## Outside Options

Most students in year 2/3/4 have either 1/2 or 1 unit of “outside” options open to them. It is your responsibility to find out about any outside courses you want to take, and no guarantee can be made about timetabling. Advice on any options in other departments should be sought from the relevant department, probably in the first case from the web-site.

The choice of outside options is pretty free (with the obvious exception of elementary maths courses), but please consult me about any outside courses you wish to take: I will need to approve your choice. You may also need to bear in mind the rules on levels of courses.

Please note that 4th year MSci students should only take modules at Master's or Advanced Level.

Please see:

## Relevant Departments

Students have taken outside options from a wide variety of Departments (including Chemistry, Latin and Psychology) but obvious choices are: the Language Centre, the Statistics Department, the Physics and Astronomy Department, the Management Studies Centre, the Computer Science Department and the Department of Science and Technology Studies. In the first place please look on the relevant web-site for information.

For information about other departments, please see their web-site or other information

## UCL Centre for Languages & International Education (CLIE)

Note that Language courses are normally taken at the Language Centre,
and are available as 1/2 unit or full unit courses. They all run throughout
the year, and you have to have an interview at the language centre to
determine your level.

## Kings College

It is possible (timetable permitting) to take courses at other London
Colleges – in particular, we have an arrangement with Kings College,
which offers various Mathematics topics that UCL doesn’t and is
fairly convenient from here – please look at their web-site.

## Maths Education Module

‘Mathematics education’ is an umbrella term that encompasses all aspects of learning and teaching mathematics in schools and in other settings. This module is for undergraduates who are in their third or final year of a mathematics degree or a cognate discipline, students who are considering teaching mathematics in the future or students who are curious about how mathematics is learnt and what educational environments support learning and participation.

The course is delivered on Monday afternoons in the Autumn Term from 2pm-5pm at the UCL Institute of Education, 20 Bedford Way. There will be opportunities for individual or small group tutorials to support assessment in the Winter/Spring Term and a revision session before the final exam in the Summer Term. Four members of the UCL IOE staff contribute to the teaching: Dr Cosette Crisan (c.crisan@ucl.ac.uk), Suman Ghosh (suman.ghosh@ucl.ac.uk), Dr Eirini Geraniou (e.geraniou@ucl.ac.uk) and Dr Melissa Rodd (m.rodd@ucl.ac.uk, programme leader), the administrator is Donald Newholm (d.newholm@ucl.ac.uk).

### Assessment

The final grade for the course is based on 50% coursework (an essay of 2000 words that is due mid-March) and 50% exam (scheduled for early May and for which the questions are pre-disclosed in March). There are four formative assignments during the course which introduce students to course expectations and assessment criteria.

### Learning outcomes

- You’ll have a better understanding of your own mathematics-learning strategies and capacities.

- You’ll be able to explain how mathematical ideas can be represented in different ways with various tools or media.

- You’ll have a coherent view on the content of the school maths curriculum and methods of teaching mathematics.

- You’ll be able to discuss wider social and political issues related to mathematics education.

- You’ll have developed your skills in presenting ideas about mathematics and education in writing; this includes expressing views, synthesising readings and presenting arguments.

### Teaching style

Each Monday afternoon students will study a central theme of mathematics education in a workshop format. Each workshop will include activities such as engaging in mathematical tasks, including practical work, investigation of the roles of digital learning technologies, listening and responding to lectures on new topics and reading and discussing mathematics education literature. The workshops will be interactive in which both students and staff contribute. The usual organisation will be a longer session – that will typically include, a short lecture-style presentation, practical work and discussion – on one main topic (1405 to 1540) followed by a 15 minute break and a shorter session on a complementary topic (1555-1655).

### Induction week 1300 Thursday 29 September 2016

A meeting has been arranged, in the Mathematics Department for 1pm on Thursday of enrolment week, so prospective students can ask teaching staff about the course and decide whether they would like to enrol. It is not necessary to attend the induction: students can start the course by attending on week 1 and attending the induction does not oblige students to take the course.

The schedule for the rest of the course:

#### Week 1, 3 Oct 2016 What is mathematics education?

#### Differences between mathematics and mathematics education

We start studying mathematics education by considering some of the foundational questions of the discipline, such as: How do people learn mathematics? What are effective teaching strategies? What mathematics ‘should’ children and young people learn? then consider what intellectual tools are needed to answer such questions. One set of such intellectual tools is provided by the discipline of developmental psychology:

#### Learning theories

Psychology and mathematics education; development of children’s number abilities from infancy.

