Chapter 5 Other Ways of Learning

Tutorials

The teaching which supplements and supports lectures, varies from place to place, and sometimes from lecture course to lecture course, but often include tutorials. Considerable resources are put into tutorials because they are a very valuable part of the learning process. These may be discussions with your tutor individually or in small groups. The format will be determined by the tutor but whatever it is you can help to get the best out of it by attending to four points, namely:

• Make sure that you bring all relevant notes, paper, pen and calculator.

• If there is work to be done before the tutorial do attempt it seriously and take your work along with you, even if you haven’t got very far.

• Get involved! Don’t be afraid to raise your real problems however trivial they may seem, the chances are that others share them. If you are really shy about asking questions yourself try to form a group and appoint a spokesperson.

Problem Sessions/Workshops

Problem sessions are usually taken in larger groups than tutorials. Problems are worked on by students during the session and help is on hand to get you over difficulties. You will probably find it helpful to work with one or two other students in the group. The same comments as for tutorials apply. It is a good idea to attempt a range of problems of varying difficulty during the session so that you may gain full benefit from the help available.

Since knowledge acquisition and skill in mathematics is a process which requires active involvement and sustained thought some institutions have developed courses that are investigation led rather than lecture led. Classes are broken down into small groups and they work on solving set problems either from a textbook or handouts. Then they all combine to pull together the themes that have been covered during the week. The idea is to encourage you the student to take more responsibility for your own learning but with the safety net that help is available when required. For such investigative learning courses it might be best to keep your own effort, individual or combined, in rough form until the strands are pulled together then they can be written up in a more formal and neat format. Our suggestions about tutorials also apply here. Such investigative work is also the basis of projects and research, so it is demanding and yet very rewarding.

Maths Support Service

Many institutes offer an independent maths support service which is available to complement your lectures and tutorials. Maths support is generally accepted to be the ‘catch-all’ name for extra-curricular maths and stats teaching which is provided in higher education institutions to enhance student learning. It is an additional resource which is not compulsory and does not bear any module credit. The exact format and mode of delivery will vary from place to place but is usually a combination of drop-in sessions, appointments, workshops and additional resources. You should find out how and when maths support runs at your institution and be sure to note the times; it can be a valuable resource and additional space to ask questions and clear up any uncertainty you have with your lecture notes and problem sheets.

Textbooks

These are often recommended by your lecturer or tutor either to supplement or to replace lecture notes. Many standard textbooks are now available as an e-book (usually via your library) but if you like to annotate the text, it may be useful to have your own copy - don’t forget to ask your lecturer about which editions are still applicable.

The most important aspect of reading is to be clear in your own mind why you are reading: to get a rapid overview of the topic in order to see what is relevant or not; to search for a specific piece of information; to come to grips with and understand a particular theorem or proof! Each of these tasks requires a rather different reading strategy. Having a clear purpose in mind when reading is one of the most important study skills that you need to develop.

Books vary widely in the notation they use and in their approach to a subject. During the early stages you should stick to books (if any) recommended by the lecturer and books which use similar conventions and notations. A ‘good’ book is one which suits you but you will probably want one with:

• lots of worked examples

• lots of exercises and problems

• answers at the back

• attractive presentation

You cannot read a mathematical textbook like a novel – you will rarely want to read from cover to cover. Learn to use the contents page and the index to find the relevant sections and pages; sometimes you may have to skim through both to find where to look. Read slowly and carefully and always with pen and paper to hand to do supplementary working.

Be prepared to go over an argument several times. If you have to gloss over a step, note it for later consideration. As always, try to understand the overall structure of an argument as well as the detailed steps. Make notes and cross reference them with your other notes on the subject. Always indicate on these notes the book from which they were taken together with the page numbers, so that you can find it again quickly if necessary.

Problems in the text often have hints (and even answers) at the end of the book; these may help you with work on problem sheets. Definitions and notations differ slightly from one book to another and from lecture notes; sometimes these differences matter, sometimes they don’t – consult your tutor if in any doubt. There may be an index of symbols and notations to help you.

Coursework

Coursework has been designed to provide substantial back up to your learning. It can often help to reinforce material already covered and, equally, can often provide a firm foundation on which to build new ideas and techniques. The feedback given to you through coursework is invaluable, read it and make sure you understand it. As always, if you have doubts, ask your tutor or lecturer for clarification.

Library

Get to know your library well; it is the source of a vast amount of information. Go to any introductory talks and tours and obtain copies of any library guides which are available. Find out how to use the catalogue, find out where the maths books are stacked and spend some time browsing to see what is there. It will repay you in the long term. Occasionally browsing may unexpectedly help you to resolve a difficulty or clarify a muddle.

Many textbooks are available online via your library catalogue, this can be a very useful way to access textbooks so find out how to use it.

The library staff are there to help you – don’t be afraid to ask. There may be librarians with a special interest in and knowledge of mathematics books.

Summary

• There are many additional ways to learn; use them!
• Be active in your participation in tutorials and workshops, it will help your understanding.
• Find out how to use any additional support such as Maths Support Services and Library services.
• You can find additional problems and examples in textbooks; start with the recommended text for your course.
• Be sure to read the feedback from any coursework; the comments and corrections are a valuable resource.