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Algebra learning benefits

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This page lists benefits of learning the subject algebra. In other words, it tries to answer the question Why should I learn algebra? |See all pages on the benefits of learning specific subjects
This page is about the benefits of learning basic algebra as taught in middle school and high school. For the benefits of learning linear algebra, see linear algebra learning benefits, and for the benefits of learning abstract algebra, see abstract algebra learning benefits.

Algebra (beginning with prealgebra in middle school and continuing to algebra in high school) is a foundational mathematical topic with widespread applicability. The following are some key ideas of algebra:

  1. The idea of using letters to represent unknowns (variables) and reason about them without knowing their true values.
  2. The concept of general algebraic rules (also known as identities) that can be applied even when some values are not known.
  3. Conversion between verbal statements and symbolic expressions.
  4. The idea of using strategies to store and manipulate equations to reveal information about variables.

(1) and (2) can be thought of as the conceptual side of algebra and (3) and (4) can be thought of as the computational side of algebra. However, this is not a clear-cut distinction.

Benefits within mathematics

All of mathematics in high school and beyond, including trigonometry, precalculus, single-variable calculus, multivariable calculus, linear algebra, and upper-division undergraduate mathematics, involves reasoning with general types of objects. The use of letters to denote unknowns and reason about them is crucial to formulating and discussing the rules. A deep understanding of algebra is absolutely crucial to learning most mathematics.

Note that (1) and (2) are a lot more widely useful than (3) and (4). All of mathematics uses (1) and (2). Most subdisciplines of mathematics use some version of (3) and (4). However, each subdiscipline has its own rules analogous to (3) and (4), so the rules learned in school algebra may not be that useful or necessary for that subdiscipline. But school algebra is still students' first exposure to efforts in the general category. So it is still likely to be quite useful.

Benefits outside mathematics

The use of letters to denote unknowns is common in notation of all sorts. For instance, a letter may be used to denote the population of a city, or the lifetime average of a sports player, even when the values aren't known to us. While it's not absolutely essential to be comfortable with this for day-to-day life, it does become quite helpful in making sense of data in any skilled work or study context.

The following subjects rely heavily on school algebra starting at different stages:

Subject Stage of reliance on algebra
Physics Most high school physics (including Advanced Placement physics) relies heavily on all aspects of algebra (including equation-manipulation. Higher physics relies on even more advanced mathematics.
Chemistry Most high school chemistry (including Advanced Placement chemistry) relies somewhat on algebra. This is in particular true of quantitative physical chemistry. Example topics are stoichiometry, kinetics, and equilibrium.
Biology Algebra shows up somewhat in high school biology (including Advanced Placement biology). It shows up more in college biology. For instance, basic algebra is used quite a bit in genetics.
Economics Some parts of high school economics (including Advanced Placement economics) use algebra. The reliance is more on the qualitative ideas (points (1) and (2) in the list) rather than on manipulation skills (points (3) and (4) in the list).
Other social sciences Algebra shows up in the experimental social sciences (studied in college) because of its necessity in understanding functions in general (precalculus material) and in statistics.
Computer science Variables are very important in computer programming, but the idea of variable as used in computer programming differs subtly from the idea as used in mathematics, so the transfer of learning must be done subtly.
Advanced theoretical computer science, including theory of computation and analysis of algorithms, rely very heavily on algebra.
Statistics Statistics is concerned with distributions of random variables. It builds heavily on algebra, conceptually and computationally.

Benefits of accelerated learning

A number of mathematics educators and mathematicians have claimed that learning algebra earlier confers significant benefits for people who are intellectually capable of doing so. In particular, people have argued that (1) and (2) (the use of letters for unknowns and the concept of algebraic rules) can be learned early on, even before people learn the formal rules for converting word problems to equations and for equation-solving. The following are some discussions of early algebra learning: