I'm a maths tutor, and my students/tutees are aged $11 - 18.$
Obviously I have limited time with students, usually one hour per week. Moreover, if parents don't see improvement over a year or two they will look for a better tutor which is undesirable for me.
I feel like students not knowing their basics well enough, like being quick at multiplication, addition, subtraction, division, and fractions, holds them back enormously in learning more difficult topics. Their learning speed in these difficult compound topics that requires quick arithmetic is massively reduced and this disrupts their learning of the main goals of the harder topic.
When I was a young kid of 4 - 7 years old (or something like that), my Mum used to play a cassette in the car of the times tables, and ever since, I have had instant recall, and this has been one of the main contributing factors for allowing me to learn the more difficult topics easier than others. [I am not comparing myself to others on this website, as most people here are also probably good/ quick at arithmetic. I am comparing myself to the general population]. This is because I don't get distracted from the learning goals of a topic when calculating $7\times 6$ is required to attain that unrelated, more difficult goal: my brain converts $7\times 6$ to $42$ in under a second, and I can get on with understanding the more difficult topic.
I was wondering if it was a good idea to give students - who are not quick or accurate enough at these basic calculations - tools, and a programme that if they stick to, will guarantee improvement in multiplication, arithmetic, fractions. And then only continue on the compound topics once they have proven their speed and accuracy in various tests? Then their newly-found instant recall will not stand in their way of learning harder topics, and might even give them a confidence boost in learning mathematics.
automatic-algebra has one-minute/$30$-second/$15$-second multiple choice tests on different aspects of arithmetic. But the difficulty and allotted time of the tests don't vary, and so the tests aren't very comprehensive/ are one-dimensional. However, I have tried that website with some students and some students do improve a bit with it and some students didn't improve much with it. So I was thinking of creating a website/webpage that was like that one but where, for example, either the difficulty of the questions increased, or the allotted time decreased, or a combination of both.
I was thinking of changing my tutoring to be a strict, hard-line approach: Either they improve so that:
- they can multiply any two numbers from their $9\times 9$ tables in $< 5$ seconds.
- Something similar with addition
- Then on to fractions - obviously more time is needed for this, but they should still need to do them quickly.
But I don't continue tutoring with them if they can't do the calculations within the time period.
Is this approach too hard-line?
Personally, I think it may be a good idea for almost every student who is not quick at these calculations. I just worry as to whether or not this will work. If they haven't bothered learning their times tables by now, and they are reluctant to do so with my instruction, then what? Do I sweep this under the rug and teach them harder topics anyway? I know that students can learn harder topics, but it just takes much much longer for them to be able to do exam questions quickly in these harder topics (because they don't have the instant recall of arithmetic operations), and this exam performant is very important when it comes to tutoring, as parents are more likely to fire me if the student has done poorly in exams.
Another aspect of this is that if I am too "hard-line" in this approach then the student may not like me (but the parents might)...
What do you think? Has anyone tried this approach in practise?