Craig Barton's excellent book [1] makes a compelling argument in favour of the 'explicit instruction' for teaching maths. Here's an excerpt: --------------- I

Craig Barton's excellent book [1] makes a compelling argument in favour of the 'explicit instruction' for teaching maths. Here's an excerpt: --------------- I was particularly proud of a guided discovery task I came up with for introducing some of the more complex laws of indices to my Year 11 class two years ago. The worksheet looked like this: https://photos.app.goo.gl/dzWPzw32hWVDLvYG8 https://photos.app.goo.gl/dzWPzw32hWVDLvYG8 Nice, eh? Again, I ask the question: what could possibly go wrong? Well, quite a lot, as it turns out. My takeaway When considering a guided discovery task, the question I should have asked myself is: what is the best that can happen? Take the laws of indices lesson. The best that can happen is that all students discover the laws of indices for themselves, leaving no gaps in their knowledge, nor developing any misconceptions, in a reasonable time frame. We can then proceed with the rest of the lesson, maybe moving on to application questions, or interleaving other topics into the examples (see Chapter 12), such as indices involving surds or fractions. How often does that actually happen? In my experience, literally never. What actually happens is that one or two students discover exactly what I wanted them to discover. They are feeling great about themselves, and rightly so – as we have seen in Chapter 2, success is motivating. A handful of students have some kind of idea what is going on, but with an eclectic mix of gaps in their knowledge and newly formed misconceptions. Some of these students are aware they have gaps and misconceptions, others are blissfully ignorant. And the rest of the students do not have a flipping clue what is going on. They are feeling confused and pretty down about themselves when they see their fellow classmates have figured it out. Any form of decent formative assessment strategy (Chapter 11) quickly reveals this disparity between levels of understanding, and as such I cannot move on with the lesson. So what do I inevitably end up doing? Teaching the laws of indices, of course! Maybe I will set those students who seem to have understood it off on the work I hoped everyone else would be moving on to – mind you, I would really like them to hear my explanation and do the worked examples, but how can I justify doing so when they have demonstrated their understanding? Hmmm… Anyway, back to the rest of the class. By this stage, I am 30 minutes into a 50-minute lesson, rattling through a series of worked examples on the laws of indices far quicker and with much less care than I should. There is zero time for the students to practise their newly acquired skills and hence consolidate their knowledge, nor sufficient time for me to do any kind of application questions which would show them the full breadth of the topic. But it is even worse than that. Even if I could somehow freeze time and spend those lost 30 minutes going through carefully structured and well-chosen worked examples (Chapters 6 and 7), I am not back at square one. I am behind square one, because my students are no longer coming at the topic with fresh eyes. Many of those who failed to ‘discover’ the key relationships have already decided that indices are difficult, and yet another area of maths that they don’t understand. It’s going to take more than my magically retrieved 30 minutes to turn that one around. And so I wave goodbye to a group of confused students trundling out of the door, promising that we will pick this up again tomorrow, assuring them it will all be fine. I am already dreading the lesson, wanting to open up proceedings by saying ‘okay, everyone, forget what happened yesterday’. In the past, I blamed my students for this – if only more of them could have figured it out. Now, I know the blame rests squarely at my feet. I never gave them a chance. [1] "How I Wish I'd Taught Maths: Lessons learned from research, conversations with experts, and 12 years of mistakes" https://amzn.eu/3BkjAsl https://amzn.eu/3BkjAsl