Children’s Mathematics

My work in children’s mathematics is informed primarily by Cognitively Guided Instruction (CGI). CGI helps teachers to understand children’s mathematical thinking and how to base teaching on their knowledge of children’s thinking. It supports all children to learn maths with understanding and leads to more inclusive and equitable classrooms.

I am currently working with a number of schools and Local Authorities in supporting teachers in developing their understanding of children’s mathematical thinking and how to apply this in practice. Typically, this involves initial development around CGI with teachers along with classroom-based support in which teachers’ learning is embedded in classroom activity.
In developing CGI in schools, my preference is to work with whole schools, or at least as many staff as possible within a school, and to support the development of practice by working collaboratively with teachers and support staff in classrooms. Whenever possible I use Lesson Study as a framework for supporting teachers’ learning. I encourage collaboration across schools and I have established opportunities for teachers to work in each others’ classrooms within and across schools and Local Authorities.


Lio’s classes on CGI address an ongoing issue for all teachers: that of being able to understand what the learner in the class thinks or understands in the area of Number Knowledge. As you become engaged with his classes and with the theoretical concepts underpinning Cognitively Guided Instruction, you start to question your own long held assumptions about people’s numerical capabilities. As you develop the confidence to take time to work with what each of the learners are bringing to the situation (and not ‘measuring the gap’ between your learners’ achievements and the expected ‘targets’ or ‘standards’) you develop greater autonomy to address the needs of each of your learners.

Prof. Effie Maclellan

Emeritus Professor of Education, University of Strathclyde

 I am the only person in UK to have studied with members of the original research team at University of Wisconsin-Madison. I have continued to study and developed this work in my own practice over the last 17 years. I continue to collaborate with colleagues in the US and I am invited regularly to share my work on CGI particularly in relation to inclusive practice, at conferences and events in the US, the UK and internationally. My published work in children’s mathematics is used for teaching in universities in the UK and across the world. I have recently been invited to collaborate on a research project on children’s counting with colleagues from UCLA and UCSB, California.

The professional development work I lead with schools is also informed by work which came about in collaboration with Dr Penny Munn. I worked alongside Dr Penny Munn at the University of Strathclyde for a number of years. Penny led the development of Maths Recovery across Scotland. We worked closely together on developing teaching programmes for teachers to learn about children’s mathematical thinking and development.

The Final report for the most recent study can be downloaded below.

Working alongside Lio has definitely developed my own confidence when teaching numeracy. Over the past two years I have noticed a significant difference in my ability to identify and analyse children’s thinking and therefore adjust my planning and assessments accordingly. Attending the CGI support sessions and keeping in regular contact with Lio has allowed me to develop numeracy in engaging and meaningful ways. Lio has always been supportive and encouraging during class visits, which has made this learning process both productive and enjoyable. Gemma Bell

Class Teacher

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