The new SAT: Math

This is the second of a series of posts about the redesigned SAT.  Yesterday's post addressed comments made about vocabulary.

About the adjustments to the math section:

When Daniel Coleman announced a year ago that the SAT would be redesigned, he listed 3 reasons:

1.     To better serve the needs of college admissions officers.

2.     To improve equity.

3.     To better align with the Common Core curriculum.

At the time, the prediction among many was three-fold:

1.     The SAT would become more like its rival the ACT.

2.     The SAT would become less of a college entrance exam and more of a high school exit exam.

3.       The new SAT would be “easier” and thus do little to distinguish between top students and above-average students.

For the math section in particular, speculation was that, like the ACT, the SAT would test topics currently included in pre-calculus.  The current SAT doesn’t test topics past Algebra II.

Since the recent announcement giving more details about the SAT that will be rolled out in March 2016, some pundits are still predicting that the new SAT will be very similar to the ACT, but I disagree.

It’s no secret that the redesign was inspired in part by the ACT’s increasing market share.  Among other things, several states have contracted to give the ACT in schools as a measure of high school achievement.  That has to be a tempting market to tap. 

One detail in the announcement seemed designed to lure back students who would have chosen the rival test.  The current SAT "penalizes guessing" by subtracting points for incorrect answers.  The ACT does not.  Students have actually chosen not to take the SAT for that reason alone, and eliminating this practice is a much-needed marketing move.  It is also a move I heartily approve.  Less time spent on this useful-only-for-the-SAT test-taking skill means more time we can spend on content and problem-solving.

HOWEVER:  In a very bold move, the College Board also announced that part of the new test will be "calculator inactive."  This will be VERY unpopular, and since calculators are allowed on the entire ACT math section many students will choose to take the ACT on this basis alone.  The College Board may have shot themselves in the foot on that one.  I, on the other hand, am pleased as punch.

In Wednesday’s announcement, they said that the math section would include fewer topics, not more.  The topics are vaguely divided into “Problem Solving and Data Analysis”, the “Heart of Algebra”, and “Passport to Advanced Math.” One presumes that each topic would then be tested in more depth.  This would be consistent with the Common Core goal of studying fewer topics in more depth and of promoting critical thinking skills.  The list of topics was very vague, but nothing in the list specifically pointed to the inclusion of pre-calculus topics.  As for the difficulty level of the questions, it’s much too early to tell.

I am ambivalent about a reduction in the number of topics.  On the one hand, does a college student really need to be able to apply the Hinge Theorem – a topic on one of the Official Guide practice tests?  On the other hand, a student who didn’t remember the theorem could reason through the problem as long as he understood the basic principles of geometry, and isn’t the ability to do that exactly what the test purports to measure?  Won’t reducing the number of topics just put a limit on the questions that can be asked?  Or would this question continue to be asked because the student can reason through it using……wait.  Geometry isn’t in the list of math topics.  Unless it is included in “passport to advanced math” – and what IS that, anyway? – then GEOMETRY IS NOT ON THE REDESIGNED SAT. 

Well, that would solve their market share problem, right there.  On the other hand, if I’m a college math, physics or engineering department, I definitely want to know if the kid remembers geometry.  So, if they leave it off the SAT, will colleges start requiring the ACT instead?  And if this test is designed to influence high school curriculum, then will geometry no longer be taught in high school?  I guess we won’t really know what the topics are until we actually see some sample questions, so I’ll try to avoid getting my panties in a wad between now and then.  Still.  It’s something to keep an eye on.

I’ll be posting about local high school students’ experience with an implementation of the Common Core math standards in a week or so once I get the SAT stuff said, but at this point it’s relevant to remind the reader that the “architect” of Common Core and the leader of the College Board are the same person.  When the announcement first came out that the SAT would be redesigned, aligning with the Common Core standards was specifically mentioned.  But in the announcement last Wednesday, College Board spokespeople and the media were strangely quiet on that point.  Perhaps because Common Core’s approval rating is currently in the toilet?

But, I digress.  One other announcement was indirectly math-related.  Oddly, the one change that seems to have resonated most with the general public is that the SAT will go back to scoring on a 1600-point scale.  I thought this was a silly thing to focus on, but then someone pointed out that this causes your math score to represent half of your overall composite instead of one-third.  That’s true.  The individual who pointed it out was bemoaning this fact (she was an English teacher) but as a math major I am pleased.  I also think it is appropriate given the current emphasis on STEM.

So, changes to the math section:  Good or Bad?  It’s too early to tell, but I confess I’m worried.

The Cost of Calculators

Before calculators, if we spotted a zero as one of the multipliers, we thought something along the lines of: “Woohoo! Less work for me!”  With today’s students a multiplier of zero barely registers. I swear I have had this exact conversation with multiple students:

Student:  (busily using a calculator to multiply a long string of numbers)

Me:  Sweetie, STOP.

