Many teachers argue that it gives some pupils a better chance of demonstrating their abilities than an exam. But Ken Boston, Qualifications and Curriculum Authority chief executive, told a maths conference earlier this month that not everyone agreed.
The consultation will see if there are any areas of maths for which coursework is a "more valid and reliable" assessment method for grading pupils. Changes will be brought in from September 2007.
Pressed on whether coursework could be scrapped, a QCA spokesman said: "If that was the clearly expressed view from the consultation, I suppose it would be."
Coursework counts for 20 per cent of maths GCSE. Half of these marks are for an assignment on using and applying maths, while the rest is for a statistical, or "data handling" task.
Data handling, introduced in 2003, has been particularly controversial, with teachers arguing that it can be reduced to teaching children to "jump through hoops". Answers are also available online.
The consultation, which will be launched by the summer, comes after Ruth Kelly, the English Education Secretary, asked the QCA to review the place of coursework in all subjects. Many schools in Wales take GCSE courses from QCA-approved English boards.
Coursework was heavily criticised by the 2004 Tomlinson report on secondary exams, which said pupils were burdened with routine assessments which were similar in many subjects.