Developing good academic practice
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# 4.2.3 Maths, Computing and Technology

In a pure mathematics examination question a first-year student is asked to state and prove Pythagoras’s Theorem.

## Level 1

The student should have previously memorised the theorem and its proof and could repeat this verbatim as the answer to the question without needing to reference Pythagoras’s original statement or the course text’s version of the statement. The theorem is essentially considered to be ‘common knowledge’ at this level, in this context and within this subject.

In a mathematical physics examination question a third-year student is asked to state and prove Pythagoras’s Theorem in 2D space and then to extend it: firstly, to 3D space; secondly, to n-dimensional space and, finally, to non-Euclidean geometries.

## Level 3

In this case, the student should state the theorem and proof verbatim but should reference the source of the particular version of the theorem and should reference the work of other researchers who have extended the original theorem.

However, a discussion of Euclidean and non-Euclidean spaces should also be included with descriptions and explanations presented in the student’s own words. Here, the theorem forms part of a wider context within a more difficult subject area and at a more advanced level, and so only certain aspects of its statement and use would be considered to be common knowledge.

In a mathematical philosophy examination question a postgraduate student is asked to analyse and discuss various forms of Pythagoras’s Theorem and the latter’s influence on our general concept of physical space.

## Postgraduate

Here the student should state and reference the sources of several different forms of the theorem, and, additionally, should provide a detailed critical analysis with extensive references to a wide range of sources that discuss the topic.

In this very broad context, within a conceptually sophisticated subject at a very advanced level, there is likely to be very little common knowledge involved. Full referencing should accompany the discussion and analysis, including references to ostensibly ‘obvious facts’, however ‘simple’ these might appear to be at first sight.

##### 4.2.3.1 Good academic practices in mathematics

How to find help with your studies

We hope that our teaching materials will make perfect sense the first time round, but the nature of mathematics is that concepts are quite hard, so most of what follows is about what to do when you find it hard.

Firstly, you should realise that almost everyone struggles with mathematics at some point. If mathematical problems could all be solved without a struggle the subject would not have the fascination and reward that it does.

Secondly, identify the nature of your problem. Is it:

- a specific piece of course text where you cannot see where the next line comes from;
- a general feeling of not understanding;
- an assignment question that you don’t know how to begin?

Struggling with mathematics is part of the learning process. Doing a course in mathematics is not just about producing assignment answers or even passing the exam or end-of-course assessment. It is about engaging and wrestling with the ideas and techniques in the course. You are likely to make mistakes, misunderstand some things and quite possibly feel stupid. Of course, you need to correct your mistakes and sort out your misunderstandings, but do not feel too stupid! Making mistakes can be a useful part of learning. You may find it helpful to refer to the book Success with Mathematics by Heather Cooke.

Do you have a general feeling of not understanding?

This is harder to cope with but still very common in mathematics.

If this happens early in the course, ask yourself whether you have taken a course before you are ready for it. Your tutor should be able to help you determine this.

Have you rushed through some material without giving it time to sink in? A good way of dealing with this is to work though some relevant problems or exercises. Write out your solutions properly – looking at the provided solution for guidance as needed. Even if this means that you are essentially copying the provided solution, it will help, particularly if you check the results and definitions used.

Try to attend tutorials. You can also make use of course forums if they are available – just knowing that others are feeling the same way can help.

If you are able to do most of the exercises but still feel you are struggling there is no real need to worry. It is likely that, as you progress through the course, ideas and techniques that seemed unfamiliar and hard at first will become clearer and fit into place. Mathematics, particularly more advanced mathematics, requires something that is often called ‘absorption time’.

Is it an assignment question that you don’t know how to begin?

Assignment questions are nearly always based closely on the course text. Indeed, most questions will clearly state which part of the course is being covered in their preamble. Many questions closely follow an exercise or example in the text, so a first step is to look for such an exercise or example and try to understand that. If you can find such an exercise or example you can discuss this with other students or with your tutor. If you cannot identify such an exercise or example you can try:

- contacting your tutor;
- posting a message on a course-based forum ;
- contacting a faculty member.

