Mathematics

"All science requires mathematics. The knowledge of mathematical things is almost innate in us. This is the easiest of sciences, a fact which is obvious in that no one's brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon" - Roger Bacon

Mathematics is unlike other subjects. In most academic subject areas the ability to read is the necessary and sufficient requirement for success in achieving a deep knowledge of the subject. In Mathematics, reading is a necessary condition but it simply is not sufficient for most people. While some with great mathematical intuition can in fact simply learn it by reading it once, the vast majority of us do not fall into that category.

We can see evidence of this in two separate reports. The first covers overall US student vs International student performance: 15 Feb 2017 Pew Research Report: "U.S. students’ academic achievement still lags that of their peers in many other countries". The second concerns homeschool students. In most subject areas, home school students perform very well. However, there is quite a gap in verbal and math performance. Examine the Coalition for Responsible Home Education report: "The Homeschool Math Gap: The Data" In every other subject area homeschool students perform above the national average for public schools. Indeed, verbal SAT scores are on par with the best private schools, much higher than that of public schools. And while homeschool outcomes on the standardized tests are above that of public schools, there is a huge gap between the math and verbal scores. One has to ask: Why? Why do we do so well in verbal areas but so poorly in the math?

The difference is in the teacher's command of and ability to impart the deep knowledge of mathematics. Math is a complex subject. Not 'hard' (as I frequently hear) but complex. Approaching certain problems using a memorized procedural attack is fine - until it isn't. The most common time it isn't fine is while teaching and the student comes up with a question whose answer lies outside memorized procedures. In other words, explaining the answer relies on the deep knowledge.

The two study numbers are starting to make sense. The US has abandoned rigorous mathematics in recent decades, (fuzzy math, reform math, self esteem goals, etc.) leading to our continuing decline in performance compared to other industrialized nations. But, the math teachers do still have degrees that concentrate in math, they may be able to (depending on the teacher) come up with deeper answers.

But what about the majority of homeschool homes? Many parents are quite a few years away from their formal math training by the time they start hitting complex math subjects - and therein likes the problem. Students can ask the darnedest questions. Being able to answer them can be extremely difficult. Commonly, a parent is forced to rely on rusty memories, probably a deficient math education, and a curriculum which (even if it is a good one) is unable to respond to dynamic questions.  I have repeatedly heard, from many home school parents, 'math is hard' - is it any wonder that our students also find it difficult if their teacher makes that statement where they can hear it?!

The proposed solution is an obvious one - a rigorous curriculum that concentrates on mathematics and an instructor who has both the deep knowledge and ability to impart it to a student. Then, math can become quite doable by anyone. Complex - yes, beautiful - yes, and it does require work and thinking. But the reward of sound thinking and logic that go with a mastery of mathematics will last a lifetime across any field of endeavor.