Find a way to make hard questions easier and easy questions harder
Don’t: Jump straight to the full worked solution when you get stuck.
Do: Find a way to use part of the worked solution to make the question achievable.
The easiest way to make sure you are studying at the very edge of your understanding is choose what you work on. Sometimes you don’t have a choice: usually because the questions suddenly get too hard. In high school maths this often happens with worded questions: some students find them a breeze but for other students this where things get out of their depth very quickly and it is not easy to find a foothold. This is where you need to find a way to make the hard questions easier.
Everybody knows you can make a question easier by using worked solutions, asking a teacher, friends or a tutor, but the key is to make sure you don’t just jump straight to the full solution. Unless understanding the worked solution is itself a challenge you should take just a small peek to get a hint and work out the rest yourself. Have a go at correctly identifying the technique that needs to be used for a question before looking up the solution, or having seen the correct technique, try working through the rest of the solution yourself. One way or another break down the difficult problems into manageable chunks. Another approach to make difficult problems easier is by trying a sequence of very similar problems, getting just enough help for each until they become comfortable without any help. If you have a bank of questions to work with this can be very effective. If you do end up needing the full worked solution, make sure you attempt the question again later without the worked solution and try again until you get it.
Maybe you are lucky enough to have opposite problem: you know the material so well that the questions are no challenge at all. You could just cruise through on auto pilot. If you’re smart you’ll find a way to make the questions challenging by setting a speed challenge or seeing how many questions you can correctly answer without any silly errors. Try out little tactics that will help speed and accuracy. Try recording just enough to make a double check quick and easy.
For Bruce the answer was yes.
Let me be clear from the outset, I am no miracle worker, this doesn’t happen for all of my students. Hopefully you can see in Bruce’s story some patterns that will help you achieve your goals.
Bruce’s case shows that with the right support and the right approach, your improvement can be nothing short of dramatic. I’ve been surprised by how often I’ve seen students improve out of sight like Bruce.
Bruce came to me in the second half of his first year at Uni worried that he’d fail. He was studying civil engineering online as a mature age student through Open Universities, and the course was great except for one thing: maths!
Maths was never Bruce’s favorite subject and it had been about 10 years since he’d studied any maths at all. He’d managed to scrape a pass in the first semester and desperately wanted to pass the second semester. Bruce lived more than an hour drive away, and every couple of weeks he would make the two hour round-trip in to Preston for a two-hour session with me.
I think because he had to sacrifice so much he was determined to get the maximum value out of our sessions together. Bruce would come extremely well prepared with a detailed list of the worked problems and topics he had trouble with. He worked hard and brought along all of his working out so we could see exactly where he had trouble.
One by one we’d knock down each of the issues he battled with and gradually over time his confidence grew. Bruce’s hard work paid off and he managed to achieve a high distinction for maths in the second semester.
There are a couple of things that Bruce did that I see consistently with high achieving students:
- He put a high value on the support he was getting – if it took that long to get there he didn’t want to waste a minute of the session. He made sure that the work he did before the session was directed at getting the best out of our time together.
- He attempted to make as much progress as he could without help before asking for help. When Bruce did get help it had real lasting impact.
- By being clear about where he had trouble and bringing his working out, we could get straight to the key issues without wasting time.
Anyone looking to maximise the benefit they receive from any of the study support they have would do well to follow Bruce’s lead. It doesn’t matter whether the support is a teacher, tutor, parent, or friend, following these suggestions will get the most out of your time together.
How about you? Have you seen someone improve dramatically or have you improved dramatically? What have you found works best?
Always, always, always concentrate on the edge of your understanding
Don’t: Spend too much time on questions that are either too easy or too hard.
Do: Make sure you concentrate as much time as possible on achievable challenges.
This is number one. Master this and you are guaranteed to improve. I’ve seen dramatic improvements in my students when they apply this with discipline.
If you have ever seen me you will know that I’m no body builder, but I’ve been told that if you work out on weights to build up muscle mass you need to push on the weights until you can push no more: all the benefit comes at the very end where the muscles are forced to reform and re-grow bigger.
It’s the same with learning: all the benefit is gained by pushing out beyond the boundaries of your current understanding. The difference is that it doesn’t have to be at the end of a study workout. If you are smart you will constantly monitor how you are studying to make sure you are neither working on material you find easy, nor material that is beyond you.
It is tempting to work away happily on questions or material that you feel confident with but that approach is not doing you much good: you are not being stretched. I sometimes see the opposite problem: students out of their depth and drowning with material that is beyond them. That only saps confidence with little prospect of improvement. You want to be on the boundary between these two places: one step further and you are out of your depth, one step back and you are in comfortable shallows. You’ll be surprised at how quickly problems that you thought were out of your depth start to seem shallow.
And if you feel totally overwhelmed by a subject pick a part that looks the easiest and choose little baby steps to get started. It can be anything: memorising the main ideas, trying to understand or repeat a worked solution, or the simplest questions you can find. Celebrate these baby steps, because in truth, for a subject you are overwhelmed by they are the biggest steps of all.
For maths and science my approach was to work through a list of questions. I’d skip any questions that looked comfortable for me, maybe just thinking them through quickly. I’d continue until I found a question that I wasn’t so sure about and then concentrate on it. The easier questions I’d leave and use them later to work on speed and accuracy.
How about you? What have you found useful to keep your learning momentum going? Or do you find it difficult? Leave a comment and share your thoughts.
I’m addicted to learning. Learning through books, learning through studying, learning by observing, and learning by doing.
So this blog is about learning. There are lots of aspects to learning that I’d love to write about, but I get paid to help people get results, so the blog is at least going to start by focusing on how to help people achieve results in their learning. Over the next few weeks and months I will post articles on what I’ve learnt about how to study effectively, share some of the stories of my students and what they did to get results. I’ll throw in a few worked solutions as well.
Do you need or want to achieve results in your learning this year? What do you find difficult? What little secrets have you discovered? Share your thoughts and questions.