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STRANMILLIS UNIVERSITY COLLEGE

BEd Year 3 Module Guide

Primary SCS3013

&SCS3056 (Aspects of…)

Mathematics and Numeracy 3

Weighting of Module 20 CATS / 10 ECTS / 5 US Credits

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This module is compulsory. Where problems arise with any particular aspect of the course you should approach the class tutor directly. General queries should be taken to the Module Co-ordinator.

Rationale The Mathematics and Numeracy 3 module is interrelated with the other components of the BEd (Primary) in its general aim of ensuring that students enter the teaching profession with the knowledge, skills, attitudes and values appropriate to professional teachers. In order to respond to the demands of the Northern Ireland Curriculum, the specific purpose of the module is to enable students to gain knowledge of mathematics at a level which will support effective classroom teaching in a context of understanding and awareness of the many factors – cultural, sociological and psychological as well as methodological – which may promote or inhibit learning, and of the place of assessment, testing, reporting and recording in ensuring pupils’ progress throughout the primary school. While the chief objective of the module is to provide for the immediate personal and professional needs of newly qualified teachers, the module as a whole will form a sound foundation for their further professional development. Content This module is concerned with the preparation of an appropriate and effective primary mathematics curriculum. Students will examine the requirements of the NI Curriculum for Mathematics and Numeracy and other relevant literature in relation to the topics addressed. Students will explore approaches to calculation, and contexts for developing knowledge, skills and understanding in mathematics. They will also extend their knowledge and understanding of assessment and Special Educational Needs within mathematics. Learning Outcomes On completion of this module students should demonstrate:

A critical knowledge and understanding of: o the NI Curriculum for Mathematics and Numeracy; o theoretical perspectives and literature informing teaching and learning

in mathematics; o approaches to calculation; o how mathematics can be developed through meaningful contexts; o the range of resources, including educational technology, available to

support teaching and learning in primary mathematics.

A well-developed ability to incorporate differentiation within their teaching in mathematics.

A personal and professional knowledge and understanding of mathematics to support their teaching.

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Transferable skills Students should have a well-developed ability to:

Organise and articulate their knowledge and understanding using specialist vocabulary;

Support their views with reference to relevant theoretical perspectives and literature;

Reflect and analyse information;

Evaluate and use ICT in appropriate situations;

Interpret graphical and tabular presentation of data in a critical and constructive way;

Collect and present numerical data;

Use graphical and tabular information appropriately;

Work effectively within a group and participate in discussion;

Organise an effective work pattern including meeting deadlines. Teaching and Learning During the study of this module students will experience a variety of teaching and learning methods and techniques. They will gain knowledge and understanding through lectures, tutorials, individual consultation opportunities, computer assisted learning, and independent study time. Relevant GTCNI Competences PC3i – have a detailed knowledge and understanding of the mathematics taught, including the centrality of strategies and initiatives to improve … numeracy and thinking skills, keeping curricular, subject and pedagogical knowledge up-to-date through reflection, self-study and collaboration with colleagues PC4 – know and understand how mathematics contributes to the NI Curriculum and be aware of curriculum requirements in preceding and subsequent key stages Aspects of the following as they relate to Mathematics and Numeracy:

PC5 – know and understand the relationship between the planning, implementation and evaluation of the curriculum PC9 – know and understand the principles underpinning the teaching of children with special educational needs … know the basic features of common special needs PC11 – know how to use educational technology to aid pupil learning and to support their professional role PC14 – set appropriate learning intentions taking account of what pupils know, understand and can do in relation to the requirements of the NI Curriculum PC15 – plan and evaluate lessons that enable all pupils, including those with SEN, to meet learning intentions, showing high expectations and an awareness of potential areas of difficulty

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PC25 – know about, and be able to use, a range of ipsative, formative and summative assessment. Appreciate their uses and limitations.

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Module Outline Foundation Stage and Key Stage 1 Topics covered will include: Approaches to teaching and learning mathematics and numeracy

Developing a quality mathematic and numeracy environment in the early years

Using a thematic approach to integrate mathematics and numeracy across the curriculum in the early years.

Developing mathematics through themes and play centres. Further develop the concept of play/ play based activity learning.

