Ambiguity

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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Significant Digits: Introduction

Our next series of posts will be about the concept of significant digits (also called significant figures), which are important in scientific or engineering calculations to keep track of the precision of numbers (although, as we’ll see, they are not what you would use when you need to be especially careful). We’ll start with the …

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Three Times Larger: Idiom or Error?

Having just written about issues of wording with regard to percentages, we should look at another wording issue that touches on percentages and several other matters of wording. What does “three times larger” mean? How about “300% more”? We’ll focus on one discussion that involved several of us, and referred back to other answers we’ve …

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