Anonymous weighs in

Here's a weird thought to ponder: across the land, future teachers are being taught that direct instruction is bad, that they should be the guide on the side, that the discover method is the best way to educate...but exactly HOW are they being taught this? Does a guide on the side help them to discover the enduring understanding that this is the best way to teach? I bet not. I bet they are being directly instructed not to directly instruct. Hmm...

The reason this came to mind is that I was remembering a curriculum writing workshop in which I was instructed (and it felt direct to me) that if a question has a single correct answer then it is not an essential question.

What has happened is that the understanding-by-design crowd has claimed the term "essential question" as their own special buzzword. I guess the common core crowd is using it too.

Tom Loveless on the algebra 2 problem

From Algebra II and The Declining Significance of Coursetaking:

...taking and successfully completing an Algebra II course, which once certified high school students’ mastery of advanced topics in algebra and solid preparation for college-level mathematics, no longer means what it once did. The credentialing integrity of Algebra II has weakened.

The declining significance of successfully completing Algebra II highlights a dilemma. Pushing students to take more advanced coursework has been a mainstay of American school reform for several decades. That prescription has worked in boosting enrollments. In 1986, less than half of all 17 year-olds (44%) had completed Algebra II, and for Black and Hispanic students, the rate was less than a third. Completing Algebra II is now commonplace. In 2012, about three-fourths of students completed Algebra II, and the race/ethnicity gaps associated with taking the course have narrowed significantly. (All NAEP data below are from the NAEP data explorer.)

Getting more students to take higher level math courses may be a hollow victory. It has not coincided with students learning more math.

Worse than you think, non-Common Core edition

After a 3-year hiatus, I have returned to my district's school board meetings. I am, once again, a regular.

It's been somewhat fun.

It's also been interesting in that I discovered, on my first night 'back,' that I had missed the board. Missed as in missed members of the board as people for whom I feel a great deal of affection. I was happy to see them again, after so long away.

Crazy!

I've spent years attempting to reform my district, and being frustrated by the administration and by whoever was currently serving on the board who wasn't someone I helped elect.

And Chris's middle school years were harrowing.

But Chris's middle school years are well behind us now, and come to find out, my essential emotion today, where board members are concerned, is: affection. I am fond of our school our school board members, collectively and individually.

I seem to feel the same way about our administrators. (That's really weird.)

Ed says I have become the loyal opposition.

Anyway, it's somewhat fun to be back.

The somewhat comes from the content of board meetings, which is never what I want. Or, rather, it's (sometimes) in the vicinity of what I want, but it's not what I actually want.

Plus, there are surprises.

Last Tuesday night's surprise was the revelation that the district does not have an early reading curriculum.

At all.

I had been assuming we had a bad one. Last I checked we have something like 18% of kids going into 'Tier 2' intervention, and I'm pretty sure that number would be 10% with a good reading curriculum. (I hope palisadesk is around to weigh in.)

So I had just naturally been assuming that we have a really bad early reading curriculum the same way we had a really bad math curriculum in K-5 and a really bad reading curriculum in the middle school.

But no.

We don't have any early reading curriculum at all.

The funny (ha-ha) thing about this is that back when Ed and I first moved to town we became dimly aware of what seemed to be chronic conflicts at the board level re: not enough textbooks to go around. Various classes didn't have enough textbooks, and somehow enough textbooks were never bought or budgeted for or who knows what, and teachers were getting in trouble for spilling the beans to parents about the not-enough-textbooks situation, until finally the then-board president took matters in his own hands and decreed that enough textbooks be ordered at once and distributed to students. That's the story I heard, at any rate.

So it's path dependency.

We have always been a district with a not-enough-textbooks problem, and we are evolving into a district with no textbooks at all.

I'm sure regular attendance at board meetings will reverse that trend.

Resources for the ACT test?

My daughter is a junior and in the middle of the test taking year. I went back through all the posts and gathered the resources on the SAT. Does anyone have a similar set of resources for the ACT test?

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.

So...to 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  http://www.hoover.org/publications/policy-review/article/7262 to refer to the state of educational research. My use of it was independent of this, and somewhat different.

Help desk, Common Core edition

Cruising Common Core materials (there seem to be lots on Prezi), I find this (slide title: "Two Types of Essential Questions: Overarching and Topical"):

Isn't there one right answer to "how many ways can we achieve the sum of 23"?

Isn't the answer: "There are an infinite number of ways to achieve the sum of 23"?