Discussion around the theories of child development that support specific teaching strategies and approaches.

Participation in activity-based seminars to aid in the identification of problems faced in the teaching of mathematical concepts.

Number to 100 Understanding Number and Number Notation:

Developing mental strategies within 100 (especially the value of 10);

Understand that the place of the digit indicates its value - grouping and exchanging, tens and units, activities/resources to support early place value

Difficulties encountered in teaching place value. Operations and their Applications

Understand the operations of early addition and subtraction and use them to solve problems, language and recording associated with early addition and subtraction

Develop mental strategies to 100 including adding and subtracting up to the addition of two two-digit number within 100

Money

Recognise coins and use them in simple contexts; early addition and subtraction of money and use the conventional way of recording money and use these skills to solve problems;

llustrate a holistic and integrated approach to teaching and learning using the topic of money in keeping with the NI Curriculum through - Integrating and developing mathematics through play, including shop play; - Using examples of problem solving, thinking skills and mathematical

language through the topic of money; integrating ICT

Time

Develop the concepts and language associated with telling the time and the passage of time for young children and explore difficulties associated with these concepts

Recognize times on the analogue clock and digital displays ; sequence everyday events ; know the days of the week, months of the year and seasons

Stages of development

Illustrate a holistic and integrated approach to teaching and learning the time in keeping with the NI Curriculum

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ICT

Developing an integrated approach

Using suitable software with reference to the topics outlined Home and school partnerships

Partnership between home and school to support mathematical development. Processes in Mathematics will underpin the course. Key Stage 2 Topics covered will include:

Perspectives on teaching and learning mathematics

Realistic Mathematics Education (RME) o Principles of RME o Realistic contexts for mathematics o Mathematical modeling o Using models and images

Fractions, decimals and percentages o Use of models in understanding fractions, decimals and percentages

Approaches to calculation o Mental methods versus standard written methods o Progressing from mental to standard written methods of calculation o Teaching and recording mental calculation strategies o Overview of the Framework for Developing Mental Mathematics Skills

(Northern Ireland Strategy for Numeracy)

Multiplication and division o Using the ‘Area’ model o Developing mental strategies for multiplication and division o Progressing to standard written methods o Interpreting remainders in division calculations

Angle o The degree as a standard unit to measure angle

o Measuring and drawing angles up to 360 o Using Logo and programmable devices (e.g. Pro-bot) to explore movement

and turning

Mathematics outside the classroom o Planning a mathematics trail

Characteristics of good practice in numeracy in the primary school o Better Numeracy (ETI)

Mathematics and Special Educational Needs

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Assessment in primary mathematics o Update on NI Curriculum assessment arrangements o Use of standardized tests o Effective use of data o Underachievement in mathematics o Count, Read: Succeed

Processes in Mathematics will underpin the course. Personal Mathematics

The personal subject knowledge and understanding of mathematics, which all students need to support effective mathematics teaching at primary level, is considered through the ‘Personal Mathematics Course’. This is an integral part of the curriculum mathematics course. Topics will be selected primarily from the area of ‘Handling Data.’ (Further details on QOL)

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Booklist Essential Reading CCEA. (2007). The Northern Ireland curriculum: Primary. Belfast: CCEA. CCEA. (2006). The revised lines of development for mathematics/numeracy. Belfast: CCEA. DENI. (2008). Every school a good school: A strategy for raising achievement in literacy and numeracy. DENI. (2011). Count Read: Succeed – A strategy to improve outcomes in literacy and

numeracy. Belfast: DENI.

Northern Ireland steering group for the promotion of numeracy. (2001). Northern Ireland Strategy for Numeracy: Teaching and learning (Primary). Belfast: Interboard Numeracy Group.

