This figure is not drawn to scale

Both the ACT and the SAT math sections are filled with figures and diagrams.  Can you trust what you see?  That depends on the test.

On the ACT none of the figures are drawn to scale.  They make this disclaimer at the beginning of the math section.  You can still trust certain aspects of the diagram.  For example, if it shows that two line segments intersect, then they really do.  Sometimes they will give you facts about the diagram that you should assume.  However, sometimes they can be mean, and looks can be deceiving.  Here are some things you CANNOT assume about the diagram. Consider the diagram below:

Unless it is stated or you can prove it given what is stated, you CANNOT assume any of the following:

• that segment AC is tangent to the circle 
• that point O is the center of the circle
• that D, O and F are collinear (in other words, angle DOF could be 179°)
• that any angle shown is a right angle, an acute angle or an obtuse angle
• that any segment is longer than, shorter than, or the same length as another based on how they look

For the SAT on the other hand, you should assume that every figure is drawn precisely to scale unless there is a note under the figure that says otherwise.  If the figure IS drawn to scale, you can use that information to eliminate some of the answer choices. Again considering the figure above:  If you are told that segment OB is 3 inches long and asked the length of segment EF you can eliminate any answer choice that reads 3 inches or longer, since EF is clearly shorter than OB. 

Does the Math SAT measure anything worthwhile?

Daniel Coleman recently announced that the College Board will begin a process of updating the SAT. Again.  The last update was in 2006. While that may seem like a lifetime ago to any teenagers faced with taking the test, it feels more like yesterday to the "old fogies" among us.  The announcement has spawned a rehash of the usual anti-test rhetoric, which tends to consist of variations on the following:

• The test doesn't measure the true abilities of students who know the material but don't "test well."
• college entrance exams are unnecessary since a college can learn everything they need to know from other parts of the application - particularly the student's GPA/transcript
• the SAT in particular is "not aligned with the curriculum"
• college entrance exams, and the SAT in particular, are too "coachable."  This gives an unfair advantage to students whose families can afford expensive courses or tutors.

The article lambasting the test in question generally ends with a call to end all testing that is standardized and/or "high stakes" immediately and directly.

My expertise is primarily in the math section.  For a discussion of the reading section, I'll refer you to this article by Erica Meltzer "Why good grades in English do not always correlate with high SAT Verbal scores."

As test prep coach, I am frequently called by a parent who assures me that her child's grades are top-notch, but he/she just doesn't "test well."  The parent seems to feel that the student knows the material, but can't show it on the test.  Usually I discover that the student understands the material at such a shallow level that he or she can only answer a question if it fits the same pattern as the questions that have always been asked in math class. Furthermore, this only works for more recent material.  Topics covered more than a year before have been forgotten because they were never thoroughly understood in the first place.  Once I've worked with the student for a few hours, I've uncovered a list of "holes" in his or her math understanding.  Salman Khan discussed this phenomenon in a Ted Talk.  (Watch the Ted Talk here.  The part about holes in understanding is in minutes 8 through 10) A child can make an A or a B on a test without mastering about 15% of the material. Since math is cumulative, these holes add up.  Eventually the student will hit a wall. Suddenly, after years of A's and B's, the student is struggling to pass math.  The angry parents will often blame the teacher since, "he was doing well until this year."

The Math SAT shines a big spotlight on all of those holes.  Let's look at an example that should be accessible even to those readers who may be math-phobes:  even and odd numbers.  At the most basic level of understanding, a student can recite the definitions of even and odd numbers and identify a particular integer as being even or odd.  At a deeper level, a student should be able to apply the definition in order to answer a novel problem, such as "a and b are both even numbers. Which of the following could be the product of a and b?"  If you truly understand what it means to be an even number, you will realize that, of the choices given, the answer is the only one divisible by 4.

Critics see questions such as the above and wail, "The test is not aligned to the curriculum!"  Really? Since when are odd and even numbers not part of the curriculum? Apparently saying that is someone's attempt to translate, "The problem doesn't look exactly like the homework," into educationalese.  Of course the problem doesn't look exactly like the homework! That was the point.

Sometimes, on one of the earlier questions, an alert student will realize that she doesn't need to perform the tedious arithmetic called for in the question because the answer will have to be even and there is only one even answer choice.  Critics wail, "The test is too easy to 'game'!  A student can get the correct answer without even working the problem!"  Having a deeper understanding of odd and even numbers isn't "gaming" the test. That IS the test! Do you really think the folks at the College Board are so stupid that after decades they haven't figured out that to prevent a student from doing that they should include more than one even answer choice? They wrote it that way on purpose.  A student with a deep understanding of math can breeze through that question and have more time for the difficult questions at the end that are more at her level.  Meanwhile, however, other students can still get a correct answer. They just have to slog through the arithmetic. Test questions such as these are brilliantly designed.

