IB Guidance on Maths Explorations

IB Guidance on Maths Explorations – Very Important

It is essential that you read all the guidance below, as well as clicking on the links to the information from the IB. The biggest mistake students make is not paying enough (or any) attention to the below recommendations. If you fail to read everything below carefully it could make the difference between getting 17/20 and getting 11/20. That’s a huge difference which could easily drop you an IB grade.

Before you choose a topic:

It is essential that you read the SL and HL guidance from the IB prior to starting your IA maths exploration – this linked site gives the full list of assessment criteria you will be judged against and also gives 9 full examples of investigations students have done. From teacher discussions, this year’s IAs for HL (summer 2014) seem to have been moderated down quite a few points – and as a result the IB have released further clarifications about marking criteria. Make sure your teacher has read these!

IB Feedback for May 2014’s HL Explorations (applicable in nearly all parts to SL)

The IB have just released their marking report for the May 2014 maths explorations.  Because this was the first year students have had to do this type of exploration there are a large number of comments from the IB giving guidance for how teachers and students can improve their grades in the future.  I would recommend reading the below comments very very carefully.  These are after all being made by the people who will be (ultimately) grading your coursework.  The rest of the text (italic) is taken from the IB report here.

Overall Summary

The majority of explorations were generally commensurate with the Maths HL content but the quality was very mixed with very few explorations in the top range. Unfortunately many explorations lacked citations. This requirement needs to be made clearly known to all teachers; otherwise students will risk a malpractice decision.

Some of the explorations were too long, sometimes because the scope of the exploration was not focused enough. On the other hand a few explorations were too short and included very little mathematical content. Some repeated topics were seen like “The Monty Hall Problem”, “Rubic Cube Mathematics” or “Mathematics behind the Pokemon game”.

A number of explorations were based on common textbooks problems and demonstrated little or superficial understanding of the mathematical concepts being explored. A few of the students however demonstrated thorough understanding and managed to personalize their explorations. Modelling explorations based on Physics problems were also abundant. The most popular topic explored was the “Parabolic Trajectory” and the “Catenary equation”.

Criterion A Summary

In general students performed well against this criterion. Some teachers seem to believe that subheadings indicating “Aim”, “Rationale” etc., are required in order to achieve top levels. Most explorations were complete and concise, however, some were far too long.

Works that were based on typical text book problems and depended a lot on sources tended to be incoherent and were difficult to follow. Any paraphrased information needs to be cited at the point in the exploration where it is used. A footnote referring to the bibliography is not enough and may lead to a decision of malpractice.

Criterion B Summary

Students did well in general on this criterion. Graphs and tables were often provided but not commented on. Sometimes graphs lacked labelling, and tables had no headings. The teacher sometimes condoned the misuse of computer notation; this lead to a change in the achievement level awarded. Some explorations lacked the definition of key terms used.

Criterion C Summary

This is the criterion that was mostly misinterpreted by teachers with a quite a few students being awarded top levels because of their commitment or enthusiasm for the subject without any of this being evident in the student work. Students who presented explorations based on common textbook problems beyond the HL curriculum, were unable to score highly on this criterion because the mathematics was not understood fully to enable them to take ownership and extend the work beyond the theory presented. Some teachers understood the criterion descriptors well and this was transmitted to students effectively.

Criterion D Summary

Some teachers misunderstood this criterion’s descriptors and must have conveyed to students that reflection was a summative of the work done. As such some explorations were written as an old “IA Task” with just a narrative about the scope and limitations of the work done and no meaningful or critical reflection. Again students who wrote a “textbook” problem investigation found it difficult to reflect on the process and or results and their significance.

For higher achievement levels in this criterion students need to consider further explorations, implications of results, compare the strengths and weaknesses of the different mathematical approaches of their investigation and also look at the topic from different perspectives.

Criterion E Summary

There was a large variety of mathematical content in the exploration, ranging from very basic mathematics to extensions well beyond the HL syllabus. A number of explorations were full of formulae which seemed to be copied from mathematical journals or Wikipedia without appropriate sources. It was not always clear whether the teacher had checked the mathematical content; this made it more difficult to understand how the achievement levels were interpreted and awarded by the teacher.

In some explorations the content seemed “forced” and overly sophisticated abstract concepts were added in an attempt to raise the quality of the exploration. Often this created a patchwork of mathematical formulae and equations that were not necessarily understood by the student. Although an exploration may take the form of a research paper, containing mathematics that is found in appropriate sources, the student needs to demonstrate a deep understanding of the mathematics being explored.

Recommendations for students and teachers

1) The exploration should be introduced early in the course and referred to frequently enough to allow students to reflect on an area of Mathematics that best suits their interest and allows them to develop an appropriate exploration.

2) Students should be provided with material to stimulate ideas for the exploration. These may include movies, short videos, photographs, experiments etc…

3) Students need to develop research and writing skills through reading and understanding different forms of mathematical writing as well as the possible assignment of mini tasks

4) Teachers should discuss the suitability of the topic chosen by students before a first draft is handed in.

5) Students should use some of the time allocated to the Exploration to explain clearly the expectations when it comes to using borrowed ideas from sources.

6) Teachers need to make it very clear to students that each and every quoted, paraphrased, borrowed or stolen reference must be cited at the point of reference, otherwise the student’s work will be referred to the Academic Honesty department that may decide on a possible malpractice (plagiarizism).

7) The teacher should ensure that the work being submitted is the student’s own work.

8) The teacher must show evidence of checking the mathematics with tick marks, annotations and comments written directly on the students’ work. This will help the moderator to confirm the achievement levels awarded by the teacher.

9) The teacher must mark a first draft of the exploration. This should provide students with written feedback. This should also lead to a discussion to ensure that the student understands the mathematics used and demonstrates this in the work.

10) Students should be discouraged from using difficult Mathematics beyond the HL syllabus if this cannot lead to some creativity or personalized problem.

11) Students should be reminded that the exploration should be between 6 to 12 pages typed in an appropriate font size (e.g. Arial 12). Diagrams and /or tables which are not significant and do not enhance the development of the exploration should not be included.

12) Candidates need to understand the difference between describing results and critically reflecting on their results.

13) Using difficult mathematics that goes well beyond the HL syllabus often results in a lack of thorough understanding and this in turn makes it difficult for the student to demonstrate Personal Engagement or Reflection.

14) Students should be encouraged to create their own questions based on their own individual interest which may include current social, economic or environmental problems in the community. Teachers are encouraged to use past explorations (TSM exemplars) and engage students in marking them early on in the process. This will clarify the importance of each criterion and the impact the choice of topic may have on the achievement levels that may be reached.

When you have read all of the above, you are now ready to choose your topic – good luck!