"Recruiting to reject"

I was reading a blog post earlier today when I came across a new phrase:  "recruiting to reject."  It refers to a practice whereby students who have a snowball's chance in the proverbial hot spot's chance of getting into a college are encouraged to apply anyway.  The college then (predictably for those of us "in the know") rejects the student.  By rejecting these students, the schools admit rate goes down and they look more competitive than they would otherwise.  This, in turn, raises the school's ranking in various lists.  I've seen this going on a various local schools, but I never had a nice phrase to refer to it by until now.

Colleges use various methods of encouraging potential rejects to apply, and I was witness to some of them on a recent visit to a local high school.  I was there to talk to the career counselor.  She wasn't in, but I happened into a room in which an admissions officer from a local public university - I won't say which one because they are both equally guilty, but if you'll note my location you'll see which two I've narrowed it down to - was meeting with a group of prospective applicants.  Among the statements she made:

"We look at your whole application."
"We really look for people who have made A's and B's, but we admit people with bad grades every year.  It really depends on your story."  (Followed, of course, by an anecdote of a kid who failed six courses, but got admitted anyway.)
"Yes, we consider your test scores, but you are more than just your score."

I had to bite my tongue.  What I really wanted to do was jump in and say, "Yes, they will admit you with substandard grades or test scores.  IF you are 6 and half feet tall and have a terrific 3-point shot. Or IF you are a Hispanic Buddhist who will be the first in her family to go to college. Or IF your family has donated money to the school in excess of seven figures."

If you want to see if you are likely to get into a school, go to a website like Cappex. It's free, but you have to sign up.  They have admission trend scattergrams that plot on a grid all of the students signed up with them who applied to a particular school according to their GPA's and test scores.

Here is a sample:

See where the blue and green dots are?  Notice those stray blue and green dots that represent students with low test scores and/or low GPA's?  Those are the basketball-players, the kids of big donors, etc.  They are NOT the applicants who are generally described as "a good kid."  As in, "You know, he's just a good kid."  If nothing about you is VERY unusual (in a good way) then you are not destined to be one of the stray dots.  Consider whether to apply accordingly.

"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?

A less-biased look at Northeastern University's "meteoric" rise in the U.S. News and World Report ranking.

College rankings have taken a big PR hit in the last year.  Some of it is deserved.  However, as has become the norm in American public discourse, people eager to jump on the “bash the latest unpopular thing” bandwagon have demonstrated a remarkable lack of critical thinking skills.  This is especially sad when the topic is higher education – an institution that should be dedicated to encouraging critical thinking.

An article recently published in Boston Magazine by Max Kutner purports to be about how Northeastern University, located in Boston, managed to rise in the rankings of the U.S. News and World Report by “gaming” the system.  Before going on, it might be useful to note that “gaming the system” is typically defined to mean manipulating the rules in such a way as to gain an advantage.  It is generally understood that the entity “gaming the system” is not breaking the rules.  Rather, the entity is typically following the letter of the rules but not the intent.  Breaking the rules would be subject to disciplinary action of some kind.  “Gaming the system” generally is not.  Despite that, it is also generally understood that “gaming the system” is an unscrupulous act designed to obtain an advantage unfairly.

The article opens with a description of the state of Northeastern University in the early 1990’s.  Their situation was dire:  the school was under-enrolled and under-funded.  There was a real danger that if they could not turn things around, they might have to close their doors.  Enter one Dr. Richard Freeland who is charged by the author with making “gaming the U.S. News ….part of the university’s DNA.”

Here is a list of the things the university did under Freeland’s administration that resulted in a rise in the school’s ranking from 162 to 98:

•       Reduce class sizes
•        Begin accepting the Common Application, which made it easier for students to apply
•        Constructed new dormitories because studies showed that student who lived on campus were more likely to graduate
•        Do some PR to boost the school’s image
•        Report the number of students each year differently to reflect the number of students on campus instead of including co-op students

Wow.  How nefarious of them.  The author emphasizes that Dr. Freeland kept his eyes on the rankings throughout the improvement process.  What he fails to acknowledge is that, while the college rankings are far from perfect, they do include some measures that legitimately affect the quality of education.  Smaller class sizes are not only linked to better learning outcomes, they are also a measure that potential students and their parents find interesting.  Surely no one thinks that making the application process more convenient and accessible is a bad thing.  And if graduation rates needed to be raised (and it seems they did) then building dormitories sounds more like “data-based decision-making” than “gaming the system.”  Oddly, the author carefully avoids telling us how much the graduation rate rose, but rise it must have – the subsequent increase in ranking could not have been obtained otherwise.  On what planet is that a bad thing?

