I think "application" is the wrong focus. The real thing to help students understand is this exact question: what is math? That remains a mystery to most students. It gets conflated with the problem of application, but…
Personal anecdote: I never understood what math "was," and this totally demotivated me to study it. I got A's all the way through high school mathematics because I was a systematic and logical thinker who had no problem…
I think "application" is the wrong focus. The real thing to help students understand is this exact question: what is math? That remains a mystery to most students. It gets conflated with the problem of application, but…
Personal anecdote: I never understood what math "was," and this totally demotivated me to study it. I got A's all the way through high school mathematics because I was a systematic and logical thinker who had no problem…