Mrs Kaembe told the BBC: "She has built classrooms at existing schools... really it's a difference in terminology".
The project, documented on a dedicated Guardian website, distributed malaria bednets, trained local village health teams in basic medical care, repaired and built classrooms and installed boreholes.
Madonna's charity, Raising Malawi, claims to have built 10 schools serving more than 4,800 children, but Mrs Kaembe told the BBC that in reality she had built "classrooms at existing schools".
She continued: "They have said... they have built ten schools in Malawi and on our side what we know is that she [Madonna] has built classrooms... these are not schools from our side and really that's the essence of the difference between her side and the Malawi government".
There is a strong ownership of COBET in the communities and on community members' own initiatives, they have built classrooms, latrines and initiated school meals.
Educators can learn new ways to build classroom community and will then see the positive impact connections and relationships with their students and families have on academic achievement.
They also become student advocates who build classroom learning communities based on mutual respect and fight for and defend their students against unfair practices and inadequate funding.
But this is where SEL can start to shift the tide as fostering social and emotional skills helps to build classroom and school environments that bring out our innate altruism.
This when we are expected to absorb £5m in council tax cuts and build classrooms for 240 more children".
Schools Mr Alexander announced plans to spend £21bn by 2020 to build classrooms for more than 275,000 new primary school places and 245,000 new secondary school places.
The training program at Rejaf received about $1 million from international donors through the United Nations, which helped to build classrooms and provide part-time trainers, particularly in human rights.
