There were a few cases in my over 10 years of tutoring math that I just could not boost my student's math marks higher and I have spent some time to observe them and compared why some of my students could pull their marks higher in a few months of tutoring but not others. I concluded that there are some conditions with those students who could not get their marks higher and if they improve on these conditions then they perhaps could also enjoy higher math marks. The problems impede students from getting higher math marks despite my tremendous efforts in trying to help them are list as follows:
1. No motivation to learn
Students have to be pushed to do work. These type of students always ask questions about uselessness of learning math such as what is the use to learn all these trinomial factoring when in fact they will perhaps never use it in their real life?
2. Can not follow steps
Concepts are taught to student but they do not seem to be able to follow the algorithm and steps on how do solve problems. Problems are done in "piece-meal" fashion. For example, student cannot find the quotient using mental math instead a separate vertical multiplication needs to be done to find it. The solving equation can not be carried out from left to right, instead a separate calculation is done on each expression so simple problem has taken the student the whole sheet to just get one equation solved. I do not know if this happens is because their teacher did not work out the problem on the board and explain clearly so the student ends up doing problems on piece by piece fashion. For example x + 3 (x-2) = 3 (x-9), the students can not do smoothly from to left, instead the student would write a few not connected steps to figure out each expression first and then assemble them together.
3. "I don't know" attitude
The student keeps on saying "I don't know" when asked to do work. They are not able to point out where they do not know or why they are do not understanding.
4. Do not even try to remember
The students seem to be so forgetful and constantly need to be reminded on whatever has been taught. The students will completely lose direction if they do not even bother to remember the identity of sine square plus cosine square is 1 since they will not have the second nature to do proof or see the way on how to do them.
5. Never master the basics
Some grade 5 or even grade 10 students never mastered the times table or still need to use fingers or skip counts to get answers then they will have problems to do factoring or trinomial factoring using cross-multiplication method since their mental math ability is too weak. So even problem like 2 to the power of 4 times 4 to the power of 2 will lose them since they cannot "see" the base 4 can be changed to base 2 and then add the exponents together to get answers.
6. Leave all notes behind
I have students who will collect all notes I used to teach them but on the other hand I also see some students leave all my written notes behind and never collect them. Don't they want to review those important points to help them in the exam? Of course, these notes are helpful, but it is too bad some students just do not care.
7. Cannot concentrate
Some students can't concentrate and get distracted so easily and often ask for more breaks than others to just get away from learning.
8. Do not want to practice
Complain about doing practice when in fact the student needs more practice to perfect the system and this is one of the reasons some students do not get high marks – lack of enough practice.
9. Only care about marks
Marks are important but if students only care about marks then they are not getting the real benefits, what they learn in how to solve problems and the willingness to do deep research and analyzing work will really benefit them in the future. Sometimes even a wrong answer can benefit students because if they did through study and came up with a wrong answer then their efforts are putting in and they can learn from mistakes. Sometimes quantity is important such as the amount of practice but if the quality of practice is not good as mentioned above for example, if they do not follow a good ritual to use LCM to get all the same dominator when doing rational equations then their calculations are error prone.
I have taught grade 10 or 11 students and I feel like to tell some of them to get back to grade 5 math and start the fractions all over again or go back to grade 9 and redo the trinomial factoring again but I think they perhaps will feel they are hurt psychologically so I just re-teach some concepts of fractions they should have known or ask them to do more basic trinomial factoring but I know it is not enough since by doing a handful of problems then they will forget in a few weeks of time.
I trained my students to do trinomial factoring from a couple of hundreds to a thousand by the time including all their day school work. With this amount of work, they will have the memory of lasting perhaps at least a few years.
A willingness to do work and learn and can concentrate and is willing to do practice by following some fine-tuned steps to avoid mistakes and do enough practice after through understanding, this is the way that a student to can get high marks in math. In addition, the student should have a good study habit to keep good notes and to review them before the exam time.
Without changing attitude and realizing what are the real problems for students not been able to improve marks and simply blame classroom teacher who can not teach or change tutor is not the real solution.
I hope that my points raised on why some students who could not do well math will alarm some students to change their attitude even when the are still young since math is an accumulated knowledge, something they did not do well as young as grade 3 in times tables will continue to hunt them in the later stage of learning like finding factors, GCF, LCM, products of primes, multiples, divisibility, decimal multiplication and the problem will resurface to high school when doing rational equations or using completing squares to get the standard form of parabola.
This is why it is so important that students must build a good and solid foundation even in elementary students as you as grade 1. The basic mental math ability is largely developed at this stage.
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