Recommended reading Haylock, D., & Cockburn, A. (2008). Understanding mathematics for young children: A guide

for foundation stage & lower primary teachers. London: SAGE. Haylock, D. (2010). Mathematics explained for primary teachers (4th ed.). London: SAGE. Other useful sources Anghileri, J. (2000). Teaching number sense. London: Continuum. Anghileri, J. (Ed.). (2001). Principles and practices in arithmetic teaching: Innovative

approaches for the primary classroom. Maidenhead: Open University Press. Askew, M. (2012). Transforming primary mathematics. Abingdon, Oxon: Routledge. Chinn, S. (2004). The trouble with maths: A practical guide to helping learners with numeracy

difficulties. London: Routledge Falmer. Cockburn, A.D., & Littler, G. (Eds.). (2008). Mathematical misconceptions. London: SAGE. DCSF. (2008) Independent Review of Mathematics Teaching in Early Years Settings and

Primary Schools: Final Report – Sir Peter Williams. Nottingham: DCSF. Drews, D., & Hansen, A. (Eds.). (2007). Using resources to support mathematical thinking:

Primary and early years. Exeter: Learning Matters. ETI. (2010). Better numeracy in primary schools: Evaluations and prompts for self-evaluation. ETI. (2010). Transition in mathematics: primary to post-primary – issues from inspection. Fox, B. (2000). Using ICT in primary mathematics: Practice and possibilities. London: David

Fulton.

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Fraser, H., & Honeyford, G. (2000). Children, parents and teachers enjoying numeracy: Numeracy hour success through collaboration. London: David Fulton.

Gifford, S. (2005). Teaching mathematics 3-5: Developing learning in the foundation stage.

Maidenhead: Open University Press. Hansen, A. (Ed.). (2005). Children’s errors in mathematics: Understanding common

misconceptions in primary schools. Exeter: Learning matters. Hansen, A. & Vaukins, D. (2011). Primary mathematics across the curriculum. Exeter:

Learning Matters. Harries, T., & Spooner, M. (2000). Mental mathematics for the numeracy hour. London:

David Fulton. Hughes, M. (2000). Numeracy and beyond: Applying mathematics in the primary school.

Buckingham: Open University Press. Koshy, V., & Murray, J. (Eds.). (2002). Unlocking numeracy: A guide for primary schools.

London: David Fulton. Lee, C. (2006). Language for learning mathematics: Assessment for learning in practice.

Maidenhead: Open University Press. Pepperell, S., Hopkins, C., Gifford, S. & Tallant, P. (2009). Mathematics in the primary school:

A sense of progression (3rd ed.). London: David Fulton. Pitt, E. (2001). Ready, set, go – Maths: A guide for teachers to help children who find

mathematics difficult experience a secure start in early number. Belfast: Interboard Numeracy Group.

Ryan, J., & Williams, J. (2007). Children’s mathematics 4-15: Learning from errors and

misconceptions. Maidenhead: Open University Press. Skinner, C. (2005). Maths outdoors. London: Beam Education. Thompson, I. (Ed.). (2003). Enhancing primary mathematics teaching. Maidenhead: Open

University Press. Thompson, I. (Ed.). (2010). Issues in teaching numeracy in primary schools (2nd ed.).

Maidenhead: Open University Press. Thompson, I. (Ed.). (2008). Teaching and learning early number (2nd ed.). Maidenhead: Open

University Press. Tucker, K. (2010). Mathematics through play in the early years (2nd ed.). London: SAGE. Way, J., & Beardon, T. (2003). ICT and primary mathematics. Maidenhead: Open University

Press.

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Personal Mathematics Cooke, H. (2007). Mathematics for primary and early years: Developing subject knowledge

(2nd ed.). London: SAGE. Haylock, D. (2001). Numeracy for teaching. London: Paul Chapman. Mooney, C., Ferrie,. L., Fox, S., Hansen, A., & Wrathmell, R. (2011). Primary mathematics:

Knowledge and understanding (5th ed.). Exeter: Learning Matters. Suggate, J., Davis, A., & Goulding, M. (2010). Mathematical knowledge for primary teachers

(4th ed.). Abingdon, Oxon: Routledge. Classroom textbooks Apex Maths, Cambridge Collins New Primary Mathematics Ginn Abacus Heinemann Mathematics Plus (Groups Work, Interactive Mental Mathematics, Maths

Investigations, Problem-solving Toolkit, Solving Problems, Talking Maths, Tough Topics, Word Problems)

Mathematics Pyramid, Rigby Numeracy Solutions New Heinemann Mathematics Number Connections, Heinemann

Periodicals

Mathematics Teaching Primary Mathematics Teaching Children Mathematics

Journals

Journal for Research in Mathematics Education Research in Mathematics Education

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Assessment To pass the module, students must pass each of the following elements of assessment. Compulsory elements

Examination (50%) – end of Semester 1

Coursework (50%) – end of Semester 2

Students must also satisfy the requirements of the computer assisted learning Personal and Professional Mathematics Course.

