# Further Mathematics Conference 2022 resources

During the spring term 2022, the AMSP held an online professional development conference dedicated to supporting teachers with:

• the teaching of AS and A level Further Mathematics
• preparing students for university admissions tests.

The presentation slides used in the welcome plenary can be viewed here.

When viewing recordings, please note that some sessions used Desmos activities to collect responses and many of these links will no longer be active. Where sessions used Desmos activities that can be translated to use in the classroom, we've included links to editable versions within the presentations.

## Matrix Multiplication: should you teach the ‘how’ or the ‘why’ first?

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 demonstrated two different ways of introducing the method. The first was the typical algorithmic approach, and the second considered plane transformations. There was an opportunity in the session to consider the strengths and weaknesses of both of these for your classroom. A familiarity with matrix multiplication is helpful for this session.

## Bringing colour to Discrete Mathematics

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 explored 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 is assumed.

## Moving pictures: using videos in the teaching of further mechanics

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, and we explored some ways in this session. As the session focuses on teaching approaches, some familiarity with the mechanics content of A level Further Mathematics is assumed.

## 2nd order differential equations and 2nd order recurrence relations: bridging the gap between continuous and discrete mathematics

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

## Getting to grips with the coefficient of restitution

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 analysed 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 is assumed.

## Logical Thinking for all 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 looked at a range of questions from different tests, discussed what the examiners are looking for, and considered how this branch of thinking can be strengthened for all A level mathematics students, not just those applying to read mathematics.

## Using Desmos for Statistics in Further Maths

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

## Introducing polar curves

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 considered 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!

## Rising to the challenge of the MAT long questions

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 addressed these questions using a selection of problems from the MAT examination.

## Dynamic 3D vectors using GeoGebra and GeoGebra Classroom

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