to avoid drill and kill, but what they are really doing is changing math into something that it isn't. They don't want math to be a filter, so they think they've found a perfect way to pump them along. The problem is that they pump along the problems until it's too late to do anything about them. The kids get separated into different math tracks (usually in 7th grade) and for those in the lower tracks, almost any possibility of a STEM career is over. By 7th grade. No amount of Project Lead The Way in high school will fix the damage. The problem isn't student motivation. The problem isn't some subtle difference in spiraling. The problem is basic school competence.

The worst part is that those students (and their teachers) will really think that it's their limitation. Kids will say that they just don't like math or that they are somehow genetically not capable of math. They are not math brains. Teach badly and then blame the students, genetics, peers, poverty or society. Pump kids along until you can't see the cause anymore.

SteveH said...

Schools will point to kids like my son who are successful without ever asking what went on at home. In two different K-8 schools my son was in I tried very hard (constructively) to get them to see the issues; to get them to define some sort of process that would ensure mastery of the basics. It never happened. They have to understand that their basic assumptions of education are wrong.

If possible, parents need to get schools to send out questionnaires to parents to find out exactly what kind of teaching/reteaching they do at home. I'm talking about things other than going to museums or making sure that kids have done their homework. I'm talking about teaching the basics. We've talked about this in the past at KTM. It's really annoying for parents to get notes sent home asking them to practice basic math facts with their kids. I'm sure that if you eliminate the kids who got help at home, Everyday Math would show very little success.

momof4 said...

I'm betting big that schools will be highly resistant to polling parents about any kind of tutoring; they want to take credit for it and don't want to consider any alternative explanations.

SteveH said...

It seems to me that the best way to confront the math problem in K-8 is to work down from the high school. For many years, our middle school used CMP for 7th and 8th grades. Parents complained that their kids were not prepared to start honors geometry as freshmen. Heck, CMP didn't even provide a proper introduction to algebra. In response, the school added more algebra to CMP. It still didn't solve the problem. This is a good approach because one can clearly see and define a specific curriculum gap. The school can't deny it. They can't say that it isn't important.

Eventually (I don't know the details), our school finally realized that they couldn't push differentiated instruction through 8th grade. They had to separate the kids in 7th and 8th grades for math. They had to offer the exact same honors algebra course in 8th grade as the high school course and use the same textbook. This forced them to get rid of CMP, probably because the school was small and they couldn't offer two separate approaches to math. This pushed the problem down to the lower grades that used Everyday Math.

This is where the push seems to end. Everything is based on doing well on the state tests, but the state tests are not good enough. I once tried to figure out the math behind the conversion of the raw percent correct scores on the state test into the "Proficiency Index" all schools use to see if they are meeting expectations. However, this has little to do with whether the schools are properly preparing kids for the top math track when they hit 7th grade. What the state tests do is to convert really bad raw percent correct scores into really nice looking percent correct proficiency indices. For more affluent communities, this is a really simple goal. Our town even points to the proficiency index to claim that it is providing a good education. They are wrong.

It seems that the only way to push improvements into the lower grades is to focus on what the schools use as the criteria for getting into the top math track in 7th grade. If that is a specific test, then those skills can be tested and tracked specifically in the lower grades. Unfortunately, many schools base the decision on Everyday Math grades and a teacher's recommendation. In any case, one could try to force a school to define exactly what that means. Those expectations can be clearly defined and handed out to parents so that they can see if their kids are on the top math track in the lower grades.

Niki Hayes said...

Brian: There are many of us working on local or limited levels who are trying to bring common sense changes to math education. I've long maintained we're like sparklers, however, and we need to become a candle with sustained light on the subject.

Parents, understandably, leave the problem when their children are out of the education system, so there's a high turnover rate among those of us in the "math wars." To try and organize a group that could consistently counteract NCTM's immense power seems highly improbable.

For one thing, we would need big bucks from someone with a big megaphone. The National Science Foundation, for example, pumped $84million in grants to NCTM colleagues during the 1990's for them to write, implement, and embed unproven math curricula, which are still destroying American math education today. The NCTM-Federal Government fingers went very deep throughout the political systems at the state and local levels, as well as within teacher training programs. Those monied fingers will not be pried loose easily.

That's why John Saxon's battle with NCTM and their political allies for 15 years is so important to recognize and honor today. To his great surprise, he became a multimillionaire as parents and maverick schools grabbed onto his traditional program, starting in 1981. He was vilified, ridiculed, and one "leader" offered to throw a party to celebrate his death. That hatred for him still exists today.

I have two goals today at age 71. I want John Saxon honored for providing successful math experiences to thousands of children (and to their parents and teachers). He and his friend, Jaime Escalante, are true heroes. ("Waiting for Superman," the acclaimed documentary about public education, should be remade to show how Supermen are actually treated by the public education establishment.) Jaime, who died recently, has been memorialized through the movie, Stand and Deliver. I wrote John's biography to memorialize him, at least in book form. My dream is for him, finally, to be honored openly. (Go to

My other goal is to keep building my Emmanuel Academy, a K-8 tutoring program at my church, with the primary use of Saxon Math and Saxon Reading and Writing methods.

Hey, being 71 means you have 50 years of work experience, so why not keep putting it to use?!

Brian BTN said...


Thanks for the input and feedback. Two comments and one bit of ammunition.

The first comment ties into what Steve said, "They have to understand that their basic assumptions of education are wrong." I read this to agree with the statement I made to the Board of Education, i.e.,

"The very philosophical foundation of Everyday Math is flawed, and must be rejected." I am going to focus my push on showing that the major tennants of EDM are wrong:
1. repeated partial learning (I like that term and the implications),
2. discovery learning (ask the BoE if they want to get operated on by a doctor who did "discovery learning" in surgery class in med school),
3. ignoring the basics and the standard algorithms (or forcing teachers to supplement, which has to be occurring inconsistently across a district - a great lead in for a discrimination law suit).
4. inch deep, mile wide; although the standards may be hard to fight (or at least that will be the next battle).

My second comment ties to Niki's thoughts on "Those monied fingers..." In the long version of my prepared comments to the BoE (which got cut because I only had three minutes to speak), I was going to comment on the ability of the insiders (monied fingers) to use jargon to confuse the issue:

"It is very easy to get caught up in, or confused by, the jargon used by the current day equivalent of Eisenhower’s Military-Industrial Complex, i.e., what I call the Publishing-Educational-Governmental Complex. This Complex does not consume the results of education; they sell the tools for that education. I would posit that the effort to sell has overridden the desire to produce good results."

My focus is going to be on results, not research. What do the middle school teachers say? What do the college professors say? What do the parents say? What are we producing out of high school, whether they go to college or to work? They need to know the basics and the algorithms, and EDM is failing in that regard.

One interesting "reason" I have discovered for EDM's success is that they must have a large number of schools using the program with incredibly small class sizes. On the front page of the EDM website (ABOUT) is the statement: "It is currently being used in over 185,000 classrooms by almost 3,000,000 students."

If I use my long division, which they obviously did not, to work this out, I come up with at most 16.22 students per class. I don't know about you, but even in Greenwich our class sizes are 20-21, if not more.

Brian BTN

Anonymous said...

Two thoughts:

1) The Saxon approach, though popular with some home schoolers, is not a panacea. In particular, the rather slow-moving drill is not particularly suitable for gifted math students, who can progress more quickly with less boredom (and, perhaps, more understanding) with the Singapore curriculum.

2) There is nothing inherently wrong with the lattice approach to multiplication. It is mathematically well founded and is as easy and quick to do as other algorithms. The problem with Everyday Math is not that they chose bad algorithms, but that they don't teach the algorithms they chose to mastery.

Barry Garelick said...

The lattice approach to multiplication was included in the original (draft) version of EM as a sidebar to highlight how place value works in another algorithm. It was not intended for students to use the algorithm in calculations. Currently, EM doesn't bother to explain how place value works in the lattice method, and presents the algorithm as a way to multiply. It is inefficient, particularly with numbers of three digits or more, and with decimals. The standard algorithm on the other hand is efficient while underscoring how place value works.

A video done by M.J. McDermott a few years ago demonstrates that the lattice method may not be as easy and quick to do as other algorithms:

Brian BTN said...

Never having used the lattice method for real calculations (although I have played with it a few times), the question I have is how can anyone say it is "very efficient and powerful", as the EDM Teachers Reference Manual does? If we look at the operations performed in the standard algo and Lattice method, the Lattice always has more operations (defined below). If I can support this, and it is very evident that it takes longer to draw a lattice as the problem becomes larger, it therefore disproves the EDM Manual assertion that "The authors have found that with practice, it is more efficient than standard multiplication for problems involving more than two digits in each factor." If there are more operations in the lattice method, AND you need to draw the lattice as opposed to two lines in the standard algo, the lattice method has to take longer.

