This is from the Common Core Standards for the 5th grade. All students are required to:
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
In the 8th grade, the Common Core requires all students to
Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
In the 9th grade:
Prove theorems about lines and angles: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
Lest you think I cherry-picked, here is the link to all the standards, K-12. Throughout, they are remarkably arcane and irrelevant in the real world.
They’re even irrelevant in high-level careers that use math. For example, I hold a Ph.D. from the University of California, Berkeley, in which I was required to take five-unit graduate level statistics courses, received an A or A+ in all five, yet never needed to use any of the above in any of the courses, let alone in my career or my life outside of work. Lest I be an anomaly, in preparation for this article, I showed the Common Core math standards to a schools superintendent, a researcher, and a psychologist and all them believe the standards are absurdly irrelevant to both professional or personal success.
The ancient argument that math “trains the mind” is beside the point. Many activities train the mind, for example, practical problem solving, which is not only more practical, but more motivating to students. They wouldn’t complain, “why do I need to know that?” if they were learning how to estimate in their head and then calculate the cost, including interest, of buying a car.
Countless students graduate from high school without such crucial math survival skills. It is the height of elitism to demand that every high school student know the Common Core Standards when they graduate unable, for example, to estimate if they can afford to fix up their apartment or the probability of winning at a casino.