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Approaches to Learning through Mathematics

Year 9

The aim of this course is for students to think deeply, work to a high standard, and communicate their mathematics with purpose and completeness — building strong problem-solving, collaboration, and research skills, alongside the independence and perseverance to keep growing as mathematicians.

About the class

This course is designed for students who already have a solid fluency with mathematical skills and are ready to apply them to real problem solving. Rather than focusing only on getting the right answer, we focus on developing the habits and skills that will serve students throughout their mathematical journey and beyond — spanning Thinking, Social, Communication, Self-Management, and Research skills.

Approaches to learning in this class

Thinking

  • Students tackle compound, multi-step problems that require them to apply what they know in new situations and think deeply, rather than simply repeating a memorised procedure.
  • The goal is genuine problem solving: working out how to approach an unfamiliar question, not just following a formula.

Social

  • Much of this work happens in groups, where students practise accepting responsibility for their share of the task, making decisions collaboratively, respecting others' ideas and approaches, and cooperating to reach a shared solution.
  • Working alongside others means learning to listen to different mathematical perspectives and negotiate a way forward together.

Communication

  • A correct answer is only part of the picture.
  • Students are asked to show their working, explain how they reached their answer, and describe any patterns they notice along the way.
  • They are encouraged to represent their thinking in multiple ways — using diagrams, numbers, colour, tables, graphs, or algebra — and to ask themselves: How many different ways can I show or explain this?
  • Students also learn to use proper mathematical conventions, so their work is set out clearly and meaningfully.
  • This moves them beyond simply stating a solution, toward justifying why it works and generalising it to other situations.

Self-management

  • Problem solving takes time, and this course asks students to embrace that.
  • Take your time.
  • Work independently and persevere — if a problem feels hard, sit with it and try a different approach before moving on.
  • Doing fewer sections to a high standard is better than rushing through as much as you can.
  • This also means being a self-starter: noticing when you need a little more practice or support, and taking the initiative to work on it.

Research

  • Exploring a problem often means investigating it like a small research task:
  • formulating questions about what's being asked
  • observing and planning an approach
  • collecting and recording relevant information or data
  • organising and interpreting it
  • presenting findings clearly at the end

I can…

Weekly homework

Continue the Exploration from class for at least 40 minutes.

Communication

Show your working, explain how you reached your answer, and describe any patterns you see. Consider using diagrams, numbers, colour, tables, graphs, algebra. Can you show or explain your thinking in multiple ways? How many different ways can you think of?

Thinking and self-management

Take your time. Work independently and persevere: if a problem feels hard, sit with it and try a different approach before moving on. If you know there is something you need more practice with, take the initiative to work on it yourself.

Explorations

  1. Stars
  2. The Gear and Loop Mystery
  3. Days and dates
  4. Time traveller's calendar

The IB learner profile

IB learners strive to be:

Inquirers

We nurture our curiosity, developing skills for inquiry and research. We know how to learn independently and with others. We learn with enthusiasm and sustain our love of learning throughout life.

Knowledgeable

We develop and use conceptual understanding, exploring knowledge across a range of disciplines. We engage with issues and ideas that have local and global significance.

Thinkers

We use critical and creative thinking skills to analyse and take responsible action on complex problems. We exercise initiative in making reasoned, ethical decisions.

Communicators

We express ourselves confidently and creatively in more than one language and in many ways. We collaborate effectively, listening carefully to the perspectives of other individuals and groups.

Principled

We act with integrity and honesty, with a strong sense of fairness and justice, and with respect for the dignity and rights of people everywhere. We take responsibility for our actions and their consequences.

Open-minded

We critically appreciate our own cultures and personal histories, as well as the values and traditions of others. We seek and evaluate a range of points of view, and we are willing to grow from the experience.

Caring

We show empathy, compassion and respect. We have a commitment to service, and we act to make a positive difference in the lives of others and in the world around us.

Risk-takers

We approach uncertainty with forethought and determination; we work independently and cooperatively to explore new ideas and innovative strategies. We are resourceful and resilient in the face of challenges and change.

Balanced

We understand the importance of balancing different aspects of our lives (intellectual, physical and emotional) to achieve well-being for ourselves and others. We recognise our interdependence with other people and with the world in which we live.

Reflective

We thoughtfully consider the world and our own ideas and experience. We work to understand our strengths and weaknesses in order to support our learning and personal development.

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