The one item in the list that sounds like it might be shady is the last bullet point in the list.  Northeastern changed their reporting methods.  Dr. Freeland realized that the metric being used by U.S. News hurt schools with strong co-op programs.  Northeastern counted significantly more students each year than were actually on campus, which made it look like the school was spending a lot less per student.  He took his case to the U.S. News statisticians who declined to change their metric, but who explained what they were doing with the numbers and why.  As a result, Northeastern stopped including co-op students who weren’t on campus in their numbers.  Is that dishonest?  I don’t think so.  I think it makes for a more accurate picture of their situation.

The article includes a list of schools caught flat-out lying on the numbers they report to U.S. News.  While the author acknowledges that this does not fall under the category of “gaming the system,” he does offer this as evidence that the rankings are irretrievably broken – an accusation the magazine denies.  Including them tends to – intentionally or otherwise – give the impression that the measures Northeastern has taken are as dishonest as these examples.

Not until the last few paragraphs do we find any evidence of actual “gaming,” and these were introduced after Freeland retired in 2006.  Northeastern stopped requiring foreign students to submit SAT scores.  Foreign students, for whom English is often a second language, can have lower SAT scores.  Not to require scores from foreign students may be a bit shady, although it has recently come to my attention that taking the test represents a true hardship for many foreign students by requiring an overnight trip to a distant city.  Some might consider dropping the requirement an effort to be more understanding.  Then in 2007, the school began a program whereby students could begin at NU in the spring – thus excluding their data from the reporting.  The author states that these excluded test scores and GPA’s are “lower” but offers no evidence for this statement.  They certainly could be, and if they aren’t, one wonders why NU would begin the program.

As a final jab, the author points out that the measures taken to improve educational quality at NU – and quality has undeniably been improved by increasing retention and graduation rates, if nothing else – has cost money, making the school more expensive.  This is undoubtedly true, but it’s an odd accusation to make.  Typically the complaint is that we don’t spend enough on education, or that when we do spend more, we don’t see an improvement in results.  Here is an example of a school that spent more – and it paid off.  The alternative was to close their doors.  Does anyone wish to argue that they should have chosen that as the more honorable course of action?  The price increase does, indeed, make Northeastern one of the more expensive options out there, but price is one of the factors every family should weigh in making decisions about where to send a student to school.

In over 30 paragraphs of writing, the author only mentions 2 possibly unscrupulous methods Northeastern may have used to improve their ranking.  He mentions several instances in which the school used metrics in the ranking to guide decisions that led to improved outcomes.  At one point the author quotes Lloyd Thacker as saying, “Have rankings contributed to anything beneficial in education?  There’s no evidence.  There’s lots of evidence to the contrary.”  As a refutation of that statement, I would point to Northeastern University.

Six Things You Should Do in College

Lately we've been hearing a lot of questions about the benefits of college in general and, more specifically, the benefit of attending a more-expensive, selective college over a less-expensive, less-selective college.  Evidence for the benefits of a college degree remains strong, but pundits are beginning to challenge the benefits of struggling to get into the biggest name school.  Evidence is mounting that what you do while in college matters more than which college you attend.

A new Gallup poll released this summer suggests that there are six choice students can make while in college that will make a difference in their Great Jobs Great Lives index.  The poll looked at five elements of well-being for 29,000 recent graduates:  social support, financial stability, physical health, sense of purpose and sense of community.  One interesting finding?  That students scored higher on the index when they had made these choices in college:

1. Do an internship or hold a summer job in your field of study.
2. Get deeply involved in an extracurricular activity.  (As opposed to shallowly involved in many activities.)
3. Do a long-term academic project - one that takes more than a semester.  It can be for a particular class, a senior thesis project, or an independent research project.
4. Find a professor that makes you excited about learning.  It doesn't have to be in your major.
5. Choose, as your professors, instructors who care about students as people.
6. Find a mentor.  This doesn't have to be someone associated with the university.

Doing these things was more important to the quality of graduates' well-being than their majors or which colleges they attended.  As you travel off to college this fall, keep these six things in mind, and look for opportunities to do them.

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.

Study materials review: Up Your Score ACT

Up Your Score for the SAT was originally introduced in the 1980's.  It is periodically updated by a fresh crop of perfect scorers.  (You can read my review of that book here.) This is the first ACT version.  It was put together by a test prep tutor (Chris Arp) and 3 perfect-scoring students who are now in college.  Like the SAT version, the book is cute and clever.  Also like the SAT version you have to wade through an awful lot of cute and clever to get to the actual meat of the advice.  As you may have gleaned from my previous reviews, I like the books that offer targeted practice.  This one does not.  It was not written as a stand-alone resource; you'd have to buy a guide with actual practice tests as well.  As of this writing (June 2014) the price isn't bad - about $14.  Still, there's no reason not to just check a copy out of the library.

There is some fairly interesting study advice that will apply to subjects other than the ACT, and, as I mentioned in a previous post, the section on punctuation is particularly useful.  If you really need to own your own copy, there is a link below.

