Student error, student and teacher misconceptions and instructional activities are interrelated in mathematics instructions.
Student error
Confidence; most students make mathematical mistakes because they feel too confident with the exams that have been done previously. Other students make mathematical errors because they do the tests in a hurry; this is done by the student wanting to do the test quickly and get the highest marks or grade possible. Other problems arise because the student read only and don’t do the practicals. Researchers recommend that the student should 20% and do 80% practice. Anyway isn’t it said that practice, practice makes perfect? Inaccuracy is another factor that leads to mathematical errors by students.
Some other problems result from the misinterpretations that the student has according to his experience. A number of students tend to think that multiplication always gives a bigger number. It may be no wonder that a student as such encounter 3+ (-8) and while some would give the as 11, some would give as -5.
Student misconceptions
Students sometimes make their own theories of which are sometimes called ‘naive theories’. These theories help them greatly in their studies. Unfortunately, some of these self-styled theories are semi-truths. These misconceptions are terrible for the wellbeing of the students because: they mess with the education since the students use them to understand new learning; and then, the learners (students) become connected to the misconceptions both in their intelligence or their emotions. An example of a misconception that is often construed by Anglo students is “Write an equation using the variables S and P to represent the following statement: “…There are six times as many students as professors at a certain university.” Use “S” for the number of students and “P” for the number of professors.”Instead of writing the answer as S=6P, a good number of students write 6S=P. Similarly, some student of Hispanic origin use their misconceptions and mostly write the above quiz as 6S=6P.
Teacher misconceptions
Mostly in the Western countries, teachers view some learners with misconceptions when they are in their young stage of learning. There are various such misconceptions like: only very clever children who have the mathematical genes can take the mathematics subject; small children are not yet ready to take the mathematics subjects; the knowledge of English is vital when learning Mathematics; when kids are learning Mathematics, mere figures and numbers are enough; Mathematics should be taught not on its own but together with another subject; the computers and other gadgets are not important when teaching mathematics; Mathematics is not of any application to kids; and that the teachers that are teaching the kids should be offered an enhanced physical atmosphere. One of the setbacks of these misconceptions is that they mess up with not only understanding but also construing the proposals that are required for the young learners in their learning classrooms (Douglas, 1992).
Instructional activities
The instructors use varying examining skills such as group discussions, investigative instructions, direct instructions and other types of personal formats. The learners gain much from the subject of Mathematics if they are educated on how they can use the Mathematical skills when they are solving the Mathematical questions. The students being in the examination room may opt to tackle the Mathematical questions when they have a small range of further clues and it may not be necessarily wait to gather further clues.
When there are instructions that are well set for the students, the students will gain the skills in no time and make much adaptive simplification than they would have if the instructions were poor. Good instructions have got two factors: the arrangement of content and the appearance of the content. Therefore the students are required to acquire skills that in the tackling of mathematical problems so that they can use them in solving varying problems in the context.
Reference
Douglas, G. (1992). Handbook of research on mathematics teaching and learning. New York: Macmillan.