My student’s teacher did not specify which topics will be taught in the coming weeks and assessed in the next exam. I was not able to teach him in advance most of the modules. This means he has several knowledge gaps so I have been trying to assist him with this problem. Due to the random nature of the upcoming assessment task, I have not provided enough assessment questions for him to practice on as I have been spending more time on trying to help him understand the topics. If you have any suggestions or feedback about this teaching method then please let me know.
Generally speaking, comprehension alone will not do much for a student’s grades. If he understands all the concepts surrounding basic curve sketching using calculus but has had little or no practice using calculus to sketch graphs then he is unlikely to be able to answer those questions in the exam. It is the familiarity with various questions types that allows for students to answer questions correctly in tests. However, it is not possible (besides with very basic topics) to answer questions correctly if the comprehension has not been acquired.
As a maths tutor we tend to prioritize the comprehension part of maths education since the practice usually happens to some extent anyway as a by-product of the homework school teachers set. Sometimes a consequence of tutoring is that students refrain from practicing the questions until their tutor explains any gaps in comprehension. This is only natural but can result in the situation where by the time comprehension is achieved there is not sufficient time to practice the actual math before an exam. This is the kind of situation you want to avoid.
If you find yourself in this situation here are a few ideas:
- First make sure that you and the student are on the same page. Be honest and explain that there is not enough time for you to practice many questions and also to explain all the content. Explain the in order to do well in the exam they will need to get some practice as well as comprehend the material. If they focus more on practice then they will probably at least succeed with the easier questions. If they focus on comprehension and not practice it will really depend on the questions they get and their ability to cross contextualise their knowledge on the spot. Get feedback from the student and formulate a strategy together.
- Suggest the possibility of having a few extra lessons before the exam but only if the student is prepared to work overtime. This is one way you get to have more practice and more comprehension. However, unless the student is prepared to do a large volume of practice questions between the tutorials, there is little point.
- You may offer some phone support to the student to keep them on track if they get stuck in your absence.
- Get the student to commit to seeing their school teacher daily (or as required) to help answer questions they get stuck with. This way you can focus more on the comprehension which is best delivered in a private tutoring environment and leave more of the practice questions to the school teacher. As long as the student consistently sees their school teacher to help answer tough questions, you can focus more on comprehension and the student might be able to get both practice and comprehension.
- If there are some smaller topics which the student is utterly unfamiliar with then you may consider leaving them aside altogether and learning that material after the exam.
- Overall you need to strategise which topics you spend your time on to maximize grades. Are any of the topics inter-related? If so, then focus in those topics may yield greater useable knowledge per unit of time spent studying. Which topics are most susceptible to rote learning and which require a great deal of comprehension? The topics which are easier to rote learn may provide you with easy marks without having to spend much time on comprehension? Which topics does the student seem to have more talent in?
