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These subject guidelines should be read M conjunction with the Assessment Criteria Overview An extended essay in mathematics provides students with an opportunity to demonstrate an appreciation of any aspect of the subject, whether it is: These are just some of the many different ways that mathematics can be Extended essay mathematics criteria or useful, or, as in many cases, both.

Choice of topic The extended essay may be written on any Extended essay mathematics criteria that hasa mathematical focus and it need not be confined to the theory of mathematics itself.

Students may choose mathematical topics from fields such as engineering, the sciences or the social sciences, as well as from mathematics itself.

Statistical analyses of experimental results taken from other subject areas are also acceptable, provided that they focus on the modelling process and discuss the limitations of the results; such essays should not include extensive non-mathematical detail.

A topic selected from the history of mathematics may also be appropriate, provided that a clear line of mathematical development is demonstrated. Concentration on the lives of, or personal rivalries between, mathematicians would be irrelevant and would not score highly on the assessment criteria.

It should be noted that the assessment criteria give credit for the nature of the investigation and for the extent that reasoned arguments are applied to an appropriate research question.

Students should avoid choosing a topic that gives rise to a trivial research question or one that is not sufficiently focused to allow appropriate treatment within a suitably sized essay. Students will normally be expected either to extend their knowledge beyond that encountered in the Diploma Programme mathematics course they are studying, or to apply techniques used in their mathematics course to modelling in an appropriately chosen topic.

However, it is very important to remember that it is an essay that is being written, not a research paper for a journal of advanced mathematics, and no result, however impressive, should be quoted without evidence of the students real understanding of it.

The following examples of titles for mathematics extended essays are intended as guidance only. The pairings illustrate that focused topics indicated by the first title should be encouraged rather than broad topics indicated by the second title.

The next examples illustrate ways in which mathematics topics can be refined and successfully approached as extended essays. Does it still play a part now we have man-made satellites?

Some other problems, perhaps in number theory and geometry, that lead to the equation could be described, with a brief history of the equation included.

Show how it is applicable in mathematical models of other real situations.

Use the decimal representation of irrational numbers as a starting point to introduce approximation by rationals. Show how a continued fraction expansion of an irrational can also provide rational approximation, and discuss error bounds and orders of approximation.

Describe how Archimedes determined the area of a circle by using inscribed polygons, leading also to his measurement of n. Continue with a description of his method of discovery for calculating the area of a parabola.

Treatment of the topic Whatever the title of the extended essay, students must apply good mathematical practice that is relevant to 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 correct level of sophistication applied to their solution.

There must be sufficient explanation and commentary throughout the extended essay to ensure that the reader does not lose sight of the purpose of the essay in a mass of mathematical symbols, formulae and analysis.

The unique disciplines of mathematics must be respected throughout. Relevant graphs and diagrams are 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 interrupt the development of the essay, and should appear separately as footnotes or in an appendix.

Proofs of key results may be included but proofs of standard results should be either omitted or, if they illustrate an important point, included in an appendix.

Frequent reference to the assessment criteria by both the supervisor and the student will help keep a sharper focus on the project.

Interpreting the assessment criteria Criterion A: It must be sufficient, but not unnecessarily long, and the various items must, after being consulted, contribute to the essay in a meaningful way. The level of knowledge displayed should reflect the mathematics acquired in the classroom and any additional information that the research for the essay has provided.

The mark awarded should reflect both of these aspects. Essays based on mathematical proof require skills in deductive reasoning and structuring; essays of an investigative nature, answering a research question or hypothesis, involve interpretative skills; while mathematical modelling requires an ability to formulate correctly a problem in mathematical terms.

In an extended essay, it should communicate clearly, not just to an examiner who is likely to be more mathematically sophisticated than the student, but also to an interested reader with a similar mathematical competence to the student.

Mathematical "name-dropping" should be avoided. It should not repeat the material of the introduction; rather, it should present a new synthesis in light of the discussion.The IB Extended Essay (or EE) is a 4, word structured mini-thesis that you write under the supervision of an advisor (an IB teacher at your school), which counts towards your IB Diploma (to learn about all of the IB diploma requirements, check out our other article).

The graphic below attempts to illustrate the change in assessment criteria for extended essays from before May (11 criteria, A-K) to what will be applied to essays from May and onwards (5 criteria, A-E).

The Extended Essay "The extended essay is an in-depth study of a focused topic chosen from the list of approved Diploma Programme subjects. It is intended to promote high-level research and writing skills, intellectual discovery and creativity. complete an extended essay (EE) follow a theory of knowledge course (TOK) Knows the regulations governing the EE & the assessment criteria. Reads & comments on first draft only – does not edit the draft. A mathematics EE means doing math as well as discussing it. The graphic below attempts to illustrate the change in assessment criteria for extended essays from before May (11 criteria, A-K) to what will be applied to essays from May and onwards (5 criteria, A-E). [I wish to thank David Ripley, site editor for the IB English B website]Below this graphic is a more detailed discussion for each of the five new criteria - especially in relation to.

[I wish to thank David Ripley, site editor for the IB English B website]Below this graphic is a more detailed discussion for each of the five new criteria - especially in relation to. Why you should consider a mathematics EE Paul Jackson provides guidelines to help you produce an excellent mathematics extended essay.

It pays to follow the new assessment criteria carefully as you write your mathematics EE. Criterion A: focus and method.

The extended essay is a research essay and the assessment criteria emphasize the importance of research skills rather than linguistic proficiency.

Although a certain level of ability in the language is. Why you should consider a mathematics EE Paul Jackson provides guidelines to help you produce an excellent mathematics extended essay. The EE assessment criteria It pays to follow the new assessment criteria carefully as you write your mathematics EE.

Criterion A: focus and method. Extended Essay Handbook ± QUEENSLAND ACADEMY for Science, Mathematics and Technology the extended essay The Extended Essay is a compulsory component of the IB Diploma program and combined with the Theory of Knowledge assessment, contributes to a possible 3 points of a maximum 45 points awarded for the IB Diploma.

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