Developing an understanding of maths in our home school math curriculum is vital in the world in which we live. Our society operates from a knowledge of computers, scientific research, understanding data, working with finances,choosing the best home loan or product off a grocery shelf, keeping in speed limits, working out fuel economy to carpeting a room, baking a cake and planning a house. Maths is everywhere and is a part of our everyday life and experiences.
Children should be taught not to isolate numbers and mathematics from the real world, but to use their mathematical reasoning and problem solving strategies to life  because Maths is not abstract, but commonly used from day to day. The way we can give our children a sense of confidence with Maths is to use Maths frequently in our discussions and present our children with real problems, helping them see the relevance and importance of working mathematically.
One way of building confidence is by practicing the basic skills often using memorization and games. Once the maths facts are learned, the effort of working out a problem should not be spent on the computation, but on conceptualizing the real life problem.
Maths shows us the beauty of an ordered world. Although our minds cannot comprehend all the complexities of the universe through maths or science, we can see that our God is a God of order and regularity. Only because of the surety of God as the creator, provider and sustainer of all things, can we be assured that 1 + 1 will always equal 2. As a God of order, He graciously uses systems which can make sense to our rational minds, and we can have confidence that as surely as the winter follows autumn, as day follows night, so the mathematical formulas will have constancy and trustworthiness. Upon this basis, we can enter the world of Maths, rely upon its laws, use it in calculations, and trust it for what it is intended. What is the intention of Maths and what should be our goal in teaching Maths? Always... the Glory of God!
As we show our children the wonders of the world, the maths in everyday things, in nature, in geography, in weather... may we turn their attention to the God who created all, even the system we term, "Mathematics."
There are different ways to understand how the knowledge of Mathematics can be taught.
Noel Weeks in his book, The Christian School An Introduction, says, "In this plan, the mathematics curriculum resembles an ascending spiral. Each topic  addition,subtraction, multiplication, fractions and so on, is done at a slightly higer level in each successive year. Thus the student receives early exposure to things that prove difficult for many, for example, fractions. He receives repeated exposure. They return every year. If he does not understand the concepts one year, he may do so the next. Thus a topic is not laboured and rigorously drilled. It is absorbed by osmosis upon repeated exposure.... Such is the idea!"
However, there are problems with this method. Firstly, the students in the lower grades are introduced to difficult concepts, perhaps too early. Before there is mastery in one operation, another operation is introduced which just brings about confusion. It also makes it difficult in a school setting, where no one teacher is responsible for seeing mastery over one operation. In the home school setting, it can be different because we can oversee our children's work, however, the introduction of too many concepts without expecting mastery, can lead to confusion and lack of confidence.
Some Spiral curriculum:
Mathematics should be taught in an ordered, sequential manner. When one concept is understood, and mastered, another concept can be introduced. Each new concept hinges on knowledge being taught prior to the new knowledge.
For example, if addition is taught and mastered and the child has a complete grasp of when addition should be used, use of addition in problem solving, and quick recall of addition facts, then subtraction is easy to teach! It is easy to teach because it is the opposite operation. 3+7=10 is the same as 7+3=10 and the following equations are simply the opposite: 103=7; 107=3.
Developmental Math (19) selfteaching workbooks  
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A Vertical/Horizontal approach to teaching home school maths, means that concepts should be taught and mastered in a sequential manner (vertical) and that there needs to be a variety of methods employed in teaching the concept(horizontal). A child cannot move forward after a quick introduction  scant explanation and a followup worksheet. Rather, they should be given concrete examples, problems, discussion, pictorial representations and real life work with the concept so they truly understand. Then, the problem is written into a an abstract equation using symbols and will be understood. Once it is grasped, children can learn rote memorization of facts so that there is quick recall. 
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