English schoolchildren do not fare well in international comparisons of mathematical, particularly algebraic, ability. I believe that this is at least partly due to algebra being traditionally taught using only symbols, ignoring the enactive-iconic-symbolic trajectory described by Jerome Bruner, which says that experiencing the way in which concrete objects behave makes it possible to learn in the abstract. I believed algebraic understanding would be enhanced by students working with concrete objects that they would be able to connect to algebraic ideas, for example, using a giftcard to represent a value that existed but was unknown to the holder. The conventional research approaches of positivist or interpretivist did not seem to me to reflect a dynamic reality in which my role was not a dispassionate external observer or interpreter. Action research is a critical theory approach that embraces the individuality of the researcher/practitioner, by recognizing practical knowledge in context ("praxis"), allowing their understanding of the situation being researched to be developed from cycles of action, reflection, and adjustment of their own practice. The benefits to me were the flexibility of reflecting and making changes, empowerment to challenge the status quo, and substantial insight into how children learn. The disadvantages in terms of generalizability and lack of conclusiveness are always factors in this sort of research, but the difficulty of creating materials, managing data, and interpreting results was more challenging than I had anticipated. My work led to the development of teaching material that has already had impact beyond my own practice. [This content is provided in the format of an e-book.]