Wednesday, September 25, 2013

Letter to the Tampa Bay Times - Common Core Standards

    This letter was written in response to the Tampa Bay Times' constantly dismissing all objectors' concerns about the Common Core Standards as coming from members of the Tea Party.  I have nothing at all against the Tea Party and what they stand for, but I'm not a member of that organization and neither are many of the other people who have voiced objections to these awful Standards.  I don't know if they'll print the letter - it got a bit long - but either way, here it is.

September 25, 2013
To: Tampa Bay Times

Common Core Standards

The people objecting to the Common Core Standards are members of many different political parties including Republicans, Democrats, Libertarians and Independents.  The TB Times does a disservice to its readers by constantly referring to all objectors as “Tea Party members”. 
In addition to the valid criticisms of being top-down, one-size-fits all, un-Constitutional, and extremely costly, many of us are very concerned with the poor quality of the Standards themselves.  We’ve arrived at these opinions through carefully reading these Standards as well as studying plentiful commentaries and articles written by professionals who give thorough and reasonable explanations for their concerns.  I agree with the experts in Math when they complain that CC puts us two years behind other countries, for example, when I can read for myself that students are not expected to achieve proficiency at adding and subtracting using the Standard Algorithm until the 4th grade. (CCSS.Math.Content.4.NBT.B.4).   This isn’t surprising given the materials and methodology pushed by the CC-driven text books and assessments, especially when one examines some of the bizarre “alternative” algorithms taking up more and more time in CC classrooms across the nation.  Far from providing deeper understanding of Math concepts, this is leading to frustration and academic disengagement even in previously very good students who loved Math.  When these students’ college-educated parents admit to being baffled by what comes home in the name of 2nd grade Math, it is obvious that something has gone seriously wrong with the schools – not with the parents.  The Language Arts CC Standards are also very problematic and fly in the face of decades of research examining the knowledge necessary to succeed in college or anywhere else.
Many of today’s CC objectors are old enough to remember having our concerns over OBE, Whole Language and Discovery Math dismissed by the news media as the paranoia of The Religious Right and other “loonies” back in the 90’s.  Then we had to listen to this same media complain about their loss of readership, the decline in literacy and the breathtaking lack of skills and knowledge in our workforce.  The fact is that there are reasonable people who have valid doubts that this latest fad is any better than the long line of previous, now discredited trends.  It is time that parents’ concerns are taken seriously – and I mean that parents should be given the right to choose a different course for their children when the public school system – again – goes off on one of its ill-considered tangents.  We need parents’ choice.

