Although she welcomes in principle any move to improve teaching of the 3Rs and disseminate good practice, she feels the extra money might be put to better use in schools, helping teachers do the job themselves.
Mrs Beeson, head of Greenholm primary school, Birmingham, believes the support will be spread so thinly - with funds for just 10 literacy and 10 numeracy centres employing two full-time staff each - it will benefit only a minority of pupils.
"Those two members of staff are going to be stretched to the limit and I wonder how much they will actually be able to achieve," she said.
Furthermore, she fears the centres may undermine the good work already being done if they operate in isolation.
"There's plenty of expertise out there already. In Birmingham we have pupil support and educational psychology units that are stretched to the point where the amount of help they can offer is quite thin on the ground.
"If the new centres are going to act as a clearing house and bring together the best ideas around, that's great. But if there's no collaboration they will be a waste of money, duplicating what's already on offer."
The Department for Education and Employment has said priority will be given to areas judged to need help in raising standards, which means Mrs Beeson's primary is unlikely to benefit.
For the past year, she and her staff have put a lot of effort into improving literacy and the hard work appears to be paying off. Fewer children than in previous years managed only a level 1 or below in their key stage 1 tests last summer and more achieved levels 2 and 3.
Although the school did not complete key stage 2 tests, there has been an increased level of interest among older children in using the library and parents have become more involved.
The secret has been a multi-pronged approach, sparked off in part by a survey last year of children's reading habits.
Although the 427-pupil school is not in a particularly disadvantaged area, the survey showed few children picked up books for pleasure and parents tended only to read with them when asked by teachers.
Mrs Beeson decided to focus her efforts on helping children enjoy books with their families. She introduced a scheme - developed by a primary school in Swindon, Wiltshire - whereby parents make story sacks containing books, an educational game and soft toys to help tell the stories.
Once enough sacks have been made, children are able to take them home for short periods.
Each brightly coloured sack costs Pounds 15 and the school is hoping to get business sponsorship and produce at least 50 by summer.
"They encourage families to interact. They keep children away from the TV, develop their speaking, listening and reading, and most of all they are fun," said Mrs Beeson.
Last September a family literacy group which meets every Monday at the school, was launched. Parents receive help with their own reading and writing and are taught how to assist their children.
Mrs Beeson has also established a book corner in every classroom and introduced literary role-play activities using funds from the parents' association.
And she has invested in a laminator and spiral binder so pupils can produce their own, professional-looking books which are displayed in the library.
She said there was a tremendous will throughout the school to raise standards in literacy and numeracy, but cash for improvements was tight.
"Money isn't everything but it certainly helps oil the wheels. If setting up new centres means taking from one to give to another I think they're a mistake. They will be targeted at schools that really need support but unless those schools want to improve, no amount of advice will make much difference, " she added.