Cross-Curricular and Integrated Learning in Mathematics
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 the learning in many other subject areas. By purposefully drawing connections across all areas of mathematics and to 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 Spatial Sense, 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 or preparing a mixture or solutions.
Similarly, algebraic reasoning is applied beyond the Algebra strand. For example, it is applied in measurement when learning about formulas, such as area of a parallelogram = base × height. 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, planning their move to the basketball hoop, and using diagonal and converging lines to create perspective drawing in visual art. 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.
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 between mathematics and other subject areas, and among the strands of the mathematics curriculum;
- improve their ability to provide multiple responses to a problem;
- debate and test whether responses 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 knowledge of other subject matter to enhance their learning of and engagement in mathematics. More information about integrating learning across the curriculum can be found in “Cross-Curricular and Integrated Learning”.