Katherine Livermore, Secretary
Independent Voices for Better Education


Sunday, August 11, 2013

Cookie Cutter Schools

It was a recent conversation with a mom from Pennsylvania (let’s call her Laura) that brought me to a better understanding of America’s “one-size-fits-all” schools and the stratifying effect they have been having on our society.  This lady lives in a very affluent, suburban neighborhood outside of Philadelphia and has 15-year old twin boys.  She described her children’s schools as “very good”, (and I thought, “Wow how lucky!”) – and then she began the litany of complaints. 
She started with how her sons were taught Math.  When they were little, the boys would come home with these bizarre homework assignments that neither she nor her husband could figure out how to help them with.  These are both college-educated professionals.  Have I seen the lattice method?  Sure have. Laura and her husband bought supplementary Math work books that had practice sheets.  Then the parents took turns almost every school night plus many hours during weekends and summer vacations at the kitchen table teaching them the correct way to solve Math problems.  Laura described these correct methods as the way they themselves had been taught which were, of course, the Standard Algorithms. 
I nodded my head – it’s the same down here.  As a tutor I have spoken to many, many parents about this same thing.  The kids would be trying to solve a division problem, for instance, and the first thing they did was start drawing all these bubbles all over the paper.  Laura saw that in her sons’ school as well. 
Or they would try to solve fraction problems, but had forgotten their multiplication facts.  About two years can separate the schools’ work on the tables (3rd grade – and we’re talking about an all too brief attempt at rote memorization) and the introduction of fractions (5th grade).  During this time, the material covered is so fast-paced, over-loaded with disconnected skills, and poorly sequenced that the gradual building of complexity in using multiplication appears to have been lost in the crowd.  Almost never do I meet a student of any age who has had enough (or any) practice in using two and three digit multipliers, while the neglect of the Standard Algorithm in division can apply to simple one digit divisors, let alone two and three digit divisor problems.  (The absence of division instruction was one of the most criticized points in the NCTM-written standards of the OBE days.  They’ve effectively done away with this function anyway, despite all our protesting.)  Once the connection between multiplication, division and fractions is demonstrated to my tutoring students, they are astonished!
It’s the logical, building-block sequencing in the practice of increasingly complex operations that helps a child internalize the basics, such as the multiplication tables or the step-by-step procedures used to solve elementary arithmetic problems. Many parents know this and believe strongly in the importance of plenty of paper and pencil work despite - or maybe because of - their not having Education degrees.  Too often, however, when these parents try to show their kids how to solve Math problems, the kids will protest that that’s not how they do it in school.  But the kids can’t do it the way the teacher showed them either, nor can they explain this new way to their parents. The books, when they come home at all, are poorly written and will have only one or two examples showing procedures which will not even cover all the different quirks and ramifications of the exercise problems the kids have been assigned to figure out.  (This is experience speaking here.)  It is lose/lose.  The end result is usually a build-up of frustration on both sides, and the child’s loss of respect for the hapless parents.
The Pa. schools don’t teach cursive anymore either.  Laura believes that cursive is very important – how can anyone sign their name if they haven’t learned cursive?   I nodded - it’s the same in Fl. They pretend to teach cursive for like two weeks or so, then it comes to a screeching halt, and the kids go right back to printing.  The printing is illegible because many schools don’t teach how to hold a pencil and, if the kids start at the wrong place and head in the wrong direction, they are not corrected.  (Dyslexia is such a lucrative little diagnosis.)  The kids end up trying to invent how to write the letters themselves which is usually backwards, upside down and in the wrong positions. 
Laura said they had the same situation up north.  Plus there is no keyboarding instruction.  She was very indignant about this.  The reason the schools give for not bothering with cursive anymore is because everyone will be typing everything.  But then they do not provide any kind of formal training in keyboarding.  In their earliest days of school, this mom took on the task of teaching her sons how to print and write cursive correctly, plus made sure they knew how to keyboard better than the default, two-finger hunt & peck.  It’s a good thing she started this so soon, because once a child has a few years practice forming their letters wrong, it’s a horribly difficult habit to break.
Spelling?  Spelling tests are gone in the schools she knows of in Pennsylvania, while in Florida, they are sometimes still seen in the earlier grades.  They are pretty hit or miss though – I’ll ask my students how they’re doing on all their subjects, and they’ll tell me they haven’t had a spelling test for a while.  I told Laura that back in the late 90’s, when my kids were still in a public middle school, the tests had devolved into a multiple choice format.  When I complained to the principal, he told me that that’s how he did it when he was a teacher.  Plus there are a lot of times where spelling is seen as unimportant, like in the kids’ daily journals.  Laura hadn’t seen any multiple choice spelling tests, but she remembers being appalled by her sons’ daily, error-filled journals and also complained about all the “rough drafts” the kids are always writing even now when they are in high school.  No one ever used to turn in rough drafts.  We turned in the best work possible, and if there were errors, the teacher marked them – in red – and we would take the papers home, fix them and turn in the corrected paper the next day.  This is how kids learn – and this has not been happening in America’s public schools for quite some time now.
Neither the rich Pa. nor mixed-income Fl. schools of our acquaintance spend significant time teaching grammatical rules, parts of speech or variety of sentence structure.  I’ll have a student recite that a noun is a person, place or thing, but be unable to identify the nouns in a sentence.  They won’t know what a verb is until reminded – but helping verbs, adjectives, adverbs – nada.  Prepositions? Please.  Verb conjugations?  Subjects and predicates?  Compound sentences?  Comma placement?  Not that either of us have seen.  There wasn’t anything she could do about her kids’ journals since they stayed in school, and she only got to glance at them during parents’ nights.  But as often as she could get her hands on her sons’ written work, Laura has been doing the correcting herself, from elementary school and right up into their high school years.  Lucky you, I said.  The Florida parents I know of almost never get to see their children’s work.  When they do, it’s the same story.  If you ask the teacher why none of the mistakes are marked, it’s to save the child’s self-esteem.  Right – like illiteracy is good for self-esteem.  And whatever happened to diagramming sentences?  Gosh – who isn’t asking that question?
We must have compared our respective school experiences for an hour.  Skimpy phonics instruction – check.  Called “coincidental” by the pro-Phonics millions, this is known as “eclectic” in Florida.  Having higher achieving children tutor lower achieving children without first instructing the little tutors in how to teach?  You bet.  Group seating and group projects – check.  They call it cooperating and collaborating in school and cheating everywhere else. 
The homework brought home veered from none at all to infantile nonsense to pointless, time-consuming “projects”.  Laura said she would prefer no homework at all to the stuff her sons spend so much time trying to get done.  I told Laura about one high school Senior I knew who spent hours designing a color chart – for her Honors English class.  This was a very intelligent young woman, but her English SAT scores were awful.  Go figure.  Sadly, she wanted to be an English major. 
Laura told me she worried about how well many of her children’s friends would do in college – the kids who did not have their parents spending so much time with them or even getting them tutoring.  Together we wondered how the kids could be learning much about History or Science when no books ever come home, and homework projects don’t seem to be teaching them anything either.  She actually has no idea what her boys have been studying in those subjects.  It is certainly hard for me to believe that schools that do such a poor job teaching the most basic of skills and knowledge would suddenly become terrific at imparting thorough, accurate, engagingly presented and politically neutral content in these areas.  According to college and university professors, as well as the American population at large, these bodies of knowledge are also being neglected in our public schools.   Generally, parents who do much of the teaching at home are hard pressed to keep up with the dearth of grade-level basic skills, and will not think to read History and Science text books with their children.
Finally, I pointed out that while we were both describing almost identical schools, I described them as “really crappy.”  What was it that made her think of them as “very good”?  Laura answered that the schools where she lives are considered excellent because all the kids get high SAT & ACT scores, and every single kid gets into a prestigious college or university.  There is no lower income cohort that does more poorly?  No flunking?  No dropping out?  No.  Every single child gets into a good college.  Wow.
I hearkened back to a couple experiences I had when my kids were still in the public schools during the beginning of OBE.  At an open house at my son’s middle school, one of his teachers and I started talking about all the changes going on, and she kept repeating the phrase, “Everything depends on the parents.”  She was staring at me intently, so I stared intently back at her and said, “If it takes a village to raise a child, when are the schools going to be kicking in with their part?”  (Hillary’s village was HUGE back then.)  “Everything depends on the parents.”  She was a good teacher and retired shortly after.
There was also the time I spoke with a representative of the Federal Department of Education.  He was down in Sarasota investigating claims of discrimination, and I was positive that the withholding of skills and knowledge from young school children was definitely discrimination.  He kept asking me if I knew of any instance of different treatment and, of course, I didn’t.  No one was being taught phonics or grammar or anything else, at least not in the public schools.  Then there was nothing he could do because, according to the law, as long as all students were receiving the same treatment, there was no discrimination.  So discrimination for all is OK?  He shrugged his shoulders – there was nothing he could do.  I yelled, "You’re getting blamed for this, you know!"   And, indeed, he did know.
This, then, has been - and continues to be - the true essence of Outcome-Based Education. With the input of this nation’s cookie-cutter schools held constant - as identical and as inferior as possible - the basis of the schools’ reputations has become the outcomes, and those outcomes will depend on how well the students’ families overcome the deficiencies of their children’s schools.  In fact, the modern school’s biggest accomplishment has devolved into an assessment of the parents’ performance.  This explains why poorly performing schools so often whine that their students’ parents are just refusing to do their jobs. It’s why one of the biggest arguments against objective teacher evaluations is that the schools can’t be held responsible for their students’ test results.  They say stuff like this with conviction!  Of course, the way things are now, the schools are all too sadly correct.
 This Darwinistic, family as destiny, survival-of-the-fittest structure has been assuring the perpetuation of an ever more rigid class system.  To a certain extent, this outcome dichotomy will break along income lines simply because higher earning parents have more of the skills and knowledge necessary to help their kids through the morass.  The illiterate, the innumerate, those whose schools have treated them shabbily in their own turn are not only unable to do the teaching themselves, but are also less likely to be earning enough to hire tutors let alone afford private school.  Our illustrious Educrats do want us to believe that everything hinges on money – because they want tons more of it.  But this is the Information Age, so it’s the families with the necessary “information” who will have the children who at least appear to be thriving in America’s cookie-cutter schools.

