runmath home Ready to Help

What are the lessons for?

A Strong Foundation in Algebra

And the lessons cover the basics in

and how to learn Numbers, Arithmetic,

Equations, Functions & Graphs,

Trigonometry, and Geometry. Besides,

in these lessons, I help the students do

practices on pattern recognition in math

using number systems so that they can grow

mathematical insights.

What algebra, though?

Elementary algebra

So it’s about how to handle or work with

math expressions.

Then, how to handle or work with them?

Handling or working with math expressions,

my students manipulate the expressions.

It’s about thus, how to manipulate

math expressions of all kinds, which include

expressions with numbers of all kinds,

variables, constants, numerals,

terms, parts, fractionals,

ratios of many kinds as trig ratios,

rates as pressures or densities

as well as speeds or velocities,

powers or radicals, logs or exponents, etc.

How then do my students manipulate

those expressions?

Doing the manipulations, they change

expressions with the equivalents,

alter, modify, expand, or reduce expressions.

So they know how to break apart an expression

or expressions and how to put them together

using the nature of the expressions. For instance,

they know how to add in an expression,

how to take it out,

or how to add and subtract the same

to change, alter, or modify an expression,

and how to divide and multiply back

the same to alter an expression so that

they get the expression they want, and thus,

can get to the solution fast enough, of course.

And running math, they do all those above,

together with others, of course. Running math,

we operate and manage math tools as rules,

laws, formulas, identities, etc.

as well as math objects as numbers, equations,

functions, powers and logarithms,

radicals and exponents,

ratios as trig ratios and percentages,

rates as speeds or velocities, etc.

So I help my students run math. Running math,

they know how math ideas get made,

how the ideas work, and how to use them.

What math idea?

Everything in math is an idea,

not a material thing.

Numbers are ideas in math,

equations or functions are math ideas.

And the same is true for lines, points,

triangles or circles in math. too.

What’s written or drawn on the paper

or screen is just a vidual aid, and for instance,

a circle in math does not exist in real world,

but exists in out thoughts. A circle in math is a concept.

And the same is true for everything else in math, too.

It all depends on how we think.

So my students run their math,

get the idea, the concept, and thus,

do achieve their conceptual understanding.

Math is not though,

just about such an understanding alone.

It’s about speed, too.

(That’s why mathematicians invented computers.)

So my students get their fluency

in the uses and applications of math concepts

and math tools, and thus,

get the right solution fast enough.

So what do I teach?

How to run math.

How to think mathematically. How to reason.

Practices on pattern recognition.

How to define ideas in math, for instance,

my students know how to define a circle in math.

So they know the mathematical answer

to this question: what is a circle in math?

“It is round.” cannot be the right answer.

And my students practice

looking at a problem or a math concept

at many different angles

and analyzing it in many different ways.

Also, they get to know how to use,

how to maintain, and how to expand

what they learn.

So my students grow mathematical insight,

and can think outside the box.

Email: runmath@gmail.com

runmath home Ready to Help

Copyright © 2012 S. R. Kim