Ambiguity

2020 and the Y0K Problem

The arrival of 2020 has brought to mind the various controversies at the start of the year 2000, also called Y2K. As a software engineer responsible for date-sensitive communications within large computer systems, I well recall being on call that Saturday, in case something went wrong. I also recall all the questions we got in …

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Order of Operations: Common Misunderstandings

Last time I started a series looking at the Order of Operations from various perspectives. This time I want to consider several kinds of misunderstandings we often see. Multiplication before division? Here is a question from 2005 from a teacher, “WRW”: Confusion over Interpretation of PEMDAS In telling students to “do multiplication and division IN …

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Integrals and Signed Areas

(A new question of the week) This week’s question, asked in January on the new site, will take us through some tricky areas of calculus, and also give a glimpse both of the value of quoting the entire problem you are working on when you ask for help, and of the interesting side discussions we …

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Awkward Sequence Problems

(A new question of the week) Having just discussed some pattern or sequence problems that were poorly posed, let’s look at some recent questions about sequences, some of which are quite complicated, and others seem to be just wrong. Two extreme patterns Here is the initial question from Zehra: Please make me understand how I …

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Uncertain Sequences

We’ve often pointed out that pattern or sequence problems, when nothing is given but a list of numbers, are not really math, in the sense that there is no one correct answer. They are psychology questions: What would a math teacher think is an interesting sequence to ask about? Mathematically, any number could come next, …

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