kitchen table math, the sequel: Wrecking rigorous math in high school, non Common Core edition

Monday, November 18, 2013

Wrecking rigorous math in high school, non Common Core edition

Lots of folks are up in arms about the "lowered" standards in high school, courtesy of Common Core. Meanwhile STEM preparation is degrading here, no CC necessary.

Let's recap:
In 2007, MN adopted "better, more rigorous!" standards that they claimed were the tops in the nation, matching MA and CA. In these, all 8th graders were required to take Algebra through the algebra of the line. This would now be called "algebra 1", and algebra 1 was no longer a credit bearing course in high school. Also in these changes, all high schoolers were required to take algebra 2 before graduation. The standards defining algebra 2 covered only those subjects expected to be
learned to mastery. These standards did not include trigonometry nor logarithms nor other kinds of mathematics.

In 2011, the standards were rolled in. The state did not change the teacher credentialing requirements for 8th grade math teachers.

The new Algebra 1 class looked like old Algebra 1 to parents. Except it's only 1/2 of the algebra they knew. And Algebra 2 is about 1/2 of the algebra 2 they knew. But there's no way to be half a year ahead, though, for most schools, and therefore, for kids. So the new alg 1 is the only alg 1, and the only alg 2 is the rest of the old alg 1 and 1/2 of old alg 2.
Content including trig, logs, complicated factoring, circular functions, all of this is now in pre calc.
Limits, sequences and series, graphing of high order functions, de Moivre's theorem, etc. is now in most APcalc classes.

Now, schools cheat this by offering a year  for AP calc AB, they claim, and a year for AP calc BC.

But this is a sham. A 5 of the AB test is mathematically no less than a 4 on the the BC,  because the BC test simply does not offer that much more material than a competent calculus course would already have offered. While it does offer new topics, it most definitely does not offer multivariate calc, which is the 2nd term of calc in any semester-based engineering or STEM calculus sequence, and the third term at any quarter based university calc sequence. recap: we in MN, without CC, teach algebra earlier now, and as a result, kids leave no better off where they did before in terms of knowledge, but a year behind the titles of the courses they are taking.  They and their parents are misled about what they know and what they have been taught when.

For the majority, they basically take pre calc, same as always. But for the honors kids who used to get a real AP course that really was the equivalent of the first semester of calculus, they are screwed. They no longer get that, or they only do by taking finding some school supposedly giving them alg 2 in 8th grade--who is qualified for that???? and then, they still only get as far as 1 term of college calc. Likely they waste a year instead of learning something for real.

This means without 2 years of supposed hs calc, they are not ready for calc based physics in college.

This can't be blamed on Common Core. This can't be blamed on ed schools, either.

This is the Cargo Cult of education (a phrase I coined here UPDATE! below) and the Cargo Cult of politics. We walk around, mimicking what real people once did, pretending that coconut headphones and a guy waving sheets as if they are semaphores on the tarmac will bring back the cargo planes.

The legislature pretended that decreeing students do something earlier was the same as doing it well.
The legislature pretended decreeing everyone take algebra 2 would make them capable of it.
The Dept of Ed pretended to concur and changed the content of the standard.
The publishers pretended to concur and changed the content of the books.
The schools pretended to concur and changed the content of the courses.
The teachers pretended to concur and gave everyone high grades.
The parents and students ...well? some pretend their schools are still great. Some are duped until college. And even then, most just want someone else to pay for the student loans they had to take for remediation, not yet angry about the remediation.
 But the kids who used to be ready for an engineering degree program are no longer ready, and are losing ground compared to their foreign counterparts.

Until people admit reality we will keep playing these games.

From the MN dept of ed Math 2007 standards FAQ
"Some algebra II material is introductory in nature and lays the foundation for future courses. Students are not expected to master such material. For example, logarithms are usually introduced in algebra II, but mastery of the fundamentals of logarithms is not expected until precalculus or college algebra. For this reason, logarithms are not mentioned in the 9-11th grade standards and benchmarks."

UPDATE: E. D. Hirsch first used the phrase Cargo Cult here to refer to the state of educational research. My use of it was independent of this, and somewhat different.


Auntie Ann said...

