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.Treatment of the topicWhatever the title of the extended essay, students must apply good mathematical practice that is relevantto the chosen topic.Data must be analysed using appropriate techniques; arguments correctly reasoned;situations modelled using correct methodology; problems clearly stated and techniques at the correctlevel of sophistication applied to their solution.There must be sufficient explanation and commentarythroughout the extended essay to ensure that the reader does not lose sight of the purpose of the essayin a mass of mathematical symbols, formulae and analysis.The unique disciplines of mathematics must be respected throughout.Relevant graphs and diagramsare often important and should be incorporated in the body of the essay, not relegated to an appendix.However, lengthy printouts, tables of results and computer programs should not be allowed to interruptthe development of the essay, and should appear separately as footnotes or in an appendix.Proofs ofkey results may be included but proofs of standard results should be either omitted or, if they illustratean important point, included in an appendix.Frequent reference to the assessment criteria by both the supervisor and the student will helpkeep a sharper focus on the project.Interpreting the assessment criteriaCriterion A: research questionAlthough the aim of the essay can best be defined in the form of a question, it may also be presented asa statement or proposition for discussion.Criterion B: introductionThe introduction should relate the research question to existing subject knowledge: the student s personalexperience or particular opinion is rarely relevant here.© International Baccalaureate Organization 2007 119MathematicsCriterion C: investigationThe number of sources that require consultation will be dependent on the research question that theessay addresses.It must be sufficient, but not unnecessarily long, and the various items must, after beingconsulted, contribute to the essay in a meaningful way.Criterion D: knowledge and understanding of the topic studiedClear evidence of understanding of the chosen content of the essay is more important than any attemptto exhibit an unnecessarily wide mathematical knowledge.The level of knowledge displayed shouldreflect the mathematics acquired in the classroom and any additional information that the research forthe essay has provided.Criterion E: reasoned argumentIn a mathematics extended essay, the terms  reasoning and  argument can apply to the essay overalland, with a somewhat different interpretation, to one or more sub-sections of the essay, such as in theproof of a theorem.The mark awarded should reflect both of these aspects.Criterion F: application of analytical and evaluative skills appropriateto the subjectThe words  appropriate to the subject are paramount here, given the breadth of mathematics today.Essays based on mathematical proof require skills in deductive reasoning and structuring; essays of aninvestigative nature, answering a research question or hypothesis, involve interpretative skills; whilemathematical modelling requires an ability to formulate correctly a problem in mathematical terms.Criterion G: use of language appropriate to the subjectThe purpose of language in mathematics is, as in other subjects, to communicate.In an extended essay,it should communicate clearly, not just to an examiner who is likely to be more mathematicallysophisticated than the student, but also to an interested reader with a similar mathematical competenceto the student.Mathematical  name-dropping should be avoided.Criterion H: conclusion Consistent is the key word here: the conclusion should develop out of the argument and not introducenew or extraneous matter.It should not repeat the material of the introduction; rather, it should presenta new synthesis in light of the discussion [ Pobierz caÅ‚ość w formacie PDF ]