"The test is too coachable!"  Hah. As a test prep coach I wish it were.  One mom took on a year-long project of attempting to get a 2400 on the SAT.  Her study regimen included just about every program or technique ever invented.  She even had a tutor at one point. Her math score barely budged. (Visit her blog on the subject here.) I have students who make dramatic gains on the math section after seeing me, and others who don't. Some students have a thorough understanding of the material, but they've never seen the types of test questions that would test a deeper knowledge.  Once you show them what these questions look like they are off and running. I don't try to explain Bloom's Taxonomy.  They think they are "gaming" the test.  Some of them, bless their honest little souls, anxiously inquire if using their new awareness is "cheating."

It is true that the students who come to see me often make dramatic gains.  And it is true that most of them have paid about $300 (total, not per hour) to do so. However, the solution to that problem is not to "fix" or eliminate the SAT. The solution is to include questions that test a deeper level of understanding on the students' every day math tests!

Critical thinking skills are enormously difficult to measure.  We want our students to learn critical thinking skills, and we would love to have a good measure to decide whether or not they are, but most tests, and in particular most teacher-made tests, assess learning at a fairly superficial level.  If I were in the admissions department at an engineering school, I would absolutely want to see a student's math SAT score. Even if the child has managed A's in math up to this point, I would want to be alerted to the holes in his understanding at the earlier levels that might keep him from continuing to perform at that level. I only hope that the SAT continues to be a test that can fill that role.

What I do

I'm sorry I haven't posted in a while.  I am hard at work trying to finish a new tutoring resource.  I have a pair of students who will need to use it in just a few weeks, so I'm on a tight deadline.  I thought I would take a moment here to explain what I do as an SAT/ ACT coach.

As a test prep coach I work with students who are working to get a better test score.  Sometimes everything goes very well and the student sees a dramatic improvement.  Sometimes the score hardly budges.  Some day I'll have to write a post about my theories on why it works that way.  

If you've tried to prepare for a standardized test on your own, you probably know:  there is an awful lot of information out there.  Some of it is contradictory.  To figure out what would work for you could take a long time.  Sometimes a student will write about how he managed to raise his score by hundreds of points all by himself.  Typically this took months.  The students who contact me for help don't have a very long time.  They only have days or weeks before they have to take the test.

There are coaches who will work with students starting in middle school.  They will meet with the student every week to work on test prep.  This process can go on for years. Over that time a family could spend thousands of dollars on coaching, not to mention hundreds of hours of the student's time. That's not my philosophy.  These tests are important, sure, but so are other activities. College admissions officers are going to be interested in how you spend your time.  They don't want to see that you spent it all on studying for one test.  I like to work with a student for a couple of months at most.  We hit the high points, brush up on some topics that they once knew but have since forgotten, and develop a testing strategy.  The whole thing typically costs around $300.  A family usually spends about what they would on a video game console.

If you are trying to decide whether or not to hire a test prep coach, just remember:  It doesn't have to take months and it doesn't have to break the bank. Find someone who shares your philosophy and fits your budget.

Another critical period in early childhood development: Movement

Each Monday I will review a different study guide or study tool. On Tuesdays and Thursdays check in for test-taking advice, tips and reminders. On Wednesdays you may find a post about standardized testing or education in general, and on Fridays articles geared to the parents of children age 0 to 13. Experience has taught me that there are many parents of young children who are already worried about SAT scores and college admissions. Some of you may find you way to this blog. This post is for you. I’m sorry it is late.

In my last Friday post I wrote about the critical period for language development in children.  Another window of opportunity that is open in early childhood is associated with movement.  Young children were designed to move!  They are wiggly for a reason. Neural pathways associated with large muscle movement are being developed from the prenatal period to about age 5. During this time you want to give your child the opportunity to move in as many different ways as possible. Crawl, climb, hop, skip, dance, balance on things, roll a ball, stretch. A toddler tumbling class might be fun, but none of this needs to be formal.

When pediatricians call for less “screen time” for preschool children, we sometimes stop to ask if sitting in front of the TV is harmful.  What if the child is watching something educational? You should consider that the problem might not be what your child is doing as he sits in front of the TV; it might be what he’s not doing.

You can read more about this here.