That's the case with the UCSMP math sequence too (the continuation of Everyday Math). Their sequence goes like this:

Pre-Transitions (which is for the majority of 6th graders)
Transitions (usually 7th)
Algebra (8th)
Geometry (9th)
Advanced Algebra (10th)
Functions, Statistics & Trig (11th)
Precalc (12)

So, even if you take their "Algebra" in 8th, you still don't get to a calculus class in high school. This way, schools can claim to give kids algebra in 8th, without actually having to provide a complete algebra course.

lgm said...

Around here it is called equality. Those "elites" that want more are encouraged to do so on their own dime.

Jennie said...

For Allison and Auntie Ann (and others here who know much more about this issue than I):
Oh dear. I have "afterschooled" my youngest for 3 years, b/c Everyday Math was a disaster for her. I had hoped to be able to stop come Algebra in 8th grade. I guess I'll be pulling out the Foerster Algebra text that I purchased on the advice of this blog.. The University of Chicago program really only covers 1/2 of Algebra 1 ??? What topics covered in Foerster aren't covered by Univ. of Chicago?

I admit that I don't really understand the problem that Allison relates. Could someone explain to me what content my current freshman - in Algebra 2 - will not be taught in the next 4 years that he should be taught? What recommendation do you have to address this gap? He loves math. He is more skilled in math than I. Online course?

Allison said...

The issue is that if he is really in algebra 2 now, THIS is what he should already have had:

And maybe, in the next three years, they'll get around to that material, or you will. But with what rigor, and with what pace? Should it take a school 2 more years (not counting the year of geometry) to teach the algebra topics he hasn't seen yet, when they used to constitute a couple months? Is he on pace to take an authentic AP calc course his senior year, or one that actually doesn't cover enough for him to get a 5 or 4 on the test?

It Should Not take them 2 years to teach a 1 semester college course.

I suggest looking also at my Dolciani post,

to see why even the Foerster book, better than a lot of choice available now, is still dramatically inferior to what was taught in the 60s or 70s.

What can you do? I'd look at the Art of Problem Solving on line courses to start. They begin with pre-algebra and go through many levels of algebra and pre calc. Then beyond that, I'd look at college calculus at a real college, not at the high school, or at least the oldest version of Thomas' Calculus and Analytic Geometry book you can find.

SteveH said...

"But there's no way to be half a year ahead, though, for most schools, and therefore, for kids."

Because you're from the land of Lake Wobegon.

"...and algebra 1 was no longer a credit bearing course in high school. ... all high schoolers were required to take algebra 2 before graduation."

What kind of torture is it to take four years to go from partial algebra 1 to partial algebra 2? Can't they see that the problem is carried-over gaps and baggage from K-8?

"..because the BC test simply does not offer that much more material than a competent calculus course would already have offered."

My son took AB last year because that's all that our school offers. He is taking the BC extra material right now independently in his first semester. When he mentioned that he would be doing this to the head of the math department at Michigan last summer, the professor said that that would take a few weeks, so what would he be doing for the rest of the semester? Studying Apostal. He finished the extra BC material in the first quarter.

My rule is that if you are majoring in that subject, never use AP to skip the low level courses. They don't match up to what you had.

SteveH said...

Our high school has only ever offered AB. That's because few students are left that can handle that material, let alone BC, even though BC is not that much more material. So far, I see no change to the top end classes in high school because of CC. Teachers have to show how the material matches up to CC, but they won't have to lower expectations. At least I haven't seen that yet.

The greater problem is whether they are going to start using watered down math textbooks in 7th and 8th grades. We got rid of CMP in middle school and went to more rigorous math textbooks because parents wanted a path that used the same honors algebra that the high school used. If students were offered a chance to get to honors geometry as a freshman, then 8th grade algebra has to use the same textbook as the high school.

Now that this has been done, the lower level math students in middle school use the same textbook, but go at a slower pace. This is good in that there is still some chance for them to recover and get back on the top math track. If, however, the middle school changes to some watered-down, real world CC-based math textbooks (with added material for the advanced students), we will be right back where we were with CMP. They will say that it's equal, but it won't be.

I believe that it was Wu who talked about the nonlinear change needed in middle school to get to the top math track in high school. When we got rid of CMP and went to proper math textbooks in 7th and 8th grades, the big split happened at the start of 7th grade. Students ended up on two math slopes. It's a tough adjustment (after 6 years of Everyday Math), but it's easier to make this change starting at the beginning of 7th grade. However, if CC now controls the textbooks in middle school, then fewer students will be able to make the bigger change in slope when they get to high school. We will be right back to where we started.

