First, a side point. "Copyrighting" something is pretty much meaningless. A patented idea must be useful and novel. You can't copyright an idea, only an expression of an idea and pretty much anything you write is automatically protected by copyright and merely has to be registered before you bring a lawsuit based upon it.
Second.
If you have a kid who is underperforming academically into late elementary school or beyond, it is much easier to bring that kid up to grade level in mathematics than it is in most other subjects because almost all other subjects (not just English, but social studies and science as well) mostly involve reading and writing.
Reading and writing are skills that are optimally learned as first languages at a very young age and involve very large universes of knowledge. Grammatical rules, for example, in practice, have far more exceptions than either teachers or students consciously realize and are actually learned mostly by example and not by logically and consciously applying grammatical rules to potential sentences. You can perfectly master every rule taught in a typical English grammar textbook according to its terms and still be incapable of communicating fluently in the idiomatic English of a native speaking of standing middle class American (or British) English.
Moreover, a large share of students who are underperforming in these areas either grew up learning a language other than English as a first language, (31% of students in the Denver Public Schools that my children attend) or learned a dialect of English other than the standard middle class white (Northern) American or (Southern) British dialect of English (e.g. African-America, South Asian, Southern, Appalachian, urban Scottish, some New York City dialects, or working class London dialects like cockney) (at least another 20% of students in the Denver Public Schools). So, getting a kid up to grade level in these subjects involves not only learning new information but also unlearning the child's native dialect or language in a way that also drives a wedge between parent and child culturally.
In contrast, the core set of information that you have to learn to master mathematics at the very modest levels considered to be grade level in late elementary school, middle school or early high school is much smaller, has far fewer exceptions to the general rules, and is learned in a part of our brains that is not so extremely biased towards acquiring information at a very young age.
Furthermore, while an underperforming math student may have to learn new things, it is very rare that an underperforming math student will have affirmatively learned many incorrect mathematical principles that must be rejected with cultural consequences before that student can learn standard ways of doing math. The rare student who has learned an alternative approach to the mainstream one to doing math will almost always be performing at above grade level, rather than below it.
Also,
because effective math instruction is so sensitive to the order in which concepts within the field of math are taught in a way that most language based subjects (even science subjects) are not, the negative educational impact of being placed in the wrong level of math class for a kid's abilities are much much worse than the negative impact of being places in the wrong level of a language based subject. A kid who is a year behind his peers in an English class will still learn a lot from the class readings and discussions even though it won't be optimal. A kid who is a year behind his peers in a math class will learn virtually nothing because he or she doesn't have the necessary foundation to learn the concepts that are being taught.
Accurate diagnostic tests and fine grained tracking of mathematics instruction is critical because if you can accurately place an underperforming child at exactly the right point in the mathematics curriculum (which often won't be shared by many of his or her peers) you bring learning per session from 0% to normal almost instantly. Learning also drops to almost 0% when material that has already been mastered is taught.
Drilling, concepts or anything else, in math, can be fruitful, but only if you are in the sweet spot of material that has not been mastered but does not have any prerequisites to mastery that have not been mastered. People hate drilling mostly because they were drilled on topics after they had already mastered them (resulting in near zero learning), or because they were drilled on topics that they only learned by rote and never really understood (resulting in lots of errors and near zero learning because the student doesn't understand the problem). Drilling on math concepts that are at the right level of instruction for the student is still work, but it isn't awful drudgery, and because it assures mastery later on, reduces the need for time consuming review later on and makes learning subsequent topics go more smoothly, so it can be efficient in the long run.
Because the amount of information necessary to go from say the 4th grade level to the 7th grade level in mathematics is pretty modest, it doesn't take a hell of a lot of focus and discipline to make progress once the student experiences the joy of being taught at a level that the child can understand but hasn't already mastered. The sum total of what that kid needs to learn to catch up from being three grade levels behind in mathematics fits in three late elementary school sized textbooks (which aren't very big and have big print and lots of pictures). Once you consolidate that material to remove review of the previous year's studies and repetition of concepts due to imperfect coordination of the curriculum at different grade levels, you are down to one and a half or two elementary school sized textbooks worth of material that you must teach to the kid for him or her to advance three grade levels.
This can be done simply by spending 1.5x to 2x times as much time on math as a typical student at that grade level. Since a typical student at these grade levels is spending perhaps 100-200 hours a year on mathematics instruction and homework, it takes only about 50-200 extra hours a year (2-8 hours a week) to make multi-year progress in one's grade level in mathematics if a student has the necessary staff support and is being taught at the right grade level. The is manageable without totally changing the rest of the kid's life, through before or after or free period tutoring and a few hours a week of summer school.
Also, because mathematics is such a focused area of inquiry, the amount of vocabulary and grammar that must be learned to profit from mathematics instruction is a very modest percentage of the total body of language knowledge that is needed to perform at grade level in reading and writing. So, even if a kid is lagging in language skills, he or she can still learn math. You do not have to be fluent across the board in standard middle class American English to understand mathematics instruction, and lots of the vocabulary and grammar that is pertinent to mathematics instruction (e.g. understanding the words for numbers) doesn't vary all that much between widely differing dialects of English.
In contrast, in language based subjects, lots of what you need to know isn't found in a few textbooks, because a lot of language mastery comes from immersion in an environment where people are speaking, reading or writing much more than half of their waking hours every day, so spending 1.5x to 2x times as much time on language mastery as a typical student simply isn't possible.
