Students in High School Who Are Missing Fundamentals in Math

There is no question that some students in high school are missing fundamental knowledge and skills that are supposed to have before passing grade 8. Working in private high schools and tutor companies in the same time very often I come across several cases were students have significant gaps in math in their knowledge. The question how student get through and pas grade 8 that way might generate many answers, because this whole process is very complex.

I think that building a solid math framework in student knowledge requires a fair amount of work both sides, teachers and students. It looks that in certain cases there’s lack of efforts from teachers to be consistent in their teaching process and in the same time lack of preparation from the students side. On the other hand it’s possible that gaps from previous math classes may not be identified in an early stage, first from students themselves, their parents and teachers as well. Many students struggle with concepts in maths and don't know why. It happens when something in a previous math topic was missed for a reason or another and didn't make sense for them.

The question is that tiny math gaps in students in an early stage are neglected often from teachers. However these gaps carry on quickly expending until in high school we meet student who can’t use operations with fractions ore can’t use inverse operations to isolate a variable. Another reason that we see students with gaps in math in high school is that both teachers and students don’t pay attention when it comes to reviewing all math concepts until grade 8. Reviewing is a process that is supposed to be done in regular basis in order not to miss anything basic which make student to struggle in high school.

I’ve noticed from my experience that most of the students struggling with gaps from previous years can’t use operations with fractions. Some of them don’t know the rules how to add, subtract, multiply and divide too fractions. Some others know that adding and subtracting fractions they have to find the least common denominator (LCD) but struggle finding it because are not familiar to find common multiples or common factors in their head. In most severe cases I’ve experienced when students still haven't memorized the multiplication table, that won’t let them to find these factors.

Another gray area in students’ knowledge to solve a question with multiple operations (add/subtract, multiply/divide). Students in this case are not able to follow the BEDMAS order. In and expression like this
3x^2+x/2×3x-7x+(5-7x)2/3   I have seen some students subtracting 3x-7x before multiplying x/2×3x 

Almost all students with gaps in math have difficulty to use inverse operations to isolate a variable. Without having a clear concept in this area they have memorize to move terms from one side of an equation to another, in order to isolate a variable but they think that this could be applied in every case and wrongly use that when terms are multiplying. In an example like this

2y+7 ×3x= 5x  I have seen some students writing 2y+7 = 5x×3x  instead of writing
2y+21x= 5x   and then  2y= 5x-21x        

The same situation is with students who don't apply the method of cross-multiplying properly.

Another area that students have gaps is when they are able to perform arithmetic operations but they can’t perform these operations with terms containing a variable.

There are several attempts that could be done to minimize math gaps in students but the main one I think is having teachers design individual learning plans, and classroom mathematics programs that provide support especially for this range of students. Helping students fill gaps in basic knowledge start by rebuilding their foundation skills by going back to operations with multiple operations, with fractions, working with variables, etc. it’s up to the teachers to guide these students with special worksheet in order to have them complete independently several exercises related to the areas they are weak. Because math builds on prior knowledge teachers have use their tutor support services and to focus their teaching process to those particular content areas that create links in students’ knowledge. That way they could ensure a solid understanding of prior math concepts to students in order to move forward.