First Education

Maths is a subject where consistent practice makes all the difference. In tutoring sessions, I often remind students that learning maths is similar to learning a sport or an instrument—the more you practise, the stronger the skill becomes.

One mistake students often make is leaving all their practice until right before an exam. This creates pressure and often leads to confusion. By practising regularly, even in short bursts, students strengthen their understanding step by step. In my sessions, I set small amounts of practice between lessons so that the content stays fresh and does not pile up.

Regular practice also helps students build speed and accuracy. Questions that once felt difficult start to feel routine, and patterns become easier to recognise. This gives them more confidence in exams, where time and pressure can be challenging.

I also encourage students to mix up their practice. Rather than only doing the types of questions they are comfortable with, I help them focus on the areas that need the most attention. That way, they build balance and are prepared for anything that comes up in a test.

In the end, regular practice is not just about passing exams, it is about developing long-term habits that make maths less stressful and more manageable.

James Valiozis

Today I had the opportunity to observe Mateus and his Year 9 Mathematics session, where the focus was on trigonometry, particularly the application of bearings. It was an insightful session that highlighted not only the challenges students face when transitioning from abstract trigonometric concepts to real-world applications, but also the importance of guided practice in building confidence.

Mateus began by revising the fundamentals of sine, cosine, and tangent, ensuring the student was comfortable with the core ratios before extending them to navigation based problems. This foundation was crucial, as many students often find it difficult to link abstract ratios to directional movement. By anchoring the lesson in familiar material, Mateus created a logical bridge to the more complex concept of bearings.

What stood out most was his use of visual aids. Diagrams were drawn, with clear emphasis on orienting from north and applying clockwise measurement. This incremental approach allowed students to see how trigonometry moves beyond the triangle on paper to describe direction, distance, and orientation in practical contexts, such as maps or navigation. The student initially struggled with distinguishing between angles inside the triangle and the bearing required from north, but through repetition and guided questioning, Mateus helped the student be more confident in attempting the questions

Another strength was his pacing. Rather than rushing through worked examples, he gave the student time to attempt problems independently, providing targeted support. This balance between instruction and practice allowed the student to consolidate their understanding while also identifying areas of misconception.

Observing this session reminded me of the value of contextualising mathematics. Bearings, while technical, become far more engaging when framed as a tool for navigation and decision-making. As a tutor, it reinforced for me the importance of blending clarity, patience, and real-world relevance in teaching. The session ultimately highlighted how effective instruction can transform abstract mathematics into a skill set students see as both useful and applicable

Tynan Philmara

The adaptive immune system is a highly specialised defense mechanism that protects the body against pathogens by recognising specific antigens and developing long-term immunity. Unlike the innate immune system, which responds rapidly but non-specifically, the adaptive system is slower on first exposure but produces a specific response and, most importantly, has immunological memory. This feature is key to how vaccinations work.
When a vaccine is introduced into the body, it contains either weakened, inactivated, or non-infectious components of a pathogen, such as proteins or inactivated toxins. These act as antigens that trigger the adaptive immune response without causing illness. B lymphocytes are activated and differentiate into plasma cells, which secrete antibodies that specifically bind to the introduced antigen. At the same time, some B cells become memory B cells, which persist in the body for years. Similarly, helper T cells activate both B cells and cytotoxic T cells, while cytotoxic T cells target and destroy any cells displaying the antigen. Memory T cells also remain in circulation after vaccination.
The first exposure through vaccination mimics the primary immune response, which is relatively slow and produces a moderate level of antibodies. However, the generation of memory cells ensures that, upon later exposure to the actual pathogen, the body can mount a secondary immune response. This response is rapid, producing a larger quantity of highly specific antibodies and activated T cells, often neutralising the pathogen before symptoms appear.
Vaccinations therefore harness the adaptive immune system’s specificity and memory, training the body to recognise and fight disease without the risks of natural infection. This principle not only protects individuals but also contributes to herd immunity, reducing disease spread within the community.

Chris Mylonas

One of the most effective ways to check understanding in maths is to ask students to explain a concept in their own words. It is not enough to simply solve a problem by following steps. True understanding shows when a student can explain why those steps work.

