Introduction

Effective teaching and learning of maths in primary schools involves an emphasis on building conceptual understanding, consolidating procedural knowledge and skill, and developing fluency. Another key component is ensuring that students develop a strong academic self-concept and mathematical identity, so that they see themselves as capable of being successful in their mathematics learning.

The following set of videos features a Year 5 & 6 class practising and consolidating their use of the strategy of bridging across a week of lessons. In addition to their daily hour of maths, this class also does 15 minutes of daily maths review (which is not shown in the videos). This class had learned the strategy of bridging earlier in the year, but had only practised bridging with addition and subtraction. On Days 1 & 2, the class reviews and consolidates concepts and procedures they had already learned, and on Days 3-5 they extend this knowledge by learning how to bridge with fractions and decimals.

In these videos, you will see the teacher, Laura, use a range of evidence-backed strategies for the effective teaching and learning of maths. These include:

• Being systematic and explicit when teaching mathematical concepts and procedures
• Using multiple representations when teaching, including concrete, visual, and abstract representations
• Building factual and computational fluency so that students can do maths with ease and accuracy, beyond just rote memorisation
• Explicitly teaching and using the language of mathematics
• Using word problems

The teacher also employs many general instructional strategies that align with the principles of effective, explicit teaching for mastery and long-term retention. Her approach involves asking many questions, providing models and worked examples, checking for understanding at every point, and obtaining a high success rate, all of which ensure that students are able to master the new content being taught and practised, recall it in the future, and apply in new contexts. Throughout the videos, the use of all these strategies is noted so that you can observe how they can be enacted in practice.

Research finds that the best way for students to master new content is by completing many, many hours of practice. For this reason, the videos deliberately show long periods of the class engaging in both guided practice, where the teacher guides the students through a range of problems step-by-step, and independent practice, where the students work without teacher guidance, but with monitoring and feedback from the teacher to ensure their practice is effective. By watching the videos, you will see many examples of extensive student practice with the new concepts and procedures being learned. Over the week, you will observe how the students’ fluency with these concepts and procedures gradually increases.

These videos also demonstrate how the teacher is able to effectively combine whole class instruction with small group work to ensure that she checks the understanding and monitors the progress of every single student in the class. Throughout the series of videos, you will observe her working with many different students to evaluate their understanding and mastery, in some cases providing additional supports and scaffolds, and in others offering increased challenge. During whole class sessions, she quickly reviews the students’ use of multiple representations (either physical materials or visual representations) to assess whether or not the students have understood what is being taught and practised. You will note how these many examples of formative assessment  allow the teacher  to respond flexibly and immediately to the students.

Finally, you will observe how enthusiastic and engaged the students are about learning and practising maths. The teacher frequently invites them to talk with their buddies about their existing maths knowledge, their thinking, and their ideas, and you will hear them talking about maths and using mathematical language during these moments. They are also eloquent and engaged when talking with the teacher about their work, and display an extremely positive attitude towards learning. They often come up with alternative ways of reaching the correct solution, and the teacher affirms the notion that different students will tackle their learning in different ways. A pedagogical approach that is both meticulously planned and highly interactive, and that involves asking lots of questions and constantly checking that the students understand and are actively participating, supports students to master the new content being learned while developing the characteristics of confident, effective learners.