# Understanding Algebraic Reasoning Algebraic reasoning focuses on patterns, functions, and the ability to analyze situations with the help of symbols. It involves generalizing, representing, and formalizing patterns and regularity in all aspects of mathematics.

Algebraic reasoning is introduced in the early grades and can help children develop the ability to learn proficiency using equations, functions, and variables. This can be done by assisting them in exploring different concepts through fun, simple, but thought-stimulating activities. It is never too early to begin teaching the foundations of algebraic reasoning for young learners.

## How Children Explore Algebra

Much of math, especially algebra, is based on patterns. Younger students can begin looking for patterns all around them as a great introduction to algebraic reasoning. Many teachers like to give students exercises that include manipulatives such as pattern blocks, buttons, keys, and coloured cubes so that students can create patterns on their desks with these materials.

Functions are also a big part of algebra. Younger students start by learning functions with input and output. An excellent way for children to learn about function is with a calculator. Teachers will show students how to turn a simple calculator into a function machine. Students are often asked to program their calculators with a function and see if classmates can guess it by viewing the outputs.

In algebra, x is often used to represent an unknown. Younger students start to work with a symbol (like a box or open square) for a variable (x), and letters representing the variable are introduced in grade 6. Algebraic reasoning becomes easier for many students to understand by making fun and interactive games. For example, students may be given three clues to help figure out the mysterious “x.” x+1=3, x+0=2, and 4-x=2. What is x? (answer: x=2)

In algebraic reasoning, students need to learn that the equal sign means “the same as”  when reading number sentences and later algebraic equations. Younger students often get confused and think that the “=” means “the answer is.” By learning the proper use of the = in algebraic reasoning, students will have a reinforced idea of balancing equations because each side has the same quantity. It can also develop their understanding of equality which is a BIG IDEA in algebraic reasoning.

## Algebraic Symbols

Using algebraic symbols is a large part of becoming proficient in applying algebra to solve problems. But, understanding abstract symbolism without a foundation of the operational sense is likely to lead to frustration and failure. Children have a natural love of mathematics at an early age, and it is vital to foster this admiration. Their curiosity is a strong motivator as they try to describe and extend patterns of shapes, sounds, colours, and eventually letters and numbers. Children can begin to make generalizations about patterns that seem to be the same or different, and this kind of categorizing and generalizing is an essential developmental step on the journey towards algebraic thinking.

## Recognizing Patterns

Through elementary grades, patterns are not only the subject of study but can also be used as a tool. Students can use patterns to help them recognize numbers as they develop their understanding of mathematics. As they explore and understand addition, subtraction, multiplication, and division, they can look for patterns that help them learn procedures and facts. Patterns in rows and columns of objects or patterns within multiplication tables are interesting to children and can help them discover their facts and understand relationships among facts.

## The Development of Algebraic Reasoning

The development of algebraic reasoning is a process, not an event. It is something that can be part of a motivating, positive, and enriching school mathematics experience if appropriately taught. At Dropkick Math, we understand that algebraic reasoning is part of exploring the structure of mathematics. The ability to reason and think proportionately is a critical factor in developing a student’s ability to understand mathematics. However, many students do not seem to grasp any real sense of algebra and often give up understanding it fully.

Due to this education gap, it has been suggested that students be given meaningful experiences in algebraic learning. But before you start thinking, “is there a math tutor near me?” it is essential to understand the way that children learn. Many students struggle with algebraic reasoning and realizing that this may be a result of the way it is being taught to them. With Dropkick Math, we use interactive tools that allow students to learn algebra easily and help them fully understand it as one of the four main pillars of mathematics.

The ability for everyone to enjoy math is why Dropkick Math doesn’t just want to tutor your child. We want to help the family better understand how math works and fill in any educational gaps in learning. Get started today by learning more about our programs and if they are the right fit for your child.