This is not nitpicking, this is a direct attack on the poor quality of material in the teacher's manual, and is reflective of a cavalier attitude toward truth and accuracy (see post above under ammunition).

And so to the proof (for n x n lattice):
Operations involved:
1. multiplications
2. additions
3. carry in multiplication process
4. carry in addition process
5. writing multiplication results
6. writing additon results

There will always be equal values for multiplications (a nxn digit multiplication will always involve n-squared multiplications), carry in the addition process (there will always be 2(n-1) additions), and writing addition solution (the answer will always have at most 2n digits).

For the other operations, the lattice requires 2n-squared (2 x n x n) additions, 2n-squared numbers to be written for multiplication results, and zero carrying in the multiplication process.

For the other operations, the standard algo requires (n(n+1)) + (n-1) + (n-2) + (n-3) + .... (n-n) addtions, as well as the same for numbers to be written for multiplication results, and (n-1) squared for carrying in the multiplication process. I tried to simplify this but failed (should have paid attention in series class), but doing it by hand for 3x3, 4x4, and 5x5 showed that the lattice method used 2,3, and 4 more operations. When you go to higher n's (yes, I used a spreadsheet), you add three operations to the difference for each increase in n (so for the 6x6, the lattice uses 7 more operations; for 7x7 it uses 10, etc.),.

So it is not as easy an quick as the standard algorithm, but I will agree that there is nothing inherently wrong with it and that EDM does not teach to mastery.

Brian BTN
Brian BTN

SteveH said...

"The very philosophical foundation of Everyday Math is flawed, and must be rejected."

Yes, I agree. The key is that you have to define the issue, not them. They will start talking about understanding and vague ideas of differentiated instruction, but you have to counter by asking for details. They will talk about balance, but what, exactly, does that mean? Do they ensure mastery of the skill part of that balance each year, or do they "trust the spiral"? If they trust the spiral, how do they know it works?

Do they point to the What Works Clearinghouse? I've had that thrown in my face. Even the WWC says that they really don't have enough data. And what do they use to claim that something "works". It's a relative improvement, not an absolute one. The WWC really does not want to be seen as irrelevant.

Do they point to students who have been successful with Everyday Math? Ask for a questionnaire to be sent home to parents so that you can subtract the benefit of parental teaching/reteaching. Do teachers send home notes to parents asking them to practice math facts with their kids. If so, that's outrageous.

I would suggest that you never argue over the standard algorithms. They are well-prepared for that. If it does happen however, ask them to prove mastery of ANYTHING. They will probably claim that the spiral allows kids to learn when they are ready. Of course, this means that if they don't learn, then there is something wrong with the kids, not the teaching. Ask them if they really think the spiral works by definition. What, exactly is their plan for ensuring mastery? Ask them when they do that for each skill. Our schools try (try!) to ensure the mastery of adds and subtracts to 20 in third grade. These kids are now so far behind by third grade that they will never catch up.

The discovery learning argument is kind of old. No one can argue against discovery. It's too vague. However, it's neither necessary or suffient. Ask them if it is possible for a student to discover things while listening to a teacher explain things. Ask them if it is possible to discover things while working alone on a homework set of 25 problems.

What they really want is NOT discovery. Discovery is really a justification for full inclusion classrooms with the teacher as the guide on the side. That's what they want. Discovery is only a cover for that. They just want a happy learning environment to make them feel all warm and fuzzy.

If your focus is on results, you have to define what those results should be on an absolute basis. I would focus on the key 7th grade (or whenever) math tracking decision. Usually it catches parents by surprise, and by then, there is nothing they can do about it. It's at that point where some parents figure out that their kids are perfectly capable of getting on the higher track, but the schools have not prepared them properly. Ask the high school to provide statistics of the highest math class (and grade) of kids who do not get to algebra in 8th grade.

Schools are so concerned about STEM that you should ask them what level of math and grades they think are necessary for students to have that opportunity in college? Ask them what specific degrees they are talking about. Look at college math requirements for these departments. Do they require differential equations? How many high school students will be properly prepared? How many of these kids have been helped at home or with tutors?

