Simply, Math is the ONLY subject which must be taught sequentially - you must master each concept in order, before moving to the next concept. In all areas of math, there are ONLY FOUR possible operations which can be performed:
When it comes to teaching Math, most homeschool parents have a limited understanding of what they actually need. Math curricula are full of unnecessary redundancy, and even privately published homeschool curricula are written to align with "standards" of public schools. In order for schools to show success rates in math, all the same age peers must test at the same level, yet testing has never accomplished such results. So in order to change the outcome of the standardized tests to show success in standards, the curriculum and the tests are continuously dumbed down. Additionally, math curricula is re-written to "new math" to further confuse the student. Rather than encouraging children to strive higher in math, they are intentionally slowed down to make it appear as if schools are improving. Worse, if a child isn't grasping the concept "at grade level", they are told that they are not good at math. Hence, children get bored and frustrated with math curricula and parents are always searching for something better.
The biggest issue with math is when it is not taught to mastery, rather a passing grade. Well, a "D" or a "C" is a passing grade. A "C" grade means that the student has missed 30 percent of the concepts, or did not master 30 percent of the concepts. When a student gets a "C" grade, they are not offered tutoring or any intervention to figure out why, they are simply passed to the next grade. Any "B" grade is considered average and good, but it is also indicative of the student not comprehending 20 percent of the concepts. Why is this so bad? Because math is sequential, it has a logical order. Concepts must be mastered before moving to the next concept. If you don't master the basic concepts, you will continue to struggle in math and not understand why. Missing 20 percent of math concepts is setting the student up to struggle in future math, and even give up on careers where math is involved because the student feels they "can't" do math.
We should understand that math is the ONLY sequential subject. It has a logical order, but we are led to believe that it must be taught by grade level because of national education “standards” which we are accustomed to following. The truth is, there should not be grade levels in Math. However, there should be mastery. Mastery is not based on curriculum volume, it is based on specific topics or concepts, one at a time. Counting and sorting should be mastered before learning addition. Addition should be mastered before learning subtraction. Subtraction before multiplication, and multiplication before division. Math should be taught at the highest level that the child can master - which is not specific to age or grade, rather by individuality. When taught to a mastery approach, students excel at their own pace which, surprisingly, often turns out to be 2-3 years ahead of same-age peers. Switching to a mastery approach can significantly improve math skills for students who are considered "behind", and especially those who have special needs.
After mastering division, there are basic skills which should be mastered in sequential order. From the youngest ages of counting and sorting all the way to college, all of the skills can be taught without a separate math curriculum, even if the parent has no math skill or the student is considered "behind".
What are those skills needed, and how do you teach it without a curriculum?
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