# Algebraic Reasoning

Understanding patterns is an integral part of developing Algebraic Reasoning. It is an essential mathematical skill introduced in the early years of learning and continues to play an increasingly important role through grades 4 to 9.

Two big ideas within algebraic reasoning point to the importance of allowing students to analyze patterns, form generalizations and record those generalizations using variables, algebraic expressions, and equations to represent relations.

Algebraic reasoning allows for the exploration of the structure of mathematics. There is a vital importance of including algebraic reasoning in mathematics instructions from a very young age so that ideas are accessible to all students.

All students have the capacity to think algebraically because algebraic reasoning is essentially the way humans interact with the world. Patterns are recognized and then generalized from familiar to unfamiliar situations. Daily, algebraic reasoning can be found in many instances. For example, comparing which internet provider offers a better contract or determining times and distances when going on a road trip. Many careers are also centred around algebraic reasoning, including software developers, architects, construction workers, and bankers.

Algebraic reasoning is about describing patterns of relationships among quantities as opposed to arithmetic. In a broad sense, algebraic reasoning is about generalizing mathematical ideas and identifying mathematical structures.

Most mathematics curriculums formally introduce algebra in the late junior grades, but experts agree that it should be fostered and nurtured right from Kindergarten. It is often thought of as being only symbolic manipulation and taught to students only in secondary grades. But more educators now agree that students should develop algebraic understanding before they are introduced to symbolic manipulation.

One of the easiest ways to think of algebraic reasoning is based on the ability to notice patterns and generalize them. It is the language that allows generalizations to be expressed in a mathematical way.

## Algebra is a Language

Students who are not as interested in mathematics may be surprised to know that proportional reasoning can be helpful in other subject areas such as science, music, and geography. It is also evident in everyday activities. On a daily basis, people use proportional reasoning to calculate taxes, investments, best deals at the stores, or even to adjust recipes.

The ability to reason and think proportionally is a critical factor in developing an individual’s ability to understand mathematics. While students may have memorized how to solve a proportion problem, this does not mean they can think proportionally.

## Learning Algebra

Research has indicated that teaching and learning algebra primarily focuses on symbolic algebra over other representations. This leads students to learn to manipulate algebraic expressions, but they do not use them as tools for meaningful communication. Most students do not seem to acquire any real sense of algebra and often give up understanding it fully.

Due to this gap in learning, it has been suggested that students be given meaningful experiences in algebra learning. This may include the exploration of multiple representations of concepts. Some educational professionals also suggest that the traditional approach to teaching algebra be reversed. This would mean that visual and graphical representation and problem-based contexts would be introduced first, followed by symbolic representation and decontextualized manipulation.

Many students struggle with algebraic reasoning, not understanding that it is simply the way it is being taught. With Dropkick Math, we use interactive tools that allow students to learn algebra easier and help them fully understand one of the four main pillars of mathematics. Students can learn not only to calculate problems but will also understand how the calculations work. Get started today by filling out our FREE online Early Indicators Check-In.

## FAQ

Algebraic reasoning is a way of thinking that allows students to see patterns and relationships in equations and to make generalizations about those relationships. It allows students to use variables and algebraic expressions to represent relations, making solving problems easier.

No. Algebraic reasoning refers to the process of solving equations and analyzing patterns, while algebra 2 is the more advanced study of equations and properties of equations. In Canada, we do not study algebra 2.

The three strands of algebraic reasoning are pattern analysis, generalization, and equation representation.