Recently, I read a blogpost of the same title as this one. The first error she posted was the same as the image for this post, and it reminded me of a conversation I had with a parent a few years ago.
As mentioned before, I teach in an online school. Our courses are designed to be asynchronous, so our students can work at any pace they want. As a result, the content is pre-designed (often by a third party) and there are limits to changes we can make.
Many times, this boils down to preferences. If there is a topic, I might want to teach it one way, but the course teaches it a different way. It isn’t wrong, per se. It just isn’t what I would use. For example, I don’t like the use of the word “cancel” in math because I think students use it too often when they don’t really know what is going on (or why they can do what they are doing). Think of it as “magic.” If I say the word “cancel,” I can do anything I want! (At least Jane Taylor agrees with me in her comment on the same post mentioned above.)
Using the word “cancel,” though is more a preference than an error (although it can be used erroneously). As a result, even though I don’t like it, I cannot request to have it changed in the course. Only errors will get changed.
So in one of the courses I taught, the curriculum used the error listed above. They would say something like √9 = ±3. I know this is wrong, so I asked for it to be corrected. It ended up not being corrected as the curriculum writers saw this as a “preference” as opposed to an “error.”
Eventually a parent called me on it. Of course, I knew he was correct, but there wasn’t anything more I could do about the content. I did let the parent know that I give students credit if they gave the answers of √9 = ±3 or √9 = 3. Unfortunately, that wasn’t good enough for the parent, so we had several conversations through email and phone. What bothered me the most is that I could not do anything about their valid concern. At least not while their student was in the course.
On a positive note, we ended up rewriting the course shortly after that, but mainly because it was an old course. As an old course, we had many, many students go though it and learn it the wrong way. My hope is that they were able to correct their thinking in later courses.
Often when working with a student on radicals, I will give them the following scenario:
If I, as the teacher or as the author of the curriculum, give you a square root symbol, then I will tell you whether I want the positive or negative version. For example, if you see √9, you know I want the positive version. If you see −√9, then you know I want the negative version.
However, if YOU as the student put the square root symbol, then you don’t know if I want the positive or negative version of the square root, so you need to give me both. In that case, a problem like x2 = 9 would need to have two solutions since it is the student applying the radical sign.