If one were trying to streamline the Algebra 2 curriculum, is there a good argument for retaining the rules of thumb by which we were all taught to graph rational functions by hand (finding asymptotes, holes, intercepts, all of that)? Or could we hand that over to graphing calculators and e.g. teach students a bit more probability theory?
@ct_bergstrom Maybe is useful to be able to logically deduce asymptotes, intercepts, singularities, etc., for reasons more important than graphing them? Also is easy to graph things with Matlab or Jupyter and not notice the singularities
@radehi @ct_bergstrom this is my thinking, too. I teach graphing rational expressions in a intro calc course in high school rather than in algebra II. It’s a warm up for thinking about the infinite (asymptotic behavior) and infinitesimal (removable discontinuities). And it’s excellent review and consolidation of basic algebra and even fractions.
@radehi @ct_bergstrom
Do you mean teach students how to use a calculator so you can teach them theories?
Is that actually a *math* class?
Then why bother teaching kids how to add and subtract in elementary school? Just teach them how to use a calculator. And don't bother teaching them how to count as toddlers because they won't need to know about numbers since we have calculators.
IMO, same thing. Teach them how to communicate with numbers rather than how to push buttons on a machine.
@ChofuAlum @ct_bergstrom Does who mean that?
More important than communicating with numbers is communicating with logical arguments. Accountants communicate with numbers but rarely show something surprising is true beyond all doubt.
@radehi @ct_bergstrom
In Florida, there was an End of Year geometry exam in high school. Teachers, students & schools were evaluated based on these exam scores. Since students could use a calculator on the exam, teachers taught students how to solve geometry problems with a calculator...... in other words, what buttons to push on the calculator to get the correct answer- so they would pass that exam.
Nobody learned any geometry. They just learned how to use a calculator.
@ChofuAlum @ct_bergstrom Feynman wrote entertaining stories about such corruption in Brazil.
@radehi @ct_bergstrom
I will suggest it's a common practice in US schools whose funding relies on performance evaluations.
'Teaching to the test' rather than teach content (in any discipline) IS the game. It's why so many graduate from high school dumb as a rock and incapable of critical thinking. While the (lucky) kid with parents that value education generally do fine, a whole lot of minds (majority) are being wasted.
@ct_bergstrom Think this is actually more important than solving equations. Intuition for how things act at x → ∞, x → -∞, x = 0, y = 0, denominator → 0 is street fighting mathematics.