Student:  (looks up)

Me:  There’s a zero in there.

Student:  Huh?

Me:  All of those numbers you are multiplying.  One of them is a zero.

Student:  Ok.  (goes back to multiplying)

Me:  STOP.

Student:  (looks up)

Me:  If you multiply something by zero what do you get?

Student:  (long pause)  Zero?

Me:  Exactly!

Student (gives me a look that says plainly, “And that applies to my life, how?”)

Me:  So you are going to multiply along and get some number. You are going to multiply that number by this zero. You will get zero.  You will multiply that zero by this number and get zero, and so on.  What will you have at the end?

Student:  Zero?

Me:  So write it down, and MOVE ON!

Book review: Math From 3 to 7

I am thoroughly enjoying Math From 3 to 7 by Alexander Zvonkin.  From the back cover:

"This book is a captivating account of a professional mathematician's experiences conducting a math circle for preschoolers in his apartment in Moscow in the 1980's."

The author kept a journal in which he described the activities he did with the children and the results - both success and failures. At the request of friends and colleagues, he edited the journal for publication. This volume is the English translation of the edited work.

I find this book fascinating on a number of levels.  First, the Forward to the American Edition describes ways in which Eastern Europeans approach math education and describes the concept of a "math circle." Apparently there are a few math circles here in the US, particularly in university towns, but it is definitely phenomenon that needs to spread.

Next, I enjoy reading about the puzzles and activities he does with the children.  The activities look like a lot of fun, and I would like to try them out. Since I no longer have young children of my own, I am considering kidnapping other people's children so I can do these activities with them.  (I would only kidnap them temporarily.  Their parents can have them back when they get tired and fussy.  :)) Many of the activities could even be extended to be appropriate for older children - even teenagers.  I would recommend this book to elementary and middle school math club advisors.

Last, I am very interested to see which concepts the students grasped and which they struggled with. In several instances you can see Piaget stages illustrated. In editing his journal, the author added some thoughts on cognitive psychology which I have enjoyed.

I wish I had read this book before I had kids.  I recommend it for anyone who lives or works with children under the age of 12.

Top SAT Scores Begin in the Sandbox

Top SAT Scores Begin in the Sandbox

In my last post I wrote about when a student should start preparing for college entrance exams. I described the parents who wanted me to start coaching their sixth-grader. (Read that post below.) As crazy as that sounds, I know that there are parents of even younger children who are already obsessing over how to maximize their child’s chances of getting into a top college. Some of you may eventually find your way to this blog. This post is for you.

I was teaching trigonometry in one of the top public high schools in the country. The class was in the middle of a test when one of my best students came up to ask about one of the questions.  Some exploratory questions on my part revealed her problem. The word problem concerned flying a kite. She had never flown one. She didn’t understand how an airborne kite would behave. It was about that time that I began to realize: American teenagers are suffering from a sandbox deficit. They have spent too much time interacting with virtual environments and engaged in structured schooling and not enough time engaged in hands-on play activities that build the concrete foundations for more advanced learning.

I proposed the Sandbox Deficit theory to a fellow attendee at a meeting for recipients of an NSF grant for STEM programs. A professor of engineering at a university in the Midwest, he shared that his department had come to the same conclusion at a department meeting. Our young potential engineers are handicapped in their studies by the lack of a basic, hands-on experience of the world that used to be universal.

There is something fundamentally wrong with having to add remedial kite-flying to the trigonometry curriculum, but that is not as horrifying as the teenagers who don’t understand how shadows work.  (Read a fellow blogger's post on that subject here.)  One wonders if some of our youngsters have ever been outside. The director of an environmental education program for honors-level high school students shared, “The first thing we have to do is teach the children how to be outside. When they come for the first session, they are all dressed inappropriately for the weather and the environment.”  The real shocker:  These children aren’t inhabitants of the “urban jungle”; all come from five of the most rural counties in North Carolina.

Everywhere I turn I see advertisements for the latest early childhood electronic learning program. Parents who elect not to enroll their toddlers in pre-school announce they are “home schooling”.  Some are actually using formal preschool curriculum. Meanwhile, formal school tasks are filtering down to younger and younger grades.

As high stakes testing adds pressure to perform academically, schools are trying to maximize classroom learning during the school day. Parents are lining up tutors and extra-curricular activities in an attempt to make sure their children have every advantage.  More and more the thing that is missing from our children’s lives is unstructured play.  Researchers are beginning to look at the learning that takes place during play, and the result of removing play opportunities from the school day.  (Read an article on the subject here.)

As time goes on, I expect that we will hear of more and more evidence of the importance of play and the necessity of scaling back students’ interactions with electronic “learning” programs. Meanwhile, as I work with students preparing for their college entrance exams, I continue to see first-hand the effects of the Sandbox Deficit.