Another thing: would this question be asked, in this way, in combinatorics? (In the time I've spent trying to learn combinatorics, I haven't encountered a question with more than one right answer. Nor did I encounter a question with an answer of infinity.)

(And how is this question "topical"?)

I am watching in amazement as Common Core rolls across the land.

It's as if every constructivist in the country has suddenly been handed a lifetime prescription for anabolic steroids.

All those years of No Child Left Behind and Adequate Yearly Progress must have created a massive pent-up desire in the breasts of America's educators to conduct mini-lessons and ask math questions with no right answer.

GRE scores by intended field of study for college seniors

Source: Educating School Leaders, p 32

Steve H on the mailing list

Have just read this comment by Steve H:

My son also has a college brochure stack two feet tall. He also made the comment that if you put your hand over the name of the college, you could not tell which one it is. (That would make a good YouTube video. Name This College.) I also liked the survey where they asked students why they got into a top college and the general response was: "I have no clue whatsoever." For others, however, it seemed like the extra oblong interest and special talent made the difference. It has to be special or at some particularly high level.

Unfortunately, the segment talks only about the most egregious application mistakes and stupid parents. I would like to be a fly on the wall when admissions people make the final decision. After they process race, gender, sports, and alumni parents, (grades are given), there will still be many to choose from - maybe one in five. what are the deciding factors? It might depend on whether you catch the eye of one of the strong or powerful admissions people. It might be your essay that does it, but it might also be your special talent.

Steve is in his year of viewing dangerously....college viewbooks are a world unto themselves.

My favorites were the ones from Grinnell, which were so striking, and so indecipherable in terms of who the intended audience was supposed to be and what message we were supposed to be taking away, that I kept scans.

What is the story Grinnell is telling prospective parents with these images?

After the mean girls reject your son, he'll gel his hair and take up violin?

And this is worth $50k a year?

By the way, if I were the parents of the three girls, I would have been furious. They are sisters whose parents -- both university professors in Kabul -- immigrated from Afghanistan. They're beautiful girls, and Grinnell had no business a) taking a photo like that and b) using it to promote the college.

Of course, maybe the parents weren't consulted. Which makes it even worse.

Younger

As the nation's schools undergo a wave of teacher retirements, some 25% of teachers have only five or fewer years in the classroom, "a precipitous decline" in experience since the late 1980s, when the typical teacher had 15 years' experience, according to a study by the National Commission on Teaching & America's Future, a Washington, D.C. nonprofit advocating teacher quality.

That may explain why some 43% of parents report being "extremely worried" about their kids' elementary-school teacher assignments, according to a poll last month of 306 parents by CafeMom, a social-networking and community website.

Dread of August: The Kids' Teacher Assignments | By SUE SHELLENBARGER | Aug. 6, 2013

This generation of teachers has been trained in pure constructivism.

According to Robert Slavin, direct instruction hard been all but dropped from teacher training by 1991.

An Interesting Common Core Exchange

Common Core and Curriculum Controversies

Something really struck me as strange during Fordham's panel discussion last week. At 54min 50sec in the video, there's a very basic, yet revealing, question posed by this young lady.

 Question: Garrett Fryer American Youth Policy Forum Was there ever a discussion, when you all were designing it, to implement it on a kindergarten level and letting it grow with the students as they aged on through each grade, as oppossed to implementing it with the entire school system nation wide? 

Answer: Jason Zimba This is something that states have each approached differently. Some states have done something more like that, some states have done something less like that. I seem to remember at one point I saw a MA plan where the grade level wasn’t the key parameter, but they had a Venn diagram, you know, what we do now the Common Core doesn’t do, what the Common Core does that we don’t, and then what sort of overlap, where we want to do it better. And they decided to take those three... in year one, we’re gonna focus on the overlap and do it better. In year two, we’ll drop things… and then in year three, we’ll add… I got the details of that wrong, but… my only point is that different states all approached it differently, and we may find out that some states were much wiser than others in this way. Singapore has a long standing, high functioning system in which they not only revise their syllabus ever so often, but they do it actually on the basis of how kids do, so think about that, a performance-based loop, a feedback loop. Which is something we are taking halting steps toward, but can only imagine. And so roughly every six years or so, they’ll put out tweaks to the thing. This year I noticed that they’ve rolled out a new thing in kindergarten. 

Lisa wonders... How in the world can one "image" OR take "halting steps toward" creating a "high functioning system" based on a "performance-based feedback loop" when we are STARTING with a top-down DESIGN by the name of Common Core?

