Topic Study Group 23 Visualization in the Teaching and Learning of Mathematics

This paper was published in the Proceedings of the 13th International Congress on Mathematical Education held at Hamburg, Germany from 24 - 31 July 2016

their implications to mathematical thinking and teaching-learning processes  Visualization and language, including interrogating the relationships between visualization, signs and language(s), including embodied aspects such as gestures and bodily actions.  Visualization in school practice and in teacher education, including research into the explicit inclusion of visualization in school curriculum, practice and assessment, and interrogating the development of visualization skills in teacher education programs.  Visualization as a social process, including research about the negotiations on visualization in classrooms as well as diversity aspects across various cultural contexts.  Visualization and research methodology, including asking questions about visualization research design and methodological approaches that foster visualization.  Visualization and theory, including research into possible overarching theoretical frameworks that could frame and orient visualization research such as embodied cognition theories, learning theories, socio-cultural theories.
This list was not meant to be exhaustive, and we encouraged contributions based on empirical research, including ongoing studies, as well as theoretical elaborations and reflections on a theme.
We received 29 submissions of papers and 13 submissions of posters from 16 countries (South America and North America, Asia, Europe and Africa), which shows a very encouraging cultural diversity. Papers underwent a peer review process that involved two submitting authors and one team member for each paper submission, and two team members for each poster submission. The review process was guided by criteria that included innovation, theory and methodology, coherence, interest for an international audience and clarity. Paper proposals could be accepted as either long or short papers. After the review process was completed, and the conference finally took place, 13 long papers and 9 short papers were presented and discussed during the conference sessions.
During the conference, we met in a blended modality (in presence and at distance) in four sessions, for a total of six hours. Onsite facilitators in Shanghai helped us to manage a reliable connection between onsite and online participants.
As TSG-23 we wanted to provide sufficient time for scientific exchange and discussion. As we had not enough time to discuss and interact with the presenters during our official sessions, we met in additional interactive sessions during dinner times (Shanghai times) in order to share moments of scientific discussion and exchange pertaining to the specific presentations. These meetings were realized only at distance and made use of the parallel rooms facilities. Throughout the four days we attempted to facilitate dialogue between participants in order to give constructive feedback to the presented studies, identify possible research themes and opportunities that emerged from the presentations. We found that the discussion time proved very fruitful in facilitating networking opportunities and sustaining the interest momentum that was generated during the presentations. At the end of the last session, we hosted a 50minute whole group reflection session to consider some research implications that arose.
The long papers (LO) were allocated 15 minutes for presentation, and short papers (SO) were allocated 10 minutes. Papers were briefly discussed in the official sessions, and then discussed in more depth in the parallel rooms during the additional sessions.
Our programme was organized around eight themes or clusters which characterized the submissions. Below we present each theme as they appeared in the programme and list the related papers in Tab.1 (on the next page).
 Theme 1: Visualization and problem-solving. This theme related specifically to research that looked at how visualisation process and mathematical problemsolving articulated with each other.
 Theme 2: Classroom interaction. This theme interrogated how issues of visualization played out in particular classroom interaction contexts.
 Theme 3: Visualization and teaching. The focus of this theme was how selected teachers used visualization tools and media (including dynamic geometry software) to teach mathematics. 

P r e p r i n t
In our last session we consolidated our deliberations by identifying possible visualisation avenues for further research that emerged. These were:  Visualisation as a cognitive process. This includes visualisation and reasoning, visualisation and imagination, difficulties with visualisation.  Visualisation and mathematising.  Visualisation and new technologies, such as interactive dynamic software, augmented reality and other digital media.  Visualisation and language, specifically the relationship between visualisation, signs, language(s), including embodied aspects such as gestures and bodily actions.  Visualisation as a social process, including negotiations on visualisation in classrooms as well as diversity aspects across various cultural contexts.  Visualisation and theory, which includes researching possible overarching theoretical frameworks that could frame and orient visualisation research such as embodied cognition theories, learning theories and socio-cultural theories. Do we have a visualisation theory?