Examination This element of the assessment consists of a 2 hour examination. There will be two parts to the examination: Part 1 will focus on the Foundation Stage/Key Stage 1 element of the course; Part 2 will focus on the Key Stage 2 element of the course. Students must pass both parts of the examination. Coursework There are 2 parts to the coursework. Part 1 will focus on the Foundation Stage/Key Stage 1 element of the course; Part 2 will focus on the Key Stage 2 element of the course. Students must complete both parts of coursework. Each piece of work must have a coversheet attached and be submitted to the Central Admin Office during week 27 (exact date to be advised). Each piece of work should be word-processed, include a bibliography and indicate the total word count. Unless assignments are submitted personally into the Central Admin Office, no credit will be given if an assignment is lost. Where appropriate the assessment criteria in Appendix 1 will be used. Please refer to Appendix 2 for guidance on referencing and citation. Further details will be provided in Semester 2.

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GENERAL REGULATIONS Once you enrol in Stranmillis University College you are considered to have entered the teaching profession, and are expected to conduct yourself in College and in schools with this in mind. Please note the following General Regulations for all University Courses:

5.8 Full-time students are required to be in attendance at the University during the 15 weeks of each semester and whatever additional time is required by the programme of study for which they are registered. Students may normally be absent from the University during these periods only where they have permission from their Adviser of Studies or supervisor or in cases of illness or emergency or where there are extenuating circumstances. 5.9 Students are expected to attend all scheduled sessions and other forms of instruction as defined by the programme of study and all scheduled examinations. Specific attendance requirements, including explicit attendance thresholds, will be stated by the School.

Please refer to the student study regulations for further information. These can be accessed at: http://www.qub.ac.uk/directorates/AcademicStudentAffairs/AcademicAffairs/GeneralRegulationsUniversityCalendar2011-12/ Attendance It is considered essential that you attend all Mathematics and Numeracy 3 classes, unless you are ill or when special permission has been granted by the Head of Department or Programme Leader. Failure to achieve 75% attendance at Curriculum Mathematics classes will normally result in failure of the module. In this case, additional coursework will be given. You are responsible for ensuring personally that your attendance at class is noted. Self-certification of illness is permitted for an absence of up to five working days. Medical absence of longer than five working days must be covered by a medical certificate signed by a registered medical practitioner. Fully completed self-certification forms or medical certificates must be submitted within three working days of returning to studies. It is your responsibility to complete the relevant absence forms within the time frame specified. Absence forms can be accessed at: http://studentinfo.stran.ac.uk/index.php?Student_Forms Please refer to the student study regulations for further information. Plagiarism The University College regards plagiarism as a serious academic offence which may lead to disciplinary action being taken against the student concerned. Plagiarised material will be deemed to be passages from other works (including internet sources) incorporated without acknowledgement and with the intention of it being taken to be the student's own work. Passages from other works may be quoted only if shown as quotations with

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acknowledgement of the sources, and similarly may be paraphrased only if the sources are acknowledged. Students may be requested to submit an electronic version of their work to be checked for plagiarism. Students should be aware that this procedure may delay processing their results Please refer to the student study regulations for further information. Late submission of coursework

Coursework submitted after the deadline will be penalised at a rate of 5% of the total mark available for each working day late up to a maximum of five working days, after which a mark of zero shall be awarded. Exemptions will be granted only if there are extenuating circumstances, and the student has formally notified (in writing) the Adviser of Studies of such circumstances within three working days of the submission deadline. Late submission of coursework forms can be accessed at: http://studentinfo.stran.ac.uk/index.php?Student_Forms Please refer to the student study regulations for further information.

