STRANMILLIS UNIVERSITY COLLEGE

BEd Year One Module Guide

Primary SCS1010

Mathematics and Numeracy 1

Weighting of Module 10 CATS / 5 ECTS / 2.5 US Credits

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Rationale This module is part of the BEd Programme designed to meet the needs of student teachers regarding the nature of teaching and the competences that underpin it. This module provides an introduction to the holistic teaching of the Mathematics and Numeracy programme, an essential and core Learning Area within the Primary Curriculum. It is interrelated with the other components of the BEd in its general aim of ensuring that students enter the teaching profession with the knowledge, skills, attitudes and values appropriate to professional teachers. While the chief objective of the module is to provide for the immediate personal and professional needs of first year student teachers regarding Mathematics and Numeracy, the module as a whole will form a sound foundation for their further professional development.

Content Students will be introduced to the NI Curriculum for Mathematics and Numeracy. They will examine the requirements of it especially in relation to the topics addressed. Basic theoretical perspectives underpinning these topics will also be considered. Students will explore different modes of mathematics learning and a range of teaching resources, including educational technology through the specified topics. This module will address the planning and preparation of appropriate lessons in primary mathematics.

Learning Outcomes On completion of this module students should demonstrate:

A basic awareness of the NI Curriculum for Mathematics and Numeracy especially within the topics addressed on the module;

A basic awareness of literature relevant to the module content;

A basic awareness of theoretical perspectives informing the teaching of mathematics;

A basic awareness of how to develop mathematical ideas through different modes of learning including educational technology available to support teaching and learning in primary mathematics;

An ability to engage in basic planning and reflection in their teaching of primary mathematics;

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

Transferable skills On completion of this module the students should have a basic ability to :

Construct and communicate oral and written arguments;

Use Information and Communication Technology (ICT) personally and within a professional context and evaluate and use ICT in appropriate situations:

Collaborate within a group and participate in discussion;

Develop a capacity to plan and manage learning and to reflect on their own learning;

Improve their own learning and performance, including the development of study and research skills;

Organise an effective work pattern;

Communicate adequately using some specialist (mathematical) vocabulary and interpret simple graphical and tabular presentation of data;

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Relevant GTCNI Competences The following professional competence will be addressed in this module: Professional Competence 3: Have a detailed knowledge and understanding of the learning area/ subject(s) taught, including the centrality of strategies and initiatives to improve … numeracy and thinking skills to all areas of learning. Professional Competence 4: Know and understand how the learning area/subject(s) they teach contributes to the Northern Ireland curriculum. Professional Competence 10a: Develop an understanding of the range of strategies for communicating with pupils. Professional Competence 11: Examine the educational principles behind the use of technology to aid pupil learning. Professional Competence 14: Learning objectives are set that take account of what pupils know, understand and can do. Professional Competence 15: Plans have clear objectives, relevant content, resources and well-sequenced activities. Professional Competence 19: Appreciate the importance of creating a safe, interactive and challenging learning environment and how others seek to create such an environment. Professional Competence 20: Use a range of teaching strategies appropriate to the age, ability, interests and experiences of pupils.

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, practical workshops, peer group discussion and debate, individual consultation opportunities, computer assisted learning, and independent study.

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Module Outline Curriculum Mathematics Introduction to the NI Curriculum Knowledge for teaching mathematics Understanding number and place value Counting Introduction to mental mathematics Sorting and pictorial representation Partitioning sets Introduction to mathematical processes Pattern and relationships Developing mathematical processes through Time, Money and 3D shape in Key Stage 2 Developing financial capability in the primary school The structure of a mathematics lesson Introduction to learning mathematics through play Different learning theories will be addressed throughout the various topics and the role of the teacher will also be considered Personal and Professional 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 and Professional Mathematics Course’. This is an integral part of the curriculum mathematics course. Topics will be selected primarily from the area of ‘Number.’

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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. (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 (4

th ed.). London: SAGE.

