section_path: Applications/Education
section_name: Education
paragraph_text: Education
  
  Algebra education mostly focuses on elementary algebra, which is one of the reasons why elementary algebra is also called school algebra. It is usually not introduced until secondary education since it requires mastery of the fundamentals of arithmetic while posing new cognitive challenges associated with abstract reasoning and generalization. It aims to familiarize students with the formal side of mathematics by helping them understand mathematical symbolism, for example, how variables can be used to represent unknown quantities. An additional difficulty for students lies in the fact that, unlike arithmetic calculations, algebraic expressions are often difficult to solve directly. Instead, students need to learn how to transform them according to certain laws, often with the goal of determining an unknown quantity.
  
  Some tools to introduce students to the abstract side of algebra rely on concrete models and visualizations of equations, including geometric analogies, manipulatives like sticks or cups, and "function machines" representing equations as flow diagrams. One method uses balance scales as a pictorial approach to help students grasp basic problems of algebra. The mass of some objects on the scale is unknown and represents variables. Solving an equation corresponds to adding and removing objects on both sides in such a way that the sides stay in balance until the only object remaining on one side is the object of unknown mass. Word problems are another tool to show how algebra is applied to real-life situations. For example, students may be presented with a situation in which Naomi's brother has twice as many apples as Naomi. Given that both together have twelve apples, students are then asked to find an algebraic equation that describes this situation (2 x + x = 12 {\displaystyle 2x+x=12}) and to determine how many apples Naomi has (x = 4 {\displaystyle x=4}).