Instruction in mathematics should support all students in acquiring the knowledge, skills, and habits of mind that they need in order to achieve the curriculum expectations and be able to enjoy and participate in mathematics learning for years to come.

Effective mathematics instruction begins with knowing the complex identities and profiles of the students, having high academic expectations for and of all students, providing supports when needed, and believing that all students can learn and do mathematics. Teachers incorporate Culturally Responsive and Relevant Pedagogy (CRRP) and provide authentic learning experiences to meet individual students’ learning strengths and needs. Effective mathematics instruction focuses on the development of conceptual understanding and procedural fluency, skill development, and communication, as well as problem-solving skills. It takes place in a safe and inclusive learning environment, where all students are valued, empowered, engaged, and able to take risks, learn from mistakes, and approach the learning of mathematics in a confident manner. Instruction that is student centred and asset based builds effectively on students’ strengths to develop mathematical habits of mind, such as curiosity and open-mindedness; a willingness to question, to challenge and be challenged; and an awareness of the value of listening intently, reading thoughtfully, and communicating with clarity.

Learning should be relevant: embedded in the lived realities of all students and inspired by authentic, real-life contexts as much as possible. This approach allows students to develop key mathematical concepts and skills, to appreciate the beauty and wide-ranging nature of mathematics, and to realize the potential of mathematics to raise awareness and effect social change that is innovative and sustainable. A focus on making learning relevant supports students in their use of mathematical reasoning to make connections throughout their lives.

Universal Design for Learning (UDL) and Differentiated Instruction (DI)

Students in every mathematics classroom vary in their identities, lived experiences, personal interests, learning profiles, and readiness to learn new concepts and skills. Universal Design for Learning (UDL) and differentiated instruction (DI) are robust and powerful approaches to designing assessment and instruction to engage all students in mathematical tasks that develop conceptual understanding and procedural fluency. Providing each student with opportunities to be challenged and to succeed requires teachers to attend to student differences and provide flexible and responsive approaches to instruction. UDL and DI can be used in combination to help teachers respond effectively to the strengths and needs of all students.

The aim of the UDL framework is to assist teachers in designing mathematics programs and environments that provide all students with equitable access to the mathematics curriculum. Within this framework, teachers engage students in multiple ways in order to support them in becoming purposeful and motivated in their mathematics learning. Teachers take into account students’ diverse learner profiles by designing tasks that offer individual choice, ensuring relevance and authenticity, providing graduated levels of challenge, and fostering collaboration in the mathematics classroom. Teachers also represent concepts and information in multiple ways to help students become resourceful and knowledgeable learners. For example, teachers use a variety of media to ensure that students are provided with alternatives for auditory and visual information; they clarify mathematics vocabulary and symbols; and they highlight patterns and big ideas to guide information processing. To support learners as they focus strategically on their learning goals, teachers create an environment in which learners can express themselves using a range of kinesthetic, visual, and auditory strengths. For example, teachers can improve access to tools or assistive devices; vary ways in which students can respond and demonstrate their understanding of concepts; and support students in goal-setting, planning, and time-management skills related to their mathematics learning.

Designing mathematics tasks through UDL allows the learning to be “low floor, high ceiling” – that is, all students are provided with the opportunity to find their own entry point to the learning. Teachers can then support students in working at their own pace and provide further support as needed, while continuing to move student learning forward. Tasks that are intentionally designed to be low floor, high ceiling provide opportunities for students to use varied approaches and to continue to be engaged in learning with varied levels of complexity and challenge. This is an inclusive approach that is grounded in a growth mindset: the belief that everyone can do well in mathematics.

While UDL provides teachers with broad principles for planning mathematics instruction and learning experiences for a diverse group of students, DI allows them to address specific skills and learning needs. DI is rooted in assessment and involves purposefully planning varied approaches to teaching the content of the curriculum; to the processes (e.g., tasks and activities) that support students as they make sense of what they are learning; to the ways in which students demonstrate their learning and the outcomes they are expected to produce; and to the learning environment. DI is student centred and involves a strategic blend of whole-class, small-group, and individual learning activities to suit students’ differing strengths, interests, and levels of readiness to learn. Attending to students’ varied readiness for learning mathematics is an important aspect of differentiated teaching. Learners who are ready for greater challenges need support in aiming higher, developing belief in excellence, and co-creating problem-based tasks to increase the complexity while still maintaining joy in learning. Students who are struggling to learn a concept need to be provided with the scaffolding and encouragement to reach high standards. Through an asset-based approach, teachers focus on these learners’ strengths, imbuing instructional approaches with a strong conviction that all students can learn. To make certain concepts more accessible, teachers can employ strategies such as offering students choice, and providing open-ended problems that are based on relevant real-life situations and supported with visual and hands-on learning. Research indicates that using differentiated instruction in mathematics classrooms can diminish inequities.

