I’m sure we have all worried about how our students are going to understand certain particularly challenging concepts, from the acute difficulty of an advanced trigonometric problem to Shakespearean irony or the mechanisms and prerequisites for photosynthesis.

However, we have little choice but to approach them head-on - sometimes with interesting outcomes.

Here are five common pitfalls I have either narrowly avoided or fallen into myself, along with some creative solutions that have helped me tackle tricky topics more effectively.

1. Cultivate curiosity

In my experience, telling students a topic is difficult immediately triggers the raising of a tangible wall of resistance to the new material.

Indeed, research suggests that the shortage of students in STEAM subjects is a result of students perceiving these subjects as being too hard.

Furthermore, telling students that a lesson will be easy has not been found to be a successful way of developing a growth mindset in students.

Besides, students see straight through such a deception, which can compromise the hard-won trust you have established.

Instead, why not try engaging students by telling them that the lesson today has some interesting material. This way, you have aroused the students’ curiosity. I found this to be particularly useful with a Year 10 class studying differentiation last year.

Students appreciated that the content was challenging, but because of how it had been framed, they viewed it as being accessible and approached their learning with more of a growth mindset.

2. Anticipate student responses

While it is always important to ensure that the resources and activities you are planning are of high quality, this on its own will not necessarily make for a successful lesson if students do not understand your explanations.

I had the privilege of taking part in a lesson study, whereby teachers collaborated to observe student responses to expositions of new topics.

Just by anticipating student responses and questions before lessons, we were able to plan our explanations better as well as anticipate many of the follow-up questions that would arise.

This plan would take the form of a flow chart, including possible student questions and responses.

After the lesson, this flow chart can then be edited if necessary to improve the delivery of the lesson in case you or your colleagues teach the topic again.

3. Don’t go solo

Don’t be afraid to talk challenging topics through with colleagues who you think can help or even just listen to you when needed.

Many of my ideas have been garnered from these conversations. You can even try relearning the topics yourself by watching video lessons and identify what you think students will find challenging.

All the while, think about what questions students may ask in response to the videos you watch.

Likewise, students often learn better from each other than they do from their teachers.

Occasionally, you can try flipping the classroom, asking students to explain video tutorials to each other.

4. Break it down

Research shows that students learn best when new information is broken down into concise steps. Ideally, this information could be broken down into groups of three.

These step-by-step instructions should appeal to all learning styles, as mixed research is coming out regarding students having specific learning styles.

It’s very important therefore to not focus on specific styles and include as many learning media as possible.

You can have visual associations and have students taking turns to read out instructions from the board.

Ultimately, you don’t want to be delivering all the information at once if it is going to take a long time. Students learn through practice.

It is better to have them practice a few aspects of a new topic at a time and develop a better understanding of a smaller amount of material than to cover too much material.

5. Practice makes perfect

Just because students performed well in the lesson, this doesn’t mean they retained their knowledge in subsequent lessons.

This is something most of us learn the hard way quite early on in our careers.

Research now suggests that students need to cover a new topic at least three times in order to develop a strong and lasting understanding. When dealing with difficult topics, this research is clearly even more pertinent.

I like to use fun and practical starter activities to achieve this. The chocolate bar starter is my personal favourite because it is student-led. Students fold a sheet of A4 paper into eight and ask different classmates to fill each block of their ‘chocolate bar’ in with interesting information about the topic.

At the end of the activity, we collect all of the most interesting points, usually generating a very comprehensive revision sheet.

These, then, are the ways I have adapted my teaching and which my students have found useful, when tackling those seemingly impenetrable theories and concepts.

But of course, it’s a continual learning process - so let me know your tips in the comments below.

Brendan McLoughlin is a mathematics teacher and head of year at the International School of Moscow. He has worked internationally for five years