It's hard to solve the triangle if you don't know what a "guy wire" is.

Happily all of my students currently studying trigonometry know that one would find a shadow on the ground, and all of them know how a kite works!  However, I did have to tell three students in a row what a "guy wire" is.

I'm not sure how we should be trying to address this problem.  On the one hand, we don't want a student who knows how to solve a triangle to miss the question because he doesn't know a non-math vocabulary word.  (And what about the ESL kids?) One solution might be to provide a labeled diagram with each question.  However, many would argue that being able to model the problem involves the student drawing his own diagram. Is there even a description of a guy wire that doesn't essentially tell the student how to draw the diagram?  And if we restrict ourselves to vocabulary that was used for examples in class, then how do we ever present a student with a novel problem?

The fact is that a word problem has to be about something.  And if the student has no experience with that "something" then it's a lot harder to work the problem.

(For more context, see this earlier post.)

Another great punctuation review for the ACT!

Up until now my favorite ACT punctuation review was Barron's ACT 36.  However, I have another favorite!  I am in the process of reviewing Up Your Score ACT: The Underground Guide.  I haven't finished it, yet, so stay tuned for the full review. However, I have reached the punctuation review in chapter 4, and it's pretty good.  The ACT 36 review is more thorough, but the Up Your Score ACT review is funnier and easier to remember.

If you really struggle with punctuation questions, choose the Up Your Score review.  If you are trying to get those last few questions for a perfect English score, go with the ACT 36 review.

A while back I wrote a full review of Barron's ACT 36 which you can read here.  I recommended that you borrow a copy for the punctuation review rather than buy the whole thing.  

Cheating on the college entrance exams

My kid went off to a prestigious college. He came home for Christmas break convinced that he was one of the few people on the planet who didn’t cheat on his college entrance exams. Apparently, everyone there had a story about his cousin’s boyfriend’s sister who cheated on the exam by doing fill-in-the-cheating-method-here. Some of the stories sounded rather unlikely to me, but the news at the time was all about that kid in ….New York was it? …who made a gazillion dollars impersonating other students and taking their exams for them.

In May of 2013 I took the SAT II Math Level 2 exam and I assure you, none of the cheating techniques would have worked. That’s not to say they never work, but the cheating techniques I hear about all depend upon having a dishonest or incompetent proctor. How prevalent is that? I don’t know. I do know that if your testing strategy depends entirely on having a bad proctor, you are likely to run into trouble.

I was recently asked to review a book entitled SAT SNEAK ATTACK: How Computer Geniuses Hack, Beat and Cheat America's Most Feared Exam by Peter Wayner. At 33 pages, it would make a better magazine or newspaper article than it does a book. The gist of it is this: 1. Poor pay causes the proctors to do a bad job. (There are no statistics on the percent of proctors doing a bad job, but since they are all paid poorly I suppose we are supposed to assume that they all are therefore doing a bad job.) 2. Because the proctors are not paying attention you can hide helpful information in your calculator, such as a dictionary. (Having your calculator out at all during the verbal sections is forbidden, so this requires a very inattentive proctor.) 3. You can also hide a program that helps solve math problems, although, based on the description, it sounded to me like this particular help would only be useful for students who would otherwise score very low in the math section. 4. Large numbers of students are cheating using this method. (Again, no actual statistics. This is based on anecdotes from college students.) 5. The author personally alerted the ETS to this egregious problem and they metaphorically rolled their eyes. 6. This means that the math help program is apparently “legal” and any test-taker would be stupid not to avail himself of this advantage.

The SAT was designed in such a way that you do not need a calculator AT ALL. You are allowed to use a calculator because too many high school students think they can’t do math without one, and because they aren’t really testing you on arithmetic anyway. The top test-takers know that using your calculator as little as possible will actually help you go faster in the math section. Spending time and money downloading some program that will solve triangles for you is pretty silly. The triangles on the SAT can nearly always be solved in your head. In the time it would take to practice using the program, you could just practice the math in the first place. But I guess then you wouldn’t have a fun anecdote about how you cheated the SAT.

You want the 700, but you don't have number sense: try this!

This post is a follow up to yesterday's post which describes the difference between a student who scores in the 700's on the math section of the SAT and a student who scores in the 500's.

So I've told my 500's student that getting a 700 on the SAT will be "a lot of work."  But what should that work consist of?  I have some activities we could do and some problems we could work, but we need to do the activities and work the problems over a long period of time so that she can actually internalize the lessons.  Unfortunately, working one-on-one with me for that period of time would be prohibitively expensive for a lot of people.  Is there a cheaper alternative?  Can someone do it on her own?