Why the American school system has become one where teaching is so degraded rather than one where all children receive equally effective books and teaching methods is the topic for another to handle.   For now, I can state - with conviction! - that Common Core is more of the same shabby treatment.  We need Parents’ Choice.

Tuesday, July 9, 2013

Orlando, Florida Anti-Common Core Protest Rally

On Saturday, June 29th, a large crowd of parents, grandparents and well-informed citizens gathered in front of one of the entrances of the J W Marriott Orlando Grande Lakes Resort and Spa to protest the Common Core Standards.  The weekend long event taking place inside the Marriott was the National Common Core Convention, where training, morale boosting and pep talking were available to educators of all levels.  They did the exact same thing when it was Out-Come Based, Blueprint 2000, and Whole Language coming in back in the 1990’s.  Pictures really are sometimes worth a thousand words, so here they are.

Thursday, June 13, 2013

Letter to Pasco County School Board & Administration

Dear (School Board, Supt. & Asst. Supt):

There has been a great deal of controversy over the implementation of the Common Core Standards.  Indeed, several of the states that had previously accepted the Standards, along with the federal money that came with them, have been reconsidering.  These Standards were often accepted without having been read by the state-level parties responsible.  Now that they’ve been examined by many more people nation-wide, including Education professionals, psychologists, parents and many groups traditionally concerned about the well-being of children, the level of concern has heightened considerably.

This isn’t just about the cost.  I’m sure most Americans would agree that if the Common Core was believed to be an improvement in our schools’ curriculum and methods of delivery, no amount of money would be too much.  The problems most evident to me and others, however, are that the materials, methods and even sequences of instruction in both the Language Arts and Math Standards would be large steps backward, and sometimes even counter-productive, just as we have been working so hard to bring about improvements in academic achievement for all students.

The number of articles, sites, and blogs, etc. addressing this issue have become very numerous, so I have chosen just a few to send to you that I felt were especially clear in explaining how these Standards could cause problems in the future for our students.  For Language Arts, there are two videos – one showing examples of 1st Grade Writing and Reading books and assignments, and the 2nd is a video of a Psychologist explaining why curricula such as this is inappropriate for young children.  I’ve also included an article by an Educator who very clearly explains why an over-reliance on informational text can be damaging to the academic development of students of all ages.  There is much written about the Math Standards as they pertain to the higher grade levels, but the problems with the Math goals begin much earlier than that.  I’ve included a couple posts from my own blog which examine the elementary level of the Common Core Standards.  Common Core books for first, second and third grades, mainly. 

A Clinical Mental Health Therapist's opinion about Common Core materials she reviewed from the video, above.

The first post below is an article about what is going wrong with today’s math teaching methods and material.  The second article answers the question, “Is Common Core going to fix this?”

