Then they see this and it is also OK:<\/p>\n
5(ab<\/em>) = 5ab<\/em><\/span><\/p>\n In most cases you can substitute various values of a<\/em> and b<\/em> and the students can see that it works. Fair enough. Then the student does twenty (mind-numbing) examples of such bracket expansion and they feel they have got it. <\/p>\n Later, they come across things like:<\/p>\n sin(a + b<\/em>)<\/span><\/p>\n And then their math teacher goes ape when the student expands it like:<\/p>\n sin(a + b<\/em>) = sin a<\/em> + sin b<\/em><\/span><\/p>\n Perfectly logical, in the minds of the student.<\/p>\n Similarly, it is logical to have the following, isn't it?<\/p>\n log(a + b<\/em>) = log a<\/em> + log b<\/em><\/span><\/p>\n Oh, and then we have functions. You know, like this:<\/p>\n f<\/em>(x<\/em>)<\/span><\/p>\n Is that the same as<\/p>\n f<\/em> × x<\/em>?<\/span> (That is, f<\/em><\/span> multiplied by x<\/em><\/span>?)<\/p>\n Why not?<\/p>\n I wish to propose an alternative notation for concepts where you cannot<\/strong> expand in the way you do with simple algebra. It might look something like this:<\/p>\n This would send a much clearer message to students that the particular function or operation does not work in the same way as simple algebra works.<\/p>\n Now, the proposed rectangle would be a nightmare given that we need to type mathematics (actually, everything is a nightmare when you are trying to type mathematics...).<\/p>\n So a more computer friendly option would be to (exclusively) use [ ] - square brackets - for such concepts, like this:<\/p>\n sin[x + y<\/em>]<\/span><\/p>\n log[x + y<\/em>]<\/span><\/p>\n f<\/em>[x<\/em>]<\/span><\/p>\n Would this work? Would it confuse everyone even more? I feel that if such a notation were to be universally adopted, then less confusion would arise.<\/p>\n [I wrote about notation before in Phase shift or Phase Angle?<\/a>].<\/p>\n
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