I'm not sure why CC doesn't deal with the different levels (CP, honors, and AP) in high school. They claim to have a strong standard for all students, but this is not the case. "College readiness" is meaningless. Many clearly state that math is not taught at a STEM level in K-6. I find this amazing. They are not hiding behind critical thinking and understanding. I was hoping that CC would show this problem, and it did, but the solution was to ignore it or hide those assumptions away.

I just checked, and it seems that our middle school math textbooks have not changed yet. If they don't change, then life around here after CC will have changed very little.

Auntie Ann said...

When CC first came out here in California, there was some question of whether its adoption, and the wording of the exact statute that implemented it, would allow for advanced students to proceed to Calculus in high school. The law in CA was apparently written in such a way as to declare what students should be learning in any given year, and there was no wording allowing for acceleration.

I haven't heard much about this since, so either the law was changed or conveniently reinterpreted to accommodate advanced students.

SteveH said...

"This can't be blamed on ed schools, either."

I disagree with this. I see this as the biggest problem for K-6. I saw a clear fundamental difference in opinion and philosophy with our schools. This was not something that could be discussed. This is their turf. They are the experts. I've referred to what I've called preemptive parental strikes. I will always remember when our son's first grade teacher told us that "Yes, he has a lot of superficial knowledge." when we naively said that he loved geography. There is also the threat of being called a helicopter parent (or worse) to keep parents in their place.

We couldn't talk about phonics. They would not even admit that it was a viable alternative. The Kindergarten teacher looked at us like we were abusive parents when we mentioned that we had our son doing math worksheets. This was not just a difference in acceleration. The first grade teacher went on and on about kids finding their "voice". Spelling and complete sentences didn't matter. You couldn't disagree without implying that their philosophy was fundamentally wrong. That's all they know - discovered on their own, I'm sure. We couldn't even begin to argue that differentiated instruction was a fairy tale.

I started to see a change in our middle school teachers who had to be certified in the areas they taught. The high school teachers are completely different from the K-6 teachers. In high school, the problem is more about allocation of resources. Will they reduce the number of AP classes so that more funds can be spent to meet the low state cutoff standards? I don't think they do this because the most involved students and parents would not stand for it. High schools have to deal with the reality imposed by colleges and careers. K-8 schools still live in their own educational and pedagogical fairyland. They love real world problems, but they live in a dream world. Our improved math textbooks hit a dead end when they ran into the pedagogical silliness and low expectations of K-6 Everyday Math.

I see no way to change what's in the hearts and minds of K-6 educators. CC is a matter of redefinition, not real change. One would think that the CC definition of NO STEM in K-6 would be a smoking gun, not that this is anything new, but it's right there in black and white. PARCC had to calibrate that their top PLD level (5 - "Distinguished") in math only means that it is likely you will be prepared to pass a class in college algebra; material students start learning in middle school!

SteveH said...

"... and there was no wording allowing for acceleration."

Acceleration happens in high school. That will never change. I hope. I see the big battle ground as middle school. Will we go backwards? Nothing in the NO STEM CC fixes K-6. This is nothing new, but I think there is a good chance of going backwards in 7th and 8th grades.

I don't know why CC never investigated the issue of full inclusion in K-6 and the implied need for separation of students. The one-size-fits-all philosophy only applies as a means to define a minimal high school cutoff. It may define a higher low end cutoff for many states, but many treat it like it defines best practices for all students? When does this change, in 5th grade, in 8th grade?

Ask the parents who fix things at home or with tutors. Parents are taught to shut-up, do it themselves, but still bake cookies and support the schools. I think about all of the conspiratorial parent conversations I've had on the soccer sidelines and at the grocery store.

Auntie Ann said...

FYI: Here's some of the UCSMP Algebra book, including the table of contents which starts on page 12 of the PDF (internally, it starts on page 10.)

And here's the Advanced Algebra sample, which has the Table of Contents on page 12 as well.

And finally, here's their Functions, Statistics and Trig sample

kcab said...

I believe the link Allison gave for content of authentic algebra courses covers both Algebra I and II. At least, that is what it says in the NMAP report where it appears on pg 16,

Auntie Ann said...

Allison's list doesn't show any conic sections. Formulas for circles, parabolas, ellipses, and hyperbolas. Or is that what they're calling "quadratic functions"?

I seem to recall looking at those equations, graphing them, finding centerpoint, radius, focii, etc., in my first Algebra class back in 8th grade.

