As a private tutor, I believe strongly in the value of thinking. My students do not always appreciate that because it means I expect them to work hard.
When some students come to me for math or physics help they are so completely lost that I have to take them back to material they were presented with earlier in the school year or even further back to topics from previous years. The parents always appreciate this but the students often wish that I would simply help them with their homework so that they can delude themselves into believing that they are keeping up with what they are supposed to be learning in class.
On the other hand, after I have been working with a student for a while and they are getting marks that both they and their parents are happy with, I like to spend time previewing future material. That way, they are less anxious about new terminology and concepts when they are eventually used in class.
However, most of my time with students is spent supporting them with what they are currently learning through their online or physical schools where topics are presented in a very traditional sequence. They seem to like that best because it’s a comfortable place to be, especially since before working with me they were often feeling very bad about themselves and the course in question. This is also the easiest place for me to be because it’s easy to address difficulties as they arise. It also reminds me of a slogan I invented years ago in response to someone’s comment about my hyperorganizedness: “I’m not in a rut. I am remaining centred in my peak-performance zone.”
The problem with this comfort zone is that exams, not to mention the real world, are not organized by topic. A major exam will not say “Now the next five questions are about conservation of momentum” or “Now apply what you know about torque to solve this next one.” Exam questions, just like real life situations, often expect a person to use everything they have learned as a metaphorical toolbox from which to draw the most relevant knowledge and skills.
For that reason, I will often say to a student, “Now take yourself back to this time last year and redo this classic fence-optimization problem but by using what you have just learned about related rates” or the opposite, “Before you get too smug about all the differentiation techniques you have been wielding so adroitly, forget about all of them and redo this last question using Newton’s quotient.” Better still, if I have been hired to help the same student with both calculus and physics I can say “Now look at that circular acceleration formula that you have so blindly placed your faith in and use what you have learned in calculus to see why it has been worthy of your trust for the past four months.”
This KQED blog post gives a good explanation of why it can be helpful for a tutor to shake things up a bit.