(Blog Reader, please see "Invented Math & Common Core Elementary Math Standards posts))

In light of these and so many other concerns and doubts as to the positive effect of the Common Core Standards on our students, IVBE believes, should any particular schools still decide to implement them, that parents with children in those schools be given the choice as to whether they desire this or some other curriculum.  It would also be in the best interests of the students that should the Common Core be seen to have a detrimental effect on a student’s learning, that the parents of that child be given the option to remove the student from the Common Core classroom.  These conditions would have the added benefit of giving teachers the choice of standards and methods as well.  This way, we would be moving closer to choices for parents, teachers, and schools instead of further away from choice, which is another fly in the Common Core ointment.

Thank-you for you consideration,

Katherine Livermore, Secretary

Independent Voices for Better Education

Saturday, April 27, 2013

New Math – Creative Estimation

Ever since the 90’s, when Outcome-Based goals were adopted by just about every public school in the United States, one of the most frequent complaints about Fuzzy Math has been the over-emphasis on estimating.  Along with insisting that students try to calculate answers using a multitude of convoluted, ultimately baffling methods, this is another way time is taken away from practicing actually solving mathematical problems with the standard algorithms.  Teaching children the familiar method of rounding to various place values, however, has taken a back seat to “creative and innovative” contrivances invented by the Experts. 

One of the “new math” estimation methods that recently came to my attention is the use of “compatible numbers”.  The following examples came from the 6th Grade text book titled Big Ideas Math (Florida Edition), copywrite 2010.  One author is Ron Larson, whose Bio includes all kinds of high-faluting accolades, including a Ph.D. in mathematics from the University of Colorado in 1970.  The second author is Laurie Boswell who teaches math in Vermont, has received the Presidential Award for Excellence in Mathematics, and – most important – has served on the NCTM Board of Directors.  The latter  (National Council of Teachers of Mathematics) is the group of alleged math experts who, among other things, don’t believe in paper and pencil exercises, have effectively done away with teaching long division, and continue to push doing even the most basic computations on calculators.  I’ve included all this information about the people who are at least in part responsible for the state of math skills in this country to show that these folks are considered at the very top of their field.  It is too easy for parents and others to become so cowed by all the degrees and awards and honors, etc. that they feel their concerns must be baseless.  What is happening in our public school classrooms, however, warrants a serious look beyond the professional glitz.  Here are some examples of what these Experts have our kids “learning”.  (I've included photos because my typed fractions are confusing.)

First the students need to know their fractions really well (my students do not).  In the first example of estimating products of fractions, 3/8 rounds up to 1/2, and 11/12 rounds up to 1 so 3/8 x 11/12 ≈ 1/2 (11/32).  In the next, 4/5 rounds up to 1, and 1/6 rounds down to 0 so 4/5 x 1/6 ≈ 0 (2/15).  

In estimating products or quotients of mixed numbers, 5 ¼ rounds down to 5, and 3 9/10 rounds up to     4 so 5 ¼ x 3 9/10 ≈ 20 (20 19/40).  In the second example given for this type of problem, 11 5/6 rounds up to 12, and 2 2/3 rounds up to 3 so 11 5/6 ÷2 2/3 ≈ 4 (4 7/16).  (I have no idea why there are no examples of estimating the division of fractions.)  (These are all found on pg. 46)

Okay.  I have no memory of estimating fractions myself, but I actually have no objection to learning the comparable sizes of them well enough to do so.  Many of today’s students do not have this solid grounding, however.  Then, to make matters even more complex, the authors introduce “compatible numbers” to the mix.

“Compatible numbers are numbers that are easy to compute mentally.” (pg. 47)

For solving 275 ÷ 3 ¾, first we round the 3 ¾ up to 4.  Then we realize that 4 does not divide evenly into 275 – so we change it.  If somehow the students have grasped how to round mixed numbers, this is where many of them will fall flat.  They are assumed to know that they can change 275 to 280 which is much more convenient for dividing by 4.  275 ÷ 3 ¾  ≈ 70 (73 1/3).  (Please understand that most of the students who come to me needing help with this kind of work do not know their multiplication tables.)

This was totally new to me, so I worked several problems (pg. 48) to see if I got them right before trying to guide one of my students through them.  As it with so many of today’s Math text books, half of the answers are in the back of the book – all the odd numbered problems in this case.  I was doing pretty well until I got to ¾ x 1/3 which I estimated as 0 (1 x 0), but the answer in the book is ½.  Then I got to 48 ÷ 6 7/12.  First I rounded the 6 7/12 up to 7 & then changed 48 to the more convenient 49 and came up with 7.  The estimated answer given in the book is 8. The actual answer is 7 5/13.

Is it any wonder?

And another interesting tidbit – this stuff is NOT on the FCAT.

Thursday, March 7, 2013

Common Core Elementary Math Standards

Let’s get this out of the way right now – the criticisms complaining that the Common Core Standards are the Federal government’s taking over of the schools - and the loss of local control - are completely moot.  That happened ages ago!  The 1990’s OBE/Blueprint 2000 goals for Reading, Math, History and Science were written by various committees at the Federal level.  That’s why the states all have such similar stupidities written into their current Math standards.  The states’ DOE’s took the Federal money along with the Federally written goals, tinkered with them enough to make them even worse and called them their own.  There was a huge uproar over Whole Language and the History standards so there have been rewrites of them, and Science is apparently still a battle ground, but the Math standards of today pretty much date to the horrific ‘90’s.  There are plenty of books and articles written about the history of education in this country which explain how and when this happened far better than I could.  What I’m doing here is examining these new standards from my perspective as a tutor, mother and grandmother in order to judge them on their own merits.