Universal Design for Learning and differentiated instruction are integral aspects of an inclusive mathematics program and the achievement of equity in mathematics education. More information on these approaches can be found in the ministry publication Learning for All: A Guide to Effective Assessment and Instruction for All Students, Kindergarten to Grade 12 (2013).

High-Impact Practices

Teachers understand the importance of knowing the identities and profiles of all students and of choosing the instructional approaches that will best support student learning. The approaches that teachers employ vary according to both the learning outcomes and the needs of the students, and teachers choose from and use a variety of accessible, equitable high-impact instructional practices.

The thoughtful use of these high-impact instructional practices – including knowing when to use them and how they might be combined to best support the achievement of specific math goals – is an essential component of effective math instruction. Researchers have found that the following practices consistently have a high impact on teaching and learning mathematics:

• Learning Goals, Success Criteria, and Descriptive Feedback. Learning goals and success criteria outline the intention for the lesson and how this intention will be achieved to ensure teachers and students have a clear and common understanding of what is being learned and what success looks like. The use of descriptive feedback involves providing students with the precise information they need in order to reach the intended learning goal.
• Direct Instruction. This is a concise, intentional form of instruction that begins with a clear learning goal. It is not a lecture or a show-and-tell. Instead, direct instruction is a carefully planned and focused approach that uses questioning, activities, or brief demonstrations to guide learning, check for understanding, and make concepts clear. Direct instruction prioritizes feedback and formative assessment throughout the learning process and concludes with a clear summary of the learning that can be provided in written form, orally, and/or visually.
• Problem-Solving Tasks and Experiences. It is an effective practice to use a problem, intentionally selected or created by the teacher or students, to introduce, clarify, or apply a concept or skill. This practice provides opportunities for students to demonstrate their agency by representing, connecting, and justifying their thinking. Students communicate and reason with one another and generate ideas that the teacher connects in order to highlight important concepts, refine existing understanding, eliminate unsuitable strategies, and advance learning.
• Teaching about Problem Solving. Teaching students about the process of problem solving makes explicit the critical thinking that problem solving requires. It involves teaching students to identify what is known and unknown, to draw on similarities and differences between various types of problems, and to use representations to model the problem-solving situation.
• Tools and Representations. The use of a variety of appropriate tools and representations supports a conceptual understanding of mathematics. Carefully chosen and used effectively, representations and tools such as manipulatives make math concepts accessible to a wide range of learners. At the same time, student interactions with representations and tools also give teachers insight into students’ thinking and learning.
• Math Conversations. Effective mathematical conversations create opportunities for all students to express their mathematical thoughts and to engage meaningfully in mathematical talk by listening to and responding to the ideas of others. These conversations involve reasoning, proving, building on the thinking of others, defending and justifying their own thinking, and adjusting their perspectives as they build their mathematical understanding, confidence, and awareness of the mathematical thoughts of others.
• Small-Group Instruction. A powerful strategy for moving student learning forward, small-group instruction involves targeted, timely, and scaffolded mathematics instruction that meets the learning needs of specific students at appropriate times. By working with small and flexible groups, whether they are homogenous or heterogenous, teachers can personalize learning in order to close gaps that exist or extend thinking. Small-group instruction also provides opportunities for teachers to connect with and learn more about student identities, experiences, and communities, which the teachers can build on as a basis for their mathematics instruction.
• Deliberate Practice. Practice is best when it is purposeful and spaced over time. It must always follow understanding and should be continual and consistent. Teachers provide students with timely descriptive feedback to ensure that students know they are practising correctly and sufficiently. Students also need to practise metacognition, or reflecting on their learning, in order to become self-directed learners.
• Flexible Groupings. The intentional combination of large-group, small-group, partnered, and independent working arrangements, in response to student and class learning needs, can foster a rich mathematical learning environment. Creating flexible groupings in a mathematics class enables students to work independently of the teacher but with the support of their peers, and it strengthens collaboration and communication skills. Regardless of the size of the group, it is of utmost importance that individual students have ownership of their learning.

