To keep myself focused on the challenges of learning, I like to regularly turn the tables and become the student.  Studying a subject that comes naturally for me would defeat the point, so I choose classes in higher math and foreign languages (both subjects that require a lot of work from me).

These days, I’m taking a free, online pre-calculus course and I’m glad I am, because it’s reminding me of some of the pitfalls that can easily sneak up on unwary teachers.  The material itself isn’t terribly difficult, but much of it is new to me.  Although I can follow each lesson without problems, putting it all together has been quite hard.  As an adult and an experienced teacher, I know I’m having trouble because the lessons are being given with very little context.  That is, the way the different mathematical techniques connect to each other and to the physical world isn’t being addressed.  From a mathematical perspective, I’d be getting more from this pre-calculus course if the material were being presented in a more connected way, but for my students, the structure of this class is great.  It’s serving as a forceful reminder that I need to put every topic into a larger context for them.

New York Academics is committed to putting every topic into a larger context for for you. Visit us at www.tutornewyorkcity.com, or call us and we will be happy to assist you  347.626.1842.

It is encouraging when a math curriculum lays the foundation for higher levels of math, while staying firmly age-appropriate.  Recently, I’ve been using Impact Math with a middle schooler, and I’m very pleased with this book’s chapter on “Stretching and Shrinking Machines.”  From my student’s point of view, she’s learning about exponents and reviewing factoring.  That’s great- but what makes this chapter a little bit unusual, is she’s also getting used to the idea of functions, which become very important, particularly in trigonometry and calculus.

I don’t have access to relevant research studies, so I can’t be sure if introducing the concept of functions in a meaningful way early actually improves outcomes when students take trigonometry, pre-calculus, and calculus, but it seems like a good bet that it will.

New York Academics can help you learn these skills. Visit us online or call us and we will be happy to direct your efforts.  347.626.1842

Trigonometry is essentially the study of triangles.  Most people don’t use trigonometry on a regular basis, but there are a multitude of fun and exciting applications of trigonometry that are out there if you look for them.  One of my favorites is using trigonometry to measure the maximum height that model rockets achieve when they are launched.  You could use any sort of rocket, from a simple water rocket to a relatively sophisticated model propelled by a solid fuel engine.

I was first introduced to the idea of teaching trigonometry along with rocketry by a wonderful history teacher I worked with.  This was in a rough school in Mott Haven (that year, approximately 4% of the students in the school were arrested for committing violent crimes).  Students were not exactly falling over themselves to excel academically.  Nevertheless, the promise of launching rockets was so alluring that a large number of them joined the club, even though they knew that they’d have to learn some trigonometry.

On the down side, actually building and launching rockets is much more time consuming than simply doing problems on a chalkboard.  (It can also be expensive, although that isn’t such a big problem because there are some pretty inexpensive ways to build water rockets.)

It is possible to find the height of a rocket with beginning trigonometry.  Most high school graduates learned the math at one point or another, but nearly everyone forgets how to do this sort of problem shortly after they finished up their last trigonometry exam.  One of the big advantages of teaching trigonometry with rockets is that it is much more memorable- even if the details fade over time, students who learn this way are likely to take an appreciation of the usefulness of math with them into adulthood.

The reaction between sugar and acid is quite spectacular.  A mixture of white powder (sugar) and a clear liquid (sulfuric acid) quickly turns black, expands, and gets hot.  It often steams visibly and pours out of the container that it was mixed in.  (There are lots of videos on youtube if you want to take a look.)  This reaction makes a very good chemistry demonstration, but it is not advisable to use this as a hands-on activity with students.  The sulfuric acid can be quite dangerous and the reaction forms a permanent crust on the glassware used, which would make it prohibitively expensive to do more than a few times.

To make the sugar/sulfuric acid dehydration reaction an effective chemistry demonstration for Halloween it should be paired with a dramatic frame story.  I first encountered it presented as a method used by a mad Victorian scientist/murderer for disposing of bodies.  The teacher spun a hair-raising yarn about bodies dissolving in acid and the murderer being caught when a detective became suspicious about the strange black crust on the bathtub.  Of course, it is not enough to merely entertain students with a scary story and a startling chemical reaction.  It is also important to teach some chemistry.  There are quite a few topics in chemistry that this demonstration can be linked to.  For younger students, it might be enough to discuss how we know that this is a chemical change instead of a physical change.  For more advanced students, it’s a good opportunity to discuss exothermic reactions, dehydration reactions, or elimination reactions.

Optical illusions are a great way to explore optics, which is a branch of physics that often doesn’t get its due in high school physics classes.  There are an almost unlimited range of optical illusions to explore.  For physics classes it is important to focus on illusions that rely on physical principles rather than quirks of anatomy or neurology.  One example of an illusion that is well suited for physics class is called “Pepper’s ghost.”   This illusion was perfected in the nineteenth century by a chemistry professor named John Pepper and is still occasionally used in theatrical performances and haunted houses.  The effect of the illusion is to cause the appearance of ghostly images to appear in glass (if the lighting is such that the glass is not visible, the image can appear to float in mid-air).  Pepper’s ghost can be used to study reflection and refraction.  It is also a good opportunity to teach skepticism of paranormal events.

