Guestblogger: @IanLoynd

**A Perfect Maths Lesson**

Teachers have the most important job in the world. At a time when expectations and accountability are at an all-time high, delivering excellence in the classroom has never been more difficult. And this is true no more so than for maths teachers. Maligned in the press for poor international performance and relentlessly scrutinised by school leaders and government, no wonder great maths teachers are becoming difficult to find. The unique demands of our subject make it tough to apply some aspects of research on teaching and learning in our classrooms and even the best of us can, at times, become cynical about our job.

*The Perfect Maths Lesson* is my antidote to the above! Rather than being a subject described as boring, irrelevant and hard, outstanding maths teachers combine their passion with pragmatism to ensure that maths is intriguing, relevant and delightfully baffling. I do not believe in mechanistic checklists of expectations which headteachers or inspectors can tick for compliance but I do believe that there are common features of outstanding maths lessons and common characteristics and habits that outstanding maths teachers share.

So, what are the essential elements of *The Perfect Maths Lesson*?

**1. Engagement**

When kids are engaged in their learning, they are more ambitious in their thinking. One of the key tasks in engaging children in maths lessons is to set the pace of the learning correctly. Too easy, too slow or too repetitive and they become frustrated. Too difficult, too fast or too busy and they become bewildered.

Getting the perfect maths lesson off to the right start is crucial to engaging learners. An effective initial activity sets the tone for the rest of the learning and can determine the success (or otherwise) of the lesson. Your pupils need to be in the habit of beginning their learning as soon as they walk through the door of your classroom. As they wait for others to arrive, it is a good idea to have a little, open-ended challenge available on the board or on their table. For example, ‘how many ways are there to make 10 pence using British coins’?

Once all the pupils have arrived for your lesson, an effective starter is needed to help them focus on learning, make them think and provide a sense of curiosity to maintain interest. It’s best to link this learning to pupils’ own lives by using contexts sensibly.

**2. Challenge**

Given the right set of circumstances, all students can make progress – particularly when the teacher is determined that they will. In the perfect maths lesson, teachers help students to appreciate that effort is required for success by ensuring that the work is perplexing, mystifying and wonderfully challenging.

Ideally, you should be aiming just beyond the point students have already reached – occupying a space right at the edge of their ability. Challenge can be woven into learning by asking the right questions in the right way. Effective questioning is a central tenet of the perfect maths lesson because deep learning begins with questions, not answers.

‘Rich’ questions encourage learners to make links with previous learning, stimulate thinking, reveal misconceptions and generate even more questions. For example, the question ‘What is a rhombus?’ is made richer by becoming, ‘In what ways is a rhombus like a rectangle and in what ways is it different’?

Finally, teachers must also find a way to help all children *think mathematically*. For many children, procedural knowledge and rote learning have led to a void in understanding which prevents them from making the expected progress. They require *conceptual* *understanding* in order to comprehend mathematical operations and relations before they are able to apply mathematical ideas to new situations.

**3. Independence**

Independence is what really connects the *teaching* with the *learning*. Direct instruction on the part of the teacher (that is, deciding the learning objectives, modelling the learning, monitoring and evaluating understanding and tying the learning together) is essential if students are to make progress. However, students learn even better when they can self-select or self-generate learning tasks, collaborate with peers and self-regulate their own learning.

Such is the fear of failure in maths lessons that pupils often choose to opt out of challenging learning and the words ‘I’m stuck’ resonate throughout the classroom. In the perfect maths lesson, getting stuck is celebrated because it triggers new learning and helps children to get better at maths. Helping learners to get themselves unstuck without relying on the teacher is an important precept for developing independence in maths lessons. Teachers need to rein in their impulse to answer students’ questions, instead responding by asking the question back. For example, if a pupil asks, ‘Why is the answer negative?’, the teacher replies, ‘Good question. Why do you think the answer is negative?’

**4. Assessment for learning**

Effective assessment is the key lever for personalising learning in maths lessons. Assessment can be done to, with or by students but, in its most emancipating form, assessment always results in the learner moving forward in their learning.

