<p>“students who are not doing well in college level calculus and physics is poor algebra skills. Mistakes in basic algebraic manipulation, cancelitis {eg. x/(x+2)=>1/2}, and inability to set up word problems. (Of course, this is likely reflected in their lower SAT scores.)”</p>
<p>THIS!!!
Algebra is the language of numbers using numerical equations to ask questions to solve for answers. Facility with algebra is crucial in life, in all math, and much science, and in most applied science and math. The ability to translate a word-based problem into an algebraic type of equation with numbers and variables is absolutely fundamental.
I so agree with you that these skills are not taught well anymore…
I was so disappointed in my Ds’ experiences with Math!
It is a form of literacy that is not achieved my many many students by the end of HS. It should be started much younger with linear equations and also the logic of geometric proofs. And HW should involve solving many more problems of a certain type with slight differences so that the patterns are seen, and it becomes fluent, like a language. Kids should also know learn to write word problems based on algebraic equations.
Serious miss these days.</p>