While a lesson may prominently feature one of these high-impact practices, other practices will inevitably also be involved. The practices are rarely used in isolation, nor is there any single “best” instructional practice. Teachers strategically choose the right practice, for the right time, in order to create an optimal learning experience for all students. They use their socio-cultural awareness of themselves and their students, a deep understanding of the curriculum and of the mathematics that underpins the expectations, and a variety of assessment strategies to determine which high-impact instructional practice, or combination of practices, best supports the students. These decisions are made continually throughout a lesson. The appropriate use of high-impact practices plays an important role in supporting student learning.

More information can be found in the resource section on high-impact practices in mathematics. 

When teachers effectively implement Universal Design for Learning, differentiated instruction, and high-impact practices in mathematics programs, they create opportunities for students to develop mathematics knowledge and skills, to apply mathematical processes, and to develop transferable skills that can be applied in other curricular areas.

The mathematics curriculum was developed with the understanding that the strategic use of technology is part of a balanced mathematics program. Technology can extend and enrich teachers’ instructional strategies to support all students’ learning in mathematics. Technology, when used in a thoughtful manner, can support and foster the development of mathematical reasoning, problem solving, and communication. For some students, technology is essential and required to access curriculum.

When using technology to support the teaching and learning of mathematics, teachers consider the issues of student safety, privacy, ethical responsibility, equity and inclusion, and well-being.

The strategic use of technology to support the achievement of the curriculum expectations requires a strong understanding of:

• the mathematical concepts being addressed;
• high-impact teaching practices that can be used, as appropriate, to achieve the learning goals;
• the capacity of the chosen technology to augment the learning, and how to use this technology effectively.

Technology (e.g., digital tools, computation devices, calculators, data-collection programs and coding environments) can be used specifically to support students’ thinking in mathematics, to develop conceptual understanding (e.g., visualization using virtual graphing or geometry tools), and to facilitate access to information and allow better communication and collaboration (e.g., collaborative documents and web-based content that enable students to connect with experts and other students; language translation applications).

Coding has been introduced into the Grade 9 mathematics course as a continuum from the elementary mathematics curriculum. The elementary mathematics curriculum outlines a developmental progression for students to develop foundational coding skills. In Grade 9, students transition to using coding as a tool to interact with the mathematics they are learning. They use the skills developed in elementary to create and alter code in a multitude of coding environments including text-based programming languages, spreadsheets, computer algebra systems (CAS), and virtual graphing and geometry tools.

Technology can support English language learners in accessing mathematics terminology and ways of solving problems in their first language. Assistive technologies are critical in enabling some students with special education needs to have equitable access to the curriculum and in supporting their learning, and must be provided in accordance with a student’s Individual Education Plan (IEP).

Technologies are important problem-solving tools. Computers and calculators are tools of mathematicians, and students should be given opportunities to select and use the learning tools that may be helpful or necessary for them as they search for their own solutions to problems.

Teachers understand the importance of technology and how it can be used to access and support learning for all students. Additional information can be found in the “The Role of Information and Communications Technology” subsection of “Considerations for Program Planning”. 

Education and career/life planning supports students in their transition from secondary school to their initial postsecondary destinations, whether in apprenticeships, college, community living, university, or the workplace.

Mathematics teachers can support students in education and career/life planning by making authentic connections between the mathematics concepts students are learning in school and the knowledge and skills needed in different careers. These connections engage students’ interest and allow them to develop an understanding of the usefulness of mathematics in the daily lives of workers.

Teachers can promote students’ awareness of careers involving mathematics by exploring real-life applications of mathematics concepts and providing opportunities for career-related project work. Such activities allow students to investigate mathematics-related careers compatible with their interests, aspirations, and abilities.

Community members can also act as a valuable resource by sharing their career expertise and supporting students in understanding the relevance of mathematics to various fields of study and careers. Career fairs, guest speakers, and job-shadowing days can provide opportunities for students to identify and explore mathematics-related careers.