They Make It Sound So Good

At first I found myself liking the new Math standards quite a bit.  After the confusing, overwrought hodge-podge of current standards, they are almost poetic in their simplicity.  In fact, the authors mention their intent to correct the “mile wide/inch deep” errors of today’s goals.  If you click below to the 2nd Grade standards, for instance, you will see a much more realistic, pared down and far more grade-appropriate list of goals that are separated into four main areas of study.  

These standards appear much more successful at assigning reasonable goals arranged according to the logical, building block sequences that would be recognized as normal by most parents.  In fact, there is a chart in the “Publisher’s Criteria” section of Resources (pg 9) that lists topics that should not be assessed before certain grade levels.  Parents will be surprised to learn that Symmetry in Geometric shapes should not be assessed (nor taught, it should be assumed) before Grade 4, and Probability should not be assessed before Grade 7.  These topics are currently to be found at much earlier grade levels in many text books, and have served to be major distractions from what should be the main jobs at the Elementary levels.  The Core authors go to great lengths emphasizing what the main topics should be in the younger grades.

The misuses of number models such as those shown in my previous blog are also addressed:

“Research indicates that students’ experiences using physical models to represent hundreds, tens, and ones can be effective if the materials help them think about how to combine quantities and, eventually, how these processes connect with written procedures.” (Adding It Up, p. 198,…). For example, base-ten blocks are a reasonable model for adding within 1000, but not a reasonable method for doing so; nor are colored chips a reasonable method for adding integers. …. The word “fluently” in particular as used in the Standards refers to fluency with a written or mental method, not a method using manipulatives or concrete representations.”

It’s always interesting to come across evidence that the Experts have been running experiments on children instead of educating them.  The above is but one example of the Core writers citing research that that has been subjecting multitudes of students to an obvious, ineffective use of manipulatives and “models”, as well as several other instructional errors, that I’ve heard parents complaining of for years.  I’m sure that besides the report Adding It Up (published in 2001 by the National Research Council), there have been many other reports, books and articles published on this subject.  I wonder how many kids were labeled as learning disabled as a result of never being adequately taught the correct way to add and subtract just so the alleged “Experts” could find out what everyone else already knows?  But I digress.

The Core authors also criticize what became known as “aspiral Math” which covered the same material year after year.  The review, or teaching, of earlier material while also teaching grade-level skills is something I deal with on a daily basis as a tutor.  I’ve had so many students come to me needing help with fractions who do not know their multiplication tables nor, of course, their division facts.  (In the quote below, I see a problem with the expectation of proficiency with the standard algorithm for division coming as late as 6th Grade.  Plus, the problem with division is not a problem with place value knowledge in my experience.  I deal with this further in my “So Bad” section.)

“The basic model for grade-to-grade progression involves students making tangible progress during each given grade, as opposed to substantially reviewing then marginally extending from previous grades. Grade-level work begins during the first two to four weeks of instruction, rather than being deferred until later as previous years’ content is reviewed. Remediation may be necessary, … but review is clearly identified as such to the teacher, and teachers and students can see what their specific responsibility is for the current year.”

“… materials often manage unfinished learning from earlier grades inside grade-level work, rather than setting aside grade-level work to reteach earlier content. Unfinished learning from earlier grades is normal and prevalent; it should not be ignored nor used as an excuse for cancelling grade level work and retreating to below-grade work. (For example, the development of fluency with division using the standard algorithm in grade 6 is the occasion to surface and deal with unfinished learning about place value; this is more productive than setting aside division and backing up.) Likewise, students who are “ready for more” can be provided with problems that take grade-level work in deeper directions, not just exposed to later grades’ topics.” (pg. 12)

It is great to see the end of measuring using “non-standard” units of measurement which had some lesson plans wasting students’ time measuring large lengths – such as room perimeters - with paper clips or pencils – this explains so many kids’ lack of skill with rulers.  In the measurement and data sections, there is mention of learning the smaller units within the larger units and using this knowledge to solve various problems (i.e. there are 12 inches in a foot, etc).  It would be refreshing to begin meeting students who know measurement facts to the point where students could add and subtract units of time, length or weight, etc.  How long has it been since kids were taught how to add 2 yards, 1 foot, 6 inches to 3 yards 2 feet 10 inches and convert the sum to the proper units?  The authors also specifically mention telling time using both digital and analog clocks – many of today’s teachers are under the impression that children do not “need” to learn to tell time with analog (face) clocks.  

The solving of word problems is given a great deal of attention.  So many of today’s children have a deep fear of these problems, which inundate the FCAT and many other state tests, because they are not explicitly taught the “clue words” to look for.

“The language in which problems are posed is carefully considered. Note that mathematical problems posed using only ordinary language are a special genre of text that has conventions and structures needing to be learned. The language used to pose mathematical problems should evolve with the grade level and across mathematics content.”   (pg 17)

The authors address the need for a math curriculum to be fully balanced between the practical and conceptual aspects of math and spend a great deal of time and effort in explaining exactly what they mean.  They make distinctions between practice exercises and solving problems while stressing the need for both.  I included the second paragraph below primarily for their examples of “conceptual problems”.  Today’s standards also make much of bringing about a student’s conceptual understanding of math, but the actuality of what is presented under that category has been so detrimental to achievement, that the phrase is starting to make people cringe.

