Short answer: Some students are already doing well in math. But mostly, students and their parents unwittingly commit to Math Hell and I refuse to accompany them there.
Long answer: See below.
A fitness client speaking to their trainer: “I don’t care if I can only bench press 30kg now. I don’t care what you think about vastly excessive weights, bad form, or injuries. Maybe other people should slowly raise the load from 30kg to 200kg, but I am a unique individual. Just teach me to bench press 200kg now!”
Nobody in the world of fitness is this stupid and any trainer hearing this would quit immediately.
So what does this have to do with math? When students are 12 or under, very little. If a student can only count as high as 10, there’s no point in trying to master 43+18, and everyone knows the student should learn how to count no matter what the teacher is doing with the rest of the class. Some skills and knowledge have prohibitively prerequisite skills and knowledge. In most fields, this is generally accepted.
In fitness, the ability to lift 100kg comes before any attempt to lift 200kg. Nobody thinks they’re so special that this doesn’t apply to them.
In figure skating, skating backward and forward comes before any attempt to do backflips or triple axles. No skater has ever said “I don’t care if I can or can’t stand on skates. Teach me backflips now!”
In math, counting past 10 comes before any attempt to learn 43+18.
Would any sane person contradict the gist of the above?
Sanity says no.
But reality says yes.
In fact, people say yes, by the millions.
Math education makes people go coocoo for Cocoa Puffs, tossing concern with prerequisite knowledge out the window.
Precalculus 11 student: “I don’t care about equivalent fractions and I don’t want to simplify the square root of 12. I don’t care about exponents. Just show me how to simplify this because I have to pass. I’m NOT going to summer school.”
Precalculus 12 student: “I don’t care if 5÷3 equals 3÷5 or not. Long-term damage of cramming? Foundational knowledge? Whatever. Just show me how to find vertical asymptotes NOW. My test is tomorrow and I need to maintain a 91% average just to apply to my desired university.”
Whether it’s back flips before standing on skates, lifting 200kg before learning to lift 100kg, or mastering vertical asymptotes before division, these requests are equally stupid and harmful. If this characterizes what you want – and most students and parents do as soon as there’s an imminent test or deadline – then I will refer you to another tutoring service, but I will send you there with a warning: Cramming fertilizes the root cause of the problem. It paves the way to Math Hell.
Yes. Hell. “Hell” is the right word.
Many students memorize and hack their way through tests for years, yielding good grades, but never mastering anything. Eventual consequences include not graduating, failing, mandatory summer school, extreme demoralization, emotional meltdowns, inadmissibility post-secondary programs, dropping out of academic programs or school entirely, career options closing off, permanent math hatred so bad that it passes on to the student’s future children, etc.
This is Math Hell.
And I won’t be part of it.
In other subjects in school, issues of prerequisite knowledge matter much less. If you’ve forgotten all about your grade 8 socials studies unit on the Roman Empire, you can still do just fine studying World War II in grade 9. Many students can get away with learning little in English 10 and 11, but if they apply themselves in English 12, they can get the marks they need for university. The idea that buckling down now is sufficient is true in most courses.
But not in math.
In math, there are no shortcuts.
A student who caught a cold in grade 4 math during their division unit might learn nothing related to division for years. They’ll completely miss out on the two meanings of division, that it’s the inverse of multiplication, fraction as division, division with negative numbers, rate as division, etc. But they can fake mastery on assessments by memorizing and cramming reinforcing the idea that shortcuts in math work. Then when they face conceptual questions about slopes, the student has years of division content to learn before they can even begin to understand slopes. Not to mention derivatives. There is no way to master the content on tomorrow’s quiz. Nobody can learn years worth of content in 1 hour of tutoring, no matter what the stakes are, no matter how high the desire is.
Hard work is not enough on that kind of timeline.
I feel bad for students and parents in these positions. I really do. I feel especially bad who do not even see that they are insisting on harmful cramming. It is terribly painful to hear that hard work won’t be enough to save the next report card, that you need to remediate years worth of content instead, that everything they’ve believed about learning math was wrong, that the marks they’ve earned in the past were not really earned.
But I’ve also learned that it is easier to talk a hungry dog off a meat truck than it is to talk some students and parents off the path of Math Hell. They don’t even believe they’re on such a path until it’s too late and they’ve reached their destination.
And that’s why I refuse so many students.