The chairs

From the "High School" section of Illustrativemathematics.org:

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary.

This video shows an excerpt of a conversation between two students comparing approaches to solving a problem and trying to understand why they got different answers and where one of them made an error.

PROBLEM:

Three halls contained 9,876 chairs altogether. One-fifth of the chairs were transferred from the first hall to the second hall. Then, one-third of the chairs were transferred from the second hall to the third hall and the number of chairs in the third hall doubled. In the end, the number of chairs in the three halls became the same. How many chairs were in the second hall at first.

I haven't watched the video, but I hope one of the approaches the two students consider involves asking the teacher what the problem means by "the chairs."

By happenstance, my students and I read the first half of G.K. Chesterton's essay on fairy tales in class today. When I say "read," I mean that my students and I read each sentence individually and out loud and then stopped so I could explain what the sentence meant and why after first asking the person who had just read to take a crack at it.

Chesterton's opening lines:

Some solemn and superficial people (for nearly all very superficial people are solemn) have declared that the fairy-tales are immoral; they base this upon some accidental circumstances or regrettable incidents in the war between giants and boys, some cases in which the latter indulged in unsympathetic deceptions or even in practical jokes. The objection, however, is not only false, but very much the reverse of the facts.

I asked my students what the words "the objection" meant. When nobody knew, I pointed out that the words "the objection" function as an anaphora: the definite determinative (the) tells you that you already know which (or what) objection because you've seen it before, in the text. It's the objection, not "an objection."

So, if you've already seen "the objection," and you've only read one other sentence, what is the objection? It's got to be inside that one other sentence.

At that point, my student who was educated outside the United States in his early elementary years (and who speaks very lightly accented English) figured it out.

..................

My answer to the Illustrated Math problem, which I arrived at on my own and without a lot of conjecturing and solution-pathway-planning and special-case mongering and the like is: 4,938.

..................

The Common Core era is going to be an unhappy one for mathematically gifted children.

I predict.

Help desk - Illustrative Mathematics

Illustrative Mathematics 

Thoughts?

Trailblazers kids in a Common Core world...

At the Irvington Parents Forum blog.

I'm waiting for the many apologies due to come rolling in from all the central administrators & board members who insisted on sticking with Trailblazers for lo these many years.

My favorite was the board member who said, during the candidates' forum, "We're not changing the math curriculum because of 20 people on a blog."

He meant list serve.

Daniel Wilingham on Paul Tough

He likes the book -- I may have to read!

Meet the new boss, part 2

I've updated "Meet the new boss." (Scroll down)

State of play, Common Core edition

Parents are in an uproar here.

We've hired a curriculum director who is a smart, fantastically hard-working true believer in the wisdom of mini-lessons and students designing their own "literacy" curriculum by choosing their own books to read for class and discussing them in pairs or pods.

A smart, fantastically hard-working true believer gets a lot more done than a dull and lazy true believer.

(Ed and I and numerous others fought to keep that position from being filled, by the way. Fought.)

So, where Common Core is concerned--Common Core as understood by a public school curriculum director--we are ahead of the curve.

Which means that after 10 years of strife over Math Trailblazers we have unceremoniously dumped Trailblazers and adopted the engage^ny math modules, which are being written and posted as we speak. No teacher has ever taught engage^ny math, no student has ever learned engage^ny math, engage^ny math does not yet exist in toto, and the vast set of engage^ny material has to be downloaded from the internet.

And this is what we're using.

Because, you know, COMMON CORE.

Those are the magic words, COMMON CORE. Once an administrator invokes the name of COMMON CORE, s/he is absolved of all responsibility for children actually learning math.

So here we are:

1. The children have no math textbooks
2. Because Trailblazers was so slow, children in later grades don't have the skills to begin grade-level engage^ny units, but they have all been forced to begin grade-level engage^ny units anyway, regardless of preparation
3. Because we've never had a scope and sequence for any subject in the district (this state of affairs finally came to light at the last board meeting, after I requested a copy of our scope and sequence) no one has any idea what skills the kids are supposed to possess 
4. Because the district has never held itself responsible for children actually learning the content being covered in class (and retaught at home by parents & tutors) there is no mechanism in place to figure out what skills kids are missing
5. Because no one apart from high school math teachers has any expertise in math, neither teachers, building principals, nor the curriculum director has any idea what the proper sequence of skills actually is & thus no idea how to assess the kids' "gaps" (lots of gaps talk amongst parents and teachers; calls to mind the early days of ktm) 
6. Although engageny promises a year-long "scope and sequence" for its curriculum "modules," the promised scope and sequence for math either: a) does not yet exist or b) does exist but is unusable by people absent a deep and hands-on knowledge of K-5 math and math curricula.

