# Mathematics (2020)

## The Importance and Beauty of Mathematics

Mathematics is integral to every aspect of daily life – social, economic, cultural, and environmental. It is part of the story of human history. People around the world have used and continue to use mathematical knowledge, skills, and attitudes to make sense of the world around them and develop new mathematical thinking and appreciation for mathematics. The relationships between cultures and mathematics are conceptualized and practiced in many different ways across many different contexts. From counting systems, measurement, and calculation to arithmetic, geometry, and spatial sense, mathematics has been evident in the daily lives of people across history.

Today, mathematics continues to be found all around us. For example, mathematics can be found in medicine, sports performance analysis, navigation systems, electronic music production, computer gaming, quantum physics, fashion design, and so much more. Mathematics skills are necessary when we buy goods and services online, complete our taxes, create art, and play sports. Mathematics also exists in nature, storytelling, puzzles, and games. Proficiency with mathematical ideas is needed for many careers, including but not limited to engineering, health care and medicine, computer science, finance, landscape design, architecture, agriculture, the arts, the culinary arts, and many skilled trades. In fact, in every field of pursuit, the analytical, problem-solving, critical-thinking, and creative-thinking skills that students develop through the study of mathematics are evident. In the modern age of evolving technologies, artificial intelligence, and access to vast sources of information and big data, knowing how to navigate, interpret, analyse, reason, evaluate, and problem solve is foundational to everyday life.

While mathematics can be understood as a way of studying and understanding structure, order, and relationships, the aesthetics of mathematics have also motivated the development of new mathematical thinking. The power of mathematics is evident in the connections between seemingly abstract mathematical ideas. The applications of mathematics have often yielded fascinating representations and results. The beauty in mathematics can be found in the process of deriving elegant and succinct approaches to resolving problems. Other times, messy problems and seeming chaos may culminate in beautiful, sometimes surprising, results that are both simple and generalizable. Most important, the beauty of mathematics is experienced when exciting breakthroughs in problem solving are made and an air of relief and awe is enjoyed. The two aspects of mathematics, aesthetics and application, are deeply interconnected.

The Ontario mathematics curriculum strives to equip all students with the knowledge, skills, and habits of mind that are essential to understanding and enjoying the importance and beauty of mathematics.

Learning in the mathematics curriculum begins with a focus on the fundamental concepts and foundational skills. This leads to an understanding of mathematical structures, operations, processes, and language that provides students with the means necessary for reasoning, justifying conclusions, and expressing and communicating mathematical ideas clearly. Through relevant and meaningful learning opportunities and through the strategic use of technology, all students are supported as they learn and apply mathematical concepts and skills within and across strands and other subject areas.

The Ontario mathematics curriculum helps establish an inclusive mathematical learning community where all students are invited to experience the living practice of mathematics, to work through challenges, and to find success and beauty in problem solving. As students engage with the curriculum, they may incorporate their prior experience and existing mathematical understanding, and then integrate the new ideas they learn into their daily lives. As all students see themselves reflected in what is taught and how it is taught, they begin to view themselves as competent and confident mathematics learners. As a result, they develop improved mathematical knowledge, concepts, and skills as well as an improved sense of mathematical agency and identity. This encouragement of mathematical confidence subsequently opens doors for all students to explore the importance and beauty of mathematics while they make connections to other subjects, explore the world, and later pursue further studies.