Monday, April 21, 2014

Euclid is rolling over in his grave.

Standardized testing has killed geometry.  All that’s left to do is plan the funeral.  True, geometry had been ailing for some time and was too weak to put up a fight.  Still, theoretical mathematicians should pause for a moment of silence and then figure out what to do next.

The objective of geometry was never understood by most modern folks.  They tended to dismiss it as the study of “shapes” and to wonder why it was included in the curriculum.  But geometry was never about shapes.  Shapes were merely intended as the vehicle for making deductive reasoning more accessible to students.  Students tended to find formal proof to be very challenging, and as the self-esteem movement grew and grade inflation ran amuck, math teachers were under more pressure to gloss over the proofs that made the subject so difficult.  Eventually, many, if not most, high school students went off to college without ever having done a formal mathematical proof.

Still, geometry problems tended to involve informal deductive reasoning:  “I know these two lines are parallel, therefore these angles must be congruent.  If that’s true, then this thing is a parallelogram and these two line segments are congruent.”  In addition, geometry continued to be a class where you had to be careful and precise about how you talked about something.  Definitions were important.  Leave out a phrase, and everything changes.

The problem is that formal deductive reasoning can be difficult to test.  Informal deductive reasoning is easier to test, but requires a great deal of background knowledge about “shapes.”  Thus the layperson thinks that “shapes” was the concept being tested in the first place, and does anyone really need to remember that a midsegment of a triangle is half the length of the side to which it is parallel?


So now the Common Core Standards and the SAT have essentially gutted geometry from the curriculum.  Only the bits about shapes that are essential to trigonometry and to transformations (since there is an increased emphasis on graphing functions by transformations) have been kept. Formal definitions and proof are no longer included.  For true mathematicians this means that real math is no longer taught in kindergarten through 12th grade at all.  What’s left is just the arithmetic and modeling needed for science and statistics.  Where will our future mathematicians come from?

Saturday, April 19, 2014

Current freshmen: Take the old SAT next year, or wait for the new version?

Current high school freshmen have a decision to make:  Take the current SAT during sophomore year, or wait until March of junior year to take the new SAT?

Up until now my advice for the timing of the test has been as follows:

Take the SAT for the first time as soon as you have completed both Geometry and Algebra II, or spring of your junior year whichever comes first.  Students often do their best on the math section while geometry is still fresh.  Taking upper level math does little to improve the math SAT score, and the math score can decline by junior or senior year if the student is on an advanced math track.  Critical reading and writing scores, on the other hand tend to increase a bit during junior year English, which is often when schools really concentrate on composition.  Therefore, students who took the SAT for the first time sophomore year, should retest at the and of their junior year to improve the verbal scores.  This generally allows for the best possible super-score with the least time spent on test-prep.

However, current freshmen who are on an advanced math track have a unique dilemma:  the test will change in March of their junior year.  If you try to test early you won't have an opportunity to retest with the same test.  On the other hand, what happens if you wait until March of 2016 to test for the first time, and run into a serious problem?  Of course, the whole thing is complicated by the adoption of the Common Core Standards.  Both the standards and the new SAT have a reduced geometry emphasis.

The options are as follows:

1.  Just take the ACT and avoid the whole issue.

Pro:  You avoid the uncertainty and confusion.
Con:  If you work slowly, the ACT may not be a good test for you.

2.  Try to get your SAT testing done before March 2016

Pro:  You can get your testing out of the way early, and avoid the uncertainty of the new test.
Con:  You will need to spend extra time (and possibly money) to prepare since you will need to make up for what you haven't yet covered in school.

3.  Wait to take the SAT for the first time in March 2016.

Pro:  This might be the best option for students who are not on an advanced math track since they would not have taken the SAT before junior year anyway.  Furthermore, if you are taking the Common Core math sequence, you may not know enough geometry to do well on the old SAT.
Con:  There is a great deal of uncertainty around the new test.  Prep materials will be scarce and/or speculative.

It would be nice if you could wait to see a sample test for the new SAT.  Unfortunately, if you plan to try to get your testing done early, this summer is the best time to work on your critical reading skills.

Maybe what you should do is work on your reading skills this summer- after all, being a better reader is worthwhile even if you don't test at all - and then you'll be prepared for whatever path you settle on.

Tuesday, April 15, 2014

The High School Common Core Math Sequence Is Broken, part II

This is a follow-up to the previous post, which you may be able to read by scrolling down.  If that doesn't work for you, check the blog archive in the right-hand column.

In the last post, I wrote about problems with the Common Core Standards.  I argued that trying to brush off criticism by saying that parents are responding to other fears – fear that my child isn’t smart enough, fear that my child won’t grow up to be like me, fear that my child’s standard of living won’t be as good as mine – fails to address very real issues in today’s classrooms.  Today let’s look at a specific example.

I am a professional tutor.  I work with some students in math, and I help others to prepare for college entrance exams.  Most of my students attend elite private schools in the Research Triangle area of North Carolina.  I expected the second week of March to be very quiet.  I planned to do some extra housecleaning and some curriculum preparation for an upcoming evening class.  On Monday evening the phone rang. 

