The Importance of Algebraic Understanding in Elementary Grades

By Sarah Alejandro

As Elementary teachers, it is our responsibility to give our students a solid foundation in all subjects so that they can develop a better understanding when they get to the higher grade levels. In mathematics, there are process standards set in place that guide students to think about mathematics content. These standards are set for every grade level so that students are able to become “successful problem solvers and use mathematics efficiently and effectively in daily life”. For instance, let’s focus on algebra. After all, algebra is the “language through which we describe patterns" (Algebra 1). This definition is similar to the process standard that expects students to “analyze mathematical relationships to connect and communicate mathematical ideas”.

In order to promote opportunities for algebraic thinking, teachers should “algebrafy” their activities. The term “algebrafy” comes from strategy that aims for teachers to use “algebraic thinking as part of their normal instruction" (Blanton & Kaput, 2003, p. 70). This can be done in grades k-12 but I would like to focus on elementary grades since it can sometimes be overshadowed. Consider the following problem that is typical of a problem found in a first grade textbook:

An octopus has 8 legs. Barry counted 2 octopi in the tank. How many legs are there?

This problem could be considered a STEM problem because the student is becoming a scientist and learning about animal characteristics as well as becoming a mathematician and figuring out how many legs there are in the tank. There are several mathematical process standards but let's focus on just two process standards. Students are expected to be able to learn multiples strategies for solving problems as well as help them understand to make connections between topics and foster deeper understanding of math concepts (TEKS). The modified problem would be the following.


An octopus has 8 legs. Barry counted 2 octopi in the tank. How many legs are there? How many octopi would be in the tank if Barry saw 3 octopi in the tank? 4 octopi? 10 octopi? Fill in the table showing your process and the number of legs in the tank.

Example of Possible Student Work: 

Number of Octopus/Octopi	Number of Legs
1	8
2	16
3	24

By having the students show their work, it encourages them to think of different strategies to solve the problem such as drawing or repeated addition. Students would be able to bounce ideas off of one another if they were to do this is pairs. Not only would they be able to learn different strategies from their partner but also see the pattern. Students could see that every time they are adding an octopus, they are also adding 8 legs. They would be able to see this in the table they are filling in.We can connect this problem to the idea of multiplication by asking the students what they noticed about the strategy they used such as a pattern. Having students look at both types of strategies, a discussion can be made about the steps they did to find the solution which can lead into repeated addition. This can help lay the foundation for lessons on repeated addition, or multiplication.

Mathematics is a stepping-stone process and students need a firm foundation. According to an article, What Does Good Math Instruction Look Like? by Nancy Protheroe, elementary grades are when children develop mathematical beliefs and a firm foundation for learning to investigate and find solutions to problems. This is why algebraic thinking is important to teach in all grades especially elementary grades.

"The foundation for K-12 mathematics is laid in the early years of elementary school. To succeed in college, this foundation must be solid"(Wilson 2014).  

Algebra 1- Algebra I. (n.d.). Retrieved February 23, 2015, from https://www.khanacademy.org/math/algebra

Blanton, M.L, & Kaput, J. (2003). Developing Elementary Teachers' "Algebra Eyes and Ears". Teaching Children Mathematics, 10 (2), 70-77.

Octopus picture taken from: http://images.clipartpanda.com/cute-octopus-clipart-OCTOPUS3.jpg

Wilson, W. S. (2014). Elementary School Mathematics Priorities. 1-10. Retrieved February 25, 2015, from http://www.math.jhu.edu/~wsw/papers2/education/14b-elem-math-priorities-preferred-09.pdf