## Saturday, October 26, 2013

### 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

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

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

And this is what we're using.

Because, you know,

Those are the magic words,

So here we are:

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.

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:

- The children have no math textbooks
- 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 - 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
- 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
- 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) - 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.

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....

## Friday, October 25, 2013

### 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

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.

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:

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

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

(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.

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:

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:

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

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

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.

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 i**s 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:

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.

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

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.

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.

## Thursday, October 24, 2013

### Help desk - How much do focus groups cost?

Does anyone know?

How much does it cost to hire a firm or an individual to run focus groups and write a report?

What I would specifically like to know is the prices for a firm not associated with the public education world to do this.

How much would it cost to hire a political polling firm, for instance?

If any of you has information, I'd love to hear.

How much does it cost to hire a firm or an individual to run focus groups and write a report?

What I would specifically like to know is the prices for a firm not associated with the public education world to do this.

How much would it cost to hire a political polling firm, for instance?

If any of you has information, I'd love to hear.

## Tuesday, October 22, 2013

### Is the S finally hitting the fan?

From Allison, on EngageNY:

The problem is the name has changed, but the song remains the same.Given the difficulty of the Common Core tests, I wonder if we'll see so many parents up in arms that .... that school boards will finally have to wake up.

Common Core is the new "new Math", unfortunately the umbrella name for everything happening in math ed these days as the standards get put in place, including things that really have nothing to do with standards.

The Common Core State Standards were, and are, a set of standards. Standards are lists of requirements. It's true that CCSSI were more proscriptive than typical standards, but they were still just standards. Standards are not curriculum. For more on this, see my post.

The CC standards in k-8 are better than NY's previous standards. That is about the end of the good I can say in NY's implementation of the new standards.

For whatever reasons, probably largely related federal funding, states adopted CCSS. Except they did so before any textbooks had been written. And before the assessments against the standards had been written.

So NY schools and teachers were supposed to magically teach from the new standards about which they had been told nothing, or use hastily repackaged curricula that wasn't really changed, or who knows what.

But help was on the way! Engage NY was created! It would be an entire curriculum online, free to everyone, digital! No need for textbooks! Isn't that great? And famous mathematicians and math teachers who are pro Singapore math had signed up to lead the writing of the curriculum on EngageNY.

At some point last spring, I saw several job reqs from EngageNY. They needed curriculum writers. I considered taking the position. Then I looked at what was already on EngageNY.

I saw a fraction lesson that was fundamentally wrong from beginning to end. I saw other lessons with equally egregious errors. I told someone who told someone high up at EngageNY. The response was, yes, it's wrong, and the writer was informed, but the writer could not understand what was wrong with it and refused to rewrite it, saying they knew it was better for kids this way.

EngageNY is still beholden to the same NYS ed people. The math people who were supposedly leads don't control the curriculum; the bureaucrats do, and are actually telling the math people what the scope and sequence must be.

This is now all called "Common Core."

Till now, the math warriors in any community were always a minority, but now everyone's child is failing math.

That said, here in Irvington sentiment in the one and only survey ever taken on the subject, was around 80% anti-Trailblazers, and the board still voted to reject Singapore Math & keep Trailblazers.

Of course, the Interim Curriculum Director announced at the time that the survey was favorable to Trailblazers. She also announced,

*again*, that the Parents Forum (me) had misled the public.

I always enjoyed that, sitting in the audience at school board meetings, being slandered via innuendo.

Or is that libeled?

I never remember which is which.

I learned the legal meaning of the word innuendo through direct personal experience of innuendo about me, purveyed by sitting members of the school board and by central administrators.

I'm going to go read the link Allison left to Wu's piece now.

### Yes, Vitamix will change your life

Just got this link from Chris....

Can a $400 Blender Change Your Life? Yes:

Can a $400 Blender Change Your Life? Yes:

“I love my Vit-a-mix,” she continued, enunciating each syllable, before launching into a highly complimentary review of the company’s return and repair policy. “I love it so much, I would recommend it to the dead!”My thoughts exactly.

### Worse than you think - Common Core edition

(Family motto)

So. My district.

No longer has Math Trailblazers.

With the predictable results.

Lost the battles--

Wrong!

My district does have good math scores, comparatively speaking, and I continue to think our math scores are 'real,' not a product of random variation. But we'll see.

The appearance of timed worksheets and better math scores coincided with our losing all the battles; that part is true, too.

It's the last part that doesn't track, the

The battle to get rid of

We have no curriculum, in my view (I'm not going to be taking this one back), and we have no textbooks. Little kids are coming home from school in tears, not knowing how to do their math homework.

When parents complain, they are told "

So I am told.

Meanwhile our new curriculum director (another battle lost) is engaged in a multi-year effort to "map" the curriculum.

When she is done, the curriculum will be modular; we will be able to swap out old units and swap in new units whenever the state passes a new curricular mandate. No word as to whether ease of unit-swapping will solve the problem of gaps.

So yesterday I asked for a copy of the district's scope and sequence, K-12.

