Why Students Develop Misconceptions in Mathematics and How to Address Them
Mathematics is a language which consists of a vast number of symbols and rules and which expresses certain relationships between things. The beauty of this language lies in its precision and the fact that it is universal. It is for these reasons that mathematics is considered to be one of the fundamental sciences.
However, mathematics is often taught in a way which does not take into account the student’s prior knowledge and as a result, students can develop misconceptions about the subject. In this essay, we will explore some of the reasons why students may develop misconceptions in mathematics and some ways in which these can be addressed.
2. Inattention to prior knowledge
One of the main reasons why students develop misconceptions in mathematics is due to the fact that their prior knowledge is not taken into account by teachers. Prior knowledge plays a crucial role in learning as it helps students to make connections between new and old information (Bransford, Brown & Cocking, 2000).
If prior knowledge is not taken into account, then students may be presented with new information which contradicts what they already know. This can lead to confusion and ultimately, to misconceptions. For example, if a student has developed the misconception that addition always makes numbers bigger, then they are likely to be confused when they are presented with information which contradicts this (for example, when adding two negative numbers).
3. Students’ stage of familiarity
Another reason why students may develop misconceptions is due to their stage of familiarity with the subject matter. When students are first introduced to a new concept, they are likely to have a very simplistic understanding of it. As they become more familiar with the concept, their understanding becomes more sophisticated.
However, if students are not given the opportunity to progress through these stages of familiarity, then they may become stuck at a simplistic level of understanding. This can lead to misconceptions as well as a lack of deep understanding. For example, if a student is only ever presented with addition problems where the answer is always bigger than the two numbers being added together, then they are likely to develop the misconception that this is always the case.
4. Teacher’s instructional activities
Another reason why students may develop misconceptions is due to the way in which the concept is being taught by the teacher. If a teacher only ever uses rote learning methods (such as drilling), then students are likely to develop superficial understandings of concepts and may struggle to apply them in novel situations. This can lead to misconceptions as well as a lack of mathematical fluency.
5. Conceptual change
If a student has developed a misconception about a concept, then it can be very difficult for them to change their understanding. This is because conceptual change requires students to un-learn their current understanding and replace it with a new one (Vygotsky, 1978). This can be a very difficult process for students and often requires explicit instruction from teachers.
One way in which teachers can help students to change their misconceptions is by using worked examples. Worked examples provide students with a model which they can follow in order to solve similar problems (Sweller, 1988). By working through worked examples with their students, teachers can help them to see how their current understanding may be incorrect and how they can replace it with a new, more accurate understanding.
In conclusion, there are many reasons why students may develop misconceptions in mathematics. However, by taking into account students’ prior knowledge, their stage of familiarity with the concept and the way in which the concept is being taught, teachers can help to prevent or address these misconceptions.