The single most difficult decision you may find yourself making with homeschooling is deciding where to start with the formal study of mathematics. Maybe this is all hyperbole and you've never struggled with this decision. If that's the case, I'd like to encourage you to think about it. Where should you start with the study of mathematics?
Mathematics is the wonder of creation condensed into a language of reason and proof. Can you translate the patterns of nature into language? Have you identified the cycles of the moon and used them to predict the future? How does a person begin to understand the world around him?
We learned from Hercule Poirot to use our brains, pay attention to details, seek help when needed, ask questions, and include others in our journey. However, he fails to tell us where to start this journey. Thus, we must look to another source: the mathematicians who've gone before us: Pythagoras, Euclid, Archimedes, and Nicomachus all have things to teach us about the study of the universe through the language of mathematics. Both Euclid and Archimedes start their books with definitions and assumptions. Nicomachus in "Introduction to Arithmetic" starts with the examination of how the ancients defined philosophy.
That is where we should start with our study of formal math as well, yet modern math textbooks contain almost nothing about philosophy. No wonder our high school students get so worked up about the why of math concepts. We need to explore the wonder, work, and why of mathematics with our children.
This Spring, as you peruse curriculum options and math texts, consider where the wonder is shown, what the work reveals, and how the why is presented to your child. This is of utmost importance for our children and ourselves as we develop and continue on this journey together.