I have been using materials from Art of Problem Solving with a handful of elementary school students, and I am struck with the fact that they place more emphasis on the number sense than they do the algorithms.  They walk students through steps toward comprehension that focus on the meaning and assume that the algorithm will come on its own.  That process works best for the advanced kids, but that is their target market.  Still, I thought they might have something useful for the high school student who has learned the algorithms, but would like to retro-actively work on the number sense.

Introducing Alcumus.  Alcumus is a free online problem bank.  Once you register, it will give you a math problem.  Get that right, and you will get a more difficult problem. Complete enough problems in a row, and you will move on to the next topic. It is somewhat similar to the practice modules on Khan academy with a couple of notable differences:  First, you will be given an explained solution even if your answer was correct!  In fact, to get anything out of this exercise, you need to carefully read every explanation to see if there was a different, more intuitive (as opposed to algorithmic) method of solving the problem.  There are a few videos to watch for more instruction, but Art of Problem Solving believes in a problem-first approach.  There are also references to chapters in Art of Problem Solving math text books. (The books can be a bit pricey.  If you have the means, buy a couple of copies and donate one to your school library.)

Try to see if these methods lead to being able to solve complicated-looking problems in your head.  (It goes without saying that you should NOT be using a calculator.)  You will be led through addition, subtraction, the distributive property - simple stuff, but there are lessons here for how to think about these problems differently.  How to use your head instead of that hand-held machine you have been using as a crutch.

Try it!  I'd love to hear how it works out!

What does a 700 student look like?

Yesterday, a student who last scored in the 500's on the math section of the SAT asked me what it would take to score above 700 by fall.  She asked me during a class change at school, so there wasn't much time to say more than, "a lot of work." However, once she had gone on to class, I asked myself:

What is the difference between this young lady, and that hypothetical person who scores above 700?

Both students have taken all of the math courses listed as prerequisites and then some.  (This is true of all of my tutorees.)  Both have good grades in math (A's and B's.)  What is true of that 700 kid that isn't true of everyone else?

The short answer:  all of the kids can tell me that a certain math fact is true, but the 700 kid behaves as if the math fact is true.  For example, all of the kids can give me a definition of an even number.  They can all recognize one when they see it (if it is written as a number and not an expression.)  The 700 kid can glance at a problem, see that 2 will have to be a factor of the answer, and eliminate the answer choices that are not even.

A 700 student can promptly tell me that 1÷ (1/16) is 16.  A 500 student will either labor through the algorithm for dividing by a fraction or, more often, sit stymied because s/he doesn't recognize that the dividing-by-a-fraction algorithm is relevant. (Note:  this most often happens when the above exercise is expressed as a compound fraction in the first place.)

A 700 student understands additive inverses and therefore doesn't sit gaping in horror if I ask him or her to add all of the integers from -25 to 26 inclusive without a calculator.

A 700 student can tell me that the square of the square root of 2 is 2 without laboring through the algorithm for multiplying square roots.  (She or he also remembers from one day to the next what fractional and negative exponents represent.)

A 500 student may or may not be able to recite the commutative properties of addition and multiplication, although he or she will confirm that numbers can be added or multiplied in any order.  A 700 student may or may not be able to recite the commutative properties of addition and multiplication  depending on whether or not she or he remembers which property goes by the name "commutative."  However, she or he will not hesitate to rearrange addends or factors to find the most efficient way to compute the answer.

A 700 student recognizes that every integer has a unique prime factorization and understands that any factor of that integer must be the product of some combination of those prime factors. If asked, the 500 student can find the prime factorization of a positive integer, but he or she will not recognize those occasions when finding the prime factorization of an integer would be useful.  If the student has found the prime factorization of an integer (with or without prompting) to be 11 x 17, and if you ask the student if the original integer is divisible by 6, the 700 student will say, "no."  The 500 student will whip out a calculator and do the computation.

In short, the 700 student has a characteristic called "number sense".  The 500 student does not.  These two students might be in the same math class, at the same school, earning the same grade, but the 700 student is only working half as hard.  Furthermore, this will have been true for years.  I am currently working with two elementary school students - brothers.  One has number sense, the other doesn't.  I can already predict what their first SAT scores will be (or perhaps would have been if the test weren't changing.)

So now you're a junior and you don't have number sense, but you want that 700.  AND you're willing to do the work.  What should you do?  Check in tomorrow for instructions.

Study Materials Review: Ultimate Guide to the Math SAT

This book does not include anything new in the way of advice.  Its formatting is not as accessible as some of the other options, and a student working on his or her own may find it intimidating.  However, it does include plenty of great problems.  There is an art to writing good SAT-style math questions, and Richard Corn (an SAT tutor in New York) has the technique down.  I still prefer Top 50 Skills or PWN the SAT for students working on their own, but if you've worked through those, and you would like some additional targeted practice, this is an excellent option.

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.