In CERME9, as a long-standing group, TWG03 “Algebraic thinking” continued the work carried out in previous CERME conferences (e.g., Cañadas, Dooley, Hodgen, & Oldenburg, 2013). There were a total of 15 papers and 7 posters with a total of 24 group participants representing 18 countries: Argentina, Canada, Cyprus, Czech Republic, Germany, Hungary, Ireland, Italy, Mexico, Norway, Portugal, Romania, Spain, Sweden, Turkey, Ukraine, UK, the USA. As we have observed in previous CERME working group reports, algebraic thinking is a “mature” sub-domain within mathematics education research (e.g., Cañadas et al., 2011). As a result, our group discussions touched on many familiar themes. Of particular interest to the group was the range of research frameworks, models and theories that participants drew on. In order to understand this diversity, we developed a categorisation of the frameworks used in TWG03 papers, where authors of TWG03 papers are given in square brackets.1