Recently, I sat through an "education town hall meeting" sponsored by a conservative political candidate in my state region.  Normally, I do not attend such things as my interest in politics has waned severely in recent years.  However, this candidate caught my interest because of the prominently displayed "Anti-Common Core" statements in the advertisements for the event.  Being very much pro-Common Core myself, I decided to do a little bit of opposition research.  I would just go and hear what the candidate had to say. 

Well, needless to say, things did not go exactly as I had envisioned.  The first sign was the presence of the leader of the state Anti-Common Core movement.  This person took over the presentation almost immediately and then my problems began.  The presentation was a well organized, well constructed, and well delivered.  Unfortunately, it was also a completely unfounded and patently untrue critique of the Common Core State Standards.  By the end of the presentation I was extremely upset and agitated, which is unusual for me.  My objection rose not from the fact of their opposition to the standards, but rather from the polished, assured delivery of complete untruths.  Now, I am not accusing anyone of lying.  The presenter and candidate might even believe what was said, but the fact of the matter is that nearly all of the information given was incorrect, misinterpreted, or untrue.  I left the meeting very disturbed by the thought that this information is being given to many people in my state and that (even presuming positive intentions) it might have a drastically negative effect on legislation and community perception of education.

Later that week as I began my summer reading list, I came across a quote attributed to John F. Kennedy when he spoke at Yale University in 1962.

"As every past generation has had to disenthrall itself from an inheritance of truisms and stereotypes, so in our own time we must move on from the reassuring repetition of stale phrases to a new, difficult, but essential confrontation with reality. For the great enemy of truth is very often not the lie-- deliberate, contrived, and dishonest-- but the myth-- persistent, persuasive, and unrealistic . . . Mythology distracts us everywhere."

This quote struck me immediately and has consumed my thoughts since.  Coupled with my experience at the education town hall meeting, it started me thinking about the nature of the Common Core Mythology (I choose the term myself).  The growth and organization of the opposition movement over the past several years has brought with it a persistent, pervasive, and to some people, persuasive mythos (Thank you, President Kennedy, for those wonderful words).  This mythology is built upon the fears and tacit acceptance of those who believe public education to be fundamentally flawed.  It is, at its core, a misinformation campaign that relies on the fears and apathy of its victims to thrive.  To those with political agendas it is a call to arms to gather support from parents afraid that their children are being destroyed or brainwashed, from disillusioned educational professionals (not just teachers, but anyone in the educational family), and from those who adamantly oppose change in any form.  I believe that those of us who understand the standards and are not afraid of them have a duty to the truth about these standards and our children.  All of this has led me to ask several questions.

                1. What is the "Common Core Mythology?"

                2. What stereotypes and truisms (both true and false) have arisen with these standards?

                3. What are the reassuring stale phrases of the Common Core Mythology?

                4. How can we come to our "essential confrontation with reality" about education and the Common Core              Mythology?

The first two questions are best answered together.  Because the Common Core Mythology is really all of the misinformation, lies (well, half-truths at the very least), and misunderstandings surrounding the standards.  It is the rehashing of old feuds and stereotypes from other eras of education reform.  Here are some statements I've heard consistently.  All of them are, at least in part, untrue.

                "Common Core is a national curriculum."

                "Common Core is federally mandated."

                "Common Core tells teachers what to do every day and doesn't let them be professionals."

                "Common Core mandates tests that are too hard for our students."

                "Common Core is brainwashing our kids with "fuzzy math," liberal ideals, and morally objectionable material."

                "Common Core requires homework that I can't even do, and I have an advanced math degree."

                "Multiplication proficiency is defined differently."

Whatever the turn of phrase opponents use, it always seems to be based in one side of a dichotomy that most people don't think about: intent versus implementation.  I've seen many different examples come through social media (particularly the "I can't help my son/daughter with  Common Core homework."), and while I don't doubt that the assignments and issues being discussed are very real and concrete, they come from teachers who have the best of intentions.  Maybe this is an integral part of the Common Core Mythology as well.  That the standards will be implemented with equal effectiveness in all schools.  This is obviously untrue, as any set of standards is subject to interpretation and any implementation plan can go awry because of the scale involved.  I am not saying that these  things are okay.  I am saying that they can and will happen, and perhaps everyone should presume positive intent before casting harsh judgments.  By "presume positive intent," I mean that teachers charged with implementing these standards in schools do not get up in the morning planning on destroying the lives and education of children.  That should be taken into account before casting aspersions on someone's work.  Perhaps a civil, reasonable conversation should be used in lieu of a stream of vitriol and bile spewed up all over Facebook and Twitter feeds.

The role of the federal government is most certainly part of the mythos, as evidenced by the first few statements above.  This is the area at the heart of most opposition positions.  However, I must be very clear on this point: these standards were purely voluntary.  With that being said, yes the federal government did step in and incentivize the process with Race to the Top funding.  While some may disagree about the appropriateness of this move, I do not believe any can deny the extent to which it enhanced the effectiveness of the Common Core State Standards Initiative.  Within a few weeks nearly every state in the union had signed on to the project.  Even the most notable exception, Texas, when viewed closely, has a set of standards very much like the Common Core.  Indiana, after backing out very recently, adopted a very similar position in their new standards.  Even the Fordham Institute rated these standards quite highly in both Mathematics and English Language Arts.