Could I help a student enrolled in a course titled “Common Core Math 2?”  Probably.  This is the first year that this course has been taught, and I wasn’t sure what was in it, but I’m familiar with most high school-level math, so I figured I could help.  Word got out, and I am currently working with a number of students all from the same class.

Common Core Math 2 is currently taught to students who, under the “old” system, would have been taking geometry.  If you will recall, I had been hopeful that certain geometry topics would be pushed to a later course, that there would be fewer topics overall, and that the topics included would be covered in greater depth.

Typically, when I get a new math student, my first question is, “Who is your teacher?”  Often that tells me all I need to know.  A handful of individuals have accounted for the bulk of my tutoring clientele.  However, the teacher this time is a veteran and a star.  She knows her stuff, both mathematical and pedagogical, so if there’s an issue, it probably doesn’t lie with her.  The reason for the sudden increase in business was apparent as soon as I looked at the homework packets.

This veteran teacher is incredibly well organized.  You can get online and see what students will be responsible for each day of the semester.  A few clicks, and the entire course was laid out before me.  I’ve never seen such a mess.  First, there are too many topics to be covered.  The list for the students to review for their midterm listed 47 topics.  FORTY-SEVEN.  Forty-seven topics had been covered in forty class periods. Some are topics that I would have voted to leave out altogether.  (Which is the incenter and which is the orthocenter?  I don’t remember from one day to the next and I teach this stuff!  Seriously, is there anyone who actually needs to know?)  Some are topics that have been pulled in from pre-calculus (Common Core 4 will replace this), and given the brain maturity required to understand them, should have been left there.  The topics don’t flow.  They don’t relate well to one another.  While I can see some of the basic principles that lessons are trying to address, it might be better to use different topics to address them.  In short, it is no wonder that students are floundering.

What went wrong?  The overall process has been remarkably opaque.  Stakeholders who should have been pulled in at certain levels of the process clearly weren’t, and it is difficult to figure out exactly what happened or where the whole thing broke down.  However, I have been paying attention to this story from the beginning.  I’ve done some poking around, and I have pieced together a story that seems plausible.  Here it is:

The setting:  For those of you who may not live here, the North Carolina educational system is fairly centralized.  Teachers are state employees and in addition to funding teacher salaries, the state gives local school systems money for busses and other expenses.  Local governments are responsible for building and maintaining school property, but the bulk of the money comes from the state.  In addition, the state jumped on the high stakes testing bandwagon before it became popular and has written and administered it’s own standardized exams since sometime in the 1980’s.  This effectively means that the state has been in charge of local curriculum for decades.

In 2009, when the Race for the Top grant was announced, we were in a recession and the state was broke.  The powers that be were scrambling for revenue sources that wouldn’t involve raising taxes, and the grant money looked awfully juicy.  Sure they had to agree to adopt some standards and then test to see if they were meeting them, but weren’t they pretty much doing that already?  Count us in!

We were awarded the grant in 2010. Now, keep in mind that the state was looking for money for everyday operating expenses.  So having spent the money on teacher’s salaries, there wasn’t any left for implementing the standards.  Best I can tell, the National Common Core Standards lump all of the high school math standards in “high school.”  It is up to the states to design the sequence of the high school curriculum. So the state wrote lists of what would be tested at the end of each year and pushed the work of curriculum design to the districts. 

Since the late 1980’s the state had developed a rich bank of curriculum resources that districts could use.  The scope and sequence of each course were spelled out with suggested pacing.  There were sample worksheets, examples of activities, and banks of test questions.  All of this was now obsolete.  In the summer of 2012 local districts were faced with having to design math courses based on lists from the state of what would be tested in January of 2013.  They didn’t have any money for curriculum design, either, so they dumped the work on the teachers who scrambled to write each piece in time to use it in the classroom.

As you can see, at every step there were ample opportunities for the process to break down.  Where can we pin the blame for this particular fiasco?  Again, because the process has been so opaque it’s hard to say.  I do believe that the teachers at the district level have done the best they can, given the mandate from the state and the time constraints.  I actually think the state Department of Instruction did the best it could, given the tight deadline and lack of money.  Where did the deadline come from?  Who said we had to have everything in place and the first tests administered by winter 2013? (And whose bone-headed idea was it to promise that we would adopt the standards without spending any money on the task??) We don’t know.  Parents see “Common Core” in the title of the course and so it’s the Common Core Standards they rail against in letters to the editor and at school board meetings.

Regardless of whom is to blame, the situation is this:  The North Carolina Common Core high school math curriculum is broken.  The scope and sequence of the topics do not reflect what we know of how students learn or of when concepts should be introduced.  Topics and concepts in each course are so numerous, that it is impossible for concepts to be studied in depth, but they will be tested as if they were. 


Arne Duncan would have you believe that the resulting poor scores mean that our little darlings just aren’t as smart as we thought they were.  Ms. Boylan would have you believe that we aren’t really upset over our little darlings’ failure to learn anything in math class, but rather that our little darlings might learn something we didn’t, while some editors in Long Island think that we are really upset over the general state of the economy.  How insulting!  North Carolina parents can recognize a mess when we see one, and this is a mess.  We can’t be faulted for misplacing the blame when the mess was made behind closed doors.  The fact remains that someone needs to clean it up.

