Teach-Primary-18.3

Having worked through these ideas, and seen that both odd and even numbers can be expressed as the sum of consecutive numbers, pupils might go on to ask themselves these questions: • Given a number, can I figure out how to express it as a sum of consecutive numbers? • Are there any numbers which cannot be expressed as the sum of consecutive numbers? • Given a string of consecutive numbers is there a quick way to work out what their sum will be? ‘Consecutive numbers’ can thus lead to a range of deep mathematical thinking, but the set-up, the initial task, is one with which everyone will initially be able to engage. This is a task that will bring as many of the pupils as possible into some ‘common ground’ from which further mathematical activity can emerge. Thus, a key question to ask when planning for adaptive teaching is: How can a task be initially set up so that the maximum number of pupils can begin to engage with it? Allowing pupils access to concrete materials that might help them start on a task is one possible strategy for creating common ground. Another is to pose a task in a way that gives pupils some choice over their entry point into it. This can mean adapting closed tasks to be more open: • Closed: Put a collection of numbers in order. • Open: Write down five numbers that can be modelled with exactly three base ten blocks. Now put them in order from smallest to largest. • Closed: Solve all the multiplication word problems on this page. • Open: Choose two numbers to multiply together. The product must be greater than 100, and an odd number. Write a problem to go with your numbers. • Closed: Complete this page of additions of fractions. • Open: Write down two fractions with different denominators. Find the sum and difference of each of these fractions. Adaptive teaching in the classroom The main actions of adaptive teaching are the ‘on the hoof’ mediations and interventions made in real-time teacher-pupil interactions. Generally, such ongoing interactions address one or the other of the following aspects of working: 1. Task completion – helping pupils to succeed in the task. Strategies that support helping pupils complete a task include: • reducing the complexity or difficult of the task, • helping pupils to focus on the most relevant aspects of the task, • suggesting some concrete materials that might help. 2. Promoting higher order thinking (mathematical activity) – helping pupils come to see mathematical generality in the specific task. As well as asking What do you notice? helpful questions include: • Can you make up an example to test what you have noticed? • What if you changed…? • Can you write down a conjecture about what you have noticed? Alas, there is no magic formula for which type of intervention to adapt at any time; too much focus on task completion and pupils may not learn anything, too much focus on higher order thinking and they may get frustrated. That’s that biggest challenge of adaptive teaching; but also the greatest joy when a decision works. TP 28 | www.teachwire.net Mike Askew is adjunct professor of education at Monash University, Melbourne. A former primary teacher, he now researches, speaks and writes about teaching and learning mathematics. What adaptive teaching is... and isn’t • Adaptive teaching involves real-time differentiation. • At its best, adaptive teaching builds on what pupils can do. Different levels of experience are seen as opportunities to learn rather than obstacles to overcome. • Pupils can succeed at tasks without necessarily learning the intended mathematics. Adaptive teaching involves formative assessment, with questions such as: Can you explain to me how you would do a similar problem? • Adaptive teaching can help pupils become self-adaptors and to develop mathematical aptitude. Adaptive questions that pupils can adopt for themselves include: What do you know? What have you seen before that is like this? • Research shows adaptive teaching that focuses pupils on the general mathematics behind a task can not only increase pupils’ success in that activity, but also have a pay-off in increasing pupil success with harder questions (see tinyurl.com/ tp-PISAQuestions ). • Adaptive teaching is NOT about catering to pupils’ supposed preferred ‘learning styles’. • A large part of adaptive teaching is carefully listening to pupils and watching them work. • Help with simpler problems is likely to be more direct. Harder problems require subtler adaptive teaching, so that the thinking is not taken away from the pupils. @mikeaskew26 mikeaskew.net