Task 7 – where, why, how???
School is tricky, nobody really expects you to be right 100% of the time, yet most people are afraid of getting the wrong answer (me included!). I think it’s going to be crucial to help students realise that it’s okay to find questions hard and get the answer wrong – more important than the right answer, is understanding where/why/how you went wrong and correcting the mistake. Getting the answer wrong is not failure, it’s learning. Learning from your mistakes is more beneficial than answering 20 easy questions correctly. On the other end of the scale, getting 20 incorrect answers and no feedback on where you went wrong wouldn’t be beneficial. Hence, computer programs like Kahn Academy that don’t pin point exactly where the mistakes were made may not be that valuable.
A few years ago on a Skiing holiday my mum suggested we all have a couple of lessons and my initial reaction was “No way! I don’t need any lessons, I hardly ever fall & can get down all the runs nicely.” I was surprised at how helpful the lesson was – feedback from the teacher really helped me improve my technique and now I have at least one lesson every time I go skiing. There’s always room for improvement! As teachers, we need to be creating a learning environment with high quality practice and meaningful evaluation that helps pupils learn, and want to learn. It’s important to motivate* and encourage students to stretch themselves and develop their mathematical thinking.
Willingham suggested that the most important advice for students is for them to test themselves the way they will be tested. At University, all of my exams were essay exams and when I was doing practice essays I found it difficult to write them so would just bullet point and think to myself ‘in the exam I’ll write this’. When it came to the exam I always struggled to write the essay and get it to flow coherently. Finding the motivation to practice my essay technique was tough, even though I knew it would help me in the exam. Should there be more emphasis on exam technique, revision and memory at school?
Regarding memory, I think it all links back to relational & instrumental understanding. If you really understand something – you’re more likely to remember it. Students might remember doing a bunch of questions on indices a couple of months ago but if they were only following rules and didn’t really understand what they were doing, how they answered those questions may not be clear. However, I don’t want to fall into a trap and think it’s going to be super easy to teach relationally and get frustrated when students don’t remember things. Topics are going to have to be revisited and there will have to be some repetition involved – we’re only human after all.
*At St Leonards & Hastings Academy there doesn’t seem to be much positive reinforcement in class (names on the happy face, achievement points etc) which I think can be a bit disheartening for the kids. I have seen teachers asking “How did you get that answer?” or “Is there a different way of doing it?” which is helpful, especially when mistakes have been made.
——Side note – Memrise is learning through repetition – there’s no understanding ‘why?’. With the unit circle Memrise tells you that sin(0 degrees) is 0, I think it would be more helpful if they showed the unit circle or the trig graphs to help you understand why sin(0 degrees) is 0.