One of the great pleasures of teaching science is that there are so many opportunities to tie in real, rigorous, science with tremendously fun hands-on exploration.  Halloween is a particularly nice excuse to pull out a big, exciting lab that still teaches really good science.

In the long-term, the best way to prepare for any test, whether it’s a high school admissions test like the SHSAT, ISEE, or SSAT, a college admissions test like the SAT, or a test to identify students for admissions to gifted and talented programs like the SCAT, is the same.  Being a conscientious, ambitious student and an avid reader pay off very well on test day.  Attending a school with high academic standards is sometimes out of an individual’s control, but it is also a key predictor of success.

In the medium-term, the best way to prepare for a big test is to take practice tests and think critically about questions you did not get correct on the first try.  Mastering techniques such as using the answer choices to help solve problems, eliminating answer choices that are obviously wrong, and referring back to reading passages when answering tricky detail questions is important, but these techniques are not secrets.  They can be learned by reading readily-available books on test preparation, by working with a private tutor, or by taking just about any test preparation class.

If there are no secrets to test preparation, is there any reason to work with a tutor?  The answer can be yes.  Working with a personal trainer can be the most effective way to meet fitness goals for many people, even though the personal trainer doesn’t possess any “secrets.”  In the same way, working with a tutor is often the most efficient way to get ready for a big test.  Tutors provide motivation and accountability and an experienced tutor knows how to get the most out of study time.

For families that can afford private tutoring, it is a highly effective option that provides convenience, saves time, and reduces stress.  However, families that cannot afford tutoring should not despair.  Independent study using commercially available test prep materials is a perfectly respectable option.

For individuals studying on their own, it is important to use high-quality study materials.  (In fact, one of the advantages of hiring a tutor is that a professional should be able to guide you towards the best study materials.)  As a general rule of thumb, it is a good idea to use official practice tests provided by the same organization that administers the test whenever possible.  For additional materials, it is often a good idea to read reviews of the available books before making a purchase.  We particularly recommend the materials published by New York Academics.  The Barron’s SHSAT book also stands out as being the best in its category.

The first book I looked at for her is Personal Finance by Karl Biedenweg.   I will review the second book, Teaching Money Applications to Make Mathematics Meaningful by Elizabeth Marquez and Paul Westbrook in a separate article.  Personal Finance is clearly labeled as a social studies workbook, not a math book, and that is accurate. It does have exercises that require basic arithmetic, such as balancing a checkbook and calculating interest. However, math is not the focus and it keeps the math pretty simple. For instance, the interest exercises assume that interest is compounded annually, which is a decent approximation of reality, but not actually true in modern banking.

The strength of this book is that it clearly introduces the basics of some important concepts such as bank accounts, insurance, home ownership, stocks, and bonds. All too often, students don’t get any formal instruction about these topics. The simple way in which math is included is probably best for most middle schoolers.  With high school students, it would be important for the teacher to use his or her judgment- some high schoolers would get a lot out of this book while others would find it condescending.  For either middle or high school students, this book is a good option for students who need to learn basic ideas about personal finance but who would be distracted or intimidated by having a lot of math in the lessons.

It is important to be aware that this book restricts itself to math that most students learn in middle school.  Therefore, it will not help motivate high school students who want to know why they are learning quadratic equations and trigonometry.  On the other hand, that isn’t the purpose of the book at all- the purpose is to introduce students to very basic information about modern financial systems.

Unfortunately, many of the activities in this workbook have the potential to be quite dry. This isn’t something that I blame the author for; insurance and municipal bonds are rarely considered exciting.  Nevertheless, having a successful class would require thoughtful modifications from the teacher.

As a tutor, I often find myself counseling families about whether they should pursue admittance to Hunter.  It is without doubt a great school, but it’s not for everyone.

There seems to be an overall impression that Hunter College High School is a math and science school.  It is definitely true that it has rigorous math and science classes, but it would be a mistake to assume that Hunter glosses over the humanities.  Perhaps the best way to convey how rigorous the humanities are at Hunter is to list some of the texts that 7^th graders read in their humanities class a few years ago.  Students read widely from original sources such as The Prince by Machiavelli, The Republic by Plato, and Two Treatises on Civil Government by John Locke (as well as many other, less well-known, documents of similar difficulty).  When considering Hunter, you should ask yourself if your child would enjoy reading and discussing primary sources of this nature.

Other classes at Hunter are similarly challenging.  Several years ago, I tutored a 7^th grader at Hunter who was understandably dismayed when she turned in writing that would have earned her an A at her old school (a well-regarded NYC private school) but, at Hunter, it was returned to her by her English teacher with masses of comments and the expectation that she would do a thorough revision.  Parents should consider whether this level of expectation will help their child flourish or feel like too heavy a burden; it can go either way.

