After reading the blog, can you think of any core concepts or terminology that we use frequently in our instruction that we do not tend to address explicitly? What are some ways that we could adapt our instruction to be more explicit about what particular commonly-used words or concepts mean?
Students faced with making sense of function notation also have to interpret the minus symbol in expressions such as f(–x) and –f(x). Many students believe that f(–x) represents "f of negative x," or "a negative input value" and that –f(x) represents "negative f of x" or "a negative output value". Some students interpret –f(x) as "the entire function is negative" and f(–x) as "only the x is negative." There are also students who interpret function notation as indicating multiplication: –f(x) means –f times x; and f(–x) as f times –x.
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