What the hell are Foundational Concepts 6 & 7 and Essential Concepts? It seems that schools are in the business of not only dumbing-down children, but also obfuscating what is being taught so parents have no idea what is occurring.
When we homeschooled our daughters, I was mostly responsible for teaching math and science, although my wife could step in at any time and teach those subjects because all of the material was basic and straight forward. Her formal education was in CompSci so she certainly had the background. My teaching math and science was just a division of labor.
One of the things we did with curriculum is what we called chunking. It's a basic idea of decomposing subject matter to be learned. There is an order to those chunks, particularly in mathematics, that has long been known to be effective for learning.
Labeling what is to be learned is very important. You do not tell a child you are learning Foundational Concepts. You tell a child they are learning Arithmetic. Yes, very old fashioned. Further more you chunk the information into a group of lessons. For instance, Addition and subtraction of single-digit numbers. By the way, it takes multiple lessons to learn this chunk. Each lesson is given a name, so the teacher and the child know exactly what is to be taught and what is to be learned.
When schools label a course with a moniker such as Foundational Concepts, we end up having an abstraction not easily understood by parents and definitely not by children incapable of abstract thought. Why hide what is being taught? Is it to keep parents from helping their children to learn?
There is a much greater problem here than having poorly a labeled curriculum; and one that I contend is the reason why so many children get lost in mathematics. The idea of withholding the teaching advanced math until the 11th and 12th grades means some children will repeat the same lessons over and over again; grade after grade. That's down right boring and unchallenging. Kids lose interest. They never see a purpose for the mathematics and its applications. They give up.
When we homeschooled our kids, we moved to the next topic in our curriculum after mastery of the current topic. Since nearly all topics built upon and used prior topics there was little need to review. It is amazing how little time needed to teach and for children learn. We were able to complete what a government school should have been teaching in a school year in a couple of months; and instruction was rarely more than 15 minutes per day.
Did it work? Yes. Before going to college they completed multi-variable calculus with analytical geometry, linear algebra, and calculus-based probability and statistics. The science they learned (Chem and Physics) was calculus-based. This isn't rocket science. It is just learning one lesson at a time and moving on after mastery.
Great post! 👍