I attended Thursday night's Common Core meeting, and the atmosphere in the room was pretty much one of controlled pandemonium.

No one knows anything, and, very clearly, no one is going to know anything any time soon.

I've seen a lot of bad math teaching in my day (a whole lot), and a lot of bad math curricula, but I've never seen anything like this.

Recent comments widget

Looks like Blogger has a new "Recent Comments" widget I'll have to figure out....

Googlemaster strikes again

In the Comments section of an earlier post (Wrong again) I was banging on about nominalizations being essential to academic writing because a nominalization lets you combine a noun and a verb and then use another verb to write about the new noun-verb combination...and Google Master made the point a lot more succinctly:

Heh. The word "nominalization" is a nominalization.

I wish I'd thought of that.

The degradation of school textbooks

We know the myriad ways Everyday Math, TERC Investigations, etc. are terrible, but the rot extends to new editions of old textbooks.

I'm often asked what algebra book I'd recommend.
The answer is Modern Algebra, Structure and Method by Mary Dolciani et. al. Copyright 1960 or 1962. But I can't recommend any edition of it written after 1970 without reservations, and the 1980s and later one should probably be pulped.

The same book title with same author has over 100 versions with over 100 different ISBNs. The old ones I recommend don't even have ISBNs.

What's the difference? Here is a tiny slice.

Modern Algebra, Structure and Method, Dolciani, Berman, and Freilich, Hougton Mifflin Co., Boston. c. 1965, 1962. No known ISBN.

This is a great book. Mathematically rigorous, 30+ oral exercises per lesson, 40+ written exercises per lesson, and ten problems as well per lesson and real content.

Chapter 3, Addition and Multiplication of Real Numbers(p. 69) begins with a discussion of axioms of equality (3.1). It states clearly:

"you learned to perform many operations with numbers because you abided by certain rules.These rules, which are statements accepted as true are called assumptions, axioms, or postulates...The first fundamental assumptions that you will meet are the axioms of equality which govern your work with equations..."

3.2 covers axioms of closure. The language is sophisticated--

"Any set S is said to be closed under an operation  performed on its elements, provided that each result of the operation is an element of S. This is known as the closure property of a set under an operation. Calculations in arithmetic are based on the often unstated assumption that the set of numbers is closed under addition and multiplication."

The text goes on to list and explain the closure properties of addition and multiplication,
explains the set of numbers of arithmetic is not closed under subtraction.

A later but still similar edition is
Modern Algebra, Structure and Method, Dolciani and Wooton, Hougton Mifflin, Boston c. 1970,
(this one has the pendulum picture on the cover.)

Yet already content is removed and moved.

3.1 leaves out all discussion of axioms of equality, relegating them to one pink box, no explanation.
The bit I quoted above, "you learned.....fundamental assumptions..." is not here at all.
The content of 3.2 and the axioms of closure are in 3.1 instead, including what I quoted above, "Any set S..." so the language that is preset isn't always simplified, but some is missing.
A discussion of how the set of odd numbers is closed under multiplication but not addition stayed in, but the statement that the set of numbers of arithmetic is not closed  subtraction is taken out.

3.3 and 3.4 in this 1970 edition are totally different, however. Their material is about
adding and subtracting real numbers on the number line, material in chapter 4 of the 1962 edition. still,  it's similar, some of it the same.

This book is one I managed to procure ten of to teach with. I need more, but so does everyone else, whether they know it or not. Anyone know if HMH ever grants permission for a fee to someone to copy their out of print books?

Then we come to lousy. Algebra, Structure and Method, Dolciani, Wooton, Sorgenfrey, and Brown, ISBN 0-395-26637-8, c. 1979 is a horse of a different color.
Gone are the explanations. Gone are the depth of problems. Gone is the mathematically deep and proper language.  Wholly new material is added and it is watered down.

3.1 is now "Rules for Multiplication". It states:

"To learn how to multiply negative numbers, notice that
2 x (-1) = -1 + (-1) = -2
3 x (-1) = -1 + (-1) + (-1) =-3
and so on."

The next sections go on to transform equations by multiplication and division,  even though in the prior books, doing those sections came after introducing the axioms of equality, closure, opposites, etc.

