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Developing your subject knowledge and teaching of mathematics

In this course we look at the underlying mathematical structures of numbers, patterns and sequences aim to develop deep understanding.
© National STEM Learning Centre
It can be relatively easy to teach a student ‘how’ to perform a mathematical task. This is often referred to as ‘procedural’ learning. Students will sometimes ask to be shown ‘how to do it’ as they find this easy as it does not involve them in doing any thinking. However, it can lead to a ‘one size fits all’ approach to mathematics and can reduce the learning of mathematics to little more than memorising an unconnected ‘bag of tricks’.

A foundation for understanding the world

There have been many studies, such as the work carried out by Professor Jo Boaler, which indicates that procedural learning is the most difficult way for students to learn mathematics. The results of her work studying the teaching and learning of mathematics can be seen at YouCubed.
Mathematics is so much more than ‘a bag of tricks’. The English National Curriculum speaks of mathematics as:
“a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.”
In this course we look at the underlying mathematical structures of numbers, patterns and sequences with the aim to develop deep understanding. The number part of the English national curriculum is comprised of different topics, which we address in this course. The common thread throughout is to develop your ability to explain number and demonstrate different properties of numbers using a range of teaching approaches.

Self-audit task

This self-audit task is for teachers and educators, to help you review your current practice and understanding of numbers. Setting a development goal and being able to assess your own development is a crucial part of professional practice, so we will be revisiting your responses to the self-audit later. Please ensure you download a PDF of your responses at the end of the task.
When completing the self-audit, there are no right or wrong answers. Answer honestly about where you are now, not where you want to be. Your answers will help you to identify what areas of practice you need to focus on the most as you progress through the course.
  1. Access the self-audit task and complete it.
  2. At the end of the self-audit, click My responses.
  3. Click Download as PDF.
  4. Save the PDF where you will be able to retrieve it to review at the end of the course.

Your development goal

What do you want to get out of this course? Think about your professional (or personal) development goal and how a better understanding of mathematics will support you, your teaching and your students. Use the comments below to record this as we’ll refer back to it at the end of the course.
© National STEM Learning Centre
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Maths Subject Knowledge: Understanding Numbers

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