# Philosophy of Education

## Philosophy of Education-better.png

My Philosophy of Education – by Brent Hanneson (creator of GreenlightTestPrep.com)

Note: My philosophy of education is actually my philosophy of mathematics education. My background and passion are in math, and although I feel the verbal instruction on this site is competently executed, I believe the course’s greatest strength lies in its quantitative content.

Research in Mathematics Education tells us a lot of people possess a fragmented and shallow understanding of the math they were taught in school. This research ranges from children leaving elementary school with a faulty interpretation of the equal sign to high school seniors who don’t understand the equation-graph relationship

Much of this confusion is the result of an unfortunate feature of math itself. That is, most math concepts require a solid understanding of earlier, building block concepts. For example, in order to learn long division, you must already know how to multiply and subtract. Similarly, to understand how decimals work, you need a solid understanding of fractions. And so on.

Given the sequential nature of math, having one bad year of math (e.g., your math teacher was one of those elementary students who didn’t understand how the equation sign works.) can make it harder to develop a deep understanding of the following year’s topics, and the year after that, and so on, until you graduate high school with the impression that certain math topics are merely a random collection of rules and formulas.

So, although the math in this course was already taught to you in elementary and secondary school, I’m keenly aware that many of you are learning a lot of these concepts for the first time. So, to ensure you complete each lesson with a rich understanding of the concepts covered, I try my best to explain:

• How and why the GRE’s core tools work (knowledge)
• How to apply one of more of those core tools to solve novel questions (strategy)

### How and why the GRE’s core tools work

Throughout their various publiucations, the GRE test-makers outline all of the basic properties and concepts the GRE tests. These core tools are crucial to your success on the quant section because every official question can be solved by applying one or more of those key tools. So, before you can apply those tools, you must understand why and how they work.

Given this, each lesson begins with the most basic building blocks, and we slowly build upon them to explain how and why each basic tool works. Once you have a solid understanding of the core tools, you’re ready to learn. . .

### How to apply one of more of the core tools to solve novel questions

I’ve answered all of the 3000+ quantitative practice questions on this site, and, for each question, I demonstrate how to apply the core tools the test-makers expect us to master.

So, rather than have you memorize dozens of superfluous formulas, I demonstrate how to solve each question through quantitative reasoning.

### Don’t be shy!

As you work your way through the course, make sure you fully understand everything taught in each video lesson before moving to the next lesson. When in doubt, ask (preferably in the comment section beneath that lesson). That’s what I’m here for!

I’ve spent the past 27 years helping all kinds of students overcome their difficulties with math (7 years teaching high school math and 20 teaching GRE math). During that time, I also earned a Masters in Math Education, because I believe mathematics is a beautiful subject, and I love helping others see it as such (or, at the very least, tolerate it until they reach their target score).