Impressions on the new practice PSAT

A few days ago the College Board posted a new PSAT practice test.  This is the practice test for the redesigned PSAT to be given in October 2015.  It is also a glimpse of what the redesigned SAT might look like. 

There has been a great deal of speculation about the redesigned test.   A number of people have opined that the new test would be an “ACT clone.”  I, myself, have speculated that the new test would be designed as more of a high school exit exam than a college entrance exam.  Quite a few pundits have pointed out that the SAT was losing market share to the ACT and thought that the redesign might be an effort to gain that share back.

Upon looking over the test, I am now prepared to make the following statements:

The writing section IS barely distinguishable from the writing portion of the ACT.  Otherwise, this test is in no way an ACT clone.  On the other hand, I do feel that this test represents a fundamental shift in purpose.

There are a number of possible purposes for giving a standardized exam.  (This would be as opposed to a teacher-made assessment.)  Here are a few:

• To document student learning (or lack thereof) of particular skills and concepts
• To distinguish among (or rank) students
• To drive the curriculum*

Prior to 2015, the PSAT’s fundamental purpose has been a balance of the first two items.  As the National Merit Scholarship Qualifying Test it has been used to distinguish top students from the pack, and it has documented whether or not students have a grasp of particular skills and concepts.  It has NOT been used to drive the curriculum...until now.  In my opinion, several of the changes were specifically designed to have an impact on the nature and content of classroom instruction.

One of the elements of Common Core language arts is a focus on having students read critically.  In an effort to have the students respond to what the author actually said – as opposed to how they feel about what they think the author said – students are being asked to point to pieces of the text as “evidence.”  In the PSAT critical reading portion, students are asked to choose the best evidence for almost every question.  Now I’m not a language arts teacher, and I don’t have any special critical reading or psychometric expertise.  However, it seems to me that this is about the same as asking the same question twice.  In other words, if you correctly answer the original question, then the answer to the “evidence” follow up is trivial.  If you missed the original question it would be impossible.  Will there be some kind of scoring mechanism that uses this question-pairing to determine when the correct answer was obtained by guessing?  Maybe.  It is more likely an attempt to make sure teachers require their students to give evidence in class.

Here is another example from the math section.  Months ago, when the sample questions were released, I noticed that some of the questions were much longer and more involved.  This represents a distinct shift.  Up until now I have told my top students, “If you are more than 3 steps into an algebra process, you probably missed something.”  One of my main criticisms of some of the test prep books out there has been that too many of the math questions can ONLY be solved with the application of tedious algebraic steps and are thus not representative of the real thing.  However, this has changed with the PSAT practice test.  It’s interesting.  If I’m a professor of mathematics or engineering I’m interested in multiple different aspects of their math skills.  I want them to have a solid grasp of the concepts, good number sense, AND I want them to be able to keep track of what they are doing through a long problem that requires many steps and sub-steps to solve.

Up until now, the major college entrance exams did a decent job of testing the first two. (The SAT was better than the ACT in my opinion.) They really haven’t attempted to do the third.  This is largely because a multiple choice or single final answer exam format is a TERRIBLE way to assess that third skill.  If the student’s answer is incorrect, you don’t know if he really can’t negotiate the process or if he just made a silly error in the middle.  Graded homework and teacher-made assessments where partial credit is given are much better means of determining whether or not the student can handle a long problem.  Both of those would be reflected in the students’ grades.  By trying to test it in this format, you add no new information.  The only reason I can come up with to include problems like this is to encourage math teachers to have students practice longer, more complex problems.

When the College Board first announced that the SAT would be re-designed, an admissions officer at a small, selective school wondered in an online forum, “Will the rSAT do a better job of distinguishing among students at the top end of the spectrum?”  This was what she was hoping for.  Other users of the forum predicted that it would not.  To do so would require a test with a wider standard deviation, and a large contingent of the (math-challenged) public believes that a wide standard deviation is inherently “unfair.”  In fact, the speculation was that the new test would do a worse job of highlighting differences among students.  Given that the redesigned test appears to have abandoned that goal altogether in favor of driving the curriculum, I’d say that admissions officers at selective schools will be plumb out of luck.

The practice PSAT is posted here: https://collegereadiness.collegeboard.org/sat-suite-assessments/practice/practice-tests

* You may be wondering what it means to have a test “drive the curriculum.”  Let’s look at an extreme example.  Throughout the 1990’s and early 2000’s North Carolina had a state writing assessment.  In fourth, eighth and tenth grades students had to write a timed essay and send it off to be scored by specially trained “experts.”  After several years of dismal results, some statisticians called “foul.”  They pointed out that the scoring methods were severely flawed, and thus that the scores were ultimately meaningless.  (By the way, the scoring methods used to score the ACT and SAT essays have some of the same issues.)  The state’s surprising response?  “Yes, we know.”  Students (and by extension their teachers and parents) suffered through this test for YEARS.  Why?  Because if there’s a writing test – even a flawed one - teachers will spend time teaching writing.  The average amount of classroom time spent on writing instruction quadrupled.  Prior to the test, some teachers had spent ZERO time teaching writing.

