This report is based on inspections of mathematics in primary and secondary schools carried out between August 2002 and April 2005. In addition to schools inspected, Her Majesty's (HM) Inspectors also visited primary and secondary schools to observe and describe aspects of best practice. This report also draws on pupils' attainment in Scottish Qualifications Authority (SQA) examinations, the Assessment of Achievement Programme (AAP), the Programme for International Student Assessment (PISA) and Trends in International Mathematics and Science Study (TIMSS). The focus of this report is on action for improvement. The starting point is the existing good practice which many schools are using to strengthen pupils' learning and to raise achievement. A number of previous reports have identified strengths and areas for improvement in learning and teaching mathematics. This report builds upon the earlier HMIE reports "Improving Mathematics Education 5-14" (1997), "Standards and Quality in Primary Schools: Mathematics 1998-2001" (2001) and "Standards and Quality in Secondary Schools 1995-1999: Mathematics" (1999). Particular questions addressed through the report include the following: (1) How good are attainment, courses, learning and teaching and leadership?; (2) What is the evidence of improvement?; (3) What are the strengths of existing good practice?; and (4) Where is the scope for further improvement? Each section of the report identifies strengths and issues common to both the primary and secondary sectors. Where appropriate, the report comments on features applicable to specific stages. The report also provides a series of prompt questions which schools should find helpful in evaluating and improving their own practice. (Contains 15 charts and 3 footnotes.)