Can I teach math to my children without a text book and not worry about gaps later on?
We homeschool our two children they are ages 8 and 10. We have used Saxon curriculum and it has always been an issue as it is dry and too rote. I want to light the book on fire and do a happy dance around it with the kids, but first need to know if I'll need it later :) Our tutor says they'll have gaps if we don't use a text.
1. Jump Math ( High Quality Curriculum and interesting)
2. Mathematical Reasoning from Critical thinking company.
The only pre-determined and gaps you would need to worry about is if you decide to send your child to a public school at a later date. Then you would want to go through the state/local standards, and spend a few months making sure your child was confident with the material expected for the next year.
There are also so many math curricula! I've been happy with a combination of Miquon and Singapore, mixed in with games, hands-on experiments, and resources like this website. No single curriculum is perfect. Saxon, in particular, has "gaps" of another sort - in my opinion it tends to teach too procedurally and without enough word problems, or other higher order thinking uses of math.
Your tutor is right. There will be gaps if you don't use a text. But the good news is that you will also have gaps if you do use a text. When you start another subject, like physics or calculus, or even solve a new problem within the same subject, you will have to hunt for some formulas, ideas, or definitions.
This is normal.
Everybody has gaps. Mathematics and science themselves are full of gaps - things nobody has figured out yet! Einstein said: "Do not worry about your difficulties in mathematics; I can assure you that mine are still greater."
But you do want to develop strong habits and practices. For example, do your kids know what to do when they realize they have a gap? Do they know how to find more knowledge if they need it to solve a problem or to understand a theorem?
When we see a gap it usually means there is a disconnect between parts. The context that reveals the connections is usually missing. There are always unrecognized gaps between the image, what it represents, and further abstraction. From facts, usually in isolation (text,) to meaning that is symbolic, then value that comes from individual experience with facts. To much room for formulas to fill gaps.
Good point about types of gaps: representation, abstraction, symbolic meaning, live experiences... The last type is the slowest to accumulate, right? Comes with maturity...
I agree. Everyone has gaps. A child that doesn't follow a particular curriculum will probably have gaps that are somewhat different from his peers who do follow a curriculum. Sometimes it makes me nervous. Then I reach for one of the math curricula that we tried and abandoned. But I quickly remember why we abandoned them and return to our very eclectic mix of living math books, logic puzzles, board games, math circles and LEGOs.