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Appendix 1: Assessment Criteria – Level 3

Conceptual Equivalent

% Pt Mark Band

Level 3 Criteria

Exceptional I High/Excellent I (in addition to criteria for Definite/low 1)

100 90

95-100 85–94

Exceptional and exemplary work showing:

A very high level of critical analysis

A very high level of insight in the conclusions drawn

An in-depth knowledge and understanding across a wide range of the relevant areas including areas at the forefront of the discipline

Very thorough coverage of the topic

Confidence in the appropriate use of learning resources to support arguments made

Definite I

80

78–84

Excellent and outstanding answer showing:

Considerable independence of thought and critical judgement with sustained critical analysis.

A well developed ability to analyse concepts and ideas at an abstract level

A thorough understanding of all the main issues involved and their relevance

A substantial degree of originality

Substantial evidence of wide, relevant and critical use of learning resources

Good understanding of complex and problematic areas of the discipline

Low I

75

70-77

Excellent answer showing:

A good level of independence of thought and critical judgement and a level of critical analysis.

A developed ability to analyse concepts and ideas

An understanding of all the main issues involved and their relevance

A degree of originality

Evidence of wide, relevant and critical use of learning resources

An understanding of the complexity and scope of the discipline

High 2.1 Definite/solid 2.1 Low/clear 2.1

68 65 62

67–69 64–66 60-63

Very good, comprehensive answer showing:

Good understanding of relevant wider issues.

Well developed arguments with evidence of independent thought

A good understanding of module material coupled with the ability to relate this to new ideas and concepts

Evidence of wide and relevant use of learning resources

Synthesis / integration of material from other modules/experience as well as the current module

Evidence of independent/autonomous learning

High 2.2 Definite/solid 2.2 Low/clear 2.2

58 55 52

57-59 54–56 50–53

Good answer showing:

The ability to draw reasonable conclusions

Knowledge and awareness of the main issues

A satisfactory understanding of module material

Little reference to resources outside module material

High 3rd Definite 3rd

48 45

47–49 44–46

Adequate answer which:

Shows fair understanding of main issues

Shows little familiarity with resources outside module material

Makes arguments that are not strong

Has a low but acceptable level of written expression

Low 3rd 42 40–43 Passable just acceptable) answer which:

Contains some relevant material

Contains significant omissions and/or inaccuracies

Recognises the aim of the question and has attempted to answer it

Marginal fail

35 35–39 Marginally failing answer which:

Meets some of the necessary requirements

Has some major inaccuracies

Shows limited understanding of the module content

Weak fail 25 25–34 Unsatisfactory answer which:

Fails to meet most of the necessary requirements

Shows little understanding of the major issues

Indicates that knowledge is vague and skimpy

Has many major inaccuracies

Poor fail 15 15–24 Poor answer in which

There are few points relevant to the question

The bulk of the answer is irrelevant/inaccurate

There are major misunderstandings of the material

Nothing of merit 0 0–14 Answer meeting none of the necessary requirements with:

Minimal or no material of value to the question asked

No recognition of the question

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Appendix 2: Referencing and Citation Good assignments acknowledge the sources of their ideas, and give full details of the works, journals, etc where they are to be found. When presenting assignments, you are asked to use the following conventions when you are referring to a publication in the text of your assignment, and when compiling your list of references.

Definitions: CITING means formally recognising, within your text, the resources from which you have obtained information. REFERENCING is the detailed description of the item from which you have obtained your information. BIBLIOGRAPHY is the list of sources you have used. 1. Books: a) Single author

in your text: ‘Bush (1986, p43) argues that ….’ In the list of references: ‘Bush, T. (1986) Theories of Educational

Management, London, Harper and Row.’ b) Two authors

in your text: ‘Bolman and Deal (1984), p27) found that …’ in your references: ‘Bolman, L. G. and Deal, T. E. (1984) Modern Approaches to

Understanding and Managing Organisations, San Francisco, Jossey-Bass.’

c) More than two authors

in your text: ‘Baldridge et al. (1978, p16) have stated that ….’ in your references: ‘Baldridge J. V., Curtis, D.V., Euchre, G. and Riley, G.L. (1978)

Policy-Making and Effective Leadership, San Francisco, Jossey-Bass.’

