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PARCC MODEL CONTENT FRAMEWORKS

ENGLISH LANGUAGE ARTS/LITERACY

GRADES 3–11



A big title for what might be important, as a whole slew of states are officially in on it.

Exercising my normal skepticism, I checked it for some of what I think should be the normal curricular phrases. One search has me wondering. I used the Acrobat Reader's find tool and asked to find uses of the words spell " and "spelling".  The word "spell" did not appear in the 98 page document, and the word "spelling" appeared once, in the sentence "In all student writing, the use of specific facts and descriptive details is emphasized, as is correct spelling and punctuation. "

Now that sentence appears in the 3rd grade section of the document. At no other grade level do these words appear.

Having seen careless spelling gradually expand into our media (perhaps largely in thanks to the not-always-correct spell checker), this scares me.

Evidently the laxity in spelling exists outside of the US. According to an article by Laura Clark in the Daily Mail out of England (see it here), a school has the following guideline in its policies: "Teaching staff are not to highlight any more than three incorrect spellings on any piece of work. This is in order that the children’s self-confidence is not damaged."

The placing of self-confidence (and its companion self-esteem) above the development of skills and knowledge that lead to self-confidence and self-esteem is another of the well-intentioned but misguided trends in education.  Feeling good about oneself has been taking precedence as a means rather than an end.

The Long Division of the Literati

Just as I feel that long division has been tossed out incorrectly, I also feel that the teaching of grammar (what's that) has gone by the wayside, especially its art of diagramming sentences.

An article from the New York Times by Kitty Burns Florey (see here) from June 2012, referring to diagramming sentences, says "First of all, diagramming is not for everyone." That hits our problem nail on the head, especially when compared with the term "Common Core": what we teach in our schools now is supposed to be for everyone.

In my experience as both a student and a teacher, what our public schools have failed to acknowledge is that there are some items that are beneficial to some, not for all, and that it is okay to teach some things in the classroom that not all students can master.

We put all New York students through Algebra 1 (whatever it is called now), force them through it all, calling them failures when there are parts they cannot handle. Those "failures" become negative marks on both the students' and teachers' records, and generally on the students' home lives as well  as we pass the buck to such things as single parent families and poverty.

What New York should be looking at are two key issues: are students' ready to learn what they are being taught? Does everybody need to master what they are taught? If we were all to recognize that some skills that need to be known and can be learned by some, but not necessarily by all, then it would be okay for a student to not succeed at that skill. Can you imagine students' getting things wrong in school and being told "that's okay."

We do it in PE quite masterfully. We take all through basketball, football, baseball, soccer, etc., identify those who want to do well and can do well, and proceed with them. We do not condemn the others and call them failures.

We have gone through a patch in the last 25 years where knowledge and skills obtainable by few have slowly been weaned out of our curriculum. This has been a downward trend. The Common Core will not change this trend.

I recommend reading "Common Core Standards Will Impose an Unproven ‘One Size Fits All’ Curriculum on North Carolina" (get it here).  This article says "Common Core Standards have been sold as a tool to raise academic standards and improve education for all students across America. However, an untested assumption underlies CCS: all students should learn the same things and have the same education."

The Common Core standards website says "The standards promote equity by ensuring all students, no matter where they live, are well prepared with the skills and knowledge necessary to collaborate and compete with their peers in the United States and abroad." Take note that equity can be obtained by bringing down the top as ell as raising the bottom.  Also take note that it says "no matter where they live". Really? ANYwhere?

More oddball division

Check out University students learn a new long division algorithm .

I am still trying to decipher what this new method really is. There is just one example given, and I am trying to decipher the recipe from it.

This paper does seem odd that it asks college students if this recipe for division is simpler or more difficult than a method they had probably learned in grade school, or at least tried to learn. ( I do believe that school mathematics often "moves on" before many skills are truly developed in the students' minds. If long division was taught initially to college students, their more highly developed brains might catch on more easily than do the brains of pre-teens.)

Another long division befuddlement

In "The case Against Long Division" (see it here), Tony Ralston gives this example of an alternate method for division:
Then, at the first step, multiply by 10, record the integer portion of 10A/B as a, subtract a from both sides to get .bcdefg… on the right and then repeat this idea to get b, c, … . When B has one, or even two, digits, the subtraction can be done mentally. Thus, for example, to compute the decimal equivalent of 3/7 we would set 3/7 = .abcdefg… and proceed as follows:

30/7 = 4.bcdefg… so 2/7 = 30/7 – 4 = .bcdefg…
20/7 = 2.cdefg… 6/7 = 20/7 – 2 = .cdefg…
60/7 = 8.defg… 4/7 = 60/7 – 8 = .defg…
40/7 = 5.efg… 5/7 = 40/7 – 5 = .efg…
50/7 = 7.fg… 1/7 = 50/7 – 7 = .fg…
10/7 = 1.g… 3/7 = 10/7 – 1 = .g…
30/7 = 4. …

and now it is clear that the sequence 428571 just repeats since once one digit of the quotient is repeated, subsequent digits must also repeat. Note that in practice students should be expected to write down just the successive quotient digits with all other calculation done mentally.

I, for one, don't picture this as easier than long division, but it doesn't really matter, as the steps taken are EXACTLY the same as in long division, just written out differently. In this case I think the presentation creates a greater chance for careless error, but that is just my opinion.