“To date, curricula have not always been balanced in their approach to these three aspects of rigor. Some curricula stress fluency in computation, without acknowledging the role of conceptual understanding in attaining fluency. Some stress conceptual understanding, without acknowledging that fluency requires separate classroom work of a different nature. Some stress pure mathematics, without acknowledging first of all that applications can be highly motivating for students, and moreover, that a mathematical education should make students fit for more than just their next mathematics course. At another extreme, some curricula focus on applications, without acknowledging that math doesn’t teach itself.

“Materials amply feature high-quality conceptual problems and questions that can serve as fertile conversation starters in a classroom if students are unable to answer them. This includes brief conceptual problems with low computational difficulty (e.g., ‘Find a number greater than 1/5 and less than 1/4’); brief conceptual questions (e.g., ‘If the divisor does not change and the dividend increases, what happens to the quotient?’);”…(pg 10)

This Is Going To Be So Bad

Once I noticed that the NCTM was involved in the writing of the Common Core Math Standards, I knew it wouldn’t do to assume the best intentions based just on the simple listing of grade level goals.  The NCTM (National Council of Teachers of Mathematics) wrote the current standards that have been wreaking havoc with American students for at least the past twenty years.  So, a-wandering I went through all the various sections:  the Key Points, the Standards for Practice, the Standards by Domain, the Resources – including the Publishers’ Criteria (very important) and so on. 

As it proved with the current standards, the authors do not often lie outright, but use misdirection, the distortion of definitions as normally understood, and very carefully worded statements designed to placate the reader (including me for a short, happy time).  The Experts are very talented and well-practiced at telling the public what they know we desperately want to hear.  It is such an old tactic - much that the Core authors have written will have us nodding in agreement so often that our inclination is to keep nodding and nodding in approval even after we sense that we should begin to question or object. 

The problems begin with their seeming to state that they have adopted the goals of countries well known for their prowess in math.  In fact," International Benchmarking" and "International Best Practices" are the by-words of this latest set of standards.  This would naturally lead us to believe that our students will be taught just like the Asian whiz kids are, but that is not exactly what the authors are saying.

“The composite standards [of Hong Kong, Korea and Singapore] have a number of features that can inform an international benchmarking process for the development of K–6 mathematics standards in the U.S. First, the composite standards concentrate the early learning of mathematics on the number, measurement, and geometry strands with less emphasis on data analysis and little exposure to algebra. The Hong Kong standards for grades 1–3 devote approximately half the targeted time to numbers and almost all the time remaining to geometry and measurement.” — Ginsburg, Leinwand and Decker, 2009

“International benchmarking provides an additional tool for making every state’s existing education policy and improvement process more effective, offering insights and ideas that cannot be garnered by examining educational practices only within U.S. borders.  State leaders can use benchmarking to augment their “database of policy options” by adding strategies suggested by international best practice to the range of ideas already under consideration. Indeed, international benchmarking should not be a stand-alone project, but rather should function as a critical and well-integrated component of the regular policy planning process.” (pg.23)

We are NOT getting the Singapore Math standards! The Core authors are almost clear in stating here and in other sections of the Common Core site that they have chosen only a select number of educational features of higher-performing countries which “can (not “will”) inform” the states’ process of developing K-6 Math standards.  They have opted to focus on the grade-level topics that these other countries target, but that does not mean that our public schools will be using any of the other academic features of these countries.  Culling inappropriate topics will do our children no good without all the rest that these other nations employ to assure their students’ success.  However, the Core folks clearly state in more than one area that the Core Standards do not adhere to International Standards to the point of mandating any particular curricula, materials nor, even more importantly, teaching methods which are very much a part of intensive teacher training and evaluation in the more math-proficient countries. 

“These Standards do not dictate curriculum or teaching methods. For example, just because topic A appears before topic B in the standards for a given grade, it does not necessarily mean that topic A must be taught before topic B. A teacher might prefer to teach topic B before topic A, or might choose to highlight connections by teaching topic A and topic B at the same time. Or, a teacher might prefer to teach a topic of his or her own choosing that leads, as a byproduct, to students reaching the standards for topics A and B.”

The phrasing makes it seem as if the benchmarking in the USA is to act more as a reference than as a mandate to the states – somewhat interesting reading, in other words.  (And, really, The Feds aren’t allowed to mandate, are they?)  The most we can expect from the statements above is that the various states will be spending gobs of taxpayer money doing (allegedly their own) Standards rewrites that will include the phrase “International Benchmarking” a lot, but won’t be actually making much use of those much better International Standards.  This becomes obvious as we continue our reading.

Another very strong clue to the bitter disappointment we and our children will be experiencing with these Common Core Standards is the severe restriction in access to the Standard Algorithms for basic arithmetic operations.  Looking at the 2nd grade goal dealing with adding and subtracting, we find:

CCSS.Math.Content.2.NBT.B.5  Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.”

