smart education

Homeschooling parents undertake the monumental responsibility for facilitating their children's education. Taking on the role of "teacher," as opposed to being a "facilitator of learning," is a potential deterrent to successful learning outcomes for parent and child, alike. The two greatest gifts a parent can bestow on their children are instilling a lifelong desire for continuous learning and helping them develop the life skill of "learning how to learn." These two elements of practical neuroscience all but guarantee the development of young minds into responsible, successful and self sufficient adults and future leaders. This applies to all parents, regardless of whether they home school or not.
John Naisbitt, American author and futurist said:
"In a world that is constantly changing, there is no one subject that will serve you for the foreseeable future, let alone for the rest of your life. The most important skill to acquire now is learning how to learn."
Many homeschooling parents may associate "learning how to learn" with learning styles. The practical neuroscience definition of learning styles is your child's preferred sensory sequence to take in information and their cognitive preference to process it.
Sensory Pathway Preferences
It's important that you, as a parent, and your child, both know the child's most and least preferred ways to take in new and challenging information. For successful learning outcomes, the inflow of information must be presented in the student's two strongest sensory pathways. Your child should pursue self-directed learning, whereby they request and select learning resources and delivery methods best suited to the way their brain is naturally wired to learn.
Sensory Learning Aids for:
Kinesthetic Children

• Allow student to move around and be comfortable while learning
• Encourage making flash cards for key learning points
• Let student squeeze a small ball or work with another manipulative, while learning

Visual Children

• Provide material to look over and read before class
• Give instructions, homework, and key learning points visually
• Minimize words and maximize symbols, pictures, charts, illustrations

Auditory Children

• Allow extra time for questions and discussions
• Suggest reading notes and study material aloud
• Encourage student to discuss and tell others what they are learning

Cognitive Pathways Preferences
Cognitive processing is required to solve problems, make decisions, and develop skills and competencies to navigate life. Your child's tendencies for Sequential and Global thinking may be established from birth or may be dependent on their environment and how you influence them. By the age of 7, the preferences for cognitive processing can usually be observed. The strongest cognitive preference should be acknowledged, while allowing opportunities to use and strengthen the least favored one. This approach helps build an integrated and balanced "whole brain." If resistance is experienced, let your child follow their natural instincts. Both Leonardo da Vinci (Global) and Isaac Newton (Sequential) have made significant contributions in the world.
Cognitive Learning Aids for:
Sequential Gifted Children

• Connect the key learning points and steps to one another to form central concepts
• Organize assignments into logical steps and sequences
• Encourage students to complete one assignment at a time
• Formal physical environments are favored: straight back chair at table, quiet, bright and direct light, cool room temperature, snacks and drinks limited to breaks

Global Gifted Children

• Explain major concepts and the big picture first; then provide the detail, if necessary
• Allow student to multi-task as long as learning progress occurs
• Provide for frequent breaks to maintain interest and focus
• Informal physical environments are favored: Casual furniture, dim and indirect light, warmer room temperature, snacks and drinks while learning

In summary, each child has distinct interests, gifts and styles for receiving and processing sensory information. Homeschooling parents can lighten their "teaching load" by helping their children become self-directed, lifelong learners. Parents can also role model what they teach, provide a smorgasbord of learning opportunities and assist with making learning resources available.

Stephen Hager is a lifelong learner, scientist, author, speaker and teacher. Along with Deanna Phelps, he is the co-creator of brain-based human development products. Their goal is to help people live better and more peaceful lives through the "power within." Since 1992, Deanna and Stephen have been developing practical neuroscience solutions for better communications, clearer thinking, faster learning, higher productivity, stress management and creative problem solving. Everything they have learned from 20 years of research and working with people is incorporated in the comprehensive and individualized Brain PathWays 14-page report. For a daily dose of practical neuroscience tips, visit http://www.brainpathways.net and sign up for Free Daily Messages From Your Brain.
Please feel free to share this article as long as it includes this resource box. ©2011 The Hadron Group, Inc. All rights reserved.

