Further Mathematics Online Conference

The method for multiplying matrices can take students a while to master. One obstacle is that there may be no obvious reason for doing the calculation in the way that we do. In this session we will demonstrate two different ways of introducing the method. The first is the typical algorithmic approach, the second considers plane transformations.  There will be an opportunity to consider the strengths and weaknesses of both of these for your classroom. A familiarity with matrix multiplication would be helpful for this session.

As discrete/decision mathematics courses include so many algorithms, there is a danger that the teaching of it can also become dry and mechanistic. However, there are plenty of ways to bring interest and variety into the discrete maths classroom. This session will explore different types of ‘colour’: historical, practical and actual colour-based problems. Some familiarity with the content of any of the current discrete/decision maths course will be assumed.

During lockdown it became harder to explore mechanics in a practical setting, and video provided a way to help students visualise motion in action. But now that face-to-face teaching is back, there are still plenty of ways that short videos can enhance students’ understanding of mechanics, some of which will be explored in this session. As the session will focus on teaching approaches, some familiarity with the mechanics content of A level Further Mathematics will be assumed.

Further Pure Mathematics and Discrete maths often seem to be poles apart. In this session we will challenge this misconception by exploring the parallel topics of 2^nd order differential equations and 2^nd order recurrence relations. We will use technology to help visualise the solutions and demonstrate some approaches you can use to help your students' understanding either of these topics better. A familiarity with solving 2^nd order differential equations would be helpful for this session.

Students often get tangled up when collisions questions move beyond conservation of momentum to needing an understanding of the coefficient of restitution. But just because a question might be about a car crash, the solution doesn’t have to look like one! In this session we will analyse a variety of situations, both possible and impossible, to explore how to support students. Prior understanding of the principle of conservation of momentum will be useful, but no knowledge of the coefficient of restitution will be assumed.

The method for multiplying matrices can take students a while to master. One obstacle is that there may be no obvious reason for doing the calculation in the way that we do. In this session we will demonstrate two different ways of introducing the method. The first is the typical algorithmic approach, the second considers plane transformations.  There will be an opportunity to consider the strengths and weaknesses of both of these for your classroom. A familiarity with matrix multiplication would be helpful for this session.

As discrete/decision mathematics courses include so many algorithms, there is a danger that the teaching of it can also become dry and mechanistic. However, there are plenty of ways to bring interest and variety into the discrete maths classroom. This session will explore different types of ‘colour’: historical, practical and actual colour-based problems. Some familiarity with the content of any of the current discrete/decision maths course will be assumed.

During lockdown it became harder to explore mechanics in a practical setting, and video provided a way to help students visualise motion in action. But now that face-to-face teaching is back, there are still plenty of ways that short videos can enhance students’ understanding of mechanics, some of which will be explored in this session. As the session will focus on teaching approaches, some familiarity with the mechanics content of A level Further Mathematics will be assumed.

Further Pure Mathematics and Discrete maths often seem to be poles apart. In this session we will challenge this misconception by exploring the parallel topics of 2^nd order differential equations and 2^nd order recurrence relations. We will use technology to help visualise the solutions and demonstrate some approaches you can use to help your students' understanding either of these topics better. A familiarity with solving 2^nd order differential equations would be helpful for this session.

Students often get tangled up when collisions questions move beyond conservation of momentum to needing an understanding of the coefficient of restitution. But just because a question might be about a car crash, the solution doesn’t have to look like one! In this session we will analyse a variety of situations, both possible and impossible, to explore how to support students. Prior understanding of the principle of conservation of momentum will be useful, but no knowledge of the coefficient of restitution will be assumed.

Reasoning, logic and proof are part of the specification for the TMUA. However, other non-maths Admissions Tests, such as the Thinking Skills Assessment (TSA), also require the application of reasoning and logic. In this session, we’ll look at a range of questions from different tests, discuss what the examiners are looking for, and consider how this branch of thinking can be strengthened for all A level mathematics students, not just those applying to read mathematics.

Desmos is a powerful graphing tool that has functions which allow you to analyse real data and visualise distributions. In this session we will demonstrate how to use Desmos for a range of topics from FM Statistics such as the Poisson distribution, paired tests, probability density functions, regression and errors in hypothesis tests. There will be an opportunity to try some activities as well as a discussion about how these can be used to support students developing their understanding.

At primary school, students are first introduced to the cartesian coordinate system to place or locate objects in 2D space and later, they learn how to plot and sketch lines and curves on the x-y plane. One of the delights of studying Further Maths is the chance for students to look at describing position in space in a different, more natural and arguably more beautiful way. This session will consider an approach for supporting further maths students with sketching polar curves; building on what students already know and making connections with familiar Cartesian forms. From simple lines and waves we can create rings, spirals, hearts and flowers!

The Mathematics Admissions Test, used by the University of Oxford and Imperial College, requires students to tackle four extended questions. What are the universities looking for in students’ solutions? What strategies do students need, and how do we help students to develop these strategies? In this session we will address these questions using a selection of problems from the MAT examination.

GeoGebra is a powerful dynamic graphing tool that can be used to visualise many of the concepts in Further Maths. In this session we will make use of the built-in 3-dimensional mode, discussing 3D vectors in particular, and how to make them interactive and dynamic. We will also use the GeoGebra Classroom platform which allows you to easily share activities with classes of students and review their interactions in real time. We will demonstrate some ready-made 3D GeoGebra files, give you a chance to build your own, and demonstrate how to assign and use GeoGebra Classroom activities with students.

Reasoning, logic and proof are part of the specification for the TMUA. However, other non-maths Admissions Tests, such as the Thinking Skills Assessment (TSA), also require the application of reasoning and logic. In this session, we’ll look at a range of questions from different tests, discuss what the examiners are looking for, and consider how this branch of thinking can be strengthened for all A level mathematics students, not just those applying to read mathematics.

Desmos is a powerful graphing tool that has functions which allow you to analyse real data and visualise distributions. In this session we will demonstrate how to use Desmos for a range of topics from FM Statistics such as the Poisson distribution, paired tests, probability density functions, regression and errors in hypothesis tests. There will be an opportunity to try some activities as well as a discussion about how these can be used to support students developing their understanding.

At primary school, students are first introduced to the cartesian coordinate system to place or locate objects in 2D space and later, they learn how to plot and sketch lines and curves on the x-y plane. One of the delights of studying Further Maths is the chance for students to look at describing position in space in a different, more natural and arguably more beautiful way. This session will consider an approach for supporting further maths students with sketching polar curves; building on what students already know and making connections with familiar Cartesian forms. From simple lines and waves we can create rings, spirals, hearts and flowers!

The Mathematics Admissions Test, used by the University of Oxford and Imperial College, requires students to tackle four extended questions. What are the universities looking for in students’ solutions? What strategies do students need, and how do we help students to develop these strategies? In this session we will address these questions using a selection of problems from the MAT examination.

GeoGebra is a powerful dynamic graphing tool that can be used to visualise many of the concepts in Further Maths. In this session we will make use of the built-in 3-dimensional mode, discussing 3D vectors in particular, and how to make them interactive and dynamic. We will also use the GeoGebra Classroom platform which allows you to easily share activities with classes of students and review their interactions in real time. We will demonstrate some ready-made 3D GeoGebra files, give you a chance to build your own, and demonstrate how to assign and use GeoGebra Classroom activities with students.