As I read this piece over once more, I realize that I, sadly, do not have an answer to my fourth and final question.  But perhaps that's just as well.  Perhaps this discussion is the beginning of that confrontation with reality.  There is much more to say.  Many more debates to be had in this fertile arena.  From here I send the discussion your way as I look forward to your thoughts concerning the Common Core Mythology.  I've begun to describe the rise and attempted to begin the fall.  Where do you stand?

How would you teach students to divide fractions?  As in, what would you do on Day 1 of your dividing fractions unit?  I've asked this question of teachers many times in professional learning settings and all too often the answer I get is . . . wait for it . . . "I'd teach them to flip the second and multiply."  Those of us who learned fraction division at some point in the last, say 50 years, are very familiar with this "standard" algorithm for dividing two fractions. 

Fraction division is not the only operation that has a "standard" algorithm, of course.  Almost all operations in math have one.  Most, if not all, of us are familiar with the Fearful Four of standard algorithms:

·         the "carrying/borrowing" algorithm for addition and subtraction of whole numbers and decimals,

·         a similar algorithm for multiplication of whole numbers and decimals,

·         Long Division (yes, capitalized) for division of whole numbers and decimals,  

·         and the dreaded "invert and multiply" for division of fractions. 

Yes, mathematics has hundreds more smaller, less well-known standard algorithms (reduction of fractions, converting between mixed numbers and improper fractions, etc.) but the four above are the biggies.  They also happen to be the four that are mentioned explicitly in the K-8 Common Core standards. 

Well, almost explicitly.

The "carrying/borrowing" algorithm is often referred to as the "standard" algorithm for addition and subtraction, but the standards do not specify that particular algorithm.  They simply say "Fluently add and subtract multi-digit whole numbers using the standard algorithm." So there has been some debate over the definition of standard algorithm, and it turns out that this definition is not universal.  Some experts and math education leaders (and I agree with them) would suggest that the "standard" algorithm for addition and subtraction should be partial sums.  The standard for multiplication could be partial products.  Both of these methods have advantages over the traditional "carry/borrow" algorithm in both connection to place value concepts and encouraging flexibility in student thinking. 

It is also worth noting that "Fluently add and subtract multi-digit whole numbers using the standard algorithm." is standard 4.NBT.B.4 (CCSSI, 2010).  This means that the standard algorithm is pushed off until 4th grade, after students have learned to add and subtract multi-digit whole numbers in Grades 2 and 3, with introductions from early Kindergarten through Grade 1.  The algorithm is pushed off until very late in students' experiences with those operations. 

Much like the punch line to a joke. 

While the punch line metaphor is perhaps unflattering, it is nevertheless effective and accurate.  Students build understanding of operations through experiences and informal reasoning, just as listeners build understanding of the amusing situation in the body of a joke, and only after having sufficient experience with and understanding of the operations are they ready to learn the algorithm with understanding, just like the listeners and the punch line.

Another aspect of this debate is whether students should even be taught certain algorithms in school.  David Ginsburg blogged about the necessity of long division, so I'll avoid that one here (but you should all read So Long, Long Division) and move on to some others.  I've no argument against the standard algorithms for most operations in elementary schools but I'll choose one that I do have an argument against: reduction of fractions (or writing fractions in simplest form for all my high school teachers out there).  This is the "punch line to bad jokes" portion of the blog.

And don't worry, I'll get to a hot button secondary example in my next post.

But first, reduction of fractions.  Before everyone piles on all at once here, I am absolutely not saying that students should not be taught how to write fractions in simplest form.  What I am saying is that we should not teach it as an algorithm and we should definitely not require students to write every single fractional answer they ever get in simplest form.  This is because in many mathematical situations, the reduced form of a fraction will not reveal enough information about the initial problem context.  Not to mention all of my statistics friends out there who will argue tooth and nail that a probability of three-fourths is absolutely not the same as a probability of six-eighths (and they are right).  That being said, I do acknowledge the necessity of reducing fractions and so I propose teaching the idea or procedure with understanding.

My reasoning for this is two-fold.  First, we spend a great deal of time in schools beating students over the head with reducing fractions and we never tell them why or require that they make sense of the actual procedure.  Time that could be better spent both exploring more important topics and showing students success instead of highlighting failure.  Distributed practice is very important, however when students are completely correct in reasoning and even calculation on a problem but receive bad marks due to an answer that is unreduced, teachers are doing them a great disservice.  We must ask ourselves what we are trying to assess about students' knowledge and be sure we aren't needlessly penalizing them for something that is quite trivial and unrelated to the knowledge base we desire.

Second, students will be much more likely to remember how to "reduce" fractions if we teach them under the guise of generating equivalent fractions.  The CCSSM focus on equivalent fractions in Grades 3-7 should be continued throughout all grades.  Students are very capable of generating equivalent fractions from almost the beginning of their study of fractions and we should nurture this instinctual understanding, not drive it out with a meaningless procedure.  Students can understand equivalent fractions in  a few different ways, all of which are very effective and still allow students to find the "simplest" form of a fraction.  One great example I've heard before is that of a reduced fraction being the "simplest recipe" in a given situation.   This idea, in conjunction with appropriate contexts, can really drive home the idea of reduced fractions with understanding.

So the moral of the story today is: teaching standard algorithms is fine if you must.  Just treat them like the punch line of a joke and don't deliver them until the end of the learning trajectory.  Remember, procedural fluency should be developed from conceptual understanding, not the other way around.

Those are some of my thoughts.  I'd love to hear your thoughts on the subject!