Margaret Jones, the association's honorary secretary, said the tests, which will be introduced from 2010, are too focused on facts and will not teach pupils how to fully understand concepts or apply them in a variety of situations.
In a letter to members to be sent out this month, Ms Jones writes: "The mathematics community does not want a basic skills test. Maths is not a set of facts to be learnt. It is a way of thinking about problems.
"We want functional maths to ensure students have the problem-solving skills for later in life.
"Just as they did with coursework, the exam boards and those directing its implementation centrally have taken functional mathematics and turned it into a travesty of what is needed."
Good mathematicians are like musicians who know their scales and arpeggios but use them to master complicated melodies rather than trot them out by heart, she argued.
"The current pilot is not about the wonderful ideas the mathematics community had when they first came together," she writes.
Pilots for functional tests in maths, English and information technology started in September.
The Qualifications and Curriculum Authority defines functional maths as knowledge that enables pupils "to take an active and responsible role in their communities, in their everyday life, workplace and educational settings", including the use of new technology where appropriate.
Sample questions from the exam board Edexcel ask pupils to order wood for a bookcase, measure up radiators for a kitchen and state how many houses should be built on a new estate.