Algebraic Reasoning

Understanding patterns is an essential part of algebraic reasoning and a skill that should be nurtured from the early years of learning. These skills form the backbone of algebraic thinking, allowing children to recognize relationships in numbers and figures. As they progress through grades 4 to 9, algebra starts to become increasingly important – algebraic reasoning can help them make sense of more complex math problems and draw correlations between their results. With this understanding, students can connect disparate elements and uncover deeper meanings within mathematical expressions.

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

How We Interact With The World

All students can think algebraically because algebraic reasoning is essentially how 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.

Algebraic reasoning is essential for many successful careers. Without algebra, critical decisions that must be made in a variety of different occupations would be near impossible.

Such careers include software developers and architects, who use algebra to create plans, designs and constructions. Construction workers also utilize algebraic skills to measure materials lengths and quantity of items required accurately. Similarly, bankers apply algebraic principles to make investments or determine financial risk and creditworthiness. In every case, algebra helps ensure accuracy—and thus success—in any field.

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Algebraic Reasoning

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 algebra curriculums are generally introduced in the later years of elementary school. However, algebraic reasoning is something that should be encouraged from early on.

Research suggests that kids learn best when given the opportunity to explore and engage with algebraic activities, so it’s clear that starting early is beneficial for their development. Investing in algebra knowledge at a young age can set kids up for success and help them gain confidence as they progress through their studies.

Children naturally love 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 toward algebraic thinking.

Algebraic reasoning 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.

Surprisingly, algebraic reasoning can be helpful in subjects ranging from literary analysis to life skills. Algebra teaches us how to identify patterns and interpret data, which are transferable skills that can help us look for trends or insights in any circumstance.

After all, algebraic reasoning uses logical steps and invites critical thinking skills that can apply to multiple disciplines. In fact, algebraic reasoning can unlock new understandings of reading texts, scientific inquiries, or humanities theories; the possibilities are endless. Knowing how algebra intersects with the rest of a student’s academic endeavours can open doors to greater success and interesting advancements in learning.

Learning Algebra

Developing algebraic reasoning is essential in today’s mathematical world and forms the foundation of higher math. It is not a one-time event but a process that can be imparted to students through an engaging, positive school mathematics experience.

This experience can be further enriched if algebraic reasoning is appropriately taught by qualified educators and practiced with enthusiasm, working to ensure educational equity so that all students have access to this important learning.

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.

At Dropkick Math Academy, our certified Ontario teachers provide an understanding of algebraic reasoning so it can become a vital part of every learner’s skillset, further deepening their understanding of mathematics and its relevance.

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 reversing the traditional approach to teaching algebra. 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 Academy, 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.


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.