“To infinity, and beyond!” - the rallying cry of the irritatingly naive Buzz Lightyear in Toy Story. Perhaps the choice of title for this book implies an equal naivety on the part of those of us who hope the numeracy strategy really will change things in the long, problematic history of British mathematical education.

Criticism of the numeracy strategy from the mathematical education research establishment has been growing. It is not research-based; it is over-reliant on one teaching style (in the teeth of the Cockcroft report’s insistence that diverse learning styles make advocacy of a single teaching approach impossible). Numeracy and Beyond explores the further charge that it more or less abandons application in favour of a narrow concentration on basic skills: Attainment Target 2 victorious over the AT1 principles of using and applying, so hard-fought, for so long. ” We believe that application is at the heart of numeracy” say the authors in their introduction. An overview of relevant research demonstrates clearly that “the problem of application” is neither new nor peculiarly British, and this is followed by a critical look at the history of application within the mathematics curriculum in England and Wales, including the numeracy strategy.

Subsequent chapters describe the work of primary teachers during the course of a Nuffield project called “Using and Applying in the Primary School”. This included visits to Japan, where the approach to application is also described and commented on. The words of one Japanese teacher could well describe many plenary sessions: “When asked about his technique of getting children t explain each other’s methods, he said, ‘Expressing other people’s ideas is the perfect way to good understanding. Children go to the board and explain, and there is no shame about getting it wrong.’” AT1 was always the most problematic area as regards teaching and assessment. We should not be surprised that an impatient government has opted for “what works” over diffuse research messages which made too little real difference in too few classrooms.

Nor am I surprised that it proves hard for academics to isolate one particular conceptual paradigm behind the strategy: it springs not from theory, but from practice. Maybe this explains why it has been more readily welcomed and understood by teachers than previous initiatives. Good teachers possess a repertoire of styles: they switch between aspects of associationism and situated cognition instinctively.

The framework does not prevent this. It neither forbids a constructivist approach, nor makes attention to application impossible if (as I do) you agree with Hughes et al that “application is at the heart of numeracy.”

But for application to happen, you must have something to transfer first. The strategy has got all primary teachers genuinely engaged with mathematics teaching and is proving a species of in-service activity in itself, along with the five-day courses. The framework is a tool such as they have never had before and has been overwhelmingly welcomed. Providing funding is maintained, I believe the initial gains can be built upon and become a permanent classroom culture change. Yes, to numeracy, and beyond! - but we need to reach numeracy first and, so far, we have not been sufficiently successful at that.

Laurie Rousham is a numeracy consultant in Suffolk.