Other useful sources Anghileri, J. (2000). Teaching number sense. London: Continuum. 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. Fox, B. (2000). Using ICT in primary mathematics: Practice and possibilities. London: David Fulton. 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.

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Lee, C. (2006). Language for learning mathematics: Assessment for learning in practice. Maidenhead:

Open University Press. Mooney, C., Briggs, M., Fletcher, M., Hansen, A., & McCullouch, J. (2011). Primary mathematics:

Teaching theory and practice (5th

ed.). Exeter: Learning Matters. Nickson, M. (2000). Teaching and learning mathematics: A teacher's guide to recent research. London:

Cassell. 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. Thompson, I. (Ed.). (2003). Enhancing primary mathematics teaching. Maidenhead: Open University

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

nd ed.). Maidenhead:

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

nd ed.). Maidenhead: Open

University Press. Tucker, K. (2010). Mathematics through play in the early years (2

nd ed.). London: SAGE.

Way, J., & Beardon, T. (2003). ICT and primary mathematics. Maidenhead: Open University Press. Personal Mathematics Cooke, H. (2007). Mathematics for primary and early years: Developing subject knowledge (2

nd 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 (4

th 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

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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 all elements of assessment.

Compulsory elements:

There will be one examination (Curriculum Mathematics) at the end of Semester 2. Further details will be provided in class and uploaded on QOL.

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

Where appropriate the assessment criteria in Appendix 1 will be used. Please refer to Appendix 2 for guidance on referencing and citation.

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 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 1 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.

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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 acknowledgement of the sources, and similarly may be paraphrased only if the sources are acknowledged. Please refer to the student study regulations for further information.

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Appendix 1: Assessment Criteria – Conceptual Equivalents Scale - Level 1

Conceptual Equivalent % Pt

Mark Band

Level 1 Criteria

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

100 90

95–100 85–94

Excellent answer which:

Is comprehensive and accurate

Is presented in a clear and cogent manner

Makes full reference to appropriate material

Makes effective use of language

Displays some of the following characteristics: o integration of a wide range of learning resources o originality of exposition or treatment o evidence of insight o critical evaluation

Definite I

80

78–84

Low I

75

70-77

High 2.1 Definite/solid 2.1 Low/clear 2.1

68 65 62

67–69 64–66 60-63

Very good answer which:

Is generally accurate and reasonably detailed

Displays a good understanding of the main principles and a reasonable grasp of details

Shows strong and coherent argumentation

Is presented in a logical fashion

Makes frequent reference to appropriate material

Makes effective use of language

High 2.2 Definite/solid 2.2 Low/clear 2.2

58 55 52

57-59 54–56 50–53

Good answer which:

Is reasonably accurate and well informed, albeit with some minor omissions or inaccuracies

Is limited to the main issues and based on a limited range of learning resources

Makes some reference to appropriate material

Makes acceptable use of language, with some minor Inaccuracies

High 3rd Definite 3

rd

48 45

47-49 44-46

Adequate answer which:

Displays evidence of understanding of the main principles in broad terms

May contain important inaccuracies or omissions

May lack a coherent structure

May answer the question indirectly or may lack supporting evidence

Makes minimal reference to relevant material

Shows poor use of language, although the meaning is understandable

Low 3

rd

42

40-43

Marginal fail

35

35-39

Failing but compensatable answer which:

Displays a very limited understanding of the aim of the question

Is sparse in material and lacking in organisation

Contains material that is inappropriately used or of limited relevance

Proceeds by way of assertions unsupported by appropriate evidence

Shows poor use of language with significant grammatical and other errors

Weak fail

25

25-34

Unsatisfactory, poor answer which:

Shows a complete lack of understanding of the question

Provides very little of any relevance and value to the question

Makes an incoherent argument

Shows poor use of language with significant grammatical and other errors

Poor fail

15

15-24

Nothing of merit

0

0-14

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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)

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

in your text: ‘Handy (1981, 2

nd edt) Understanding Organisations,

Harmondsworth, Penguin Books

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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.

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.

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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.