My student isn’t challenging herself and lacking the motivation to do so. Right now I’m just trying to work at harder problems with her to show that she is able to tackle much more difficult questions. Are there any textbooks at a year 8 level that you could recommend for more challenging problems? This is because I find that the current textbook my student is using doesn’t have enough questions marked as difficult.
Not sure about textbooks at a year 8 maths level, so many different ones to chose from and the word “challenging” is a relative term. Certainly Cambridge textbooks are excellent for year 11 and 12 – there are “extension” questions in each exercise and these questions are seriously challenging! Perhaps there is also a range for junior grades.
Some more ways to tackle a lack of challenge:
- If the student is in year 9 and learning trigonometry, for harder practice, grab a year 10 textbook. The year 10 book will have a revision on year 9 trig which will be useful and possibly harder questions. Also, teach year 10 trig itself if you have time. Although not directly relevant, understanding year 10 trig will help to develop their ability to “think in terms of trigonometry” and will be a massive help if learned properly. Also, this serves as a massive ego boost for the student which also helps results and motivation.
- Teach the student topics from year 8 which they have not learned in class yet. Ideally it would be either the very next topic or a topic which is relevant to the current one such that comprehension of the current topic is improved as a consequence of learning the future topic. This approach is similar to the previous point only the student does not have to wait until next year to directly apply the “extra” knowledge. In the coming months her class will cover the topic you have pre-taught and she will know the work before any of her peers. Hopefully, such an ego boost will engage her further and encourage more study.
- Teach her ahead those topics which are central to mathematics and will help with all topics. The best example of this is algebra/arithmetic. Regardless of what topic she is currently studying (or in what grade of high school) it will necessarily presume knowledge of arithmetic and algebra. Typically the errors students make in tests have a high proportion of silly or algebraic mistakes. Algebra is the grammar of mathematics and if she is to master it at a young age then learning maths will be easier in general for the rest of her academic career. Slowly you can work your way up to year 9, then year 10 algebra – she may be reluctant at first but inevitably she will experience the benefit of such knowledge herself and develop an appreciation for what you have done.