Introduction To Mathematics
Mathematics plays an important role in everyday life. The process of solving problems in most aspects of life involves mathematical skills and is embedded in the history of humankind. All cultures have used and continue to use mathematical knowledge and competencies in making sense of their environment. Mathematical values and habits of mind transcend numbers and symbols to help people connect, create, communicate, visualize, and reason as part of the complex process of problem solving. These habits of mind provide a needed framework for analyzing novel and complex problems from multiple perspectives, generating possible solutions, and testing the viability of solutions. Math habits of mind, developed early in life, enable the appreciation of the mathematics in the world around us and generate confidence in our ability to solve everyday problems with no doubt or fear of math.
The observation, learning, and practicing of mathematical thinking provide a means for making sense of our surroundings. For instance, the use of puzzles and games to investigate the logic of mathematics can build a constructive mathematical disposition and a self-motivated and confident student with unique and individualized mathematical insights. Whether students choose a deeper or broader study in mathematics, the design of the Mathematics curriculum ensures that they are able to pursue their individual interests and passions while establishing a strong mathematical foundation.
Big Ideas
1. Mathematical relationships can be generalized and represented in multiple connected forms. This includes linear, quadratic, rational, trigonometric, and calculus-based relationships. Algebra, graphs, tables, and symbolic rules all provide models to describe patterns and change.
2. Operations with numbers extend to more abstract structures. The principles governing whole numbers apply to rational numbers, powers, radicals, polynomials, and beyond. Fluency with operations grows from concrete arithmetic to symbolic manipulation.
3. Proportional reasoning is foundational across mathematics. It underlies ratios, rates, fractions, similarity, trigonometry, and many modelling contexts, enabling indirect measurement and comparison.
4. Geometry and measurement describe spatial relationships. Properties such as similarity, surface area, volume, and trigonometric ratios allow us to measure, compare, and reason about shapes in two and three dimensions.
5. Data analysis helps us interpret and make decisions from information. Understanding averages, variability, and representation helps us evaluate reliability and draw meaningful comparisons.
