Critical thinking in mathematics involves the ability to compare, evaluate, critique, justify, test, and validate ideas, representations, plans, or solutions using logical arguments, criteria, and evidence. It requires metacognition in learners, enabling them to solve mathematical problems and situations, communicate their reasoning effectively, and make ethical decisions.
- Learners research, use, and think about a variety of ideas and information strategically, efficiently, and effectively to make decisions and choices.
- Learners evaluate their own and others’ ideas, as well as possible solutions, by considering different perspectives, biases, and the validity and relevance of supporting sources.
- Learners use inductive reasoning to explore and record results; to analyze mathematical ideas, problems, and situations; to make observations and generalizations from patterns; and to test these generalizations based on criteria and evidence.
- Learners recognize that certain math beliefs influence how they perceive themselves as math learners.
- Learners demonstrate a willingness to reconsider their own thinking and to consider others’ thinking about mathematical ideas, problems, or situations.
- Learners ask relevant and clarifying questions to further learning and enhance comprehension of mathematical ideas, concepts, problems, and situations.
- Learners make judgments based on thoughtful criteria to then make decisions and solve mathematical problems and situations, enabling them to take action in an informed manner.
- Learners use deductive reasoning to solve mathematical problems and situations, reach new conclusions based on what is already known or assumed to be true, and make ethical decisions.
Creativity in mathematics involves flexible thinking, curiosity, and risk taking, as well as making connections to prior knowledge among learners; this allows learners to come up with innovative solutions to a variety of mathematical problems and situations by considering them from a new angle or by formulating new hypotheses.
- Learners embrace a learning environment of trust and respect that encourages them to make choices, take risks, and think flexibly—allowing them to make decisions and take action.
- Learners wonder, ask questions, and contemplate different mathematical ideas and concepts.
- Learners solve mathematical problems and situations using different ways to arrive at innovative solutions.
- Learners enrich and refine their reasoning by considering others’ ideas.
- Learners formulate, adjust, and refine their plans for solving mathematical problems and situations by looking at them from a new angle.
- Learners validate and adapt plans, ideas, strategies, or solutions, while persevering through obstacles, so they can improve at solving mathematical problems and situations.
- Learners 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 involves the development of mathematical literacy that enables the application of mathematical 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 generate solutions to an issue from a variety of perspectives.
- 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.
- Learners 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.
- Learners 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.
- Learners 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.
- Learners empathize with others whose ideas are different from their own and appreciate solutions to mathematical problems or situations proposed by others.
- Learners 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.
- Learners realize that their mathematical knowledge and skills will serve not only to improve their own quality of life but also that of others.
- Learners 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.
- Learners 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 involves the learner’s belief in their ability to approach and complete tasks, solve mathematical problems and situations, and persevere in the face of mathematical challenges. It also involves the learner’s ability to engage positively in reflective practices about their learning in order to set goals for self-improvement.
- Learners believe in their ability to learn and understand the world of mathematics and its impact on their daily lives.
- Learners recognize the elements that shape their identity as math learners, and they see themselves as mathematicians.
- Learners allow themselves the time they need, and they implement strategies that foster a growth mindset to develop a positive relationship with mathematics.
- Learners consider reflecting on their own decisions, the efforts they deploy, the experiences they have, and feedback from others as learning opportunities to improve their knowledge and skills in mathematics.
- Learners reflect on their mathematical learning to set goals and make informed decisions that affect their well-being.
- Learners 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.
- Learners are willing to take risks, ask for help, and persevere, despite obstacles.
- Learners 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.
- Learners develop their autonomy, value their voice, and commit to their role in becoming lifelong mathematics learners.
Collaboration in mathematics involves adhering to a culture of exchanging ideas and viewpoints in order to improve, both collectively and individually, and to learn from and with others to develop and apply new ideas in mathematics.
- Learners collaborate with others, value diverse points of view, and consider a range of ideas and perspectives when contributing to mathematical exchanges.
- Learners participate actively and fully 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.
- Learners value the contributions of others, making room for different points of view that will foster mathematical exchanges.
- Learners 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.
- Learners show a willingness to compromise and change their opinions when presented with convincing arguments during mathematical exchanges.
- Learners make sense of mathematical concepts and ideas by co-constructing their understanding with others.
- Learners support others and take responsibility for their roles throughout the learning process and in the execution of mathematical tasks.
Communication in mathematics involves the learners’ ability to share 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, and to challenge their attitudes and beliefs about mathematics.
- Learners express their mathematical ideas and emotions about mathematics, taking into account non-verbal cues and adjusting what they say according to the context.
- Learners 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.
- Learners understand how their words and actions shape their identity as mathematical learners and shape their relationships with others.
- Learners 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.
- Learners 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 creating a culture of mutual communication.
- Learners recognize and accept that the ways they learn and represent their understanding may be different from those of others.
- Learners make sense of mathematical ideas, problems, and situations, and deepen their understanding by making connections among their own language, mathematical terminology, and mathematical conventions.
- Learners contribute to mathematical exchanges and express their thoughts and emotions about mathematical ideas in a positive and respectful way, whether in person or online.
- Learners defend their points of view and their mathematical reasoning while accepting the points of view and reasoning of others in a constructive and responsible way; they understand how these exchanges benefit themselves as much as they do other members of their learning community.