Students may need support to comprehend the wide variety of professions and careers where mathematical concepts and processes are used. For example: 

• fractions and imperial measures are used in various trades and daily activities; 
• rates and percentages are used in banking, investing, and currency exchange; 
• ratios and proportions are used in architecture, engineering, construction, nursing, pharmacy practice, hair colouring techniques, and fields related to culinary arts;
• algebraic reasoning is used in the sciences and computer programming;  
• geometry and measurement concepts are used in construction, civil engineering, and art; statistics are used in real estate, the retail sector, tourism and recreation, conservation, finance, insurance, sports management, and research.

Students should be made aware that mathematical literacy, problem solving, and the other skills and knowledge they learn in the mathematics classroom are valuable assets in an ever-widening range of jobs and careers in today’s society. More information can be found in the “Education and Career/Life Planning” subsection of “Considerations for Program Planning”. 

Classroom teachers hold high expectations of all students and are the key educators in designing and supporting mathematics assessment and instruction for students with special education needs. They have a responsibility to support all students in their learning and to work collaboratively with special education teachers, where appropriate, to plan, design and implement appropriate instructional and assessment accommodations and modifications in the mathematics program to achieve this goal. More information on planning for and assessing students with special education needs can be found in the “Planning for Students with Special Education Needs” subsection of “Considerations for Program Planning”.

Principles for Supporting Students with Special Education Needs

The following principles guide teachers in effectively planning and teaching mathematics programs to students with special education needs, and also benefit all students:

• The teacher plays a critical role in student success in mathematics.
• It is important for teachers to develop an understanding of the general principles of how students learn mathematics.
• The learning expectations outline interconnected, developmentally appropriate key concepts and skills of mathematics across all of the strands.
• It is important to support students in making connections between procedural knowledge and conceptual understanding of mathematics.
• The use of concrete, visual, and virtual representations and tools is fundamental to learning mathematics and provides a way of representing both concepts and student understanding.
• The teaching and learning process involves ongoing assessment. Students with special education needs should be provided with various opportunities to demonstrate their learning and thinking in multiple ways.

An effective mathematics learning environment and program that addresses the mathematical learning needs of students with special education needs is purposefully planned with the principles of Universal Design for Learning in mind and integrates the following elements:

• knowing the student’s cultural and linguistic background, strengths, interests, motivations, and needs in mathematics learning in order to differentiate learning and make accommodations and modifications as outlined in the student’s Individual Education Plan;
• building the student’s confidence and positive identity as a mathematics learner;
• valuing the student’s prior knowledge and connecting what the student knows with what the student needs to learn;
• identifying and focusing on the connections between broad concepts in mathematics;
• connecting mathematics with familiar, relevant, everyday situations and providing rich and meaningful learning contexts;
• fostering a positive attitude towards mathematics and an appreciation of mathematics through multimodal means, including through the use of assistive technology and the performance of authentic tasks;
• implementing research-informed instructional approaches (e.g., Concrete – Semi-Concrete – Representational – Abstract) when introducing new concepts to promote conceptual understanding, procedural accuracy, and fluency;
• creating a balance of explicit instruction, problem solving within a student’s zone of proximal development, learning in flexible groupings, and independent learning. Each instructional strategy should take place in a safe, supportive, and stimulating environment while taking into consideration that some students may require more systematic and intensive support, and more explicit and direct instruction, before engaging in independent learning;
• assessing student learning through observations, conversations with the students, and frequent use of low-stakes assessment check-ins and tools;
• providing immediate feedback in order to facilitate purposeful, correct practice that supports understanding of concepts and procedures, as well as efficient strategies;
• providing environmental, assessment, and instructional accommodations in order to maximize the student’s learning (e.g., making available learning tools such as virtual manipulatives, computer algebra systems, and calculators; ensuring access to assistive technology), as well as modifications that are specified in the student’s Individual Education Plan;
• building an inclusive community of learners and encouraging students with special education needs to participate in various mathematics-oriented class projects and activities;
• building partnerships with administrators and other teachers, particularly special education teachers, where available, to share expertise and knowledge of the curriculum expectations; co-develop content in the Individual Education Plan that is specific to mathematics; and systematically implement intervention strategies, as required, while making meaningful connections between school and home to ensure that what the student is learning in the school is relevant and can be practised and reinforced beyond the classroom.

