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The Fear of Mollycoddling
Recently I was a guest at a planning meeting for a certain school and ended up in a session where we discussed how we can better support students in terms of their wellbeing. We were shown a news report highlighting the fact that the suicide rate in professionals of this particular discipline is four times higher than the general population. One of the major factors mentioned in the news report was that professionals in this discipline are very unlikely to seek support from anyone when they are struggling, having been trained too well to be self-sufficient while they were students.
A function is not a graph
When students learn about functions at school, we spend a lot of time forging the connection between functions and graphs. We plot individual points, and we find x-intercepts and y-intercepts. We use graphing software to investigate what the coefficients do to the graph, and discuss shifting along the x-axis and y-axis. We make reference to the graph to define derivatives and integrals. Some teachers help students to recognise from the formula of a function what general shape its graph ought to have, such as recognising that a quadratic function must have a parabola-shaped graph. (I wish this last point was much more strongly pushed, actually.)
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