For math, we are going to try Singapore's math approach. Undoubtedly, they lead the world in mathematics competence at the grade school level. But in all honesty, I could care less about who does better on standardized tests. Testing is not real life, nor practical.
DH and I heard, read, and watched good things about Singapore's philosophy and practice. Their Ministry of Education's rationale for mathematics instruction aligns very well with our approach to the subject:
"Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual competence in logical reasoning, spatial visualisation, analysis and abstract thought. Students develop numeracy, reasoning, thinking skills, and problem solving skills through the learning and application of mathematics. These are valued not only in science and technology, but also in everyday living and in the workplace."
This review breaks down the general topics for each grade level and gives some other details. Their method of instruction differs greatly from the typical American (Saxon) method taught in most classrooms, but because my kids will not know otherwise, I think this will be an easier and more logical approach. It's more like how I remember my mom teaching me math when I was little with understanding of how numbers work, remembering tricks of manipulating numbers, and not just memorization (though she drilled me on that too).
I am concerned with the format of the typical Singapore curriculum because it uses workbooks and Bean at times can loathe writing, though he can do it legibly. I have two tentative solutions. One is to do it more orally and the other is to buy a number stamp set so he can stamp the numbers and then trace them. Most importantly, I want him to have a love of learning and a basic grasp of math. I'm willing to forgo the battle of writing for a little bit, and then gradually I'll have him do it more and more. Tey is an amazing writer already at just under 3.5 years old, so I am less concerned about him with that. I'll work on this number recognition, sequencing, understanding quantity etc. and then ease him into Singapore.
So we've purchased the curriculum, which at this point I'm thinking will likely be our only one or one of few subjects that resembles a typical school-like approach to a subject (with a textbook and my teaching the material). I anticipate that more of our time we will be using math more practically: measuring while cooking, figuring out how much more money we need to buy something from the store, etc. With other subjects, I'm exploring other approaches, but that is for another post.