CHAPTER 10

Report Writing and Presentations

Aims and objectives

In this chapter we discuss the ways in which the conclusions we derive from our models can be communicated to a wider audience.

10.1 Introduction

In the previous chapters, we hope that we have shown you that modelling is fun, exciting, challenging and rewarding. We may build models for enjoyment or to help us to make sense of the world around us but very often we build models in response to a request for help with a practical problem. Ultimately, we need to communicate our conclusions to the person or persons who asked for our help in the first place. These may be our employers, clients or friends and it is almost certain that they will not be mathematicians. They will only want to know what conclusions we have come to from our model and what advice we have to offer.

In this chapter, we focus our attention on how to communicate our conclusions and also how to explain the way in which we obtained our conclusions. This can obviously be done in two main ways: in writing and verbally. In practice, it is a good idea to use both. We shall refer to them as the (written) report and the (verbal) presentation. If we want our modelling efforts to be turned to good practical use we must make sure that our communication is effective. We might develop a very good and potentially very useful model but, if we do badly in communicating our conclusions, we may fail to convince anybody of its worth. With mathematical models, we need to take special care because we shall very often be communicating with people who have less mathematical training than ourselves.

10.2 Report writing

How much we write and how we say it will depend partly on how large the problem was and for whom the report is intended. We shall describe an ‘average’ report based on a straightforward problem. The guidelines which we describe should not be taken as absolutely rigid rules; some of the sections described can be shuffled around to suit a particular report.

The first point to make is that the report should have a well-defined structure. This will make it more likely that the intended message will get across to the reader and will make it easier to pick out parts of the report that may be of particular interest.

We can divide the structure into three sections, to be assembled together in the following order.

1.Preliminary.

2.Main body.

3.Appendices.

Each of these sections will be further divided into subsections of unequal lengths.

Preliminary

We start with the front cover which will carry the first important item of information – the title of the

report. The title should be clear and direct, avoiding any technical jargon, and should be as brief as possible. It should contain the essence of what the report is about. The title page, which may be either the first page or the front cover itself, should contain the title, the names of the writers, their official capacity (if any), the organisation which they represent and the date of issue. The format will look similar to

On the next page an acknowledgement or thanks to persons or organisations which have helped in the investigation may be inserted. Following this should be the contents, listing the headings and subheadings of all the sections of the report and quoting the relevant page numbers. Appendices and illustrations should also be included in the list. As well as outlining what the report contains, the contents also communicate the structure of the report.

After the contents, there should be a summary. This constitutes a report in miniature covering all sections of the main report and it could be used as an ‘abstract’ for people who do not require the detailed information provided by

the whole report. You should write the summary after the main report is finished and try to contain it within a single page.

If the reader is impressed by the contents and summary, he or she may be ready to read the main report but in some cases, e.g. a senior person with little time, he or she might consider it sufficient simply to ask for conclusions and recommendations. It may be a good idea therefore to include in the summary the main conclusions. (Full conclusions are given as the last section in the main part of the report.) These should sum up the results that have been obtained from the model and what the implications are. There may be recommended courses of action, offering advice based on the interpretation of the results produced by the model. In effect, we are providing a short-cut through the report, i.e. title–contents– summary and conclusions, as an alternative to reading the full report.

Before we leave the preliminary section, we have a further page to add, namely a glossary of variable names together with units of measurement and symbols used. Any particular variable or parameter should of course be represented by the same symbol throughout the report. Also included should be an explanation of any abbreviations used in the report.

Main body

This should start with a problem statement explaining the background to the problem and why the model was developed. The objectives of the investigation should be clearly stated here. (This subsection may alternatively appear in the preliminary section of the report.) You need to remember that whoever reads your report will look at the conclusions to see whether the objectives have been achieved; so you must ensure that they relate.

In developing your model, you will have made a number of simplifying assumptions. These should now be listed carefully and clearly. Include all the assumptions that you had to make in order to make progress with the model together with those assumptions that you decided to make in order to keep the

model simple. There is obviously going to be a link between the assumptions and the final conclusions obtained and you could be challenged on the validity of the assumptions. You should be prepared to defend them if necessary.

It is very likely that some data are included in the report. Present the data clearly and accurately using tables and graphs and also give the source. If there is a large amount of data, this would be best put in the appendix.

The next subsection will probably be the longest in the whole report. It will explain the development of the model from the assumptions and the derivation of equations, etc., which completes the formulation. There may well be a number of diagrams involved also.