Not sure why I didn't do that years ago. It's funny how there are always some lines you feel you can't cross. I'm reasonably certain the district doesn't

I do remember, I think, asking for copies of a math syllabus back when C. was in middle school -- I think Debbie S. may have done the same. I'll check. I think we were both told we couldn't have copies of the syllabus, but the details are hazy now....Actually, as I think about it, the then-Assistant Superintendent finally sent me a syllabus, which I discovered was for the old class with the old textbook. The district had adopted new textbooks that year, and as far as I could tell no one had written down a syllabus based on the book teachers were actually using.

I'm going to have to go through my old emails one of these days...

In any event, where the possibly apocryphal Irvington scope and sequence is concerned, now's the time. Presumably the high school classes have syllabuses (

Beyond that, I don't want to hear that young children are coming home crying over math and

The problem isn't

Crying and blogging.

I have to check in with Allison, who is I think on top of the NY situation vis a vis

I love knowing someone in

UPDATE 10/26/2013: We have replaced Math Trailblazers with "math modules" from engagny, which somebody downloads from the internet. The engageny curriculum has yet to be completed, so...let's say we have replaced Math Trailblazers with part of a curriculum. A brand-new, never been taught, never been learned from math curriculum you have to download from the internet.

So. My district.

No longer has Math Trailblazers.

*Does*have timed worksheets.With the predictable results.

Lost the battles--

*all*of the battles--won the war. That was my conclusion.Wrong!

My district does have good math scores, comparatively speaking, and I continue to think our math scores are 'real,' not a product of random variation. But we'll see.

The appearance of timed worksheets and better math scores coincided with our losing all the battles; that part is true, too.

It's the last part that doesn't track, the

*lost all the battles, won the war*part. Normally when people lose all the battles they lose the war, too, and that's what happened here. We lost all the battles,*and*we lost the war--and we got better math scores in the bargain because somewhere in there, after ten or twelve years of parent uprisings, we got timed worksheets.The battle to get rid of

*Math Trailblazers*culminated in the district getting rid of*Math Trailblazers...*and replacing it with*.*__nothing__We have no curriculum, in my view (I'm not going to be taking this one back), and we have no textbooks. Little kids are coming home from school in tears, not knowing how to do their math homework.

When parents complain, they are told "

**COMMON CORE**" and sent to EngageNY. Some children have gaps because of**COMMON CORE**, parents are told. The younger kids will be in better shape than the older kids because they started**COMMON CORE**from the get-go & didn't have to suddenly shift over to**COMMON CORE**when the state commanded schools to shift over to**COMMON CORE**.**COMMON CORE**,**COMMON****CORE**:**COMMON****CORE**is the problem, and**COMMON****CORE**is the*explanation*of the problem, too.So I am told.

Meanwhile our new curriculum director (another battle lost) is engaged in a multi-year effort to "map" the curriculum.

When she is done, the curriculum will be modular; we will be able to swap out old units and swap in new units whenever the state passes a new curricular mandate. No word as to whether ease of unit-swapping will solve the problem of gaps.

So yesterday I asked for a copy of the district's scope and sequence, K-12.

Not sure why I didn't do that years ago. It's funny how there are always some lines you feel you can't cross. I'm reasonably certain the district doesn't

*have*a scope and sequence--a friend of ours was told so directly when he asked for one maybe 15 years ago--and for some reason I've felt I shouldn't put people on the spot by asking for something I'm pretty sure they don't have.I do remember, I think, asking for copies of a math syllabus back when C. was in middle school -- I think Debbie S. may have done the same. I'll check. I think we were both told we couldn't have copies of the syllabus, but the details are hazy now....Actually, as I think about it, the then-Assistant Superintendent finally sent me a syllabus, which I discovered was for the old class with the old textbook. The district had adopted new textbooks that year, and as far as I could tell no one had written down a syllabus based on the book teachers were actually using.

I'm going to have to go through my old emails one of these days...

In any event, where the possibly apocryphal Irvington scope and sequence is concerned, now's the time. Presumably the high school classes have syllabuses (

*syllabi*) and it's time for the community to see what K-8 has.**UPDATE**: We don't have a scope and sequence and never did. Confirmed in BOE meeting of 10/22/2013.Beyond that, I don't want to hear that young children are coming home crying over math and

**COMMON CORE**did it.The problem isn't

**COMMON CORE.****Children crying about math in Irvington long pre-dates**

**COMMON CORE.****Heck,**

*parents*crying about math in Irvington long pre-dates**COMMON CORE**.Crying and blogging.

I have to check in with Allison, who is I think on top of the NY situation vis a vis

**COMMON CORE**math.I love knowing someone in

*Minnesota*who can explain my own state education department's math situation to me.UPDATE 10/26/2013: We have replaced Math Trailblazers with "math modules" from engagny, which somebody downloads from the internet. The engageny curriculum has yet to be completed, so...let's say we have replaced Math Trailblazers with part of a curriculum. A brand-new, never been taught, never been learned from math curriculum you have to download from the internet.

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