Most of my students come to me in grade 11 for their first year of IB mathematics (either SL or HL). One of the big challenges I face is transitioning students from "practice" to "problems". I define practice as repeating the same skills over and over until you get good - for example, learning how to complete the square. "Problems", on the other hand, are new questions that require a student to combine multiple mathematical concept in new ways to work towards an answer.
Many of my students have been raised on "practice" but have limited exposure to "problems". This is a serious "problem" for them when they begin the IB mathematics curriculum. My assessments are almost entirely made up of problems, not additional practice. Early on it is not uncommon for a student to approach me after a test and say something along the lines of, "It's not fair, I haven't seen that problem before." Needless to say, I have little sympathy and proceed to explain the difference between "practice" and a "problem".
Eventually, they understand that it is going to be a real "problem" for them if they do not learn how to solve actual mathematical "problems". They come around, but it takes time and "practice". In the end, they eventually get a sense of what real mathematics is all about.
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