This is misleading; the public will assume that this indicates the learning of the Standard Algorithm because that method uses place value as well as the relationship between adding and subtracting to solve problems. The truth lies in the distinctions the authors themselves apply in their use of language.  Accordingly, our public school 1st, 2nd and 3rd Graders are to be subjected to the same confusing, ineffective, multiple-strategies methodology that our students currently struggle with.  The actual wording: “Fluently add and subtract multi-digit whole numbers using the standard algorithm,” is not seen until Grade 4.  Multiplication using the Standard is delayed until 5th Grade, division until 6th Grade.  All four basic operations using decimals wait for the Standard Algorithm until 6th Grade.  The grade level sections on fractions – and all the “conceptualizing” that goes with them – I found very confusing as I searched in vain for any mention of the use of the Standard Algorithm.  Far from being balanced in juxtaposing procedure and concept, as claimed by the authors multiple times, the Core tilts so far toward “concept” for so many years that procedure is in grave danger of ever being achieved.  Surely many 4th Graders will have given up hope of ever performing the super complex function of - adding.  Are we really supposed to believe that the Experts think it takes four years to grasp the ideas behind adding and subtracting?

Much like today, students are also to try to figure out how to solve problems on their own without benefit of explicit instruction.  According to the Experts, this will take a great deal of perseverance on the part of the students – students must not be allowed to give up, which of course they would be pretty likely to do since they are not to be taught the skills nor knowledge it would take to solve them.

Under CCSS.Math.Practice.MP7  “Look for and make use of structure:
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, …”  

Very young students struggling to add - because of teachers insisting that they use ten different, inane methods to do so- might Not notice the above fact.  It would be far easier for a student to “notice” patterns such as this if taught the Standard Algorithm from the beginning, but that is not to be.  It would be even better if an instructor would point this out to the kids explicitly using several different examples which would naturally lead the students to find similar patterns on their own.  We wish.

 Below is another indication of the same as the authors distinguish between problem-solving and practice exercises.  The only thing students learn from trying to solve problems they lack the skills and knowledge to solve is frustration and a hatred of Math

“…. in working exercises, students apply what they have already learned to build mastery. Problems are problems because students haven’t yet learned how to solve them (Italics are mine); students are learning from solving them. Materials use problems to teach mathematics. Lessons have a few well designed problems that progressively build and extend understanding. Practice exercises that build fluency are easy to recognize for their purpose. Other exercises require longer chains of reasoning.”  (pg 17)

The most chilling statements I found on the entire web site, however, were these:

“…. each standard in this document might have been phrased in the form, “Students who already know A should next come to learn B.” But at present this approach is unrealistic—not least because existing education research cannot specify all such learning pathways (Italics are mine). Of necessity therefore, grade placements for specific topics have been made on the basis of state and international comparisons and the collective experience and collective professional judgment of educators, researchers and mathematicians. One promise of common state standards is that over time they will allow research on learning progressions to inform and improve the design of standards to a much greater extent than is possible today. (Italics are mine.)  Learning opportunities will continue to vary across schools and school systems, and educators should make every effort to meet the needs of individual students based on their current understanding.”

“These Standards are not intended to be new names for old ways of doing business. They are a call to take the next step. It is time for states to work together to build on lessons learned from two decades of standards based reforms. It is time to recognize that these standards are not just promises to our children, but promises we intend to keep.”

What kind of "lessons learned" would have these folks withholding skills and knowledge for even longer than happens now?  Put another way, why does this look like dumbing our kids down even more?  Because this isn’t about education – this is about the states getting big bucks to do yet more experimenting.

There are plenty of mathematicians, other education experts and no small number of parents who know exactly how to successfully teach math and in what sequence.  They know that the Standard Algorithms for the four major arithmetic operations can be successfully taught at grade-appropriate levels beginning with 1st Grade with no sacrifice to the understanding of the concepts of numbers or functions.  But apparently they were not the ones in charge of writing the Common Core Standards.  Despite all the yammering by everyone from President Obama on down about the importance of the STEM skills and knowledge, these Core authors are not in the least interested in educating our public school children.  A large percentage of our children are not to have access to a future in STEM-related jobs, and the United States is not to have access to the majority of its children's highest potentials.  The  Educators are far too busy doing research – and not in a way that will help this nation at all.  

There is, of course, even more being written on the Core’s errors in teaching Math at the higher levels which I’m not qualified to address.  There's quite a bit about the Language Arts Standards also.  I’ve read very good articles on this topic at Education  While some states have spurned the Common Core, many states have begun using the new standards, and the detrimental effects are being described in detail by experts and by parents of suffering children.  Please especially see:

Thursday, February 7, 2013

Invented Math

Question:  Will the Common Core Standards Fix This?

It’s a rare thing anymore for me to meet a student who knows how to subtract correctly.  Many of them subtract upside down, at least for part of the problem.  I am not talking about little 1st graders who are just beginning to learn;  most recently I am talking about having met a 2nd grader closing in on third grade, a 6th grader, and an 8th grader all doing the same thing.  Faced with a problem such as 92 – 18, too many of today’s students will place a 6 in the ones column and an 8 in the tens.  The 8th grader started reaching for his calculator when I told him he was wrong.  He’s been using a calculator for 3 - 4 years now and knows how to do absolutely nothing without it.  That young man opted for an after school tutoring program when he saw I wouldn’t allow him to use his calculator - nor count on his fingers.  (I’m hoping they’ll finally teach him how to do something besides push buttons.)  The 2nd grader will be fine, and the 6th grader is learning the multiplication table with mini lessons on adding & subtracting using the age-old, efficient procedures everyone grew up with before the Educators started foisting New Math on us. 

