Student error often comes as a result of inattention to the differences between the knowledge they now acquire with the one they had prior to. Before students come into contact with new knowledge, it is an indisputable fact that they have a prior knowledge which is either related to it or not. Basically they have got a foundation on which they begin building on the new concepts and ideas that they are now being taught. They come to the classroom with these delusions and that any new modifications will unsettle what they already know.
Mathematics teachers need to always try to stress the links between the prior and new knowledge so as to bring about a smooth transition of knowledge. The teachers ought to map out the requirements, in terms of materials and background information, for a particular lesson and explain to students the connection between the two extremes as well as outlining the importance of the two. Getting rid of these delusions cannot be realized by simply re-teaching the class or providing additional tuition. Pointing out to the learners where they get it wrong or where they can improve their knowledge will neither help. Identifying the misapprehensions among the learners and instantaneously zeroing in on a deliberate dialogue on it will prove to be a vital solution. Giving leading inquiries by employing an all round way of thinking is a preeminent answer.
Both students and teachers equally contribute to the many misconceptions in mathematics. For instance in a maiden lesson they both perceive it as a fresh start to education in mathematical studies while the students are intrinsically aware that they possess prior knowledge and understanding. However some of this understanding is flawed and inappropriate. Moreover some learners hold detrimental principles regarding the study of mathematics as one of the pillars in gaining literacy. Using a teaching standpoint that encompasses indulging the learners to assist them identify erroneous understanding and deep held foregone conclusions would go a long way in halting these barriers sooner than hampering excellent education. Furthermore it is evident that the learners usually synthesize what they are taught in class to generate individualized significance. These deliberate actions to develop a framework for learning provides not a single chance to realize a great comprehension but for incomprehension as well.
Teaching mathematics at all levels of learning regularly involves a lecture hall, learning room or laboratory tutoring in which the educator is regarded as a specialist in the field and the learners assumed to be acquiring the know-how. Flaws like this end up mystifying and annoying both the learners and the educators. Moreover, the learners’ stage of familiarity with mathematics and their attitudes to studying contribute to their uptake of new information and concepts as well as the impetus to work hard.
Instructional activities in mathematics also contribute to the errors and misconceptions. Most lessons in mathematics are challenging with regards to the quantity of concepts that must be grasped and that there is a short or no time allocated to scrutinize the learning process. The connection linking the learners’ knowledge with the lesson’s components can be unsuitable in many ways.
It is a usual belief that students are prone to get the wrong idea about the teaching due to their inaccessibility to proper tools to identify mistakes but as comprehension rises, confusion happens at profound points for example the amateur to the expert. Good acquisition of knowledge necessitates an opportunity to study and to incorporate the prior knowledge with the new one as well as evaluating its reliability and significance.