In my tutoring sessions, I often pause after a question and ask, “Can you explain to me what you just did?” At first, many students find this uncomfortable, but with practice they begin to use their own language to describe the process. This reveals how well they grasp the concept and highlights any gaps that need addressing.

For example, when working on fractions, a student might say, “I made the denominators the same so I could add them together.” This simple explanation shows that they understand the reasoning rather than just applying a formula. If they cannot explain it, that is a sign we need to revisit the idea more clearly.

Encouraging students to use their own words also builds confidence. They begin to see themselves not just as learners, but as people who can teach and explain. That shift is powerful, especially when exam pressure makes students doubt themselves.

When students can explain maths in plain language, they have taken the first step towards mastery.

James Valiozis

Today, observed James’ year 7 Maths, as it was the last week, and Owen didn’t have any class work James focused on revision – ensuring that all the content that was taught throughout the semester was well understood and remembered this included, fractions, area and volume, and algebra. Throughout this revision, James identified that Owen struggled and was not as confident in completing worded questions across all topics, he was able to confidently complete more basic questions where the information was given, but struggled to fully comprehend how to extract information for worded problems.

Therefore to help Owen, James focused most of the lesson was based on completing worded problems ranging from easier questions to more challenging. James was super clear when reading the question and really helped him to understand by begin to help him through using the board to help him identify key words and formulas and asking him to explain why he approached the question instead of just telling him to answer. By the end of the lesson, Owen was a bit more confident on answering these questions and was able to complete them more independently.

James also went over factorisation with Owen as he forget the concept , James did this through showing Owen factorisation tree, using the white board again to help explain this concept and make it understandable reminding Owen on how to complete it, he then completed questions on his own. James ensured that the holiday homework was based on worded questions and factorisation to make sure that he has a clear understanding of the next term and is he is ready for next term if these questions potentially come up in next exams or in future years.

To finish the class, he ended with uni a fun game they enjoy playing. Overall James was very clear, using the board to reinforce his ideas and teaching, which really helped owen understand his revision.

Daniella Antoun

I had the opportunity to observe Luka’s Year 10 Mathematics session, which centred on trigonometry, with particular focus on solving problems involving bearings, angles, and sides of right-angled triangles. The lesson began with a recap of the trigonometric ratios — sine, cosine, and tangent — before applying them to more practical navigation-style contexts. Bearings were introduced as a way of expressing direction, and the teacher demonstrated how trigonometry could be used to calculate distances and angles when moving between points on a map.

Luka engaged well with the material, particularly when the problems were framed in real-world terms. He was able to identify the key sides of the triangle (opposite, adjacent, hypotenuse) and select the appropriate trigonometric ratio when solving for unknown side lengths. When tasked with finding unknown angles, Luka showed confidence in rearranging the formula, carefully using the inverse trigonometric functions on his calculator. The introduction of bearings provided an additional layer of complexity, as it required Luka to link his trigonometric calculations with compass directions and standardised angle measurements from north. While he initially found this challenging, he improved as the teacher modelled step-by-step worked examples.

Overall, the session was an effective demonstration of how trigonometry can be taught through scaffolded examples that connect to practical applications. Observing Luka’s learning emphasised the importance of contextual problems, such as bearings, in motivating students and showing the real-world value of mathematics.

Alexander Nikitopoulos

I recently observed Joel working with one of his students and was struck by how thoughtfully she ran the lesson. From the outset, he was very confident and knowledgeable about topic areas from the get-go. He also planned, making sure his student would leave with learning opportunities and areas to work on for the week ahead, while leaving confidently knowing the previous content they had completed during the session.

Joel’s explanations were also very clear and concise. He used everyday language, defined new terms as they came up, and regularly paused to confirm that the student was following along and learning along the way, as he took a hands-off approach, which is a perfect approach for tutors to take from my own learning. Rather than correcting errors straight away, he posed guiding questions that helped to see the source of a mistake. When working through problems, he modelled his own reasoning step by step, letting the student watch his thought process unfold as well as imitate his process with their own working later on.

His time management was equally impressive. He moved the lesson forward at a steady pace, spending just enough time on topics of need as well as practising what they were learning during the session.