Of course, the high expectations at Hunter are not limited to humanities courses; math and science classes are similarly challenging.  When I was tutoring that same 7^th grader I said, “Huh… I’ve never seen this math taught anywhere else” so many times that it turned into a running joke between us (and this was after I had almost a decade of experience working as a full-time tutor).  Indeed, I was startled by both the scope and difficulty of the math curriculum in nearly every lesson.

If you are not sure if your child would enjoy attending Hunter College High School, you might consider purchasing the “Very Challenging Math Worksheets” published by New York Academics and available at shop.tutornewyorkcity.com.  These worksheets were written with gifted middle school students in mind.  They are quite difficult but also playful.  The problems require creative thought more than drudgery; if your child gets satisfaction from working through them, he or she would likely get satisfaction from attending Hunter.

When I am tutoring students who will be taking the Hunter College High School Entrance Exam, I try to give the children and parents an idea of what they might be getting into if they are accepted and decide to attend.  This way, they can make a truly informed decision.  That’s not to say I try to make the tutoring process a slog- quite the contrary.  Just as attending Hunter College High School should be challenging and exciting rather than burdensome, I do my very best to expose my students to interesting, challenging materials that will draw them in, pique their curiosity, and stretch their abilities.

Fortunately, there are several, often-overlooked sources of high-quality scrambled paragraph questions.  One source is the handbook for the Thomas Jefferson High School for Science and Technology.  Since the test to get into this school is very similar to the SHSAT, it is possible to use the materials for one test to study for the other test.  Conveniently, this handbook is available for free download.

Another good source of scrambled paragraphs are the practice tests developed by New York Academics, which are available at shop.tutornewyorkcity.com.   These tests have been very carefully developed and edited to have valid scrambled paragraph questions.

Highly motivated students may wish to consider forming study groups in which they write scrambled paragraph problems for each other.  Writing this type of problem can provide great insight into how they work, and it can make solving scrambled paragraphs easier.  Of course, solving the scrambled paragraphs created by other people in the group is also valuable practice.

I argue that both sets of skills have a place in education.  Indeed, when I am teaching math I make sure to use aspects of both philosophies.  But, I’m concerned that what I see as practical math necessities are seldom taught with any thoroughness.

How is it possible that people can sign up for credit cards without understanding the shocking power of compounding interest? How can people have obtained mortgages without fully understanding the implications of interest rates?  How can I go out to dinner with friends who have graduate degrees, but who nevertheless struggle to calculate a tip?

I would like to see math taught as a much more practical subject.  Budgeting, accounting, saving, and borrowing are math ideas I’d like to see explicitly taught in every middle and high school.  Unfortunately, few schools address these issues in any depth.  Part of the reason is that standardized tests do not cover these topics in any details.  Like it or not, school curriculums (especially in math and English) are intensely influenced by standardized tests.  In middle school, high school admissions tests such as the SHSAT, ISEE, and SSAT loom large.  The state tests given to all students in public schools loom even larger.  In high school, the SAT, ACT, and NYS Regents exams are what determines curriculum.

The testing regimen that students experience emphasizes relatively abstract math skills, but this is not the only reason practical, every day math is given short shrift.  The other reason is that algebra, geometry, and calculus are far more prestigious than budgeting and accounting.  When schools propose teaching practical math, there is often a strong push-back, and people accuse the schools of “dumbing down” their curriculums.  I think that’s wildly inaccurate.  There’s no reason at all that motivated students can’t learn basic life skills and calculus, too.  But there are a great many reasons why dis-interested students should not be forced into higher math, especially when they haven’t even learned the mathematics that constitutes a set of important life skills.

The SCAT is a private proprietary test and official sample exams are not available.  This means that the exact content and emphasis of the test is not well known, especially when compared to larger, better known tests such as the SHSAT, ISEE, SSAT, and SAT.

At New York Academics, we believe that the best way to be prepared for the SCAT is to go into it with a strong background in English and math.  In other words, the candidates most likely to be successful are those go to schools with strong academics, who read widely and deeply, and who do not merely complete their school work, but who actively think about it.  But what does specific test preparation for the SCAT look like?  In the short term, test preparation for the verbal portion of the SCAT consists of becoming thoroughly familiar with analogies and learning techniques for solving them.  A crash course in learning vocabulary words is not terribly useful; the English language is simply too large for a week or even a month of daily vocabulary study to have a perceptible impact on a test like this.  For the math portion of the test, it is important for students to learn potential useful shortcuts that work with quantitative comparison questions.  These shortcuts are not the sort of techniques that are emphasized in most school rooms, so it is helpful for students to learn and practice them before walking into the test.

Materials to help students practice analogies are plentiful but quantitative comparison questions for elementary and middle school students are scarce.  SSAT prep books have some, Becoming a Problem Solving Genius by Edward Zaccaro has some, and there is a package of quantitative comparison questions available at shop.tutornewyorkcity.com.  If a student is having trouble with the format, all of these resources should be used.