Monday, April 14, 2014

The High School Common Core Math Sequence is Broken

There has been a great deal of criticism of the Common Core Standards in the past year, and the discussion is getting heated.  On one side we have accusations of a federal take-over of local educational systems and myriad examples of nonsensical homework assignments.  Some of the responses from the other side have been interesting.   First we have Arne Duncan accusing “white suburban moms” of fearing that their little darlings “aren’t as brilliant as they thought they were.”  Then there’s the piece by Jennifer Finney Boylan (“A Common Core for All of Us”) claiming that Common Core opposition is rooted in the fear that our children might not turn out to be carbon copies of ourselves.  Now most recently we have an editorial from Long Island Newsday that tells us our concerns about Common Core are really “the fear that the fundamental promises of American society are eroding, that the next generation will not be better off.”

At some point I need to poke around and see if anyone is writing about why Common Core proponents are trying to make their case by insulting millions of parents.  (Surely they realize they’re outnumbered.)  But for now, lets just say that parents don’t have their panties in a wad over some vague angst. They are upset over what they see happening to their children in the classroom.

When the Common Core Standards were first announced, I saw two promises that gave me reason to cheer:  First, there would be fewer topics taught in greater depth.  Second, school districts would have the option of eliminating the traditional algebra I, geometry, algebra II sequence in favor of a system where the algebra and  geometry topics are mixed and taught in an order that recognizes some things are better left until student’s brains have matured.  I have spent years watching the math curriculum (geometry in particular) get watered down until it was meaningless because we tried to teach too much too soon, and I was looking forward to adopting a model that had long been used in Europe and Canada.  I knew there would be bumps in the road on the way to implementation, but I thought that if we could all just hang in there, we would eventually end up with something really effective.

Then reports started to flood in from parents and teachers.  Children are miserable.  Teachers are exhausted. The failure rates on assessments are high.  Whom do we blame? It’s hard to say because what we are looking at is likely a mixture of the standards themselves, local implementation of the standards, and a culture of high stakes testing that pre-dates the standards.  And yes, a bit of resistance to change to season the stew.

Part of the problem is that the path from the standards to the day-to-day workings of an actual classroom has been very opaque.  Some of the blame that has been cast at the national Common Core Standards might be more accurately pointed at a more-local agency.  That doesn’t change the fact that something will have to change.  Brushing away the criticisms by libeling parents and teachers is not a valid or viable solution.


Next up:  A look at a particular course in a particular school district as an illustration of what may have gone wrong.

Tuesday, March 11, 2014

The new SAT: the Essay

This is the third post in a series on the redesigned SAT.  The first two were on vocabulary and the math section, respectively.

It was interesting to see what the news media chose to focus on when they did their bullet points for the redesigned SAT.  As headlines and/or sound-bites, many chose variations on “The new SAT will drop the essay requirement!”  That they would trumpet this particular change is understandable.  The SAT essay has been widely loathed since it was first introduced in 2005.

Criticisms of the 25-minute essay section abound:  Writing a coherent essay in such a short period of time on a random prompt that was sprung on you at the last second is a very artificial task.  How often does that come up?  Even college blue-book exams – the closest real-world situation - will have essay questions specifically on the course material.  And don’t get people started on how they are scored.  Anecdotes abound about how kids who can afford coaches are at an enormous advantage because coaches teach you how to use really bad writing to get a top score.  Dropping the essay requirement was popular and a good marketing move.

However, "drop the essay requirement" may be misleading.  The SAT still has an essay.  However, now the style of essay has changed and it is "optional."  Changing the style of the essay is a good move. The new style is much more the kind of writing that you might expect to do in the workplace:  Take this data and write a quick position summary.  ETS has already test-driven this essay style on the GRE, so they should be able to implement it on the SAT with few hiccups.

As far as being "optional" goes, the more selective colleges will "require" it, just as they now "require" the "optional" ACT essay.

While it is true that the method of scoring the essay has always had issues - and likely still will - there are two points to consider here:  First, American kids need to be writing more and when you include essays in assessments, the curriculum will include more writing instruction.  Second, colleges have always been able to read a student's actual essay.  They don't have to rely on the score as a measure of an essay's quality.  In fact, the essay score has always had only a slight impact on the students Writing component score in addition to being reported as a separate score.  Many colleges disregard the entire Writing component score altogether while others downplay it.  Yet, they have required the essay anyway. Keep in mind that this will probably be the only sample of writing accessible to the admissions committee that is guaranteed to have been written by the applicant.  Admissions officers all claim they can spot an adult-written essay from a mile off, but can they really?  And what is to prevent a student from paying his classmate to write a better essay?


So the essay is still there and those applying to selective colleges are stuck with it.  However, the task should be a better example of a real-world writing situation, and practicing for it may pay off even after the SAT is over.

Need help with the current SAT essay?  Try this: