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Key Ideas in Mentoring Mathematics Teachers

Develop as a mentor of early career maths teachers through engagement with robust and up-to-date mathematics education research.

Key Ideas in Mentoring Mathematics Teachers

Develop as a mentor of early career maths teachers

On this course, you’ll be led by experts from the UCL Institute of Education as you learn how to support less experienced maths teachers.

This course offers high-touch support from the course educators, including one live session in Week 3, as well as in-course discussion to help you boost your own subject knowledge in teaching secondary school students and apply new research to your teaching practice.

As a mentor, you’ll use your personal experience to reflect upon and develop further your practice as well as share your expertise with new teachers.

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Skip to 0 minutes and 8 seconds Hi, my name is Cosette Crisan. Hi, I’m Eirini Geraniou, and we are both mathematics educators at the UCL Institute of Education in London. We have both worked on teacher training programmes for a number of years, and we are undertaking high quality research in mathematics education which continuously informs our own practice. I am currently leading the master’s in mathematics education programme and contribute to the training of secondary school mathematics teachers. And I’m currently leading one of the training of secondary school mathematics teachers programmes and contribute to the master’s in mathematics education programme at UCL. We are the designers of this online short course which is aimed of the development of practising experienced mathematics teachers as mentors.

Skip to 0 minutes and 54 seconds This course is suitable for you if you are a mathematics teacher of 11 to 18-year-old students with at least three years of teaching experience. Teachers with such a background draw on their wealth of knowledge about what works and is effective in teaching and learning, and reflect upon how best to mentor others. Such wisdom of practice is an invaluable source and body of knowledge indeed. This course will further enrich your wisdom of practice with evidence from mathematics education research about various aspects related to the teaching and learning of specific mathematics topics at school level.

Skip to 1 minute and 30 seconds We hope that by undertaking this course, you will experience the benefits of research-informed teaching practice, which in turn, will also support you in mentoring less experienced colleagues.

Syllabus

  • Week 1

    Introduction to the course

    • Welcome and course overview

      A welcome to the course and overview of the content in each week, followed by a justification of how this course supports the development of a research-informed approach to mentoring.

    • Getting the most from the course

      For many, studying online and asynchronously may be a new experience. With these steps we offer some guidance around studying online with us and the tools you'll need. Image: Jimwrenholt CC BY 2.0

    • Introduce yourself

      An opportunity to introduce yourself, meet other learners, and talk about your experiences and what you hope to gain from the course. Image: Jimwrenholt CC BY 2.0

  • Week 2

    Fostering Algebraic Reasoning

    • Introduction

      Algebra has been known to cause a number of difficulties for school students, leading to disengagement and even negativity towards mathematics as a subject. How can we support our beginner teachers in resolving this issue?

    • Mathematical Relations

      Having the ability to identify mathematical relationships and express them using algebra is at the core of algebraic thinking and reasoning.

    • Algebraic Language

      Pupils' difficulties with using algebraic notation is well-known and justified in relevant research. In this activity, you will reflect upon your own expertise and decide upon the best advice to give to a beginner teacher.

    • Solving Equations

      When teaching 'solving linear equations', pupils' difficulties, such as with syntax, algebraic language, the application of rules, and how to decode algebraic expressions, need to be carefully considered.

    • Fostering Algebraic Reasoning: Reflections and Concluding remarks

      An opportunity to reflect on your learning during this week.

  • Week 3

    Fostering Geometric Reasoning

    • Introduction

      The activities below model how engagement with research empowers teachers to recognize the challenges pupils might have in learning geometry, providing thus a stimulus for consideration of how to better support their learning.

