Timeline for Should high school teachers say “real numbers” before teaching complex numbers?
Current License: CC BY-SA 4.0
10 events
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| Dec 3, 2019 at 19:28 | comment | added | lukejanicke | @Kevin You make a convincing argument that I could side with. Respect for choosing the (apparently) dissenting side. As you can see in the comments, it can be risky to do so. But you tackled the heart of my question head on. I do think sometimes it is wise to be judicious and deliberate about when and how you roll out new language. I am particularly sensitive to this as half of my students are EAL. | |
| Dec 1, 2019 at 17:11 | comment | added | Xander Henderson♦ | @Kevin The problem, I think, with your analogy, is that many students mistakenly believe that the equation $x^2+4=0$ has no solutions. When discussing an equation like this, it is necessary to specify that this equation has no real solutions (though it might have solutions in some larger space). By contrast, "We're going to use microscopes today" says nothing about the existence or non-existence of other kinds of microscopes (though, personally, I wouldn't have any problem mentioning electron microscopes, then letting Google finish the job). | |
| Dec 1, 2019 at 7:21 | comment | added | user21820 | @SueVanHattum: Thanks for your comment, but just because I am critical of something does not imply that I am unkind. I commented only because it is a disservice to mathematical education to draw false analogies and conclude that using the term "real number" is "basically opening a door that you're hoping nobody is curious enough to try to go through.". I want this site to be a good pedagogical resource, not filled with opinions that may engender poor teaching. | |
| Dec 1, 2019 at 1:14 | comment | added | Sue VanHattum♦ | Dear @Kevin, welcome to the site. (@user21820, the rules are, we are kind to one another here.) Personally, I do like saying something about the lay of the land, ie saying a bit about "other microscopes types" or other number systems bigger than the one we're playing in. | |
| Nov 30, 2019 at 20:21 | comment | added | Kevin | Geez. My answer was "completely flawed", and I was somehow able to be "even more wrong" with a subsequent comment. I can understand disagreeing with the analogy, though I think you're wrong and missing the point. But the way you're expressing your disagreement is pretty darned aggressive (let alone to someone who's posting on this site for the first time.) | |
| Nov 30, 2019 at 19:25 | comment | added | user21820 | That is even more wrong. Even in modern mathematics, the cube root of 2 is not a bunch of values. Either you take a principal branch-cut, or you say "a cube-root", not "the cube-root". And for high-school and real analysis, we define the cube-root to be the inverse of the cube operation on the reals. And there is no "begging". Who says I don't want to answer? If a bright student asks, further discussion can and should be done separately if it would not be suitable for the rest of the class. | |
| Nov 30, 2019 at 19:07 | comment | added | Kevin | Do you teach 7th graders that the cube root of 8 isn't just 2, but also -1+Sqrt(-3) and -1-Sqrt(-3) - before they learn about imaginary numbers, let alone complex number algebra? Or do you just teach them that the cube root of 8 is 2? Again, unless you're prepared to go into just what real/imaginary mean, using that terminology is begging a question you don't want to try to answer. | |
| Nov 30, 2019 at 16:44 | comment | added | user21820 | The analogy is completely logically flawed. There is nothing false in saying "we are going to be using a microscope" if we are in fact going to use an optical microscope. On the other hand, it is absolutely false to say "there is no $x$ such that $x^2 + 4 = 0$", unless we specify precisely what $x$ is, such as "real $x$". | |
| Nov 30, 2019 at 5:55 | review | First posts | |||
| Nov 30, 2019 at 7:29 | |||||
| Nov 30, 2019 at 5:53 | history | answered | Kevin | CC BY-SA 4.0 |