In 3.8, the total explanation of axioms is given:

"Many rules or number properties have been stated earlier in this book. Some are axioms. Others are theorems. An axiom is a statement that is assumed to be true. A theorem is a statement shown to be true by using axioms, definitions, and other theorems in a logical development. The axioms that account for the rules or properties used in working with real numbers are listed below."

And then there is a list. No explanation of closure at all, no explanation about the use of axioms.

Exercises are far cry in content. Six oral exercises as opposed to 30, 20 written, except with nearly all of the work done for you (2 column proofs, steps provided, you fill in the property)
no problems at all about what sets are closed under what operations.

Nonetheless, I did find 30 of these, and we use them. It still has more problems and exercises than nearly any other book these days. But the teacher really uses the other 10 books as the base.

Even worse is Algebra, Structure and Method, Dolciani, Brown, Cole, ISBN 0-395-43053-4, c. 1988.

This book managed to drop an entire chapter by Chap 2. Chap 2 "matches" the old chap 3, Addition and Multiplication of Real Numbers. But it has no mathematical language. No use of "set", no explanation in general about closure, nothing of the kind.

Now, chap 2, Working with Real Numbers", begins with

"The rules used in adding and multiplying real numbers are based on several properties that you can take for granted.  For example, the following statements are accepted as facts.
1. Every pair of real numbers has a unique (one and only one) sum that is also a real number.
2. Every pair of real numbers has a unique product that is also a real number.
3. When you add two real numbers, you get the same sum no matter what order you use in adding them.
4. When you multiply two you get the same product no matter what order you use in multiplying them."

It doesn't get much better. No precision, no formalism.

Worse, the whole thing above is misleading. Nowhere does it explain that various subsets of the reals *aren't closed* under addition or multiplication. Nowhere does it ask students to determine closure.
Nowhere does it even explain a set.

Now, I just compared 3.2 for ease. I didn't cherry pick for the most egregious. But every page, every sentence is rewritten in these later editions. The relationship to the 1970 work is not recognizable.

This phenomenon is known in college level math and physics books, certainly--my 2nd ed Thomas (no Finney yet) calculus is a thing of beauty. My 3rd edition Kittel Thermal Physics is too. The later editions are dreadful. But most people don't know this about high school texts.

Suffice to say, the 1970 books will be even rarer now that people know to look for them, but if I were homeschooling or running a small class, I would spend the premium for the oldest you can possibly find, and junk anything from the 80s on.

Steve H on Common Core in his town

from Steve:

In our town, life is going on just about the same. We still have Everyday Math and only those kids with help at home will get to algebra I in 8th grade and have a chance of getting to a STEM career. High school kids still pack their schedules with honors and AP classes while ignoring the meaningless state tests. The CC PARCC test will be no different. Students worry about the PSAT and SAT, but ignore the state tests. They are meaningless for them.

However, there are still many kids who will now have to meet these state test standards to get their high school degree. These are tests that try to judge one's thinking and understanding abilities, not just mastery of basic skills. They are the ones most hurt by these fuzzy tests. Classroom teachers should be the ones best able to judge these qualities, but it's now turned over to test makers who try to boil that ability into a few understanding-type questions on the state test.

Why should students fail to graduate high school when they pass high school courses but flunk a fuzzy state test? This is a failure of the school or the test. Why should minimal passing grades be based on fuzzy understanding rather than mastery of basic skills? How do these tests give teachers any feedback on how to improve? When my son was in first grade, I was a member of a parent-teacher team that evaluated our state test results. The test gave thinking-type questions where they (magically) split the results into areas like number sense and problem solving. Rather than directly test to see if students can add, subtract, and handle percentages and fractions, they test to see if they "understand".

So here we were sitting around a table discussing what could be done to fix a lower school score in "problem solving". The answer was to spend more time on, you guessed it, problem solving. If they tested something directly, like fractions, that would give them much better feedback. But then again, they should be doing that already. A state test should only be used as a last-resort check for systemic school failures, not as a means to check for "understanding".

The downside to CC is that many more will point to it as rigorous path that is meaningful to the development of their kids. I'm also waiting to see if our 7th and 8th grade math texts are watered down. A few years ago, we managed to get rid of CMP and replace them with the same strong algebra textbooks used by our high school. Common Core might now force us into a less rigorous path.

I attended the SRO Common Core shindig in my district last night.

Irvington kids are going to be inferencing for 13 years.

Inferencing and problem-solving because, in the real world, math has more than one right answer.