The development and formulation will be followed by the solution of the equations, including an explanation of the solution procedure and any com-

puter software used (either specially written or standard packages). It may also be of relevance to mention the computer hardware used. If much algebraic manipulation and/or numerical work is involved, it may be better to postpone some of it to the appendices.

Having come to the end of the solution stage, we shall be ready to present our results. These could range from very brief (a single number or statement) to many pages of graphs or tables. If there are many pages of results, it is probably wiser to put them into the appendices. Do not produce a large volume of results if they are not really useful. The main point is that they should illustrate the conclusions and provide information that could be of use.

You may wish to sum up your conclusions and recommendations here instead of or as well as in the preliminary section. Do not forget to say something about the possible accuracy of your results and the sensitivity of the conclusions obtained to the parameter values used and the assumptions made. You may wish to criticise your own model here, pointing out its limitations.

Finally there could well be a section outlining possible extensions, generalisations and suggestions for further work.

Appendices

This is the section into which detailed information relevant to the subject of the report can be put. We may have given the impression that it is some kind of ‘dustbin’ into which we put things which are rather inconvenient. The point, however, is to enable an interested reader to study the information in greater depth than is possible in the main body of the report. It is also possible to include in an appendix items of information such as graphs or tables which are frequently referred to in the report and would otherwise have to be repeated several times.

In the main body of the report, you may have referred to, or directly quoted, or used data from published sources. These should be listed under a heading ‘References’, including author names, book or journal title and volume number, page numbers and date of publication. You may also know about books or articles not mentioned directly in the report but containing relevant material either as background reading or further reading. These should be listed under the heading ‘Bibliography’.

Summary

Normally the following headings will appear in a written report but not necessarily in the same sequence. Your particular report may involve special factors which require a different sequence or you may decide to leave out some of the sections.

Graphs, tables and illustrations.

References and / or bibliography.

Back cover.

General remarks

Before starting on the report, spend some time thinking. If you know who the readers are going to be, ask yourself ‘What do they need to know?’ and ‘What do they know already?’ Make rough notes of particular points that you want to make sure are in the report. Consider the purpose and scope of the investigation and aim for a report which is appropriate in length for the importance of the work that has been done. Also consider the time available for preparing the report and divide it up between thinking, planning, writing and revising. Decide on the style of writing, bearing in mind who your readers are going to be. If they are strangers to you, be appropriately formal but not too pompous or pedantic. Try to choose a style which is clear and informative remembering that the object is to communicate what you have done.

While constructing the report use, if possible, a word processing package such as Microsoft Office so that revisions can be easily and quickly made. Make sure that all pages are clearly numbered and always start new sections, subsections or topics on a new page. Give sections and subsections headings which are underlined. Also underline any points requiring special emphasis in the report. It is a good idea to use a numbering scheme such as

5 BODY OF REPORT

5.1 Problem statement

5.2 Assumptions 5.2.1 First assumption etc.

The merit of a numbering scheme such as this is that it makes it easier to cross-refer from any part of the report. Do not go too far with it, however; for example a section such as 5.2.1.5 could well put off the reader.

Each graph or table should have its own page and be clearly titled. If possible, place them next to the section of text in which they are discussed. Be neat and well organised and make sure that the grammar and spelling are correct. If they are not, your reader will quickly be distracted even though you may have something good to say. Avoid long sentences (30 words or more) and do not use complicated words when simple words will communicate the meaning equally clearly. Also keep paragraphs reasonably short and well spaced. This makes a more effective visual impact than large blocks of print.

Consider revising your report after putting it on one side for a while. Read through your first draft and consider the following questions.

Is the report objective?

Is it likely to create a good impression?

Does the writing match the needs of your readers in style, vocabulary and level of mathematics? Is the report positive and constructive?

Is the title page complete and well laid out? Is the summary clear, brief and accurate? Is the layout clear and easy to follow? Does the report read well?

Are any essential sections missing?

Are the sections in the most suitable order? Do the headings stand out?

Is the problem clearly stated?

Is the level of detail appropriate?

Have you included all the facts and no unnecessary information? Are the sources of facts clear?

Do the conclusions follow logically from the development? Are possible solutions abandoned without reason?

Are symbols, etc., suitable and consistent?

Are there any statements whose meanings are not quite clear? Are facts, figures, calculations and drawings accurate?

Are the most important points sufficiently emphasised? Are there any faults of logic or mistakes in spelling?

If you feel that the answers to any of these questions are not satisfactory, make the necessary revision