As students learn mathematics the understanding they get on what they are being taught can be very different from what the teachers expect. Students always get the wrong ideas of what is being taught to them. This is one of the major challenges for teachers in understanding the ideas the students come up with and deciding what to do about them. Learners are oftenly presented with the problem of making sense of their experiences, experiences from school and the outside environment and this always leads to them making mistakes (Elaydi, Titi, Saleh & Abu-Saris, 2002).
These are honest attempts to capture the essence of what they are learning. Mistakes can be divided into two; as misconceptions and as errors. Mistakes can be done through errors, hasty reasoning, loss of concentration and also when one fails to notice the importance of a problem. Sometimes however misconceptions about a topic are the reasons for these mistakes. In this case the mistake occurs because of a student having constant alternative approaches to mathematics meaning the student has not understood something about mathematics.
Sometimes the mistakes are as a result of a student over generalizing ideas while seeking a constructive meaning of their experience and because their ideas are based on partial concepts or local generalizations they end up making mistakes because they have limited knowledge. Mostly these kinds of mistakes are necessary steps in their learning process (Elaydi, Titi, Saleh & Abu-Saris, 2002). An example of a misconception is multiplication always makes things larger or that the equals sign means makes.
In some cases misconception arises from a students personal experience or from incomplete observation from teaching. Students usually attend classes fully equipped with theories they have created from their daily life experiences. Most of them are usually misconceptions. Misconceptions are a problem in two main ways; they interfere with the learning process and students are usually emotionally and intellectually connected to these misconceptions because they constructed them they only give them up reluctantly.
Repeating a lesson or trying to make it clearer usually doesnt help actually it would not be uncommon for them to return to their misconception. So simply lecturing on a particular topic will not help students give up their misconceptions. Teachers must participate actively in helping the students dismantle these misconceptions and help them construct new conceptions ideal to guide them in the future (Keeley & Rose, 2006). There are several steps involved in the drawing out of the contradictions in students and in helping the students reconstruct their concepts.
They include probing for qualitative understanding, probing for quantitative understanding and probing for conceptual understanding. Probing for a qualitative understanding usually involves asking proper placed questions then looking out for any misconception. This can point out where the students misconception stems from it could be from a linguistic confusion or from a naive misconception. An example of a question asked can be, are there more students in a school or teachers?
Such a question can lead a teacher to identify misconceptions in students and deal with them accordingly. In this process the teachers do not provide the correct answer to the students instead they let them solve the problems themselves but provide guidance and instructions that help them reach a constructive answer (Keeley & Rose, 2006). This way students use construction of concepts as a form of effective learning method. Therefore an active class discussion helps the students air their misconceptions and overcome them using the teacher as a guide.