English language learners are working to achieve the curriculum expectations in mathematics while they are developing English-language proficiency. An effective mathematics program that supports the success of English language learners is purposefully planned with the following considerations in mind.

• Students’ various linguistic identities are viewed as a critical resource in mathematics instruction and learning. Recognizing students’ language resources and expanding linguistic competence enables students to use their linguistic repertoire in a fluid and dynamic way, mixing and meshing languages to communicate. This translingual practice is creative and strategic, and allows students to communicate, interact, and connect with peers and teachers using the full range of their linguistic repertoire, selecting features and modes that are most appropriate to communicate across a variety of purposes, such as when developing conceptual knowledge and when seeking clarity and understanding.
• Students may be negotiating between school-based mathematics and ways of mathematical reasoning from diverse cultural and linguistic backgrounds. They may have deep mathematical knowledge and skills developed in another educational cultural and/or linguistic context, and may already have learned the same mathematical terms and concepts that they are studying now, but in another language. 
• Knowledge of the diversity among English language learners and of their mathematical strengths, interests, and identities, including their social and cultural backgrounds, is important. These “funds of knowledge” are historically and culturally developed skills and assets that can be incorporated into mathematics learning to create a richer and more highly scaffolded learning experience for all students, promoting a positive, inclusive teaching and learning environment. Understanding how mathematical concepts are described in students’ home languages and cultures can provide insight into how students are thinking about mathematical ideas.
• In addition to assessing their level of English-language proficiency, an initial assessment of the mathematics knowledge and skills of newcomer English language learners is required in Ontario schools.
• Differentiated instruction is essential in supporting English language learners, who face the dual challenge of learning new conceptual knowledge while acquiring English-language proficiency. Designing mathematics learning to have the right balance for English language learners is achieved through program adaptations (e.g., accommodations that utilize their background knowledge in their first language) that ensure the tasks are mathematically challenging, reflective of learning demands within the mathematics curriculum, and comprehensible and accessible to English language learners. Using the full range of a student’s language assets, including additional languages that a student speaks, reads, and writes, as a resource in the mathematics classroom supports access to their prior learning, reduces the language demands of the mathematics curriculum, and increases engagement.
• Working with students and their families and with available community supports allows for the multilingual representation of mathematics concepts to create relevant and real-life learning contexts and tasks.

In a supportive learning environment, scaffolding the learning of mathematics assessment and instruction offers English language learners the opportunity to:

• integrate their linguistic repertoire rather than engage in language separation, and select and use the linguistic features and modes that are most appropriate for their communication purposes;
• discuss how mathematical concepts are described in their language(s) and cultures;
• draw on their additional language(s) (e.g., some newcomer students may use technology to access mathematical terminology and ways of solving problems in their first language), prior learning experiences, and background knowledge in mathematics;
• learn new mathematical concepts in authentic, meaningful, and familiar contexts;
• engage in open and parallel tasks to allow for multiple entry points for learning;
• work in a variety of settings that support co-learning and multiple opportunities for practice (e.g., with partners or in small groups with same-language peers, as part of cooperative or collaborative learning, in group conferences);
• access the language of instruction during oral, written, and multimodal instruction and assessment, during questioning, and when encountering texts, learning tasks, and other activities in mathematics;
• use oral language in different strategically planned activities, such as “think-pair-share”, “turn-and-talk”, and “adding on”, to express their ideas and engage in mathematical discourse;
• develop both everyday and academic vocabulary, including specialized mathematics vocabulary in context, through rephrasing and recasting by the teacher and through using student-developed bilingual word banks or glossaries;
• practise using sentence frames adapted to their English-language proficiency levels to describe concepts, provide reasoning, hypothesize, make judgements, and explain their thinking;
• use a variety of concrete and/or digital learning tools to demonstrate their learning in mathematics in multiple ways (e.g., orally, visually, kinesthetically), through a range of representations (e.g., portfolios, displays, discussions, models), and in multiple languages (e.g., multilingual word walls and anchor charts);
• have their learning assessed in terms of the processes they use in multiple languages, both during the learning and through teachers’ observations and conversations.