The flip side of mathematics, however, is that
pretty much the only way that it can be learned at even the modestly advanced levels of middle school mathematics is through intentional instruction from someone who has already mastered the subject-matter being taught.
Also,
it is easy to get off track in mathematics and once you get off track you are doomed to learn almost nothing at all until intensive personalized instruction gets you back on track. If you change schools mid-year to a school that teaches math subjects at your grade level in a different order, you may miss critical skills needed to understand instruction in the following year. If you are sick for a couple of months (or miss class due to disciplinary issues or to care for a sick sibling or parent or extended family member) and don't make a concerted effort to catch up immediately, you will have to repeat the year of instruction in misery with younger smarter at math kids who aren't your peers, while spending most of the year on boring and useless review, or will advance with your peers and learn nothing in the next year because you lack the prerequisites.
If you only earn a C or D in a math class, you are pretty much guaranteed to fail the next math class that builds on your current math class; gaining anything less than complete mastery from a math class is basically worthless. If you have ADHD which makes it hard for you to sit still and listen during lectures in a math class, you will fail that math class and every math class that follows. If you have a lousy teacher in a math class who advances you to the next level with a tolerable grade without actually teaching you the material, you are doomed to struggle and probably fail the next year no matter how good the teacher who is trying to teach at grade level is in the following year. For example, changing schools midyear harms a student's math performance more than it harms a student's language arts performance.
http://uknowledge.uky.edu/cgi/viewcontent.cgi?article=1180&context=gradschool_diss
In a typical central city school district like the Denver Public Schools which my children attend, the percentage of students who face one or more of the impediments above or are simply assigned to the wrong level mathematics class by school officials and can't promptly correct the inaccurate assignment is a very large percentage of the total student body. For example, seventy three percent of DPS students qualify for Free and Reduced Lunch, and poor students are much more vulnerable to occasional disruptions in their educations at some point over twelve years than more affluent students. Eight percent of students change schools midyear in DPS as a whole, but in some schools in DPS as many as one in six students do. And, the percentage of students who change schools at least once or twice during their school careers is much higher.
In contrast, you can totally screw up iambic pentameter during a Shakespeare unit and still perform just as well in the short story unit that follows, or completely fail to grok the Russian Revolution and still not be at a disadvantage in learning the causes of the American Civil War.
If your parents were also bad at math, you also can get almost no help from them with your homework, which is rarely the case in language based subjects.
So,
prompt school initiated intervention when a kid stumbles in math in an environment where parental instruction or parent funded and driven tutoring and stable lifestyles aren't like to make math missteps rare and prone to self-correction is also crucial. Poor performance in math needs to be addressed decisively the very week or month that it happens, not once final grades for a semester or even midterm grades are assigned, or the long term costs will be huge.
You can master reading and writing through osmosis from your peers and pleasure activities without ever having to really consciously study after the early elementary school years, and this is precisely how a lot of kids do master reading and writing and other subjects in practice. But, you can't do this with math.
So, a kid who is not connecting with teachers in the course of the classroom experience not only will fall behind grade level in math, but will learn absolutely nothing and furthermore be rendered incapable of learning math in ordinary classroom settings in future years as a result. But, a kid who is not connecting with teachers in the course of the classroom experience in language mastery based courses will just fall a little behind each year because he or she will pick up a lot of the concepts and vocabulary from his or her peers unconsciously by interacting with them, even if he or she gets nothing out of the classroom experience, and will be able to pick something up if that child reconnects with the classroom experience in later years.
Similarly, if a high school graduate is admitted to an open admissions college but is not ready for college level reading and writing, it is almost impossible to bring that student up to speed in enough time to prevent that student from dropping out of college out of the frustration of not being able to take any of the college level classes being taken by his or her peers. It could easily take several years for a student needed remedial reading or writing upon entering college to reach freshman in college level reading and writing skills, if the student ever acquires them. And those skills are needed in almost every class.
In contrast, if a high school graduate can read and write at a college level, but is a year or two behind the college level in mathematics (i.e. finished only Geometry or Algebra II in high school), it is much more doable to get that student to master a year or two of high school math while otherwise taking college level course work with his or her peers, over 12 months or so. And, since most college students outside STEM fields only take one or two years of mathematics in college itself, an incoming student who is a year or two behind in math upon entering college can still complete those years of math at the ordinary high school pace, plus one year of college level math at ordinary college level pace by the end of two or three years (or less with summer school).
Because math is much easier to make progress in than other subjects for students who are behind grade level is also a natural place to being to instill earned confidence based on real achievement and not just hype, and to develop hope in academically underperforming kids that they are capable of functioning academically. This, in turn, can help them summon the drive to take on the much more difficult and incremental task of trying to progress in reading and writing at more than one grade level a year, even though it may take several years of disciplined work there to catch up by even one grade level in that part of their studies.
In short then,
a math first approach that starts with intensive mathematics instruction for kids who are academically below grade level, is an excellent approach to take for reasons that are deeply and fundamentally related to the intrinsic differences between learning math and learning other subjects.
Also, a math first approach teaches otherwise academically underperforming kids something that will be useful to them in life, even if their academic performance in other subjects never catches up to their peers and they don't continue their schooling past high school (as will often be the case). While one can doubt the practical benefit of learning calculus or more advanced mathematics outside STEM fields that require college educations, the practical benefits of lower level middle school and high school math skills in daily and professional life are significant.
