**The textbook:**first, let's learn about what a logarithm is, and fill in the blanks - a lot. Then, the laws, which we'll only learn if we practice simplifying meaningless expressions - a lot. Then, a bit about equations and application problems. Then change of base. Each in its own nice little sub-chapter.

**Me:**Lets learn about logs, a'ight? What they are and ooh look they seem to obey a bunch of rules, I wonder if we can use that to solve equations and for applications?

Bottom line is, it seems so utterly

*pointless*to learn about logs, and log laws and then practice manipulating logarithmic expressions. Why would I let my students*wait*to see the power of log laws in solving equations that previously left them dumbfounded? I'm even wondering, why teach them the change of base formula, when they can handle any equation just using basic log laws? If there ain't a need, why go there?
I definitely agree about change of base formula. I didn't teach it this year, I just taught them how to rewrite logs in their exponential form, then solve the equation by loging both sides. It was so much better I think because it got them practicing solving equation techniques while just trying to evaluate a simple logarithm, and it let them discover the change of base formula for themselves with no direct teaching.

ReplyDeleteYes, I think your approach makes good sense. The textbook approach has some sense as well, I suppose the authors are thinking "if we break it into bite-size chunks it won't feel so overwhelming". Instead, I often find students feel overwhelmed by the sheer number of subsections, as in "OMG we covered 4 subchapters today? We're moving too fast!". I dream of a textbook with only, say, 8 chapters - and actual text! Like in a physics book, or something.

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