Overall, Joel demonstrated a well-balanced blend of preparation and clarity, and an approach that kept the student engaged. This made the session both efficient and encouraging, letting the student walk away benefiting from the session that had just finished with new knowledge and a comprehensive understanding of the content covered.

Lucas Sinnott

When I first started tutoring, I thought my job was to give students all the answers. If they were stuck on a maths problem, I’d walk them through every step. If they forgot a key term in an essay, I’d fill in the blank.

But a moment stands out to me that I learnt about the skill of tutoring. One of my students I was tutoring for maths, kept running into the same mistakes repeatedly after I had corrected him and tried to remind him about it. Then I decided to try another approach. Instead of explaining, I decided to give small prompts and reminders in an attempt to activate a moment of realisation or memory in his brain from previous sessions. At first, it may have felt awkward, but after a minute, he tentatively had a spark in his mind, and actually remembered after having forgotten a couple of moments before.

Since then, I’ve embraced a more hands-off style. I still guide students, but with questions and small prompts rather than direct answers. I might ask things such as: “Which formula could apply here?” And it’s amazing how often they already know the next step; they just need the space and time to find it in their brain.

This approach builds more than academic skills. Students grow confident in their ability to tackle hard problems and start recognising their own thoughts. They learn perseverance and learn more independent skills they’ll carry into university, work, and everyday life.

Lucas Sinnott

Today I had the opportunity to observe Luka working with a Year 10 student on the topic of linear relationships. The session was an excellent example of how mathematical concepts can be used when they are linked to real-world applications and explained in progressive, accessible steps.

Luka began by revisiting the general form of a linear equation, y=mx+c Rather than rushing into abstract algebraic manipulation, he encouraged the student to interpret these terms visually by plotting examples on the Cartesian plane. This step was particularly effective, as it grounded the algebraic symbols in a picture the student could immediately recognise.

A highlight of the lesson was Luka’s use of contextual problems. He framed linear relationships in everyday settings, such as calculating the cost of ride-share fares or predicting phone plan charges based on a fixed rate plus usage. By doing this, he helped the student see that slope represents a rate of change while the intercept captures a starting value. The student initially struggled to articulate why the line’s steepness changed with different values of m, but through questioning and repeated sketching, Luka guided them toward understanding slope as a measure of sensitivity: the greater the slope, the faster
y changes with respect to x.

The pacing of the lesson balanced explanation and practice well. Luka would model an example, then hand over to the student to attempt a similar problem. This strategy ensured active engagement and allowed him to provide immediate feedback. Importantly, he encouraged the student to verbalise their reasoning at each step, which not only clarified their thought process but also revealed gaps in understanding that Luka could address on the spot.

What stood out most in this session was the emphasis on linking algebra to interpretation. Too often, linear relationships are treated as purely symbolic exercises. Luka showed how to integrate both the visual and practical dimensions, making the concept more intuitive and less intimidating. It was a reminder of how effective tutoring blends clarity, relevance, and patience to deepen student learning.

Tynan Philmara

I was lucky enough to observe Kate’s session with her maths student. I was really impressed with how she effectively used the centre resources, seeking out specific documents to match areas her student needed help with. She also made sure that her student would have adequate homework and practice materials over the course of the week, and pointed out specific questions that might challenge him. When she was going up to print, I admired how she kept the student engaged, working on a challenging question so he would always be working over the course of the session.
I also admired how she used clear, plain language and asked specific questions to point him towards the correct answer. She defined all the terms she was using, and stopped to check if he was understanding and taking in the information. When he made mistakes, she wouldn’t immediately correct him, but would instead ask questions so that he understood where he had gone wrong. She would also work the questions out in real time in front of him, explaining as she went.
She was extremely efficient at planning the session time, and ensured they were moving on quickly from complex questions so they didn’t waste time on unnecessary content.
Finally, I was intrigued by how she managed the personality and unique needs of the student. The student was reasonably shy and not very communicative, and would not always make it clear if he was understanding something. Kate relied on aspects of body language and small comments he made, and made sure to check in quickly. She was sensitive to his signs of frustration, such as sighing, and handled them gently and empathetically. She attempted to motivate him by making jokes, and it was clear they had a close relationship.

Jemima Smith