Don't ever concede EM's success. It is fundamentally flawed. The only way it could be successful is by reducing expectations and slowing down the coverage ... at the expense of more able kids. Institutionalized low expectations.

SteveH said...

"... EM doesn't bother to explain how place value works in the lattice method, and presents the algorithm as a way to multiply."

Yes, the lattice method is just thrown in there. Everyday Math goes out of its way to not teach the standard algorithms. They introduce partial sums and partial products, but they never go to the full, most efficient (standard) algorithm. Their goal is NOT any sort of full understanding of what's going on. Their goal is to give the basic concepts of what's going on. They don't believe in the need for mastery because kids have calculators. However, real understanding of what's going on involves hard work. Having a conceptual understanding is not enough. Don't buy their argument that they care about understanding. They have an extraordinarily simple idea of rote learning and understanding. They see little linkage between mastery and understanding. That is one of their biggest flaws. You might get away with that with basic math skills, but it fails miserably when you come to manipulating rational expressions.

As I've always said, they use calculators as avoidance tools rather than magnification tools. Calculators, used properly, should allow one to tackle more complex problems and to raise expectations by focusing on more complex ideas. Schools use them to do the opposite.

"This is not nitpicking, this is a direct attack on the poor quality of material in the teacher's manual, and is reflective of a cavalier attitude toward truth and accuracy..."

Exactly, and that should be the focus. Don't get drawn into an argument over the merits of the lattice method versus the standard algorithm. I could come up with a detailed analysis of why the standard long division algorithm teaches so much more understanding and number sense, but they really don't care. The want the students to select a favorite algorithm and make it his/her own. OK, but what, exactly, is the level of mastery they require? While my son was taking EM, I don't remember that ever happening. Perfectly capable kids got to fifth grade without knowing the times table using any sort of technique.

It's an issue of competence, not pedagogy. If you argue too much about pegagogy, you fall into their trap. Focus on the top end algebra in 8th grade path, not the low state profiency to nowhere. If they dispute that, ask them to define (back through K-6) the content, skills, and grades necessary to get to algebra in 8th grade.

SteveH said...

"In particular, the rather slow-moving drill is not particularly suitable for gifted math students, who can progress more quickly with less boredom (and, perhaps, more understanding) with the Singapore c

My son was bored with the standard pace of Singapore Math. When I taught him algebra and geometry at home using the Glencoe series, I could never take them at the standard pace. We would cover a whole chapter in an hour or so. I would give him problem sets and he would go off and do them on his own.

No curriculum is satisfactory for advanced students, and you don't even have to be gifted. Now that my son is in a regular high school math class, he deals with the slow speed perfectly fine. At least the content is proper.

In terms of K-6, Saxon makes it easier for schools to be competent at a proper level. The needs of gifted students are another issue. Schools have to allow for true acceleration.

SteveH said...

Let me also say that I never pulled out the big guns (of competence) with my son's schools. I've always tried to be constructive - with very little effect. It's very difficult to draw a line in the sand while your kids are in the school. Also, it can take years to figure out what's going on. Catherine drew a line in the sand and I give her very high marks for that. It would be interesting to hear if she would do it differently if she had to do it again.

Even after my son graduates from high school, it would be a difficult thing to do in our small town. (I think it must be easier in larger towns or districts.) People are extraordinarily funny when it comes to K-8 public schools. I don't think they want the issues clarified. Parents who have different ideas of K-8 education just keep quiet. If they can afford it, they send their kids to other schools - and they still keep quiet. The issues are VERY personal. Full inclusion is very personal. Even teachers know that differentiated instruction doesn't work unless you lower expectations. You have to believe that the more able kids "will do just fine". It's a dream world. Increase the range of abilities in a classroom but talk about how teachers can get all kids to learn at their best levels. The sorry excuse you hear when it doesn't work is that "public schools have to teach ALL kids." Apparently this has to happen in one age-tracked classroom.

Allison said...

Niki said:
-- You quote some Saxon lessons to show how "unlinear" they are. What you don't explain to those who have never used Saxon is those topics are "introduced," with 5 problems out of 30 on that particular topic found in their written practice/homework.

Hi Niki,
There's a difference between constant repetition and coherence. My objection is with the idea that distributed practice makes up for a lack of coherent structure. I quoted the exact order by which topics are "taught" in Saxon Intermediate 4. That order is the problem, and no repetition of material in previous lessons or future lessons will fix it.

