Module descriptions
Module descriptions for the Mathematics and Secondary Mathematics Education Teacher Degree Apprenticeship BSc (QTS).
Contents
Year 1
Differential and Integral Calculus
This module provides a fairly rapid introduction to calculus. Calculus underlies almost all areas of mathematics and a great deal of science and engineering. The aim of the module is to provide a solid grounding in this fundamental branch of mathematics for students who have a limited mathematical background. Most of the module material occurs in A-level mathematics: the treatment here will be slightly more advanced. Topics covered include functions and graphs; differentiation; exponential functions and logarithmic functions; integration; approximate or numerical integration; simple differential equations and applications.
Linear Algebra for Data Science
The aim of this module is to provide an introduction to vectors, matrices, and least square methods, all basic topics in linear algebra, in the context of data science.
Introduction to Learning and Teaching Mathematics
This module focuses on the learning of mathematics, gradually transitioning to the learning of how to teach mathematics. Apprentices examine key mathematical concepts that commonly challenge secondary school and early university students. The module introduces research on misconceptions and common errors in mathematics, along with teaching strategies to enhance student understanding. Principles from educational neuroscience and psychology will provide insights into how students learn mathematics. Throughout the module, emphasis is on connecting undergraduate mathematics knowledge to effective teaching of the secondary school mathematics curriculum, with a focus on the transition from key stage 4 to key stage 5.
Professional Practice 1
This module introduces the context of the professional practice of teaching in secondary schools. Apprentices deepen their understanding of core issues around professionalism, professional identity and the nature of the work that teachers do. Taught sessions at IOE are extended by directed activities completed in apprentices’ workplaces. Apprentices complete an online Professional Practice Portfolio which showcases their progress over time, including feedback on their teaching and related activities (e.g. planning, assessment).
Year 2
Calculus and Linear Algebra
This is an introductory module on Mathematical Methods and their Applications for students of Economics, Statistics and related disciplines. The emphasis of the module is on techniques rather than full rigour and this is developed through the use of many examples.
Topics covered include differentiation, integration, infinite series, functions of several variables, and elementary matrix theory.
Mathematical Analysis
This module is an introduction to Mathematical Analysis, one of the most important and well-developed strands of pure mathematics with many elegant and beautiful theorems, and also with applications to many areas of mathematics, theoretical statistics, econometrics, and optimisation. The aim is to introduce apprentices to the ideas of formal definitions and rigorous proofs (one of the fundamental features of modern mathematics, and something that is not familiar from A-level), and to develop their powers of logical thinking.
Introductory Statistical Methods and Computing
This module provides an introduction to statistical methods and interpretation of data, along with associated computing, and some expertise in applying quantitative methods in the Life and Physical Sciences.
Topics covered include confidence intervals and significance tests applied to one and two sample problems by parametric and non-parametric methods; goodness-of-fit and contingency tables; correlation and regression; use of computer software for statistical purposes.
From Learning Mathematics to Teaching Mathematics
This module encourages apprentices to explore mathematics as an interconnected system of ideas. Focusing on key stages 3 and 4, the module emphasises relationships between mathematical concepts to foster a deeper, integrated understanding. Apprentices critically engage with research on teaching and learning mathematics, reflect on their own experiences, and explore key pedagogical issues. They examine the evolving role of mathematics in the global landscape and develop essential competencies such as mathematical digital competencies and data literacy.
Professional Practice 2
This module builds on the foundation established in Professional Practice 1, further developing apprentices' understanding and practice of teaching in secondary schools. Apprentices deepen further their understanding of core issues around professionalism, professional identity and the nature of the work that teachers do. Taught sessions at IOE are extended by directed activities completed in apprentices’ workplaces. Apprentices complete subject-specific school-based tasks and receive ongoing feedback, with progress documented in their online Professional Practice Portfolio.
Year 3
History of Mathematics
The history of mathematics is not history alone, nor is it mathematics alone, but a subject requiring sympathy for and knowledge of the techniques of both disciplines. The aim of this module is to provide a survey of mathematical thought from the earliest times up to the early nineteenth century, so that students may see, for example, how Archimedes obtained his famous bounds for π and how non-Euclidean geometry was discovered. While the material of the module is delivered in the lectures, with additional notes provided, students are expected to read some primary sources from the set anthology of mathematical writings as well as specific chapters from the standard histories. The basic requirement for the course is a good understanding of high school calculus, algebra and geometry but there are also one or two more challenging topics which demand a slightly higher level of mathematics. It is also advantageous to have a good command of written English.
Critical Perspectives on Mathematics Education
This module explores key issues in mathematics education across different educational levels. Apprentices deepen their understanding through critical reflection on their own experiences and engagement with various educational theories and evidence related to teaching, learning, and curriculum design. This module encourages apprentices to articulate the role of mathematics in schools, critically evaluate relevant learning theories and policies, and compare curriculum designs across contexts.
Practitioner Enquiry Project
In this module, apprentices design and conduct a small-scale practitioner enquiry focused on secondary mathematics teaching. The module builds on prior learning, emphasising values-led and research-informed practice. Apprentices formulate enquiry questions, gather and evaluate robust evidence, and engage with enquiry methods, ethics, and data analysis through guided readings and reflections. By examining classroom practices and their impact on school students’ learning, apprentices refine their teaching methods and identify opportunities for improvement. The module culminates in a comprehensive professional enquiry report, equipping apprentices to enhance student learning and promote effective, reflective teaching practices.
Professional Practice 3
This module builds on the experiences gained in Professional Practice 2, further advancing apprentices' understanding of teaching in secondary schools. Apprentices continue to expand their experience through an enhanced teaching placement in a second school in the summer term. They undertake a range of subject-specific tasks and receive regular feedback from experienced professionals. Apprentices’ progress and reflections are recorded in their online Professional Practice Portfolio, showcasing their development as beginning teachers.
Year 4
Special and Inclusive Education
This module equips apprentices with the skills to understand and support children and young people with Special Educational Needs and Disabilities. Apprentices become familiar with the different theoretical approaches of a typical development which inform practice in the education and care of children and young people with a variety of difficulties. Apprentices look at how these difficulties manifest, how they are diagnosed and how they can be explained based on literature and research. They also explore what works in terms of interventions for these difficulties.
Professional Practice 4
This module builds on the knowledge and experience gained in Professional Practice 3, further embedding apprentices' understanding of teaching in secondary schools. Apprentices will continue to refine their skills in planning, assessment, and classroom management while completing a range of mathematics-specific tasks. Apprentices receive ongoing feedback from experienced professionals and will document their progress and reflections in their online Professional Practice Portfolio, demonstrating their readiness for the next stage of their teaching career.