#### Week 2, 10 Oct 2016 Mathematics, individuals and society

#### Mathematical reasoning

Influenced by philosophical enquiry, we ask: if education is to develop students’ capacity in mathematics, how do we characterise mathematical ways of thinking? What is recognised by others as mathematical thinking?

#### Cross-cultural issues

We shall investigate how different understandings of mathematical reasoning impact on teaching &/or learning mathematics and how social forces and students’ emotions contribute (or otherwise) to mathematics learning and participation in mathematics.

#### Week 3, 17 Oct 2016 Language and communication

#### Multiple representations

We shall study important aspects of language in the learning and teaching of mathematics, for example: the language used to produce a definition and also the ways teachers and students talk in class. Furthermore, communication of mathematics invariably uses ‘multiple representations’ (e.g., symbols, graphs and diagrams) of mathematical concepts.

#### Algebra

Using the example of school algebra: what aspects of ordinary language as well as other representations are important for learning?

#### Week 4, 24 Oct 2016 A mathematics curriculum

#### Introduction to the idea of a curriculum

By analysing the evolution of the mathematics National Curriculum (England) this session is focussed on how a curriculum evolves or is designed. We also consider what influences curriculum design from politics to commercial forces.

#### Interpreting the curriculum for teaching

You will have the opportunity to work on tasks that introduce some school statistics topics.

#### Week 5, 31 Oct 2016 Pedagogy of Secondary School Mathematics

#### Pedagogy

An introduction to ‘pedagogy’, ‘pedagogical content knowledge’ and educational theories related to teaching mathematics.

#### Application of pedagogical principles

We shall consider ideas for teaching proportional reasoning and trigonometry.

*Reading week*

#### Week 6, 14 Nov 2016, Cross-cultural influences and inclusivity

#### Historical and cultural sources

We shall compare how people are taught in various cultures – historical and geographical – and different ways of thinking about similar topics. We will consider how different traditions influence mathematics education including how social media and digital technologies are having an impact.

#### Special educational needs

You shall be introduced to the Warnock Report and special educational needs in the educational system in England. By thinking about learners with particular special needs, we consider good ways to teach mathematics to them – and arguably to others.

#### Week 7, 21 Nov 2016, Assessment in School Mathematics

#### Aspects of assessing mathematical progress of learners

We shall consider details of National Curriculum requirements, what ‘marking’ can be in practice and will discuss of the nature of assessment.

*Practical work*

Doing some marking – marking scheme challenges and issues of agreement.

#### Week 8, 28 Nov 2016, Digital Technologies and School Mathematics

#### What’s happening in schools

How might digital technologies can help or hinder mathematics learning in various areas of the school maths curriculum from calculus to coding?

#### Software for learning geometry

A practical session, using the digital learning resource Geogebra (geogebra.org) to investigate problem solving in Euclidean geometry.

#### Week 9, 5 Dec 2016, School Visit

#### School visit

We shall be visiting a local school to observe mathematics lessons.

#### Discussion

Reflection on mathematics education in practice!

#### Week 10, 12 Dec 2016, 2-3:45pm only, Review and Evaluation

There will also be a revision session on **Monday 24 April 2017** **from 2-4pm**

### Background reading

There will be several papers distributed for reading during the course. For background and supplementary reading here are three books we recommend:

Johnston-Wilder, S., Johnston-Wilder, P., Pimm, D., & Lee, C. Learning to Teach Mathematics in the Secondary School: a Companion to School Experience. Routledge, 2011.

Singh, Simon. The Simpsons and their Mathematical Secrets. Bloomsbury Publishing USA, 2014.

Watson, A., Jones, K. & D. Pratt, D. Key Ideas in Teaching Mathematics: Research-based guidance for ages 9-19. Oxford University Press, 2013.

## Modules Treated as Maths Modules

Note that the following will normally be considered as Mathematics options rather than outside options. However, you still need permission from the relevant department to take the module and if you want to take several of these you will need to discuss your entire choice of options with me.

STAT3101 Probability and Statistics 2

STAT3102 Stochastic Processes

STAT3004 Decision and Risk

PHAS2222 Quantum Physics

PHAS3226 Quantum Mechanics

Mathematics Education module (IoE)

Suitable Mathematics modules taken at Kings or other London college.