In the world of mathematics education, certain language choices can have a significant impact on students’ understanding and comprehension. One such choice that often leads to confusion among students is the use of the word “times” when teaching multiplication.
The problem arises from the ambiguity of the word “times” itself. In everyday language, we often use it to mean “repeated addition” or “groups of.” For example, if we say “3 times 4,” it can be interpreted as “3 groups of 4” or “3 repeated additions of 4.” While this interpretation serves well in simple cases, it can create a conceptual barrier for students when dealing with more complex multiplication problems.
When students are taught that “3 times 4” means “3 groups of 4,” they may struggle to transition to more abstract representations of multiplication. As they progress to larger numbers and begin working with variables, stating multiplication problems solely in terms of “times” can hinder their ability to generalize and apply mathematical concepts.
One common misconception that arises from this confusion is the belief that all multiplication problems involve “groups.” Students may incorrectly assume that the concept of multiplication is limited to situations where items are arranged in equal groups. This can lead to difficulties in understanding the associative and distributive properties of multiplication, as well as the concept of multiplying fractions or decimals.
To prevent this confusion, educators should strive to introduce multiple representations of multiplication from the early stages of learning. This includes emphasizing the use of symbols such as “x” or “•” to denote multiplication, as well as using phrases like “multiply by” or “multiply with” instead of solely relying on the word “times.” By exposing students to different ways of expressing multiplication, they can develop a more flexible understanding of the concept.
Moreover, teachers should incorporate real-world contexts into multiplication lessons to help students see the broader applicability of this operation. For instance, instead of presenting a problem as “3 times 4,” teachers can frame it as “If you have 3 bags of candy, with each bag containing 4 pieces, how many pieces do you have in total?” This approach helps students connect multiplication to situations beyond just grouping or repeated addition.
In conclusion, the use of the word “times” when teaching multiplication can indeed confuse students. By introducing alternative expressions and providing meaningful contexts, educators can help students develop a deeper understanding of multiplication. Empowering students with a flexible mental schema for multiplication is crucial in their mathematical journey and lays a solid foundation for their future mathematical exploration.