It isn’t hard to figure out how this has been happening – the standards used by Florida, and many other states, have the teachers trying to cram so much material into the kids that there is no time for them to actually learn anything.  The curriculum has everyone flying from one disconnected area to another, often spending no more than a week on any one topic, no matter how complicated, and no matter what the students’ skill set.  One week it’s the four operations with fractions, the next it’s converting decimals to percents – this with kids who hardly know what a fraction is and who have the same problems as above with the four basic operations even with whole numbers. 

Compounding the problem is a lack of emphasis on teaching the standard algorithms for arithmetic operations.  By “standard algorithms” I mean the step by step procedures we older folks all learned as kids.  For instance, with a 2-digit subtraction problem, the student will subtract the ones column first, borrowing if the bottom number is bigger than the top, then subtract the tens column.  (The Experts make a big deal out of calling borrowing and carrying “regrouping” or “exchanging” as if this clarifies matters.  I don’t care if they call it seizing and hauling as long as the kids learn how to solve the problems.) 

Instead, we have parents as well as students struggling with the results of nonsense such as Florida’s 2nd grade standard MA.2.A.2.2 which states: “Add and subtract multi-digit whole numbers through three digits with fluency by using a variety of strategies, including invented and standard algorithms and explanations of those procedures.”   The key phrases are “variety of strategies” and “invented” algorithms.  This translates to the classroom as an enormous number of methods that must be learned for even the simplest tasks, and they really do mean to have the kids try to invent their own strategies for solving math problems.  This reminds me of how they expected kids to “invent” spelling or “construct” the meaning of text during the dark days of Whole Language.  I am not kidding.  Below is just one quote that can be found by Googling math algorithms.

“Invented strategies are flexible methods of computing that vary with the
numbers and the situation. Successful use of the strategies requires that
they be understood by the one who is using them—hence, the term invented.
Strategies may be invented by a peer or the class as a whole; they may even
be suggested by the teacher. However, they must be constructed by the

The Experts must have gotten tired of waiting for the 7 year olds to come up with algorithms that took a series of geniuses a few centuries to figure out, so they decided to be creative and innovative and invent some themselves.  Under the seductive guise of helping children understand the concepts of math, it’s as if they were trying to make math as hard and horrifying as possible.  Below is one of the more counterproductive “invented algorithms” I’ve seen so far:

To solve 35 – 9, the student is supposed to cross out one of the tens and fill in the bottom block of ten ones with ten little boxes.  Then the student is to cross out the top 5 boxes in the top block of ones plus 4 in the bottom block.  This leaves 2 tens with 6 ones in the bottom block.

The next problem, which is recreated on the back of an envelope, is set up to solve 63 – 28.  The students are to cross out 3 tens, filling the bottom block of ones with ten little boxes (I used slashes).  Then the student is to cross out the 3 ones in the top block plus 5 ones in the bottom block which leaves 3 tens and 5 ones as the answer.

The above were taken from a second-grader’s worksheet with the appropriate standard (above) written in the upper right corner. (Publisher: Houghton Mifflin Harcourt)

The expanded form is popular for far too long in a student’s career.  This looks like:

15 + 39
10 + 5 + 30 + 9
10 + 30 + 5 + 9
40 + 10 + 4
50 + 4

This can go even further and look like this at a higher grade level:

34 + 27 = (3 x 10 + 4) + (2 x 10 + 7)              expanded form
= (3 x 10 + 2 x 10) + (4 + 7)                            associative and commutative properties
= (3 x 10 + 2 x 10) + 11
= (3 + 2 + 1) x 10 + 1                                      distributive property
= 6 x 10 + 1 = 61                                             simplified form

And there are these (for 3rd Grade):

     I found the paragraph under this example pretty interesting.  The kids are instructed to work in pairs or groups, hence the "shared" algorithms.  And the remark about how adults use the method that starts with the 1"s - silly grown-ups!

    And there are these:

If you would like to explore the wonderful world of invented math, all you have to do is Google something like: “Standard algorithm for addition”.  Give yourselves plenty of time, there’re just tons of these examples out there.  I clicked on a couple dozen – they would start off with showing the requested standard procedure and then go off on their flights of fancy.  Many of the sites that exhibit alternative algorithms for basic math have university addresses and are put up by folks who no doubt consider themselves the “Experts” in their fields.  This is not a reason to believe that their opinions deserve any special kind of respect, especially since all their theorizing is proving to be such a dismal failure for so many children.  Should you feel yourself being swept up in their seemingly high-minded, intellectual sounding, jargonistic gobbledy-gook, just remember, it’s people just like these who brought our children travesties like Whole Language and invented spelling – indeed the entire dumbing-down era of OBE and Blueprint 2000.

The public schools are confusing the introductory modeling of math concepts with the methods for performing the functions, and the resulting mish-mash isn’t working.  In fact it’s proving to be detrimental to the academic progress of American students.  This is why we keep having to import so many foreign born, and educated, students to fill up the higher education seats in American Universities – we’re not even teaching our kids how to add and subtract correctly.  And the jobs – the high end, math dependent jobs.

And guess what?  Singapore schools teach their students the standard algorithms!  Duh!

So – are the Common Core Standards going to fix this?  Maybe not.  We’ll be taking a close look.