Case Study: Calculus and Peer Pressure

Taking Calculus in High School is very different from taking it in college; particularly from a social point of view, especially for AP and Honors courses.

For example, I hear from my students about the egos and social pressure, shaming and boasting that goes on in some of the AP classes.  Most of the students already know each from earlier years and thus can be too comfortable playing out certain kinds of immature agendas. 

One particularly insidious example is when a student gets a high score, he boasts that he did not prepare for the test, and will offer pseudo-sympathetic words to another student who worked hard, but got a lower score.  

Marisa, a senior in High School, started tutoring part way into the second semester, at a time when students often begin worrying about the Calculus AP exam.   She was very bright, but had been a target of the situation mentioned above.  (Although the braggart did finally confess that he had in fact prepared for the test.)

She was fully capable of passing the AP but her confidence had suffered from a few social interactions, making her nervous to the point of affecting her ability to learn some of the new material in class.  I knew it was time for some confidence building !

For example, while working on a problem involving lots of Algebra steps and messy fractions, I just might intentionally make an arithmetic error and ask Marisa to help check my arithmetic.  When a student finds my error, it makes her feel good, and I see the pride building.  

Or, when she begins to understand the material, turn the tables, and ask her to pretend I don't get it, and explain it to me. I always ended sessions with a list of her wins.  

Case Study: Patience and Perseverance

J.S. began tutoring in preparation for SAT Math during the second semester of his sophomore year in High School.  He had received a Math score in the 500s (approximately 73rd percentile) on the PSAT, but had his sites set on getting a scholarship to specialized program, which requires a score over 700.  We met once per week for slightly over a year.

J.S., even though he wanted the help and was enrolled in honors classes, he was not exactly thrilled at first about having to carve out extra time to prepare.  Over a period of months, he seemed less resistant to the idea, even began to enjoy the sessions, and welcomed the additional help he also incidentally received with Algebra 2 and with the verbal sections of the SAT.

We did practice "mini-quizzes" and full practice tests as we progressed, and J.S. was happy to see that his scores were inching upwards.  We even met for sessions at various intervals over the summer to keep him "tuned-up."

About halfway through his junior year, he achieved a score of 680 on the SAT Math, putting him in the 95th percentile nationwide.  We were very happy!  But.....a family member wanted J.S. to try once more to break the 700 mark; the reasoning was that it was well into the "scholarship zone" at top schools.

So, we dug in again for a couple more months, producing a final score of 740, approximately 98th percentile!  As a bonus, his verbal score also rose to the high 600s.

Perseverance works!

Case Study: Are you open to new approaches?

Not long ago, I met with a new student whose goal was to reach a perfect or almost-perfect score on the Math portion of the ACT.  She was only a few points away, so it was time to put on my "detective hat" to see how we could squeeze out those last few points.

I began by explaining that there might be some surprising ways to accomplish this, and they might be easy to implement--"low-hanging fruit" I call them.

First, I had to check her out on something that may surprise you--basic Math facts!  What?!?  For an honor student getting an A in her Calculus course?  Yes, I test everyone for this, regardless of age, gender, or academic standing.  In fact, it turned out that she did not know some of the basic Math facts (like 8+5), and was losing valuable testing time punching them into the TI-84 graphing calculator, not to mention "mental space."

Now, I can understand where someone could find this a bit embarrassing, so I know to tread lightly, and tell the student she is in good company;  at least 50% of my Math students of all levels, have gaps in the basic Math facts and/or fraction operations.  I consider it part of my job, to uncover any skeletons and usher them out of the closet.  It's also very easy to fix, usually in less than two weeks, which is where the "low-hanging fruit" idea comes in.

I have found that many students who are looking for personalized help with Math have some form of "skeleton" that needs to be exposed and dismissed, be it a missing skill or some limiting concept.  Being open to this kind of discovery can make it easier for you to reach your academic goals!

Grandma is a Mathdork?

"Every student is different."  But I'm not here to bore you with platitudes.  Everyone does learn in a different way, and everyone can benefit from the right fit for tutoring and test prep.  Some students look for a tutor with a specific background, specific interests, and of a specific age. Sometimes I wonder, though, is this a reactive motivation, rebelling against the approach taken by a teacher you don't love?  I believe student is really seeking is that elusive human element, a rapport with the person in whom she is investing hopes for achieving academic goals. 

Think about a grandma--less agenda, right?  Non-judgmental.

So what is good about a grandma tutor?  Here is what I have been told:  minimal invested ego;  I have proved or disproved my abilities long ago, and am free to focus on the student.  My style is student-centered as opposed to "program" centered. Who is this about? I work for you!  

I also work with non-academic factors that influence both learning material and performance on tests; I know what is important to teach along with the how-to.

SAT: Strategy vs Achievement

Most of us would agree that the SAT is a "different animal."   But what do we mean?  It's not like schoolwork, not like a test you may have to take in your Algebra, Geometry, or Calculus class.  So, in a way, very few students are actually prepared, since much of the material may be presented in an unexpected way.

Years ago when I was teaching High School, I would often include on a test, one problem (maybe for extra credit, maybe not) that my students had not seen before.  It would require applying what they learned, going a level of abstraction above the specific processes that were taught. Many of the SAT Math questions fall into this category, and both students and parents ask--why?  Why are they torturing our kids, who work so hard for their GPAs, and then have to take on additional challenge? Why isn't SAT Math taught in school?

There are several answers to this question:  First, the "A" in the SAT stands for "aptitude," which is different from "achievement."  Many students can achieve high grades by working hard and memorizing methods of doing problems, or even by doing lots of extra credit work.  Arithmetic, basic Geometry, and beginning Algebra can be learned in large part by how-to.  But, advanced word problems and complex Algebra cannot.  While some basic problems are included in the SAT, the makers of the SAT are testing for skills that go beyond how-to, testing a student's deeper understanding of concepts and how the pieces fit together.

Second, schools are already extremely pressed for time in covering required topics, and typically might not have time to work on test prep during regular school hours.  A third consideration is that practice is an important component of preparation, and practice also means time--possibly lots of time--depending upon the student's goal scores.

Why is motivation so important?

Imagine you are a hiring manager or business owner, and job applicant is sitting across the desk from you.  Perhaps you interviewed another job-seeker earlier in the day, who had some awesome credentials:  graduated from a top university, great GPA, etc.  But, he had seemed a bit complacent.  The person sitting in front of you now, however, is a bit less comfortable, even a little nervous.  You notice she is observing the contents of your office, and she is making an effort to maintain a smile.  She really wants this to go well, and as you converse, you begin to understand she really wants this job.  Her credentials aren't quite as impressive as the previous interviewee, but they are acceptable.

I don't know about you, but all other considerations being equal, I would likely hire #2.  Why? She seems more motivated!  And I want someone who will get things done.  Solve problems. Motivate others.

This is not an employment website, of course.  But many of the exams you may sit for are testing more than your knowledge on a particular topic--they are designed in part to test how you perform under pressure, and how far you can push yourself.  Will you keep your cool during finals week?

To show your potential, for the vast majority of students, you will need to prepare, because the testing experience is so different from classwork and homework.  The students who are motivated to take the time and effort to prepare will necessarily do better on the exams.