    • Working with diagrams

      This activity provides the stimulus for consideration of how to support students to talk and reason about geometric figures. Image: Jimwrenholt CC BY 2.0

    • Visualising

      This activity considers the role visualisation plays in one’s geometric reasoning, and the importance of being pedagogically aware of what pupils ‘see’ when they ‘look at’ diagrams. Image: Jimwrenholt CC BY 2.0

    • Invariance

      Invariance is a central idea in geometry. Most of the theorems could be seen as the result of studying a figure and noticing what change is permitted that leaves some relationships or properties invariant. Image: Jimwrenholt C

    • Fostering Geometric Reasoning: Reflections, Learning Live, and Concluding remarks

      Here is an opportunity to reflect on your learning during this week.

  • Week 4

    Fostering Numerical Reasoning

    • Introduction

      Negative numbers, fractions, multiplication of negative numbers or division of fractions, are known to have caused a number of difficulties to school students. How can we support our trainee to resolve these issues?

    • Negative numbers and the minus sign

      This activity addresses some of the challenges in students understanding of negative numbers Image: Jimwrenholt CC BY 2.0

    • Fractions

      Students' difficulties when working with fractions are well documented and justified by relevant research. In this activity, you will reflect upon your own expertise and decide upon the best advice to give to a beginner teacher.

    • Developing fluency with times tables

      Knowing times tables is important and should be taught in schools at a young age to ensure fluency for later mathematics.

    • Fostering Numerical Reasoning: Reflections and Concluding remarks

      Here is an opportunity to reflect on your learning during this week.

  • Week 5

    Fostering Functional Reasoning

    • Introduction

      The activities below model how research-informed subject and pedagogical knowledge about functions and related school mathematics topics empower teachers to recognize the challenges pupils might have in learning about these topic.

    • Knowledge about functions

      The first activity provides the stimulus for re-collection and re-engagement with the more advanced, formal definition of a function of a real variable.

    • Graphical representations of functions

      This activity highlights the challenges in teaching about functions in ways that have been found by research to be accessible to students, namely through connecting different representations of functions.

    • Square roots

      This activity uses knowledge about functions to settle an ambiguity about the square root.

    • Fostering Functional Reasoning: Reflections, Learning Live, and Concluding remarks

      Here is an opportunity to reflect on and share your learning during this week and with the participants in this online community.

When would you like to start?

Start straight away and learn at your own pace. If the course hasn’t started yet you’ll see the future date listed below.

What will you achieve?

By the end of the course, you‘ll be able to...

  • Improve your subject knowledge for teaching mathematics appropriate to the range of secondary school students (11-18 years old)
  • Engage with relevant educational research and understand how it can be applied to you
  • Apply educational research findings to your own practice as a mentor and that of your mentees
  • Contribute to a community of mathematics mentors

Who is the course for?

This course is suitable for those who have been teaching mathematics at secondary school level for at least three years. This background is needed as mentors draw upon their observations and wealth of knowledge as experienced teachers to suggest effective and workable approaches for maths lessons.

This background is necessary for mentors to draw upon their observations and knowledge as experienced teachers.

What software or tools do you need?

We recommend that you can access GeoGebra on the device you are using to access the course. The application is based online and offers a free download for a number of its tools.

Live sessions will be delivered at two points during the course. To participate in these it is recommended that learners source a device with audio input or separate headset.

Who will you learn with?

I taught mathematics at secondary school and university levels for over 25 years. As a mathematics teacher educator I currently work with mentors of early career teachers in over 60 schools in London.

I have been a mathematics educator for over 16 years and my goal is to continue to offer my support to the mathematics education community and mathematics teachers through valuable research work

Who developed the course?

UCL (University College London)

UCL was founded in 1826. It was the first English university established after Oxford and Cambridge, and the first to open up university education to those previously excluded from it.

What's included?

This is a premium course. These courses are designed for professionals from specific industries looking to learn with a smaller group of like-minded individuals.

  • Unlimited access to this course
  • Includes any articles, videos, peer reviews and quizzes
  • Certificate of Achievement to prove your success when you're eligible
  • Download and print your Certificate of Achievement anytime
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Get a taste of this course

Find out what this course is like by previewing some of the course steps before you join: