One of the important elements of the scope and sequence is the intention to correct students' understanding of the equals sign, or hopefully even prevent the need for correction in the first place. For many children, the equals sign is mistakenly perceived as a directive to perform an operation, commonly interpreted as "add it up." This misunderstanding becomes evident when students encounter equations such as 5 + ? = 7. In these instances, many students mistakenly add five and seven, as they have been conditioned to see the equals sign mainly in its typical position—preceding the final result of an operation.
The Equals Sign: A Relational Symbol
What these students often miss is that the equals sign is fundamentally a symbol of balance and equivalence. It serves as a relational symbol, indicating that the quantities on either side of it are the same, or "equal." This concept is not being explicitly taught, leading children to fill in the gaps with the simplest interpretation: performing an operation.
Mathematics is fundamentally about understanding relationships. From the very beginning, children need ample opportunities to explore the relationships between quantities. This exploration should be supported with materials, images, and the use of procedures. Understanding the equals sign is crucial in this process, as it sets the foundation for more complex mathematical concepts later on.
Equality and Mathematical Relationships
The equals sign in an equation signifies a relationship of equality and balance. This understanding is foundational and integral to grasping more advanced mathematical concepts. When students comprehend this, they can also understand the relationship between the equals sign and other mathematical symbols like the less than and greater than signs.
In efforts to simplify learning, many educators resort to gimmicks, such as portraying the less than and greater than signs as "crocodile mouths." While these methods may seem helpful, they often lead to further confusion. Explicit teaching of these concepts is far more effective than relying on such gimmicks. When in doubt, clear and direct instruction is the best approach. Just tell them!
It wasn't until I wrote the scope and sequence five years ago that I truly began to reflect on the meaning of "equal." Over time, I've come to realise just how critical this foundational understanding is.
Last year, I introduced my Year 1 and 2 class to vertical algorithms. This method wasn't initially part of the scope and sequence, but it seemed a natural progression from our work on expanding larger numbers. It dawned on me then about the importance of the "equals line," reinforcing the relational aspect of equations—a simple yet often overlooked piece of knowledge.
In my current Year 1 and 2 class, most students initially perceived the equals sign as "add it up." This clearly indicates the necessity of addressing this misconception even earlier on.
By reinforcing the relational meaning of the equals sign, we can provide students with a more solid foundation in mathematics, preparing them for future learning and understanding.
By the end of last week, they were showing a great growing understanding, showing the relationship between the numerals we write and the Woodin patterns we learn.
I love this little guy when we are exploring equality, his mouth moves to show the relationship between amounts, I think this has been my best buy in many years!
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