d) A single author’s chapter in an edited collection

in your text: ‘Al-Khalifa, F. (1989, p22) reported that …’

in your references: ‘Al-Khalifa, F. (1989); Management by halves: women teachers and school management’ in de Lyon, H. and Widdowson-Mighiuolo, E (eds) Women Teachers: issues and experience, Milton Keynes, Open University Press

(The conventions for joint and multiple authorship of chapters are as above)

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e) If a book has more than one edition, make clear in the references which edition you have used

in your text: ‘Handy (1981, 2nd edt) Understanding Organisations,

Harmondsworth, Penguin Books 2 Articles in Journals – Single author:

in your text: ‘Hoyle (1982, p27) states that …’ in your references: ‘Hoyle, E. (1982) ‘Micropolitics of educational organisations’

Educational Management and Administration, 10(2), pp87-98.’ (Note that you should provide the volume number, in this case 10, the part number where available and page numbers.)

(The conventions for joint and multiple authorship of articles are as above)

3 Government Publications:

in your text: ‘It was stated that (DES, 1985, p43) that …’ in your references: ‘DES (1985) Better Schools, London, HMSO.’

CD-ROMs:

The citing of information from computer databases varies. If you have, for example, been using a CD-ROM to obtain journal references you only need to cite the journal as your source of information, not the CD-ROM.

eg Royal Institute of British Architects. (1998) Architecture and Design Illustrated. London, RIBA (Multi-media CD-ROM)

If the information you are using is only available as a computer database you should cite it as follows:

eg Gray, J.M. & Courtenay, G. (1988) Youth cohort study (computer file). Colchester: ESRC Data Archive (distributor)

Citing URLs (Uniform Resource Locator/Internet Address) in a Bibliography: There are a number of approaches to citing work from the Internet. We have chosen a style which fits with the Harvard style in order to maintain consistency. The following points should be noted:

Be consistent throughout – fit with the Harvard style.

Cite enough information for the reader to locate the citation in the future. Occasionally, the URL for an electronic journal article may be excessively long as it will contain control codes. It is sufficient in such cases to just include enough of the URL to identify the site from where the journal came.

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Many Web documents do give an author. If the information is not explicit you may find it in the header of the HTML encoded text (although that may reflect who “marked up” the document, rather than who actually wrote it.) You can view the header by choosing the option to view document source (a choice available from the view option in Netscape). Otherwise use the title as the main reference point as you would with any anonymous work.

If a document on the web is a series of linked pages – what is the title of the document? Do you cite the main contents page, or a particular page you are quoting from? This is a grey area.

You should cite the date the document was last updated if this is apparent, or the date when you accessed it if not.

In Internet addresses punctuation is important and the stops and commas in a bibliographic citation may confuse the reader: hence the common convention of using < and > to delineate the start and end of an URL.

World Wide Web Documents: Remember that Internet based material may only be available for a short time and hence may not be suitable for referencing. It is advisable to keep a personal copy as evidence that the information existed.

Include the following information, the order of which is:

1 Author/Editor 2 Year 3 Title. Underlined or emboldened or in italics (be consistent throughout the

bibliography) 4 (Internet) 5 Edition 6 Place of publication 7 Publisher (if ascertainable) 8 Available from: <URL>. Note general points about URLs. 9 [Accessed date]

eg Holland, M. (1906) Harvard System [Internet] Bournemouth Available from:http://www.bournemouth.ac.uk/servicedepts/lis/LIS_Pub/harvardsys:html [Accessed date 22 August, 1997]

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Useful Hints and Common Conventions:

Ibid. (Latin) is used as a ditto instead of repeating the previous reference.

Eg Lashley, C. (1995) Improving study skills. A competence approach. London, Cassell

Ibid. p 155 Ibid. p 170 Op.Cit. (Latin) is used after an author’s name to mean the same work as last cited for this author.

Eg Bennett, C. (1996) Researching into teaching methods in colleges and universities. London, Kogan Page. Manger, J.J. (1995). The essential interent information guide. New York, McGraw Hill. Bennett, C. op. Cit. P175

Et al (Latin) commonly used as an abbreviation for “and others”. Eg Bennett, H et al. (1990) Managing Education. London, Falmer Press.