Our extensive research has provided incontrovertible evidence of the significance and value of Children's Mathematical Graphics, for children's understanding of the abstract symbolic system of mathematics. This has been acknowledged in government and independent reviews. However, in England and in most countries, our findings are consistent with what Millet and Johnson observed is 'a worldwide trend ... typical teaching is assumed to be the total or significant use of a commercial mathematics scheme' (cited in Maclellan, 2001, 76).

     More recently, Baroody et al., (2019) found that there has been a significant increase in the use of worksheets at the expense of play. With respect of children's learning, many of our concerns have been voiced by other researchers, the use of worksheets leads to:

• Low-level activities of the ‘fine-motor’ skills type - such as colouring in and tracing over - that require little or no mathematical thinking 
• Significantly, both published and teacher-made worksheets prevent children from making sense of the standard, abstract symbolism of mathematics, since they deny opportunities to make meaning through their own marks and written methods and to ‘translate’ between their informal symbols and the standard forms. 

• Brooker's (2002) "systematic observations... suggests also a particularly low level of commitment while children are occupied with worksheets. Most children treat the completion of such sheets as a self-standing task unconnected to any learning activity with which they may be associated in a teacher’s mind. Rather, the sequence of actions involved in ‘doing a worksheet’ appears to be one of the more mysterious aspects of learning to be a pupil ... Children are required to sit at a table and complete the tasks when summoned…  Children have little idea what knowledge or skills they are acquiring, or demonstrating." 

• We have found no published research evidence that printed worksheets support young children's understanding of the 'written' language of mathematics, orthal they deepen children's mathematical thinking.

References

Baroody, A. J., Clements, D. H., & Sarama, J. (2019). Teaching and learning mathematics in early childhood programs. In C. Brown, M. B. McMullen & N. File (Eds.), Handbook of Early Childhood Care and Education (1st ed., pp. 329-353). : Wiley Blackwell.

Birbilli, M. (2017). The pedagogy of worksheets in early childhood settings: Teachers beliefs and practices.

Brooker. L. (2002). Starting school: Young children learning cultures. OUP.

Maclellan, E. (2001). Representing addition and subtraction: Learning the formal conventions. European Early Childhood Education Research Journals 9,(1), 73-84.

Millet, A. & Johnson, D. (1996). Solving teachers' problems: The role of the commercial mathematics scheme. In D. Johnson& A. Millet (eds.). Implementing the mathematics National Curriculum. Paul Chapman.

Worthington & Carruthers (2003). Becoming bi-numerate: Study of teachers' practices concerning children's early 'written' mathematics. Paper presented at the European Early Childhood Education Research Association Conference, University of Strathclyde.