Mr. Ralston, further down in his writings, claims that the long division algorithm is no better than the almost defunct pencil-and-paper square root algorithm. From my perspective, the reason the square root algorithm was marginal in school mathematics is because 1) it is time consuming, with a number of false starts for weak arithmetic students; 2) rarely tested, probably because of its time consuming nature; and 3) rarely needed since perfect squares and radical notation "ruled".

What I find scary about this long division issue is that the reformers are claiming that long division itself is irrelevant. By this logic, no one will learn it, helping to firm up the calculator dependency that is taking over. Skills will mean less and stock in batteries will mean more.

PS: I should add that Tony Ralston is (was) a computer science professor at SUNY Buffalo. His algorithm as exampled above is easily programmable for a single digit divisor, provided it is recognized that the integral part of the quotient is identified first. Otherwise, his algorithm needs many more examples in order to be understood.

More on Long Division (and short division, too)

There has been an article out for a few years titled "Long division is so last century" (find it here), In this article she quotes Lawrence Spector of Manhattan Community College as follows: "Spector says that long division "belongs in the history of mathematics" because short division is so much simpler and faster.  I have to say I absolutely agree with him!"

 

This is absolutely scary! Not because short division is incorrect or improper or not effective, but because it is merely a short way of writing long division, which in itself was shortened by leaving out some trailing zeroes.

 

I am of the strong belief that long division can be understood better as it relates more directly to the commonly known distributive law of multiplication over division (more on that in a future blog entry.)

 

The web site Ask.com, in response to the question "What is the Difference Between Short and Long Division?" replies by stating: "The difference between long division and short division is that Long division is a typical procedure suitable for dividing simple or complex multi-digit numbers. It breaks down a division problem into a series of easier steps, whereas short division requires neither complex technology nor mental gymnastics; it is only suitable if the divisor is small - typically less than 10."

 

I believe this reply to be extremely misleading in three ways: it fails to recognize that the "mental gymnastics" in short and long division is exactly the same, it claims that long division "breaks" a problem down, when that is exactly what short division is also doing, and it confuses "small" divisors with single digits divisors (after all, .674327 is much smaller than 1)

 

Wikipedia is a bit more precise, when it says "Short division is an abbreviated form of long division."

 

Needless to say, long division is greatly misrepresented, misunderstood, belittled, and unappreciated. Could it be that no one got rich teaching long division but a lot of people got rich selling calculators?

 

Click here for a comparison of a long division example and the information it contains.

Long Division (continued)

In yesterday's blog entry, I left out mention of an excellent article entitled The Role of Long Division in the K-12 Curriculum written by David Klein of California State Northridge and R. James Milgram of Stanford.  You can find there article here.

Within this article they stress California educational politics, but their arguments transcend the region. I do have to confess that readers with a lack of comfort with numbers will probably not finish this article (but I pointed out yesterday that familiarity with our number system along with addition, multiplication, and subtraction, is a prerequisite to handling long division).

Please remember that long division is an algorithm that historically became the standard process for doing division. It also is an excellent tool in discussing the differences between terminating, repeating, and non-terminating non-repeating decimals, which help distinguish between rational and irrational numbers, which is muddled up by hand-held calculators.

For the record, students with hand held calculators have big trouble handling our national debt (in dollars and cents it's 15 digits long). Ask a student to divide the debt equally among the 50 states and see what they do.

More to come...

Long Division as a Symptom

Laurie H. Rodgers, in an article entitled "In defense of long division: Pro-reform professor capably shows why reform math doesn't work" has given a strong defense of long division, and has done so while helping to show that the math reforms (coalescing nationwide the in Common Core State Standards) are not necessarily for the better. (Her article can be found here.)

Speaking of long division, I will add to Ms. Rodgers' argument by using a quote from her article: "Many don’t even know their basic multiplication facts.."

Long division, when it is taught, is generally the last of the four basic operations. As an algorithm, its use and fluidity depends greatly on the user's knowledge of basic multiplication facts. It also relies heavily on subtraction. We all know that multiplication and subtraction are largely taught in their relation to addition. Thus virtually all one's basic number knowledge comes into play in constructing long division. Weaknesses in addition, subtraction, and multiplication will all help in crashing the edifice known as long division.

When confronting long division, anyone with weak mental arithmetic skills in the other operations will generally "mess up."

As a high school teacher I made a point when analyzing a student's work of trying to detect the specific error(s) that caused students' solutions to be in error. I wish I had kept good solid data, because the fact was that the vast majority of errors (my sense is 80% or more) were caused by faulty addition, subtraction, and or multiplication. (Leaving out the errors based solely on conceptual weakness). And this was in the calculator age in the New York Regents program.

Speaking of calculators, I found students "dial wrong numbers", get erroneous calculation results, and have no clue that they were off. Even adding 23 and 2, for example, a student might hit the multiplication button, and then write down 23 + 2= 46, and let it stand.

Needless to say, I hold the position that our educational systems are having students race through arithmetic so we can get them to "higher thinking skills" where all the alleged importance is. I believe this if more time, energy, effort, and resources were spent teaching children all about numbers, the higher order items along with a love of math would follow in due course.

I suspect the English Language standards are missing the mark as well, since I have searched through them and I have not yet found a reference to "spelling".  The first grade has a standard that says "Write opinion pieces in which they introduce the topic or name the book they are writing about, state an opinion, supply a reason for the opinion, and provide some sense of closure."  In essence, first graders will be writing book reviews. Without being able to spell?