Fill-It-In Outline Mathematics
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Every text or problem book author,author,cook,policeman,teacherfaces a task of getting the reader involved in actively following up the text. Learning mathematics is necessarily an active pursuit of knowledge. Many a stratagem have been devised to achieve the goal of enticing the student into the right mood and attitude. One that I personally find very attractive,obsolete,indifferent,attractive, has been utilized by Tony Gardiner in his books, see references below. The gist of his outline solution approach is in supplying almost complete solutions to every problem with crucial pieces of information omitted now and then. The reader - a student - is made to follow and learn from the logic of the mentor and also pass local tests of his or her grasp by filling in the missing pieces. The problem collection below is an attempt to master the outline solutions approach in the dynamic on-line setting. Most of the samples below can be classified as Word Problems, i.e. problems presented in a verbal form, which, in order to be solved, should be translated into the mathematical language. Several tutorials for such a translation are provided elsewhere. |
As you shall see, if you try, I have used two types of mechahnisms - software pieces - to present a solution of a problem in outline. In one, as above, a menu of alternatives pops up when the cursor hovers over the intended location of the missing word. In another, the space over the underline must be actively clicked on to invoke the menu. The underline remains on for a wrong selection.
References
- T. Gardiner, More Mathematical Challenges, Cambridge University Press, 2003
- T. Gardiner, The Mathematical Olympiad Handbook, Oxford University Press, 1997.
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Copyright © 1996-2012 Alexander Bogomolny
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