My "assassin's" story didn't just amuse yr11 Jim; it helped him avoid getting division mixed up. His confidence was also boosted when I backed him up in challenging his class-teacher's use of ratio for probability (without damaging my colleague's credibility). Being able to offer innovative alternative approaches, and maximising this opportunity in 1:1 tuition, is a forte of mine. I kick-off with diagnosis, for which I find open-ended starters very useful, such as "How many juggling balls might we get in this lorry?" Actual juggling is also a fun way to demonstrate the learning cycle; I make on-the-spot decisions about which tracks to follow.

Yr9 Elly's key issue, for example, emerged to be lack of confidence in basic sums, so we lingered on times tables with more emphasis on sums tricks (which she welcomed with glee), without worrying her at this stage about being able to choose the sums herself.

In contrast, some students are soon ready for a volume algebra route.  Open-ended, flexible approaches risk leading onto muddy tracks; but it's well worth the risk because (a) the adventure generates enthusiasm and (b) it allows me to model how making mistakes or needing to back-track to find an easier way needn't hold us back.

Brett struggled for years with exam stress, making class tests difficult to face – despite lots of support. I managed to calm him down away from the classroom enough to complete a test; partly by treating it as a test not just of him but also of his teacher, and also by maintaining a calm atmosphere, encouraging him to tackle one question at a time. He was pleasantly surprised that he did most of the test. It was good to be able to reinforce this through 1:1 invigilations and in -class support.  Brett found it helped to treat exams as far less critical than he used to.

A carefully judged balance of repeated "push" and "pull" worked wonders for yr9 Elly at transforming her frequent time-wasting into sustained enthusiasm for the maths, and seeking out affirmation from me.  She started to engage with the maths in class far more often.

Many students worry about looking "stupid". Yr7 Dell called himself “dumb” and repeatedly resisted encouragement to engage, thus avoiding the risk of "failure".  Lack of confidence is sometimes masked, as when I at first overlooked Jarod's weakness because he had shown high ability. One simple strategy for boosting confidence is to re-word the way we talk and think about mistakes. "That's wrong; so this doesn't work for you" can be so much better than "You're wrong…."

It's also wonderful to find strong maths, as with Max, where I was able to stretch and enthuse us way beyond my juggling-lorry opener.  It was like "playing with maths", moving from basic volume and big numbers, to using standard form to compare, then index investigations; and shape sizes algebra, which led to equations, where I uncovered some surprising gaps in Max's understanding.

The prize for common maths mixups might go to Area and Perimeter, which many students confuse simply because they rush into an algorithm. So I emphasize "Stop, think: area means number of squares…" before asking "What sum will find this out?" Or I offer memorable words or actions to emphasize the distinction.  Another simple but effective way of "making things stick" is just to write mneumonics (eg. "area squarea") or examples repeatedly in various visually creative ways (a "doodle page").  Learning a skill or knowledge is only the half of it – the big challenge is how to avoid things falling off our "memory hooks".  My teaching plans are peppered with "recall" reminders. I had a “eureka” moment with Harvey when I suddenly discovered that the best way for him to remember the f irst stage result in a multi-stage head sum is not to give an extra split-second pause to try to remember it (as helps many people), but just to talk himself through his working.