Strategies used to differentiate instruction and assessment for English language learners in the mathematics classroom also benefit many other learners in the classroom, since programming is focused on leveraging all students’ strengths, meeting learners where they are in their learning, being aware of language demands in mathematics, and making learning visible. For example, different cultural approaches to solve mathematical problems can help students make connections to the Ontario curriculum and provide classmates with alternative ways of solving problems.

English language learners in English Literacy Development (ELD) programs require accelerated support to develop both their literacy skills and their numeracy skills. These students have significant gaps in their education because of limited or interrupted opportunities for or access to schooling. In order to build a solid foundation of mathematics, they are learning key mathematical concepts missed in prior years. At the same time, they are learning the academic language of mathematics in English while not having acquired developmentally appropriate literacy skills in their first language. Programming for these students is therefore highly differentiated and intensive. These students often require focused support over a longer period than students in English as a Second Language (ESL) programs. The use of students’ oral competence in languages other than English is a non-negotiable scaffold. The strategies described above, such as the use of visuals, the development of everyday and academic vocabulary, the use of technology, and the use of oral competence, are essential in supporting student success in ELD programs and in mathematics.

Supporting English language learners is a shared responsibility. Collaboration with administrators and other teachers, particularly ESL/ELD teachers, and Indigenous representatives, where possible, contributes to creating equitable outcomes for English language learners. Additional information on planning for and assessing English language learners can be found in the “Planning for English Language Learners” subsection of “Considerations for Program Planning”.

When planning an integrated mathematics program, educators should consider that, although the mathematical content in the curriculum is outlined in discrete strands, students develop mathematical thinking, such as proportional reasoning, algebraic reasoning, and spatial reasoning, that transcends the expectations in the strands and even connects to learning in other subject areas. By purposefully drawing connections across all areas of mathematics and other subject areas, and by applying learning to relevant real-life contexts, teachers extend and enhance student learning experiences and deepen their knowledge and skills across disciplines and beyond the classroom.

For example, proportional reasoning, which is developed through the study of ratios and rates in the Number strand, is also used when students are working towards meeting learning expectations in other strands of the math curriculum, such as in Geometry and Measurement and in Algebra, and in other disciplines, such as science, geography, and the arts. Students then apply this learning in their everyday lives – for example, when adjusting a recipe, preparing a mixture or solutions, or making unit conversions.

Similarly, algebraic reasoning is applied beyond the Number and Algebra strands. For example, it is applied in measurement when learning about formulas, such as $$\textit { volume of a pyramid }= \frac{\textit { area of the base } \times \textit { height }}{3}$$. It is applied in other disciplines, such as science, when students study simple machines and learn about the formula work = force × distance. Algebraic reasoning is also used when making decisions in everyday life – for example, when determining which service provider offers a better consumer contract or when calculating how much time it will take for a frozen package to thaw.

Spatial thinking has a fundamental role throughout the Ontario curriculum, from Kindergarten to Grade 12, including in mathematics, the arts, health and physical education, and science. For example, a student demonstrates spatial reasoning when mentally rotating and matching shapes in mathematics, navigating movement through space and time, and using diagonal converging lines to create perspective drawings in visual art and to design and construct objects. In everyday life, there are many applications of spatial reasoning, such as when creating a garden layout or when using a map to navigate the most efficient way of getting from point A to point B.

Algebraic and proportional reasoning and spatial thinking are integral to all STEM disciplines. For example, students may apply problem-solving skills and mathematical modelling through engineering design as they build and test a prototype and design solutions intended to solve complex real-life problems. Consider how skills and understanding that students gain across the strands of the Grade 9 Mathematics course, such as Financial Literacy, Number, and Data, can be integrated into real-life activities. For example, as students collect financial data relating to compound interest, and examine patterns in the data involving compound interest, they apply their understanding of exponents and non-linear growth to generalize rules that can be coded in technology programming environments. This process allows students to create a variety of mathematical models and analyse them quantitatively. These models can then be used to support discussions about what factors can enable or constrain financial decision making, while taking ethical, societal, environmental, and personal considerations into account. 