Introducing LaTeX
For those of you who are unfamiliar with the idea, mathematical typesetting is the means by which mathematicians produce documents that contain complicated mathematical expressions. It's not possible to typeset things like integral signs and summands in basic word processing systems: instead, the mathematician relies on a special typesetting language, which interprets commands as instructions to reproduce particular mathematical symbols and does so cleanly and elegantly.
LaTeX is the de facto typesetting language in modern use and is used by mathematicians and teachers around the world to write articles, create notes and print out question sheets. LaTeX usually seems quite peculiar to the uninitiated. It is not a WYSIWYG (what you see is what you get) processing system, like Microsoft Word, but rather a behind the signs document markup language: the resultant document appearance bears little resemblance to what the author actually types. Say you wanted to typeset an integral into your document. Then you would so by writing something like:
$$
\int_0^1 x^2=\frac{1}{3}.
$$
The language used consists of instructions to the typesetting system; the two dollar signs "$$" tells the typesetting system that an inline equation is about to be inserted: the "\int" command tells it that an integral sign needs to be produced and the follow-up "_0^1" informs it what bounds should be used; the "x^2" specifies the integrand; and the "\frac{1}{3}" tells it that a fraction, with numerator 1 and denominator 3, needs to be produced. The final "$$" tells it that it can stop worrying about producing mathematics, as the equation has been entirely specified.
LaTeX may seem odd at first, but it is a powerful program with a lot of features and the capability to reproduce nearly every mathematical symbol that is out there.
Why LaTeX is a great tool for learning mathematics
When I was an undergraduate mathematician, I never really got into the groove of learning my subject until I discovered LaTeX. I did what the vast majority of students do when they first go to university to study mathematics: I went to lectures, I took notes and I muddled my way through various question sheets. What I discovered was that I struggled in subjects where a full set of typeset lecture notes wasn't provided by the lecturer. For some reason, reading my own notes that I took in class rarely helped the material to sink in. Even when I took the time to sit down and write them up properly, I still found them a difficult tool to learn with.
At the end of my first year, I'd figured out the problem. It turned out I learnt best when I had a proper set of typeset lecture notes sitting in front of me. The problem was, not all lecturers were forthcoming with their own notes, and in subjects where the lecturer decided that he wasn't going to release them, I had to muddle through as best I could without. By the end of the first year, I decided I'd had enough, and took the problem into my own hands. I learned LaTeX and started to type up the notes for courses where they were missing. Immediately I experienced a massive upsurge in my performance as a mathematics undergraduate. My grades improved, my grasp of the material became more solid, and I enjoyed the subject much more.
Aside from the fact that I just enjoyed the actual process of typesetting itself, I attribute a large part of my eventual graduation with a first class degree to LaTeX and the notes I produced using it. LaTeX is a great tool for letting maths sink in and the major reason why is simple: when you get competent enough with it, it allows you to put all your focus and attention on understanding the material as you write it up.
This is in direct contrast to what happens when you write material up by hand. If you're anything like me, you're probably a bit of a perfectionist. So when it comes time to write up a definition, theorem or proof by hand, there's a big part of your mental focus dedicated to not making a mistake. There is no feeling worse than getting to the end of your second side of notes and slipping up somewhere, putting down a "y" instead of an "x", or something even worse. Sure, Tipp-Ex can solve the problem to a certain extent, but it is usually problematic to do so and distracts from the flow of your work. Because you're on guard for this eventuality (and it inevitably happens, no matter how hard you try!), you can't focus your attention fully on what is at hand, which is learning advanced mathematics.
LaTeX removes this problem, by allowing you to have as many drafts as you want. There are no distractions when working with LaTeX. In your head, you know that any error, no matter how egregious, can be fixed quickly, usually by just hitting backspace a couple of times. You can therefore focus fully on the task of understanding the mathematics, safe in the knowledge that if you make an error, you can undo it painlessly. This also makes LaTeX a great tool for revision, because if you're reading through your notes and you stumble across something that is just catastrophically wrong, you can replace it in no time with something that makes sense.
The advantages of learning mathematics using LaTeX far outweigh the learning curve required to get used to it. I would encourage any mathematics student with a perfectionist streak to give it an earnest shot. It worked for me, and it might just work for you.

Josh Gallon is a recent mathematics graduate from the University of York and walked way with a first class in his Masters of Mathematics. He is the creator of the website undergraduatemaths.com, which provides courses on various mathematical subjects at the undergraduate level.