Today, I had the great opportunity to observe David!

During the session, I observed David teaching a student the topic of index laws in mathematics. His approach was structured and systematic, beginning with the definition of indices. He explained that an index, or power, is a concise way of representing repeated multiplication. To establish this foundation, he provided straightforward examples. Once the basic idea was clarified, David introduced the laws of indices in a progressive sequence. The first rule he addressed was the multiplication of powers with the same base and reinforced this with numerical examples. Importantly, he did not present the rules as abstract statements alone, but linked them to concrete calculations to ensure comprehension.

David then moved to the law of division, expressed as he highlighted how this arises from cancelling common factors in numerator and denominator, which made the result intuitive rather than arbitrary. This progression helped to reduce the common misconception that negative indices lead to negative numbers. Throughout the lesson, David’s teaching was characterised by clarity and encouragement. He frequently prompted the student to attempt problems independently, intervening only with guiding questions when difficulties arose. This fostered active engagement and reinforced the student’s understanding.

Overall, the session demonstrated effective mathematics teaching practice. The emphasis on logical reasoning, step-by-step explanation, and student participation created a clear and supportive learning environment. By connecting each rule of indices to underlying mathematical principles, David ensured that the student developed both procedural fluency and conceptual understanding

Maria Kargas