All four of these articles involve opinions about good teaching, particularly as related to teaching mathematics. While there are similarities, there are also massive differences. For example, page 11 of the article by Paul Lockhart seems to de-emphasize the importance of planning a lesson while Gian-Carlo Rota (now deceased) emphasized the importance of planning as part of his “total openness” policy.
There are three primary components of the research paper. First, compare and contrast Lockhart’s Lament and In Defense of Mindless Rote. As part of this you should provide summaries of each, with clear indication of the main points conveyed by each author. You should discuss similarities and differences, both between the goals of the different authors as well as the teaching styles and techniques they suggest. Second, provide an analysis of Lockhart’s Lament and In Defense of Mindless Rote. Use additional research, such as refereed journal articles or books, to support or contradict the opinions of each of the authors. Third, conclude with your own opinions about how best to teach mathematical concepts. Again, journal or book sources should be used to support your case.
Note that neither of the first two components of the paper should include your own opinions. In these two portions, you are reporting on the work (and opinions) of others. The third portion is the place for you to state and defend your opinions.
The entire paper should be well organized, carefully cited (both in the paper and in a list of references), and should avoid plagiarism, poor grammar, spelling mistakes, etc. You should use at least five sources in addition to the ones given here.
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