Road Map

Foreward

This post concerns my road map to success, I've used this approach to take students in the 30% range to the upper 90% ranges. My serious students have gone on to achieve the highest grades in South Africa for the Cambridge IGCSE syllabus. I will share the recipe I've come to use, thanks to my years of experience and past failures. We learn from each other every day and I will continue to refine my recipe for success as time goes on.

Here is an index of what I'll cover:

  • Tuition - Are all tutors equal?
  • Practice - How do we fit in?
  • Teamwork - How do we work together?
  • Patience - What result can be expected?
  • Willpower - Keeping a tight reign over the undisciplined mind.
  • Success - We (really) are the champions!

Tuition - Are all tutors equal?

If your success in mathematics hinged on simply getting a tutor then any tutor would do and, if the responsibility of success rested on the shoulders of the tutor alone, every child would automatically pass when interacting with their tutor (presumably twice weekly). However this isn't true, so why is it that some tutors are superior to others? Why do some students increase their grades by 60% while others struggle to attain 60%?

I'm going to try to break down what I believe good tutoring involves. If a tutor wasn't more than a knowledge transfer terminal, computers would already be teaching in our schools. The interpersonal skills a tutor develops through experience and practice is often what changes the dynamic of a tutor-student relationship. Some examples of these interpersonal skills are:

  • Active listening
  • Teamwork
  • Responsibility
  • Dependability
  • Leadership
  • Motivation
  • Flexibility
  • Patience
  • Empathy

When a student feels that their tutor is giving them their all; each lesson, every lesson, a healthy respect and friendship flourishes. We must try to be firm but fair and truly understand the stresses of our kids today. They're not just dealing with Mathematics, some are dealing with 10 other subjects and are being given workloads from each one.

Practice - How do we fit in?

Let's be honest, Mathematics is a (beautiful) practiced art which means that it requires loads of practice at home. If I explain a concept to you (let's say trigonometric ratios of how to understand tan (graphically) with relation to sin and cos) then ask you to attempt a difficult question, chances are you're going to get it wrong. This is become the human mind needs more than just information transfer, it needs time to accept the concept and time to build the neural pathways linking the idea to the mechanical process required to solve it. These pathways grow by practicing the mechanical process of solving the problem. It's pattern recognition and it often leads to fundamental understanding of abstract concepts because your mind dwells on the idea for many more hours than if you weren't to practice at all.

I do my best to provide homework packs for every concept, starting off easy and ramping it up to downright torture because I believe that when my hardest questions are easily answered that tests and examinations become formalities and mathematics becomes enjoyable. Winning always feels better than losing, when your child starts winning at math their mind begins to freely open to the ideas of more abstract concepts and more difficult work.

 

Teamwork - How do we work together?

To make the most of our time we must work together. Teamwork is essential as, mathematics as previously mentioned is like music, sport or cooking a great meal. It is a practiced art. Anyone cutting corners is discovered in the worst way possible (in a test or exam) further weakening their desire to try and excel and making the student feel as if their back is to the wall. Often a simple concept was lacking last year and many other concepts hinged on it (simplification of expressions for example) causing anxiety when in class and sitting their tests and exams. We need to isolate these missing concepts and fill in the blanks.

We do this by attending classes, completing the homework packs on the website, taking the quizzes issued at the end of a section and by joining our forum to further the understanding of concepts by asking questions, answering question and interacting with other fellow students.

 

Patience - What result can be expected?

Results in Mathematics varies from student to student. The result relies on past experiences, previous understanding, previous interaction with teachers, math anxiety, perception of the art, mechanical understanding etc. As you can see, it's not a simple "join and thrive" situation and this where patience comes in. If we're working together as a team, we can expect growth. However this growth won't be overnight (and in some cases it may - if you're this case, you're lucky!)

Here we see neurons making connections in a time lapse over 170 hours: 7 days!

For example, the growth from 20% - 60% is rapid. You child will pass their exams within 3 months. The growth from 60% - 80% is gradual, increasing 5% - 10% per term, and the final jump to 90%+ often
never happens if practice is reduced, concentration isn't addressed and diet isn't correct. To earn 97% for your Mathematics year, you will need to become a well oiled computational machine, totally
possible but difficult to attain. Only 20% of my student base have the desire required to reach it. You can be the 20%.

Willpower - Keeping a tight reign over the undisciplined mind.

Have you heard of the term "monkey mind"? It's the Chinese term "Xinyuan" or Sino-Japanese "Shin'en" 心猿, is a Buddhist term meaning "unsettled; restless; capricious; whimsical; fanciful; inconstant; confused; indecisive; uncontrollable".

Controlling the mind is a tough thing to do. Gurus, monks and scientists spend their lives trying to accomplish it, some days they win and some days the monkey mind stays in control. In our case it takes the form of ideas that creep up that say "just rest, you don't need to do your homework!" or "you already know this, you don't need to pay attention." When these ideas creep up, we have to nip them in the bud. Discipline grows as you practice it, this is why many ex-marines are now motivational speakers. Their training (tested by being given repetitive opportunities to quit) showed them that their desires to achieve victory could surmount any odds or any negative / unconstructive thought. While our mission is different, our mindset must be the same: unyielding, relentless and ready to triple check our work.

Success - We (really) are the champions!

As Lao Tzu said "a journey of a thousand miles begins with a single step" which for our purposes translates to just because you've passed one test / exam does not mean you can stop taking steps in the right direction. Practice requires an investment of time, allocation of time requires willpower. Together we're going to make your journey into the mathematics (a journey within your own mind) as exciting, deep and beautiful as it can be. I can't wait to get started!

Wisdom: Galileo Galilei

“Mathematics is the language in which God has written the universe”

"Measure what is measurable, and make measurable what is not so."

"All truths are easy to understand once they are discovered; the point is to discover them."

"You cannot teach a man anything; you can only help him find it within himself."

I’m a self taught mathematician who started studying mathematics when I was 24 years old. I had a basic understanding of high school mathematics at the time, but I never knew the complexity and beauty of math until diving deeper into the history of mathematics. It became an enjoyable pass time and I was asked to help family friends by tutoring their kids. That was 6 years ago now and my hobby has become my business. I’m currently studying multi-variable calculus, discrete mathematics and reading books the following Math related books: “How to Think Like a Mathematician – A Companion to Undergraduate Mathematics” by Kevin Houston, “The Joy of x” by Steven Strogatz and "Introduction to Mathematical Philosophy" by Bertrand Russell.

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