I recently started giving maths lessons and it seems like I am at my wits end. My own background is: I'm a masters student in physics, already did several tutorials for younger students, especially for a course on mathematical methods in physics. Of course, some years ago when going to school myself, I was helping some of my friends with school maths, so teaching school maths is also not entirely new to me.
However the current situation really gives me a headache. The pupil is going to 8th grade, the current topics are simple systems of two linear equations in two variables and the intuitive methods of solving them. The problem which I and the pupil are facing is however another one: She really has a hard time doing simple calculations with numbers, multiplying, dividing, working with fractions. It is not a problem of understanding. Given a big amount of time she can do all the calculation using long division and multiplication.
However she is entirely missing what I would call "intuition for numbers", i.e. she doesn't see if one number is a multiple of another (i.e. she doesn't notice that 8/4 can be simplified to 2), she doesn't know the most useful fraction to decimal fraction conversions (i.e. 1/4=0.25). She knows the 10x10 multiplication table in principle, but it takes a huge amount of time till she recalls the result. Sometimes she even needs some seconds to calculate 2x3=6.
You can imagine that it is very hard teaching new topics in such a situation. A week ago we discussed the methods for solving systems of linear equations and I intentionally gave only examples with small coefficients and such that no fractions appeared at all. The result was that she understood the topic very well and could solve such exercises. However, if in an exam she encounters exercises with higher numbers or examples where fractions will pop up during the calculations, she again won't be able to solve them.
And now I'm really stuck and don't know how to proceed. Make her learning the multiplication table by heart? But she already knows it, sort of. However, doing operations with numbers in her head just doesn't work properly. Returning to standard exercises from 6th and 7th grade? Takes a huge amount of time and doesn't really solve the actual problem since the exercises will be diluted with other concepts which are not of importance now.
Thanks for any hint, Michael