 Hello. There are lots of different situations where you need to practice something during math lessons. This is a brief introduction to how you might use practice tasks to develop the mathematician as well as the mathematics. Practicing is a familiar idea in most maths classrooms and something that both learners and teachers report spending a lot of time on. However, there are lots of different meanings conjured by the word practice. Suppose you wanted to practice long multiplication. It might be helpful to pause the video and reflect on what comes to mind for you when you think about that practice. You might have imagined a certain type of textbook or worksheet practice, and it's not to say that there's no place for that kind of work. And I personally have no problem with nice exercises, but I'd like to question whether learners might benefit from other types of practice. We want students to be fluent with procedures and sometimes they just need to practice stuff. But what if we could practice in interesting ways that allow learners to develop as mathematicians, asking questions, making conjectures, being organised and systematic and justifying their ideas? The role of attention is a key consideration when thinking about practice. An issue with some practice is the learners' attention is placed entirely on the skill to be practiced. In order to become fluent, the procedure has to move from being a conscious, effortful act to something unconscious and effortless. In this case, the attention is given to some higher level task with the practicing going on underneath. Dave Hewitt and I have been thinking about the idea of practice through progress. Practice through progress allows learners to gain fluency with the maths they need to practice, but also make progress in other areas, so the skill needs less and less conscious attention. We've been thinking about this in two ways, progressing through the curriculum and progressing as a mathematician. We know that there's a lot of content in the curriculum and the first type involves practicing old ideas through new content, kind of intrinsic interleaving. So once you've taught multiplying fractions say, you make sure they crop up when you do area or perimeter, solve equations or draw graphs. The second type involves the progression in terms of conjecturing and generalising about mathematical relationships. This is the second type I'd like to think about now. Let's think back to that imagined task on long multiplication. You might have imagined a page full of questions that looked something like this. It's likely when completing a task like this, the attention will be entirely focused on the process will get in the answer. What happens if people can already do this? What is to be gained from further practice? You might offer an extension, but this has the disadvantage of creating extra work and teachers might end up preparing extension material that's never used, or alternatively only the fastest learners ever use. This could widen the learning gap and narrow the experience in some classrooms. Compare this with the following task. You might have noticed that the calculation uses the digits five, six, seven, eight, nine. If you rearrange these into a three digit by two digit multiplication, what combination gives the biggest product? How do you know? Is there a strategy for any five digits? Pause the video. Try and notice what happens for you as you work on this task. What other questions could you ask? This task was designed with five principles in mind. Exploration of the task offers the opportunity to gain further insights in related areas of mathematics. Learners have an element of choice, opportunities to notice mathematical patterns and relationships and make conjectures, opportunities to justify and prove, mathematical situations that can be adapted and extended. As you continue to work on the task, consider how these principles apply. You might find some aspects surprising. If you think you've finished, try and justify your answers and begin to work on some of your own variations. Here are some variations you might like to try. Reflect on your experiences of working on these tasks. What issues are around for you? What actions will you take going forward?