Do you remember learning your first language? Probably not- at least not the basics. Instead, you listened, and through subsequent trial and error figured out what worked and what didn't. When you were a two-year-old and kept getting corrected when you said 'The dog go home' you were learning the rules, but organically, within a relevant context. In fact, it was never a question of 'either-or.' Rules and context went together naturally. You certainly didn't think things like, 'When a singular subject is connected by or or nor to a plural subject, put the plural subject last and use a plural verb.'

About The Number Man

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 pretigious 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.

Lots of people sing, but not too many call themselves singers. Yet, we enjoy songs, and we especially enjoy it when someone performs them well. It's an important part of our lives.


In much the same way, this holds true for mathematics. Although I am a math teacher, I am not a true mathematician. That is not to say I don't have training in or an aptitude for or experience with mathematics, just that I have not dedicated myself to it in a way that I feel I deserve to be called one. Still, it pervades our lives to such an extent that it is necessary we each be proficient, at least to a degree that helps make our lives easier.


Traditionally, Math has been taught in schools very much in the manner of foreign languages; that is to say, in a highly -structured, rather than organic, manner. Without getting into detail, it is obvious why this has been so- it is much easier to organize lessons and to assess student growth when there are easy guidelines to follow. Teachers develop rubrics, and teach rules, because it's easy that way.


Do you remember learning your first language? Probably not- at least not the basics. Instead, you listened, and through subsequent trial and error figured out what worked and what didn't. When you were a two-year-old and kept getting corrected when you said 'The dog go home' you were learning the rules, but organically, within a relevant context. In fact, it was never a question of 'either-or.' Rules and context went together naturally. You certainly didn't think things like, 'When a singular subject is connected by or or nor to a plural subject, put the plural subject last and use a plural verb.'


Yet this is how we learn a foreign language in school. No one believes that it is the best way, but it's undoubtedly the easiest way in order to expose the maximum amount of people with the least amount of effort. And let's face it, that's a big deal for a school.


Unfortunately, I have seen so many students who learn mathematical rules this way, in a vacuum. A chapter test might have only seven or ten major concepts in it, and a student might think he knows each and every one, but if he doesn't know when to use each one it's as if he knows nothing. Teachers are part of this problem, because they often get so caught up in teaching the language they forget to teach why the language is there to begin with and what it can do. The basis of true mathematics is in understanding the context of each and every problem and seeing how rules and formulas have grown and developed naturally from those problems. If a student can learn how a rule has developed, he'll be able to apply it properly when the time comes.


Typically, there are two types of math problems a student might encounter: those that show you know how to use a rule, and those that show you know which rule to use. The latter of these, at certain levels, might be called 'word problems.' Typically, students hate them because they're not very good with the rules to begin with, and the teacher is now asking them not only to use a rule, but to use the proper one. Of course, they find the former boring because- like foreign language rules- they're dry, without context or meaning.


Think of a home improvement project- you have to know both what you're trying to accomplish (the goal) and which tool does what (the skills). Mathematical problems are the same. You first must know what you're trying to do, then you have to use the right tool for the right job. You don't use a saw to hammer nails, and you don't use the quadratic formula when you're solving a proportion.


understand that the rules they learn are simply tools, and that in solving real problems they must consider not only their proper use but also their proper application, the challenge of mathematics would be more appealing.


It's not easy, but that is why it's worth it. Ultimately, as in anything, the teacher's role is extremely incidental to the central role played by the student. If the student doesn't look for easy answers, but instead for deep understanding, then- ironically- learning math becomes much, much easier.

Any math problem? Ralph will be happy to help you find your way. Please use the box provided to put in your math questions. We will make sure that you will receive your answers quickly. This service is free of charge and operates on a first come first serve basis.

In a hurry for your answer? Need to brush up on your math skill? Can't solve a (math) problem? Have a quiz/exam coming up?

The Number Man is available for tutoring, both in person and via skype at a friendly hourly rate! Please contact him to set up your session.

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Math Tutorial links

• Introduction
• Finding your own way
• Knowing The Words Pre-Algebra, Algebra
• Variables and Equations - Pre-algebra, Algebra
• Postulate , aka Axiom, what is it? - Geometry
• Math Made Easy The Number Man Ralph Schatzki

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