To pre-order the practice book for the redesigned SAT:

"Young people today can't make change" just took on a whole new meaning

About 20 years ago, I was standing in the checkout line at a cafeteria-style restaurant.  Everyone in line was over the age of 30 because that style restaurant mainly appealed to the older generation.  The checkout clerk, who was probably in her early twenties, rang up the man in front of me, and he handed her a 20 dollar bill.  She punched in the 20.00 and hit return.  Just at that instant, the electricity flickered.  The cash register momentarily went dead and then came back on, but the transaction was lost.  The clerk didn't know what to do.  At first the people in line thought she wasn't sure if the transaction had been recorded or if she needed to repeat it, but that wasn't the problem.  She didn't know how much change to give him.  She remembered the price of his meal.  She knew he had handed her $20.  She couldn't tell what the change should be unless the cash register told her.  Everyone in line knew exactly what the change should be, but she couldn't risk taking our word for it.  A succession of managers was called to the scene until they found someone old enough to know how to make change for a twenty without electronic aid.  Until yesterday that was my "young people don't know how to make change" story.

Yesterday, I was at the cash register paying for an item that cost $7.42.  I reached into my purse, grabbed a ten-dollar bill and then poked around in my change pocket.  I pulled out a quarter, a nickel, a dime and two pennies.  I dropped the change into the palm of the checkout girl and then handed over the bill.  She set the bill aside, spread the coins across her palm and stared at them for 20 seconds or so.  She stared for so long, I began to worry:  Had I grabbed a third penny instead of the dime I was aiming for?  Is she trying to find a tactful way to tell me I've given her the wrong amount?  Finally she looked up, held out the coins and asked, "Is this 42 cents?"

My first thought was:  what in the world would have happened if she had needed to give ME 42 cents in change?  If she can't count out 42 cents, what would she have done?  Grabbed random coins, and if I complained add more random coins?  Call a manager? I wondered how she had been handling this problem up to now, but then I realized:  I may have been the very first customer she has ever had that paid for something in cash.

We are rapidly becoming a cash-less society and as we do, the ability to count change is becoming obsolete. Money-counting lessons will eventually be dropped from the school curriculum, and my question is:  Will this have unintended repercussions?

I frequently have this exchange with my students:

Student:  (staring at 75 ÷ 25)
Me:  How many quarters are in 75 cents?
Student:  Oh. Right.  Duh. (writes 3)

Coinage is an excellent medium for practicing all sorts of math skills that have applications in other places, but how many of those applications will continue to be relevant?  Do we need to be able to do things like divide 75 by 25 in our heads?  Much of the math in the current high school curriculum is unnecessary for the vast majority of adults.  We teach it anyway because we want to leave the door open for our students to choose those careers that need math.  However, there are other things going on when we study math.  What we learn shapes our brains.  For a long time we justified teaching geometry proofs by telling students that proof by deduction teaches us "how to think."  Geometry proofs have largely been dropped from the Common Core curriculum.  (You can read my elegy here.)
Will we see changes for the worse in students' overall cognitive functioning?  Will becoming a cash-less society have an adverse effect on our brains?

READ, dangit!

There exist SAT and ACT tutors who fill out a form after the test outlining for parents why the student didn't get the score they wanted.  I think it's a CYA thing, and I can see the motivation, but it seems a bit mean.  However, if I DID fill out such a form, "Doesn't read enough" would be one of the check-boxes.  "Didn't do what I told him to" would be another, and for many students this would amount to the same thing.

Students (and their parents) are told the importance of reading over and over again.  We all know we should be reading, but many people -- teenagers in particular -- don't.  Even if a student is a big reader, sometimes they don't read a wide enough variety of texts.  How many times have you heard, "They can read ANYTHING! It doesn't matter!  Find something they enjoy!"  This is only true up to a point.  When it comes to college readiness, the ability to read non-fiction at a college level is crucial.  However, you can't count on colleges to teach the student how to do this.  They expect their students to arrive already reading at a college level.  In fact, college entrance exams are specifically intended to measure the ability to do this.  High schools haven't traditionally done such a great job either.  They tend to focus on the types of fictional reading the practice of which will come in handy if you major in English Lit.  The Common Core Standards are supposed to address this issue.  We'll see.

When I get a student who needs work in the reading section, I usually assign reading homework.  I send home articles that were written "for grownups."  The students get to choose what to take home, although I encourage them to choose articles on topics they know little about rather than articles they think they would enjoy.  This is the homework that is least likely to get done.  I'm not sure why.  Is it because they can't bring themselves to read "boring" stuff?  Is it because they don't see the immediate connection between the assignment and improving their test scores?  Is it because the improvement is not as immediate or obvious?

An aside--  If you are reading this, and you are one of my current students:  I can tell when you didn't really read the article.  I may have chosen not to embarrass you, but I know.

Usually when a child's reading score is low, it's because he really doesn't read all that well.  You can't fix that without reading.  So, READ, dangit!

Check back tomorrow for some specific reading suggestions.

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 12^th grade at all.  What’s left is just the arithmetic and modeling needed for science and statistics.  Where will our future mathematicians come from?

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 much 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 as early as January of 2013 (for block schedule high school courses.)  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 enough 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 who 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.

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.