Teaching mathematics as a narrowly defined subject area places limits on the depth of learning that can occur. When teachers work together to develop integrated learning opportunities and highlight cross-curricular connections, students are better able to:

• make connections among the strands of the mathematics curriculum, and between mathematics and other subject areas;
• improve their ability to consider different strategies to solve a problem;
• debate, test, and evaluate whether strategies are effective and efficient;
• apply a range of knowledge and skills to solve problems in mathematics and in their daily experiences and lives.

When students are provided with opportunities to learn mathematics through real-life applications, integrating learning expectations from across the curriculum, they use their lived experiences and knowledge of other subject matter to enhance their learning of and engagement in mathematics. More information can be found in “Cross-Curricular and Integrated Learning”. 

Literacy in Mathematics

Literacy skills needed for reading and writing in general are essential for the learning of mathematics. To engage in mathematical activities and develop computational fluency, students require the ability to read and write mathematical expressions, to use a variety of literacy strategies to comprehend mathematical text, to use language to analyse, summarize, and record their observations, and to explain their reasoning when solving problems. Mathematical expressions and other mathematical texts are complex and contain a higher density of information than any other text. Reading mathematical text requires literacy strategies that are unique to mathematics.

The learning of mathematics requires students to navigate discipline-specific reading and writing skills; therefore, it is important that mathematics instruction link literacy practices to specific mathematical processes and tasks. To make their thinking visible, students should be encouraged to clearly communicate their mathematical thinking, using the discipline-specific language of mathematics, which provides educators with the opportunity to correct student thinking when necessary. The language of mathematics includes special terminology. To support all students in developing an understanding of mathematical texts, teachers need to explicitly teach mathematical vocabulary, focusing on the many meanings and applications of the terms students may encounter. In mathematics, students are required to use appropriate and correct terminology and are encouraged to use language with care and precision in order to communicate effectively.

More information about the importance of literacy across the curriculum can be found in the “Literacy” and “Mathematical Literacy” subsections of “Cross-curricular and Integrated Learning”. 

Transferable Skills in Mathematics

The Ontario curriculum emphasizes a set of skills that are critical to all students’ ability to thrive in school, in the world beyond school, and in the future. These are known as transferable skills. Educators facilitate students’ development of transferable skills across the curriculum, from Kindergarten to Grade 12. They are as follows:

• Critical Thinking and Problem Solving. In mathematics, students and educators learn and apply strategies to understand and solve problems flexibly, accurately, and efficiently. They learn to understand and visualize a situation and to use the tools and language of mathematics to reason, make connections to real-life situations, communicate, and justify solutions.
• Innovation, Creativity, and Entrepreneurship. In mathematics, students and educators solve problems with curiosity, creativity, and a willingness to take risks. They pose questions, make and test conjectures, and consider problems from different perspectives to generate new learning and apply it to novel situations.
• Self-Directed Learning. By reflecting on their own thinking and emotions, students, with the support of educators, can develop perseverance, resourcefulness, resilience, and a sense of self. In mathematics, they initiate new learning, monitor their thinking and their emotions when solving problems, and apply strategies to overcome challenges. They perceive mathematics as useful, interesting, and doable, and confidently look for ways to apply their learning.
• Collaboration. In mathematics, students and educators engage with others productively, respectfully, and critically in order to better understand ideas and problems, generate solutions, and refine their thinking.
• Communication. In mathematics, students and educators use the tools and language of mathematics to describe their thinking and to understand the world. They use mathematical vocabulary, symbols, conventions, and representations to make meaning, express a point of view, and make convincing and compelling arguments in a variety of ways, including multimodally; for example, using combinations of oral, visual, textual, and gestural communication.
• Global Citizenship and Sustainability. In mathematics, students and educators recognize and appreciate multiple ways of knowing, doing, and learning, and value different perspectives. They recognize how mathematics is used in all walks of life and how engaged citizens can use it as a tool to raise awareness and generate solutions for various political, environmental, social, and economic issues.
• Digital Literacy. In mathematics, students and educators learn to be discerning users of technology. They select when and how to use tools to understand and model real-life situations, predict outcomes, and solve problems, and they assess and evaluate the reasonableness of their results.

Transferable skills can be developed through the effective implementation of high-impact instructional strategies. More information can be found in “Transferable Skills”.