Are they still in there somewhere?

Glen said...

@Auntie Ann: Our Silicon Valley K-8 school district just had its Introduction to Common Core meeting last night. A six-person panel, including the district super, addressed a packed audience of parents and told us about the changes coming with CC.

The super started off the meeting with a statement that the transition to Common Core would not result in any reduction in faster courses of study or some such wording. I *think* this meant that, among other things, the advanced math track in middle school wouldn't be canceled. We have an advanced math track, where a few 6th graders (whose parents make enough fuss) are allowed to start in pre-algebra instead of "6th grade math," and there is a bigger "AS" (advanced studies) English track that lots of kids get into without much difficulty.

I wasn't comfortable with the number of times the marvels of differentiated instruction were emphasized by others on the panel, so I'm not totally convinced they won't convert any advanced tracks into "normal track but differentiated," while claiming that it is the same. I couldn't ask, either, because so many other parents had questions, but this was an audience that was CLEARLY intensely interested in maintaining advanced tracks. (The majority were Asian.) They would have rioting in the streets if they canceled our advanced tracks. At one point, the English teacher on the panel responded pointedly that she taught AS English and, "as we keep saying, the AS English program is not going away." But then the middle school math dept. representative on the panel kept making comments about how "acceleration is overrated," so we'll see.

The main emphases were that math has been "a mile wide and an inch deep," and with CC they are going to switch to teaching fewer things in greater depth. Also, the English program was going to do less fiction and more non-fiction, more parsing of difficult readings, more writing that argues a position using sources instead of personal feelings, etc. The AS English teacher described the changes as, "I personally like assigning them to write lots of stories, but I'm going to have to start assigning more non-fiction, academic-style writing."

Sounds good to me.

momof4 said...

Stories? Gag. Writing about personal feelings? Gag. Please, get on with the more difficult reading and academic writing - hurry! Let the kids who want to navel gaze or write stories do their diaries and stories on their own time. I also hope the history teachers assign more and better reading and writing. Bottom-line, though, I forsee massive efforts to avoid all of the above as much as possible, while watering down math and backing off acceleration Sigh

kcab said...

@Auntie Ann - So far as I know, that content would be included under quadratic functions on that list. I remember parabolas, etc being covered in my kid's algebra I class last year. Looking at the CCSM standards - references are under the geometry section.

Must be the season for meetings about Common Core - I'll be going to two this week, one at the middle school and one at high school.

Allison said...

You an read the MN standards here.

They were so vague that then the state wrote benchmarks, which effectively are cut and paste examples so you can teach to the state test. says "Identify the vertex, line of symmetry, and intercepts of a parabola corresponding to the quadratic function..."
that's the algebra 2 standard.

No mention of conic sections, hyperbola, or ellipses per se in the standards. Meaning none of that is in algebra 1 or 2. If it is taught, it is in pre calc now.

VickyS said...

Allison, when does trig get taught in MN? When does it come in via the CC in other states? I'm tutoring a student in a basic physics class, and during the first month they did problems involving vector addition. She's lost because she has never seen trig functions, much less inverse functions to get the angles. It's not rocket science to teach this and it is probably one of the few math subjects non-STEM people might actually encounter alter on!

Anonymous said...

"Writing about personal feelings? Gag. Please, get on with the more difficult reading and academic writing - hurry! Let the kids who want to navel gaze or write stories do their diaries and stories on their own time."

I suspect they're encouraged to write about personal feelings not for purposes of navel-gazing, but rather so the schools can monitor them for any politically-incorrect attitudes and target them.

Anonymous said...

Even worse. Schools should concentrate on academics; it's not as if they're doing so wonderfully well with any subgroup (academic or demographic) that they should be spending time on feelings and attitudes.

Allison said...

Vicky asked?

Allison, when does trig get taught in MN? When does it come in via the CC in other states?

Inside the MN geometry standards, there is a small amount of trig.

In MN, the "new alg 2" (which teaches quadratic functions) comes in 9th, geometry in 10th, and "pre calc", where you lesrn alg 2+trig comes in 11th.

This is one of the geometry standards:
"Know and apply properties of right triangles, including properties of 45-45-90 and 30-60-90 triangles, to solve problems and logically justify results.
For example: Use 30-60-90 triangles to analyze geometric figures involving equilateral triangles and hexagons.
Another example: Determine exact values of the trigonometric ratios in these special triangles using relationships among the side lengths."

