Mathematics is one of the most crucial skills for a person almost anywhere in the world today. Mathematics is the bedrock for fields such as science, engineering, business, and technology. Whereas 200 years ago the main gateway skill for success in life was reading, today, math has become just as critical as reading for success in the world. Skill in mathematics translates to skill in computers and technology. But what’s the trajectory for learning mathematics? How do children grow up to learn it?
In early years, children’s mathematical learning is primarily confined to number sense. Number skills that are taken for granted in older children are noticeably absent in younger kids. While a young child may be able to mimic counting from 1 to 10, in most cases they don’t really understand what those numbers mean cours particuliers maths. Younger children typically can’t usually distinguish between groups of objects with similar numbers, such as 8 pennies versus 9 pennies. It’s actually believed that humans are born to learn with a logarthmic sense of number, meaning it’s natural for us to distinguish between 1, 2, 4, 8, etc., but not between 100 and 101. That’s a skill that has to be taught.
As kids start in school and continue through elementary school, their numerical and mathematical skills get more concrete. As we are living in a base 10 world, students spend much of their time learning arithmetic (addition, subtraction, multiplication, and division) of the base 10 number system. Most children also learn best visually at this age. That is why you will see many classrooms utilizing tools such as base 10 blocks to learn the base 10 system, manipulatives to learn fractions, and the number line to learn positive and negative numbers. Kids also start to learn geometry skills. Again, these tend to be more concrete in nature, such as learning how to measure, the names and dimensions of shapes, even tessellations.
As students move into puberty and beyond, there ability to think abstractly grows substantially. For many students, middle school is the time that abstract thinking becomes easier to grasp. For others, it’s not until high school. That’s why many schools offer kids both the opportunity to take beginning algebra either in middle school or high school. As a young person’s ability to understand the abstract grows, they can better grasp the concept of an unknown or variable. This gives them the capability to solve a variety of algebra problems such as solving equations. In American high schools, it’s common to follow first year algebra with a year of proof-based geometry. The idea is that students are now capable of more advanced logical reasoning skills necessary for proofs. While some students enjoy the experience more than others, there’s no doubt this same kind of logical reasoning is common to the sciences, computer programming, the law, and more.
As students finish high school and move into college, they take a variety of paths with their mathematical “careers.” While some may only have to take a single general education math course, many others start learning a specific set of skills focused on their career. This could be anything from the advanced calculus and differential equations of engineering to the statistics necessary for a business career. Regardless of which direction they go, students will build on their early foundations of number sense, geometry, and abstract reasoning skills.