I’m a big fan of Steven Krantz. His book on teaching mathematics is the one I recommend most to beginning maths lecturers. The second edition is a must have since it contains short replies to his book from other lecturers, some of them highly critical. Currently, I’m reading his recent book A Mathematician Comes of Age. This is concerned with how a mathematician becomes mathematically mature. From the back cover: “It describes and analyzes how a student develops from a neophyte who can manipulate simple arithmetic problems to a sophisticated thinker who can understand abstract concepts, can think rigorously, and can analyze and manipulate proofs.” I must admit I’ve been diving in and out of the book at random and although I don’t agree with everything he says (or agree with the inclusion of certain topics – why are North Americans so concerned about “Math anxiety”?) there are thought-provoking passages every page or so. The parody of the Evolution of Teaching Math on page 49 is very funny and includes 1980s: A framer sells a bag of potatoes for $10. His production costs are $8 and his profit is $2. Underline the word “potatoes” and discuss with your classmates. Leaving aside the humour, I particularly like the section on Reading and Thinking (p95): It has been observed [No reference given – KH] that the key things that a good teacher does are engage the students in the learning process pace the students teach the students to read Now, reading mathematics is something I’ve thought about and try to get my students to do, see Chapter 2 of How to Think Like a Mathematician (follow the link for free samples of chapters 3 and 4). Like in HTTLAM Krantz mentions the importance of reading with...