The use of a learning continuum, based on the objectives for the lesson, is an effective way of helping students to be clear about how they can make progress in maths. It allows them to assess where they are in their learning journey and where they need to go. In this way, the emphasis is on the pupils’ continuing learning journey over the course of the lesson (or series of lessons), as opposed to believing that they are simply able to ‘do’ or ‘not do’ maths.

Because the process of learning is a journey, it is important to remind students to frequently check their own progress in relation to the distance travelled towards the learning outcome. Dedicated Improvement and Reflection Time (DIRT) means spending quality time in your lesson returning their work, letting them read your comments, soaking in the feedback *and then responding to it*.

**5. Relationships for learning**

The challenge for maths teachers is to help pupils enjoy their maths lessons (even if it isn’t their favourite subject) because positive emotions are essential for learning. Dopamine is the number one, learning-related, memory-boosting neurochemical – and a teacher’s best friend. Managing the emotional climate of your classroom to produce the right levels of dopamine in learners’ brains means that they will have no choice but to learn, whether they want to or not! The most effective means of achieving this is through reward or the anticipation of reward. In a maths lesson, rewards might include a joke, opportunities for movement, a puzzle, group work, a giggle, a game, listening to music or a curiosity or surprise.

The fear of failure is amplified in the maths classroom because children believe that, above all other subjects, failure in maths is the worst of all failures. In the perfect maths lesson, then, the teacher must obviate the fear of failure. Indeed, we must encourage students to fail better! Maths teachers can convey a growth mindset to students by using language carefully and communicating praise with purpose.

*So, there we have it!* If you’d like an insight into the ‘how to do it’ (and why it works) of outstanding lessons, get yourself a copy of *The Perfect Maths Lesson*. Having observed hundreds of brilliant teachers during my career, this little book neatly summarises their best ideas, unashamedly stolen, tried and tested.

If you are looking for ideas to breathe new life into your lessons or tops tips to gain that elusive ‘outstanding’ judgement, you’ll find plenty in *The Perfect Maths Lesson*. My aim in the book is to provide practical ideas and common-sense methods that can help every teacher to be excellent, and uncover the essential strategies that help teachers appear to walk on water!

*Ian Loynd is a teacher, school leader, governor, author, educational consultant and trainer. Follow Ian on twitter @IanLoynd or visit www.ianloynd.com*

This guest post has a lot of common sense and would make a useful read when getting ready to go back to school in September. There are no doubt more details in the book, so I may decide to invest in a copy. The only thing that I may disagree with is the part about gaining an ‘outstanding’ judgement – it shouldn’t be the objective of a lesson, but I understand what is perhaps meant by this.

Thanks for the comment, I will hand over to Ian for a response : )

You’re right, of course, Tim. The premise of the book is about getting it right for inspectors by first getting it right for the kids we teach. Grab yourself a copy and your fears will be allayed! Actually, the inspectorates in England and in Wales have a lot of very helpful stuff to say about maths teaching – much of which resonates with my own thinking. As a rule, if we can apply research on teaching and learning to our classrooms and get our kids making great progress as a result (and loving maths at the same time) then we’re onto a winner. For most teachers, however, that dreaded observation is a real fear and so, in writing the book, I hope to alleviate some of that worry. Happy kids, happy teachers (and probably some good grades too)!

I use the phrase “Are your lessons CRAP?” as a way of remembering the key ingredients of a good maths lesson:

Challenging

Rapport with students

Assessment for learning

Pace (this is similar to engagement above)

I’m pleased to see that this almost matches your checklist above

LOVE IT!!! : )

Would you like to guest blog about “CRAP” lessons at some point?

Thanks! Yes it would be a pleasure to write something about CRAP lessons (some of my colleagues would say I have delivered enough of them!!) Email me with the details.

Also thanks to @IanLoynd for a brilliant post – I ordered his book yesterday and can’t wait for it to arrive!