Study Materials Review: College Panda SAT Math

I am often introduced to a new resource by my students.  That's how I became aware of The College Panda SAT Math Advanced Guide and Workbook.  The students was one for whom I would usually recommend PWN the SAT Math Guide: an advanced math student who has covered most of the material but who needs practice with looking at problems from different angles.  He had already been through PWN the SAT and was looking for more problems.  Somehow he stumbled across College Panda.

The tag line on the back of the book reads, "If it's not in this book, it's not on the test," and that's pretty nearly true.  This is a comprehensive book with a LOT of problems.  The problems represent a wide range of styles and difficulties and are nicely divided into categories so you can target your problem areas.  The problems also "feel" right.  The most difficult problems in each sections tend to be a tad more difficult than the most difficult problems on the SAT.  That's a good thing.  (Actually, in a few spots the problems resembled those on the SAT Math II subject test.)

The book does not include any practice tests to work on strategy or timing, so you will need access to some practice tests for that purpose.  (The same company has helpfully provided a book of practice tests in case the 7 - as of this writing - provided by the College Board aren't enough.  I haven't taken a good look at it, yet, so you can expect a review of that eventually.)

If this book has one weakness, it is that it is light on strategy.  It consists of examples, practice problems, and annotated answers.  There is little in the way of advice about timing, approaching multiple choice questions, or anything else that might fall under the category of "testing tip."  The author, Nielson Phu, seems to feel that the road to a perfect math score shouldn't involve any sign-posts for students who can't answers questions through sheer math prowess.  While I agree with that in principle, even the best math students needs a toolbox of techniques to pull out for when she or he doesn't immediately see how to approach a problem.  Students in the 600's to low 700's might get the most out of this book when used in conjunction with a tutor.

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:

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.)