So hopefully that is inside the unit circle.

Nothing beyond sine, cosine, and tangent are in the standards.
"Apply the trigonometric ratios sine, cosine and tangent to
solve problems, such as determining lengths and areas in right
triangles and in figures that can be decomposed into right
triangles. Know how to use calculators, tables or other
technology to evaluate trigonometric ratios."

But it isn't before 2nd term soph year. And it doesn't have to be in geometry at all--it just has to be in some required course.

Anonymous said...

Why does Trig have to come up before 11th grade pre-Calc (or what used to be known as College Algebra/Trig). Yes, Geometry prepares you for Trig, but the heavy0duty stuff used to come in 11th grade, even for advanced math students.

Auntie Ann said...

You have to have trig either concurrent to or preceding the taking of physics. You can't do much with vectors if you can't get beyond 3-4-5 triangles.

Auntie Ann said...

"The Texas Board of Education has given preliminary approval to a plan that will eliminate algebra II as a high school graduation requirement for more students.

"The Texas state legislature gave unanimous approval to the change back in May as part of a huge overhaul of the state’s graduation and high-stakes standardized testing regime, reports The Dallas Morning News.

"Proponents of the elimination of the algebra II requirement and other academic requirements say the change provides more choices. Now, they say, more students can learn a trade or focus on practical career training if they want."

allison said...

And continuing Auntie Ann's point, because physics is now First. As in taught before bio and chem. Google Physics First.

momof4 said...

At my older kids excellent HS (outstanding math/sci program), the upper-level AP physics (A&M, BC IIRC), was calculus based, so all students were required to have concurrent enrollment in AP calc BC. As with all of the sciences, students had to have taken the honors course first, which required concurrent enrollment in pre-calc (aka Elementary Functions and Analytic Geometry). Both the calc and the physics (also AP chem) were really college-level and had double periods every day. That was 20 years ago now, but the last time I looked at the website, the sequence is still the same (except they re-named the pre-calc course, which was referred to as EFAG).

Anonymous said...

You CAN teach a full, honors-level physics to students who have not had trig. My school moved trig into later in the 11th grade pre-calc class (without mentioning that to the physics teachers). But it takes only 20 minutes to teach enough trig to then handle a wide range of vector problems. You just have to emphasize the component method because they won't see law of sines or law of cosines until the spring.

In fact, while I wouldn't want to see physics moved to 9th grade, I'd be happy to teach it before chem. So much of chemistry makes no sense until you've had physics. -- Phil

Anonymous said...


Anonymous said...

"This can't be blamed on ed schools, either."

college *mathematics* departments
routinely promulgate a *lot* of
worse-than-useless rituals designed
to *replace thinking* about
whatever calculations are being

most "remedial" classes are devoted
*mostly* to suchlike opposite-of-math
rituals, indeed. but it's not just there.

*many* of the students i grade papers
for in linear algebra... having somehow
passed 4 quarters of calculus (so-called)
still have no clear idea what "=" means.

i'm not kidding. everyone else who
marks their papers knows this too
but i'm the only one talking about it.
no damn wonder. trying to do stuff
right *will* get you fired.

textbooks? any competent instructor
will *routinely* need to correct
*major blunders* in any lower-division
text (and this is creeping upward).
clear and correct notations are
suppressed in favor of harder-
-to-understand *verbal* presentations
that few students will ever even
*try* to reproduce accurately
(usually this is in some sense for the
best since the verbal version will
have bugs not present in the code).

this system can't be saved;
the enemies of clarity have won.

vlorbik (his mark)
(once & future blog)

Catherine Johnson said...

Hi Vlorbik!

Allison - that is horrifying!

Good Lord.

Here's the 2006 use of cargo cult education at the old ktm, by Becky: Cargo Cult Lucy From Becky

Catherine Johnson said...

this system can't be saved;
the enemies of clarity have won.

Well…one more reason to be a regular at school board meetings.

Our curriculum director is a master at slinging the lingo …. so my job is to get up and parry in plain English.

I'm basically providing the comic relief.

The ridiculous thing is that the curriculum director **is** doing **some** things I have desperately wanted the district to do for years (interim assessments, for instance!)

I get the feeling she may bring in a real reading curriculum (although that would be so miraculous that I'm not placing bets).

I think she might be better off not blowing smoke.

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