# Short Course in Primary Mathematics

Thursday January 17, 2013 – Saturday January 19, 2013

Avari Towers, Karachi, Pakistan

Description:

**Introduction**

The 3-day course’s objective is to increase your **confidence, effectiveness, knowledge and understanding of approaches to teaching Mathematics at the Primary level**.

Over the three days you will work on your own understandings of mathematics and think about what the structures of mathematics suggest about how it might best be taught. We will explore tensions between the ways people (for example parents or text-book writers) might want or expect maths to be taught and how it might be taught to maximise understanding and creativity. Embedded in the sessions will be opportunities to explore issues such as sequencing and planning teaching, and particular pedagogical questions such as the organisation of problem solving and group work.

The course will include formal presentations, individual and small group tasks, discussion and reflection.

**Subjects to be covered**

• Expectations of Mathematics

• Teaching, Learning and Assessment of Mathematics

• Resource management and quality assurance

**Course Features**

• The course draws on expert knowledge and research on teaching of Mathematics

• High quality facilitation will be provided by an expert trainer. It is designed to achieve rich collaborative learning through drawing on participants’ own experiences and insights in relation to teaching

• Study materials will be provided to guide, support and challenge participants’ thinking and practice. These will take the form of, for example, conceptual frameworks and analytical tools which participants can use in their teachings. Participants will be encouraged to reflect on their learning as they progress through the programme, and to apply it to their future practice.

**Course Assignment**

During and following the course you will be asked to engage in a mathematical investigation in which you develop your understanding of an aspect of mathematics and explore its teaching in your professional context – we will discuss the nature of the assignment in more detail during the course.

Certification

*Participants who fulfil all course requirements will be awarded a Certificate of Completion.
*

**Outline of the course***Day 1: Counting and calculating: approaches and challenges*

During day one we will consider the basics of number from counting to calculation strategies. We will cover:

• stages in learning to count,

• difficulties associated with learning to count,

• the ways in which counting and number recognition develop to enable basic mental calculations,

• strategies that teachers might use to support the development of more complex mental calculation strategies and informal written strategies,

• developing these into written forms of calculation

• ways of extending and further exploring calculation strategies

We will explore the difficulties of traditional expectations and formal methods of calculation and why consider why a more principled approach might lead to greater mathematical understanding and flexibility. We will also think about why this might feel difficult and ways of developing professional resilience.

**Day 2: Place value and measures**

During day one we restricted ourselves to integers (whole numbers). In day two we will think about the numbers between the whole numbers and the ways in which these are used in measurement. The difficulties children have in developing understandings of place value and measure will be explored. Is it possible to use these difficulties as starting points for teaching? Can they be used creatively to develop understanding rather than worried about as things to ‘avoid’ or ‘fix’? During the day we will explore:

• the nature of the number system including rational numbers

• place value (especially decimals) and difficulties with this

• conservation of measures

• the unit

• inaccuracy/continuousness

• directly and indirectly observable measures

• links to place value

• Shapes (Two and Three Dimensional)

*Day 3: Multiplicative and proportional thinking, and the beginnings of algebra*

Today we will extend our work on rational numbers to thinking about multiplicative and proportional thinking to challenge and develop additive thinking. We will also consider the ways in which the early stages of algebraic thinking can be brought out of work in the primary classroom. These ways of thinking are central to mathematics but are often experienced as more difficult by many people. Over the course of the day we will cover:

• multiplicative thinking – what makes it different to additive thinking

• proportional thinking – particularly ratio and percentages

• different ways of thinking about fractions

• function machines and ‘what’s my rule?’ games

• developing awareness of pattern

• explaining, justifying and proving

• describing and generalising

• the use of unknowns

**Course Leader**

**Dr Tamara Bibby**

Tamara Bibby is a Lecturer in Learning and Teaching in the Faculty of Children and Learning, Institute of Education, University of London. She is programmed leader for the BEd in Education and teaches Masters and Doctoral courses on Teaching and Learning in Classrooms and Psychosocial Studies. Her early career was as a Primary School Teacher and Mathematics Consultant in Inner London and she is particularly interested in student and teacher experiences of learning. Her recent ESRC funded research enabled her to follow a group of primary school children across three academic years. This work has enabled her begin to unpack the processes involved in the mutual production of learner identities in one primary school. Tamara has also researched the ways in which specific maths curriculum, policy and practice issues impact upon generalist primary teachers – the intersections of policy, curriculum and teachers’ personal and professional lives – and how teachers’ accommodations to policy impact classroom/pedagogic relationships.

Publications

• Bibby, T. (2010) Education – an ‘impossible profession’? Psychoanalytic explorations of learning and classrooms. London: Routledge.

• Bibby, T. (2010) ‘What does it mean to characterise mathematics as ‘masculine’?: bringing a psychoanalytic lens to bear on the teaching and learning of mathematics’ In M. Walshaw (ed.), , Unpacking Pedagogy: New Perspectives for Mathematics Classrooms. . Greenwich, CT: Information Age.

• Bibby, T. (2009) How do children understand themselves as learners? Towards a redefinition of pedagogy. Pedagogy, Culture and Society.

• Bibby, T. (2009) ‘How do pedagogic practices impact on learner identities in mathematics? A psychoanalytically informed response’ In L. Black, H. Mendick and Y. Solomon (eds), Mathematical Relationships: identities and participation. London: Routledge.

• Bibby, T. (2008) ‘The experience of learning in classrooms: moving beyond Vygotsky’ In T. Brown (ed.), The Psychology of Mathematics Education: A Psychoanalytic Displacement. Rotterdam: Sense.

• Bibby, T. (2002) ‘Shame: an emotional response to doing mathematics as an adult and a teacher’, British Educational Research Journal 28(5), 705-722.

Further information

• Bibby, T. (2002) ‘Creativity and logic in primary school mathematics: a view from the classroom’, For the Learning of Mathematics 22(3), 10-13.

• Brown, M., Brown, P., and Bibby, T. (2008) ‘Brown ‘I would rather die’: reasons given by 16-year-olds for not continuing their study of mathematics’, Research in Mathematics Education 10(1), 3-18.

• Stobart, G., Bibby, T., and Goldstein, H. (2005) Moving to two-tier GCSE mathematics examinations: An independent evaluation of the 2005 GCSE Pilot and Trial (Final report). QCA.

Further information

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