If you do discuss approaches to assignment questions with fellow students – or indeed anyone – you can still submit a solution. You should write it out on your own, using the course text as the basis for your answer. In general you must complete an assignment yourself and not submit a joint effort.

External resources

Libraries have traditionally been the place to go for extra material. You should be aware that titles of mathematics books can be particularly misleading – even a book entitled Elements of Number Theory may be a graduate text. You should also be aware that, although most mathematical notation and definitions are international, it is possible that the book you have found is using some notation differently from the course text. If you happen upon an exercise or example that is essentially the same as an assignment question you should behave as suggested above. Namely, if you do read it, do not copy the solution, but go away and write it out for yourself, using the course text as the basis for your answer.

Nowadays the internet provides an extremely rich source of mathematical material and you can browse this in much the same way as a library book. Do be alert to the origin of the material as it may not have been through the refereeing and editing process of a text. You should treat any worked examples and exercises that closely match an assignment question in the way described above.

In general, remember that you need to practise constructing your own answers to prepare you for the exam or for future courses.

Frequently asked questions

## Question 1

Why do we need ‘Frequently Asked Questions’ for mathematics, statistics and mathematically-based sciences and technologies?

## Answer

Because there are some specific issues that are not appropriate for the generic document.

## Question 2

What is plagiarism in mathematics, statistics and mathematically-based sciences and technologies?

## Answer

It is the same as in other academic areas: if you deliberately submit an assignment that contains work that is not your own, without indicating this to the marker (by formally acknowledging your sources), you are committing ‘plagiarism’.

## Question 3

Am I allowed to work on an assignment with other students?

## Answer

Yes. However, submissions must be written up individually, away from the group.

## Question 4

Am I allowed to copy from the course material when an assignment question is much the same as an exercise?

## Answer

It is to be expected that the layout and your mathematical workings will be similar in format to those in the course material. Indeed, these will provide a guide as to how much detail you should give in your solutions.

## Question 5

How do I refer to definitions, theorems and formal mathematical statements?

## Answer

If the definition, theorem or formal mathematical statement is in the course material, simply say whereabouts in the course material or handbook it occurs. If it has a name, such as ‘Lagrange’s Theorem’, use the name. For example ‘in Unit 4 Theorem 2.3 on p26’ or ‘HB p32 Lagrange’s Theorem’.

If a definition or theorem comes from elsewhere quote it exactly and give details of the book, article or web page (give date accessed). Do not try to write definitions, theorems or formal mathematical statements in your own words. The wording is necessarily very precise and usually is best left unaltered.

## Question 6

Can I post an assignment question on an ‘ask a question’ website, even if I don’t copy the answer but just use it to help me?

## Answer

No. This may be a breach of copyright. If you are struggling with an assignment question then try:

- contacting your tutor;
- contacting a faculty member who provides additional tutorial help for your course and whose contact details are given in the course information.

## Question 7

I use books and the internet to supplement my studies. Is it acceptable to copy an answer to an assignment question from a source such as a book or the internet if I give a reference?

## Answer

No. You may not be awarded any marks for an answer that is not your own. If you have read through such an answer, you should write your own answer away from the source consulting only the course material.

## Question 8

Can I use a calculator or computer to help with calculations?

## Answer

You can use a calculator to do numerical calculations. Any calculation that cannot be done on a calculator should be done by hand, unless the instructions for your course or the assignment question say that you can use a computer. This is part of your learning, and there will be marks allocated for working. However, it is a good idea to use a computer to check your answer, where possible.

## Question 9

Can I use a calculator or computer to sketch graphs?

## Answer

You should not use a graphics calculator or mathematical software to sketch a graph, unless the instructions for your course or the assignment question say you can. In some courses it is not even acceptable to use graphics software such as the drawing facilities in Microsoft Word – you need to check the instructions for your course. However, it is a good idea to use a graphics calculator or computer to check your answer where possible.

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