Algebra’s X-Factor: Why It Is Difficult To Learn Algebra
A comic strip from Maths 360 Secondary 2 textbook explains the use of algebraic terms, p67
It can be argued that learning algebra is akin to learning a new language. Language in itself is the combination of symbols (such as the alphabet) to express and communicate a coherent idea and message. Algebra, similarly, uses a new set of symbolic notation to communicate Mathematical expressions, introducing alphabetical letters to represent variables in a calculation. Juxtapose this to arithmetic, which is about the absolute computation of specific numbers.
To the student, algebra is an entirely new concept. It represents their first foray away from mainstream Mathematics. It is their first departure from arithmetic. Not surprisingly, there has been considerable resistance by students when it comes to learning algebra. Most fail to see its practical purpose, saying that it “has no real use in daily life”. “I’m not going to use algebra when I’m washing the dishes or when I’m playing football,” said one secondary school student. Further up in junior college, another student said, “It won’t be relevant to what I want to study in university or my future job for that matter.”
In these casual, preliminary assessment of attitudes towards algebra, we see a skew towards dismissing algebra for its lack of real-world applications. There are, however, more latent and intrinsic problems in the study of algebra. Teachers across the country, and abroad, have reported students from primary to secondary school or throughout grade school with difficulties in grasping the fundamentals of algebra.
In order to help our students cope with the learning of algebra, let’s shift our focus to the following 3 possible reasons that hinder their understanding when learning algebra:
(1) Abstract nature of algebra
With algebra, students have to visualise multiple possible answers for a given algebraic expression. Where “24 + 7 = 31” used to be the brand of calculation students would work with every day in school, they now have to contend with a new approach to Mathematical expression.
Now, they have “24a + 7b = 247” – with “a” and “b” representing an entire new dimension in calculation – one in which identifying the algebraic expressions of “a” and “b” can be a range of numbers, inclusive of both integers and rational numbers, as well as rational and irrational or complex numbers. Where arithmetic uses real numbers to find an absolute answer, algebra uses symbolic notation to represent the wide Mathematical possibilities of an equation.
A 2004 study on algebra students by Koedinger and Nathan found that their (the students’) biggest struggle was understanding the letter symbolic form of the algebraic equations presented to them. It stated, “The language of symbolic algebra presents new demands that are not common in English or in the simpler symbolic arithmetic language of students’ past experience.” This is also the root cause of several other problems, such as difficulties in understanding the equal sign.
Extracted from Maths 360 secondary textbook, p91
(2) Difficulties understanding the equal sign
At their first exposure to algebra, most students would see the equal sign as a sort of invitation to perform calculation. When they see “3 + 4 = “, they understand it as the beginning of an addition process that ends with the expression of the number seven to close that equation. However, the equal sign is foremost a sign of equivalence, and many algebraic equations utilise it to hint at the Mathematical characteristics of its variables.
(3) Use of symbols
First-time learners find it difficult to grasp the concept of symbols used in algebra. In many ways, algebra invites a sort of reverse-engineering style of Mathematics. First-time learners of algebra tend to have difficulty in mentally approaching a problem such as “7 + x = 24”. While this is related to their difficulty in understanding the equal sign, it is also a matter of students finding the use of symbols in Mathematics rather alien. More students were able to process the equation when x is replaced with a blank (i.e., 7 + ___ = 24). While it does not take too long for students to get past these issues with algebra, it does account for a disillusionment or poor attitude towards the concept. If educators can get students to embrace the use of symbolism, and the intricacies of algebra, we might be able to produce a new generation of Mathematically inspired learners.
Second Handbook of Research on Mathematics Teaching and Learning (2007) by Frank J. Lester
Approaches to Algebra: Perspectives for Research and Teaching (1996) by Nadine Bednarz, Carolyn Kieran, Lesley Lee