(Archive Question of the Week) One of my favorite questions, from 2001, asked about how to convince a skeptical friend, when a clear mathematical result goes against their intuition. Why should they believe the math? It led me into thoughts about the relationship of intuition to math, whether (and when) math can be trusted, and …
In a class on symbolic logic, students are taught the truth tables that define the “logical connectives” ∧ (and), ∨ (or), ¬ (not), and → (if … then). Everything makes sense until they are told that if p is false, then is true whether or not q is true. How can we say that “If pigs fly, then 2 is …
The other day a student I was helping face to face asked how she can know when to check for extraneous solutions of an equation. I gave her a quick version of my standard answer, and the light went on! Today I want to share these thoughts here, because they are very important in several …
(New question of the week) Here is a recent question from Fida, another long-time “patient” of ours at Ask Dr. Math:
(New question of the week) Now that we are receiving questions at the new site, we will be periodically posting some of those questions and answers, in addition to going back to particularly interesting questions from the old archive. This question (which I have slightly edited) came to The Math Doctors earlier this month, from …
Why Must the Number of Variables Equal the Number of Equations? Read More »
(Archive question of the week) One day back in November, as I entered the community college where I teach, a man came in behind me with his son, probably about 3 years old. It was the first snowy day of the year, and the father stood on the mat wiping his feet, while the little …
Last time, we discussed how you know whether to add or multiply (or something else) in compound probability problems (like finding the probability that you will flip heads and roll an even number). But as I’ve said before, it’s often easier to remember a formula if you know why it is what it is. I’ll …
Last time, I talked about students’ difficulties carrying out divisions that involve a zero, which reminded me of another issue that sounds almost the same, but is quite different: division of a number by zero. Students often either forget the rule they were taught, or they don’t believe the rule, or they just wonder about …
I now want to start looking more deeply at some specific questions at various levels, starting with arithmetic, then algebra and geometry. Students learning arithmetic (and their parents) tend to think in terms of following some rote procedure, just because “that’s the way it’s done”. Modern educators try to focus more on deep understanding, so …
In the first post, I gave a small sampling of questions we’ve had from students, parents, and teachers, all related to school, and discussed how we like to deal with these. But we also get many questions with no direct relation to school. These may come from people who actually use math in their work …
A Sample of Ask Dr. Math, Part 2: Questions Outside of School Read More »