The approach in current Saxon books above grade 3 is one that is bewildering. Every day, a different concept, as if *the concepts in mathematics do not build on each other.*. Yes, the procedures are given and practiced. But they are given without explanation of what it meant, and given in such an order as to imply that math is like a cookbook where the recipes are in alphabetical order by ingredient--as if there is no notion of a purpose to what is being taught.

Mathematics education is like building a house where you can work and live comfortably-- a place where once the structure is solid, allows you to spend time roaming around, getting work done, playing, resting, etc. The building of the house must be done from the ground up, bit by bit. You don't put in the windows before you build the walls. You don't build the cabinets before you put on the roof.

Saxon's order is as if to say that we practice nailing up some of the frame, and tomorrow, we move on to nailing on the roof. We distribute practice on nailing, you see, and that's what is important.

But a structure built this way will not be load bearing. It may LOOK like a house, but it is NOT a house.

What I find even more bewildering is how anyone could read page after page of lessons ordered in that fashion and not notice a problem. It's an emperor-has-no-clothes moment--- one must be pretty sophisticated to not notice the obvious.

Now, Saxon's name isn't listed as the author of those books; Stephen Hake and others are. It may be that these books are miles from the original content. It happens quite a bit--Dolciani's books have been ruined in that way (see e.g. "Mathematics: Structure and Method" or "Thermal Physics" by Kittel and whomever else is now listed.) So it may be that all sorts of Saxon defenders haven't seen what's currently published under their moniker; I don't know.

As to the value of distributed practice, I would add that it also comes at the expense of just teaching the material. A lesson where 5 of the 30 problems are new and 25 are review is unhelpful to teaching the new. 5 is not enough to ground the concept. It should be far far far more. Review is not the place to explore the content. By only showing 5, and then reviewing a smorgasbord of prior work for 25, little depth can ever be explored and understood by the students.

I have more complaints about the procedural work of Saxon, and the weak or nonexistent reasoning offered, but that seems best for a different post.

Anonymous said...

SteveH said
"My son was bored with the standard pace of Singapore Math. When I taught him algebra and geometry at home using the Glencoe series, I could never take them at the standard pace."

We kept the pace up in the Singapore books by just doing the workbooks, not the texts and certainly not the extra practice books. That was not our original plan (we bought all the texts and workbooks), but the problems in the workbook were straightforward enough that the texts were only consulted about once a year (usually to figure out the notation used in a problem statement).

I found that the Singapore texts did a good job of introducing new material while practicing the old, gradually increasing the complexity of multistep problems from year to year. Even now that my son is in AoPS Calculus, I'm still pleased with our decision 10 or 11 years ago to start him on Singapore math rather than the curriculum his school was using.

Michael Weiss said...

And don't forget, other than Wu's class, there are no *math courses in elementary ed* at the undergrad level in our nation at this time, and merely a handful of pedagogical math methods courses in education depts that have any math content for k-6 at all.

Okay, that's just manifestly untrue. What on earth are you talking about? Here are four Universities in one region in one state, all of which have mathematics courses for elementary teachers that are taught in math departments, by mathematicians, completely separate from the methods courses which are taught by the ed schools. None of them match your description.

Michigan State University:

Oakland University:

Wayne State University:

University of Michigan:

Niki said...


Stephen Hake was hired by John in 1983 because he had been using the same methodology in the middle school grades that John had introduced with his Algebra series in 1981. Stephen's program was thus refined with John's methodology and with his editorial input.

Your complaints/arguments are identical to many who haven't used Saxon materials at all or as John had asked them to be used. He discovered (yes, there is "discovery" in math education) that what worked for kids didn't always make sense to adults. That's what many teachers slowly admitted as they became committed to Saxon Math.

John's mantra was always, "Results matter!" That is, is the student proficiently ready for the next level? Did the program carry him/her when the adult didn't, such as with weak teachers and/or absent parents? (A textbook series is often the one constant in a child's life of learning today.) My opinion on any program, therefore, is unimportant until I see the results of that program on the student, not only at the end of one year, but at the end of high school. Is that student ready for the workforce or college without the need of remedial education? The fact is the academic results of those who have used Saxon are legend, especially compared to the garbage we've seen published since 1989 (not including Singapore Math).

