Thank for your response. That's actually hugely insightful. > We are well aware that most of our students are not majoring in maths and will not go on to tea

Thank for your response. That's actually hugely insightful. > We are well aware that most of our students are not majoring in maths and will not go on to teach it. Most of them at my university will go on to be engineers, so we teach for that in their courses, light on proofs and derivations and focused on grounded practical knowledge and techniques. One important part of why I have this opinion, mathematics is poorly taught to the lower 95th percentile, is historical. Historically, pre 1950 & the GI Bill only the wealthiest students (who sat at the back of the class, partied, and generally focused on Latin not the hard sciences), and the most able students, went to university. The reason I find that's incredibly relevant is this Hackernews post. Easily my favourite of all time. https://news.ycombinator.com/item?id=32974959 https://news.ycombinator.com/item?id=32974959 In my mind, the consequence of all that is teaching the 5% is a well worn, highly polished process. Hundreds of years of effort has been invested in the 5%. For the 95th, barely a few decades. And even then, many academics I find take the elitist point of view. In my experience, your department's point of view is very much the exception. A majority of academics I find follow one of two options: -> The lazy option. -> Train my future graduate students, bugger the rest. IMO, the methodologies for training that lowest 95% are not at all developed. Arguably for example, one theory I have is proof based mathematics should be introduced in Grade 7. Proof based mathematics is the simplest, quickest, easiest way for an engineer to learn a new piece of mathematics. A proof is a quicker, and more time efficient, teaching tool than 5 exercises. Is my theory. And yet, the status quo is only pure mathematicians need to know proofs.