Geometry is a subject that asks you to think logically. This is not an easy thing to do, of course, and we've all known
people- including lots of adults- who are unable to do this. If you understand the jumping off point of the class,
though, you'll at least be off to a solid start.
At this point, of course, even a sainted mother would probably give up, since the initial lesson has been
"It just is, alright. Don't ask why."
Let's leave the remainder of this encounter to our own imaginations, shall we?
The point is, one can always ask "why." At some point, we don't have the answers anymore since our knowledge is
finite. But the question itself can be asked indefinitely.
A child learns at some point, of course, that his parents don't know everything, and begins to learn based upon
observation, trial-and-error and all sorts of other methods. In fact, some might say that experience is the best
teacher. (This is not always true. There is always some give-and-take here. A child should know the consequences of his
actions, and in many cases a little bit of hurt can go a long way toward teaching a child never to do something again.
I'm not, however, going to apply this philosophy to teaching my child to cross a street.)
Geometry is not like that, however. Everything in geometry is based upon a simpler, more basic rule before it.
About Your Math Tutor
Ralph Schatzki has taught high school algebra, and geometry, as well as trigonometry and statistics.
Referred to as "Mr.Ralph" at Ruamruedee Internatioal School Bangkok, a prestigious school where he
taught for many years, he prides himself in being able to identify areas on which students need
improvement and in giving them the tools they need to succeed at math.
Ah-ha! you say: where do we start? We can always ask why and get to something more and more basic, so what are
the beginning rules based upon? (since at some point we just can't explain further)
Well, they're not based upon anything at all. It's like your mother finally saying to you, "It just is, ok," or,
"Because I told you so." It's a little bit disconcerting, then, that this entire branch of mathematics is based upon
nothing more than that.
These are the postulates: the things we simply accept without proof. Without them, we have nothing to build
upon. Hey, we have to start somewhere!
Really, though, all knowledge is like that. It's just that geometry makes this big to-do about how everything in
it is so logical and based upon something else and that it's infallible or something.
I always like to say that at the far end of the universe is a race of alien mathematical idiots, whose entire
geometry textbook is devoted to proving the postulates we simply accept as given on page 1. At the other end of the
universe is a race of alien mathematical geniuses whose postulates are the most difficult problems in our book. In the
end, this is just another way to illustrate the idea that there is a continuum and we simply pick an arbitrary point and
- The shortest distance between two points is a straight line.
- Two points determine a unique line.
- If two distinct lines intersect, then their intersection is a point.
- Three noncollinear points determine a unique plane.
- If two planes intersect, then their intersection is a line.
Definitions are also like postulates, in that we determine the definition of something. We don't seek to show
it- we just accept it. Definitions and postulates are where we start: they're the ground on which we build. Don't
question the ground: accept it.
But question everything else!
If you have particular questions, then, what's most important is for you to be able to explain to me your understanding of it
so that I can see where you are. That way, I'll know where your Point A is, and I can direct you to Point B.
Contact me, and we can set up an appointment to get you on the track to success!
Please contact me to set up an appointment so we can get to work as soon as possible.
Whether you want to ensure your child a strong foundation in math, if he is struggling
and needs some help to get back on track, or even if he wants some enrichment to move
ahead, I am ready to do whatever it takes to apply my expertise and help him reach his
potential and excel. I can promise that each and every student I teach benefits from
my attention and experience.