Product reviews for Conceptual Maths

Mattock’s Conceptual Maths provides a real focus on the understanding of concepts and the need for teaching for understanding. Key to this are the connections made between different concepts, subconcepts and procedures. Representations repeat to support connecting ideas and these are repeated across numerous concepts. For example, repeated representations show clear connections between multiplication of integers and multiplication of surds and how these ideas link to those of factors, multiples and equality. As a primary practitioner, I do not understand surds. However, I can clearly see how the ideas connect and how what I teach at a primary level supports and is developed by maths teaching at secondary level.

I also particularly like Mattock’s focus beyond number and calculation. While Conceptual Maths naturally begins with these building blocks, chapters on measures, shape and data allow explicit opportunities for teachers both new and experienced to think more deeply about how to teach these areas for understanding – something that is certainly less of a focus in primary mathematics literature. The discussion of measuring turn is particularly fascinating and has supported me in thinking more deeply about how we introduce degrees and protractors in Key Stage 2. Clear connections are made between proportion in an early chapter and conversion of units of measure in a later chapter, meaning the reader can pinpoint and explore the linked concepts with ease. The same representations are used to allow connections to be made and these have made me think even more deeply about how we teach units of measure in primary mathematics.

The layout of Conceptual Maths allows for clear and easy reading: concepts are linked to subconcepts, which are in turn connected to procedures rooted in the concepts. Each concept starts with prerequisites and link concepts, providing a clear path and supporting teachers in seeing relationships. Within this, Mattock puts emphasis on alternative methods and strategies meaning that more novice teachers of maths can gain a depth of understanding. For example, column addition is brilliantly explained through representations, but Mattock also emphasises the importance of other methods and strategies, depending on the values. 

In a time when we want teachers to be thinking deeply about concepts and promoting depth over breadth when it comes to challenging our quicker-grasping learners, this book provides the stepping-stones for this. As I have mentioned, more novice teachers can quickly develop an appreciation for the connectedness of mathematics and gain a depth of understanding to support teaching. More expert teachers have opportunities to think more deeply about a concept through a raft of excellent, carefully chosen example tasks peppered throughout Conceptual Maths. 

Overall, I think that any teacher of mathematics at any level of experience will benefit from Conceptual Maths. Trainee teachers would understand the complex connections between mathematical ideas, and the links between those taught at primary and secondary. More expert teachers can gain further insight into how one concept connects to another and how deep conceptual understanding is key if we want learners to apply the principles of, say, integer addition to working with fractions or surds. The depth activities woven throughout provide excellent thinking opportunities for new and experienced teachers alike, whatever phase is taught. I cannot wait to share this book with colleagues from all areas of mathematics teaching.