Education and Early Childhood Learning

Creativity in mathematics involves the adoption of flexible thinking, curiosity, risk-taking and making connections to prior knowledge, enabling learners to formulate new hypotheses or view mathematical problems and situations from a new perspective in order to arrive at innovative solutions.

When creativity as a competency is applied in mathematics, learners

• embrace a learning environment base on trust and respect that encourages them to make choices, take risks, and think flexibly—allowing them to make decisions and take action
• wonder, ask questions, and contemplate different mathematical ideas and concepts
• solve mathematical problems and situations using different ways to arrive at innovative solutions
• enrich and refine their reasoning by considering others’ ideas
• formulate, adjust, and refine their plans for solving mathematical problems and situations by looking at them from a new angle
• validate and adapt plans, ideas, strategies, or solutions, while persevering through obstacles, so they can improve at solving mathematical problems and situations
• seek and use feedback from others to develop and consolidate their conceptual understanding, deepen their reasoning, and reflect on their processes for solving mathematical problems and situations

Citizenship in mathematics mathematics involves the development of mathematical literacy that enables the application of ideas and concepts in a variety of everyday contexts, awakening learners' curiosity about their role as citizens who can actively contribute to society, think critically about the world, make informed decisions, and propose solutions to issues from a variety of perspectives.

When citizenship as a competency is applied in mathematics, learners

• use mathematics as a means of developing their understanding of a range of complex social, cultural, economic, and political issues, and to help them reflect on them
• mobilize their mathematical knowledge and skills to analyze and understand issues related to discrimination, equity, and human rights by investigating or proposing solutions to a variety of mathematical problems or situations related to these issues
• mobilize their mathematical knowledge and skills to explore, analyze, and understand the impact of the interconnectedness of self, others, and the natural world by investigating or proposing solutions to a variety of mathematical problems and situations related to this issue
• show interest in others’ approaches to mathematics and to different points of view, experiences, and worldviews, allowing them to better understand and solve mathematical problems and situations
• empathize with others whose ideas are different from their own and appreciate solutions to mathematical problems or situations proposed by others
• interact and learn with others in person or online in a responsible, respectful, and inclusive manner by welcoming and valuing diverse viewpoints, and by considering a range of ideas and perspectives when contributing to mathematical exchanges
• realize that their mathematical knowledge and skills will serve not only to improve their own quality of life but also that of others
• engage in meaningful mathematical inquiries, individually and in collaboration, in which they ask themselves and others questions so they can find equitable solutions and make ethical decisions
• appreciate how mathematics can be used to make and justify ethical decisions that lead to responsible and sustainable actions that affect themselves, their community, and the world

Connection to self in mathematics encompasses the learners’ confidence in their ability to undertake and complete tasks, solve mathematical problems and situations, and engage positively in reflective practices that enable them to set goals and make progress.

When connection to self as a competency is applied in mathematics, learners

• believe in their ability to learn and understand the world of mathematics and its impact on their daily lives
• recognize the elements that shape their identity as math learners, and they see themselves as mathematicians
• allow themselves the time they need, and they implement strategies that foster a growth mindset to develop a positive relationship with mathematics
• view reflection on their decisions, efforts, experiences, and feedback as a learning opportunity that helps them progress in mathematics
• reflect on their mathematical learning to set goals and make informed decisions that affect their well-being
• believe that their ability to learn, their talents, and their skills in mathematics will continue to improve throughout their lives through their hard work, perseverance, and effort
• are willing to take risks, ask for help, and persevere, despite obstacles
• demonstrate the ability to make changes and adapt to new mathematical contexts, knowing that they will learn from their mistakes and build on their personal strengths
• develop their autonomy, value their voice, and commit to their role in becoming lifelong mathematics learners

Collaboration in mathematics involves adopting a culture of exchanging ideas and perspectives, in which learners learn from and with each other in order to progress individually and collectively, develop their mathematical reasoning, and implement new ideas to solve problems.

When collaboration as a competency is applied in mathematics, learners

• collaborate with others, value diverse points of view, and consider a range of ideas and perspectives when participating in mathematical exchanges
• participate actively in learning experiences by sharing thinking and learning strategies with others to confirm or extend understandings of mathematical ideas; they respectfully voice their opinions, ideas, and conjectures
• recognize the value of others' contributions, allowing diverse perspectives to enrich mathematical exchanges
• practise active listening, question their own and others’ mathematical ways of thinking, and ask questions of others to deepen their understanding of mathematical concepts and ideas
• demonstrate openness by agreeing to compromise and change their views when presented with convincing arguments during mathematical exchanges
• make sense of mathematical concepts and ideas by co-constructing their understanding with others
• support their peers and take responsibility for their roles throughout the learning process and in the completion of mathematical tasks

Communication in mathematics involves the learners’ ability to express their mathematical ideas, reasoning, and solutions in a variety of ways, including orally, in writing, concretely, graphically, and symbolically, and in various contexts. It enables learners to clarify and validate their ideas and reasoning, while encouraging them to question their attitudes and beliefs about mathematics.

When communication as a competency is applied in mathematics, learners

• express their mathematical ideas and emotions about mathematics, taking into account non-verbal cues and adapting what they say according to the context
• present their mathematical ideas visually, orally, in writing, graphically, or symbolically, taking into account the conventions related to the mode of communication used, their audience, and the types of communication contexts, while using clear, precise mathematical language
• understand how their words and actions shape their identity as mathematical learners and shape their relationships with others
• look for oral, non-verbal, or visual cues during exchanges to improve their understanding of terminology, what others are saying, ideas presented, and various solutions to mathematical problems and situations
• seek to understand different points of view and different solutions to a mathematical problem or situation by observing, practising active listening, and asking clarifying questions, thereby contributing to a culture of mutual communication
• recognize and accept that the ways they learn and represent their understanding may be different from those of others
• make sense of mathematical ideas, problems, and situations, and deepen their understanding by making connections among their own language, mathematical terminology, and associated conventions
• contribute to mathematical exchanges and express their thoughts and emotions about mathematical ideas in a positive and respectful way, whether in person or online
• defend their points of view and their mathematical reasoning, while welcoming those of others in a constructive and responsible manner, recognizing that these exchanges enrich learning for themselves and other members of their community