I will be happy to send you a free copy of his biography, which gives many testimonials by teachers and administrators as well as factual research results, plus an explanation of his philosophy and methodology. You have to promise to read the book, however. If you agree, send me your mailing address to

Allison said...

That my complaints are identical to others is not a statement against interest. I've met many parents of children who hit the wall in algebra after having come from Saxon. Many of them scored well as proficient procedurally up until algebra, yes. But that's not the only result that matters. The students understand none of why they do what they do, and collapse later--at algebra, or maybe a bit farther. Most can't do STEM college work. They can't even explain place value to me, let alone fractions or decimals.

I've met more whose children collapse before then. Their kids hate math because of how it's taught. Those results matter too.

I can teach a child to ride bicycle with training wheels. But they are hobbled by it. It minimizes their risk, but prevents them from learning how to lean, so they can't handle the vehicle at real speed.

Worse, I haven't seen at all that Saxon works when the teachers are weak. That is precisely when I see a terribly bad result, one where everyone is struggling by pre algebra.

I guess we will have to agree to disagree. Given my current bookshelf of 30 or so books I promise myself I'll read but haven't yet, I doubt I'll get to yours. So thank you for the offer, but it might go better to someone else.

Allison said...


Parker and Baldridge are good texts, but they aren't what I meant. They serve a good purpose, no doubt, and I am happy to see those courses being taught with those texts, but they aren't mathematically deep. They aren't math textbooks. Perhaps I need to describe the difference differently?

Liping Ma talks a great deal about the understanding of US teachers vs. Chinese ones. She makes a great deal out of their ability to discuss place value. The US teachers talk just fine about tens and ones, and on first pass, it seems like she's making a big deal out of nothing. Intuitively, place value is easy, right? Swap ten ones for a ten, etc. But she keeps digging and finds out that they can't speak deeper about place value. Much like a college student who dimly understands but who says "yeah, right, that's what I said" when a professor corrects him because he can't see what he doesn't know, the US teachers didn't have a deep understanding. Parker and Baldridge help teachers get to a certain level, but not beyond that. They are not demanding enough of the math for it to go beyond that. Wu's book does.

We can debate whether everyone needs to go past Parker and Baldridge or not some more, but what I was speaking of is a vastly different course than the ones you showed me.

The Wayne St. course might be taught by a mathematician, but Mathematics for Elementary Teachers: A Conceptual Approach is not a mathematically deep book. It draws on the NCTM standards, which don't inspire confidence. "an emphasis on learning via specific, realistic examples and the extensive use of visual aids, hands-on activities, problem-solving strategies and active classroom participation." is not an emphasis on mathematics.

I looked at length at U Mich's math dept site. While the course you link to is in a math dept, only one version of the undergrad math concentration --one for a secondary level cert--requires the first course in that sequence. That appears to be an alternative to receiving a math major, not in inside a math major. This concentration has more math in it than some, but again, it's not for elementary certs.

The listings for that concentration look a lot like inquiry courses, iirc: "The students are engaged via constructing collective explanations of key mathematical topics."
Not sure that's the same idea at all.

It'd be nice to see real syllabi.Also nice to know how many ugrad math majors actually take these courses as electives.

Michael Weiss said...

I'm not a big fan of Parker & Baldridge, either; I agree that it is fairly thin on content. More worrisome, even though the authors explicitly deny (in the introduction) any intent to teach pedagogy, the book is just filled with monolithic and unsubstantiated claims about "the way children learn" and "the right way to teach" math.

But you know, you can't really judge what goes on in a (college) classroom from its textbook. In my classes at Oakland U. the official text is Billstein. The manner in which I "follow the text" is (how to put this delicately) rather hypothetical. That is, the list of topics we go over roughly correlates with the chapter and section headings in Billstein, but the organization and presentation within those topics is radically different. And I know that much the same is true at MSU, UM, and WSU, as I have first-hand knowledge of faculty at those institutions.

In any case my point was not about textbooks. It was a response to your claim that "other than Wu's class, there are no *math courses in elementary ed* at the undergrad level in our nation at this time, and merely a handful of pedagogical math methods courses in education depts that have any math content for k-6 at all". That's just outrageously false, as all of the courses I listed are content courses, not methods courses (which preservice teachers also have to take in addition to their content courses), taught not in education departments but in math departments by honest-to-goodness real-life mathematicians.