Evaluations of professional development programmes often seek to represent definitive outcomes, with phenomena posited as discrete, bounded and independent entities, and researchers positioned as external actors. An alternative is to understand the complexity of these relationships as entanglements by applying Baradian concepts. The value of this is illustrated through the example of the evaluation of the Mathematics Teacher Exchange (MTE). The MTE is a transnational professional learning programme, part of a policy described as learning from East-Asian mathematics teaching to introduce 'teaching for mastery' in England. Four instances of entanglement are analysed. The first two of these relate to the entanglement of evaluation processes and the mastery innovation in knowledge production. The other two examples are entanglements and diffractions that are found in changes in pedagogical practice related to mathematics representations and ways learners are grouped in classrooms. Although the transnational nature of the MTE is unusual and specific to the current English context, similar entanglements may be found in more locally generated teacher change initiatives and in their evaluation. Thinking in terms of entanglements adds another conceptual tool for sociomaterial and related analysis and also draws attention to our ethical responsibility for these relationalities.