International Portal of Teacher Education

Source: ZDM Mathematics Education, Volume 52 Isuue 5, 943–958

(Reviewed by the Portal Team)

The authors have included the use of collaborative mind mapping activities as an alternative to threaded forums in the elementary mathematics education program at Western University.
They have done this for over three years in two different courses: a computational thinking in mathematics education course, and a mathematics teaching methods course.
In this paper, they present a grounded theory developed from these experiences of collaborative mind mapping.
The emerging theory responds to the question:
How do preservice mathematics teachers construct mathematical and pedagogical knowledge while they interact through three different tools for online collaborative mind mapping (i.e., Popplet, Mindmeister, and Mindomo)?

Participants
In this research, the authors implemented a multiple case study (Stake 2005) of collaborative mind mapping, carried out in the undergraduate elementary mathematics teacher education program at Western University.
Participants were enrolled in blended courses (using online activities as a support for face-to-face learning), where some of the online activities used collaborative mind mapping for knowledge construction.
Students used different mind mapping tools and received different scaffolding techniques in terms of prompts and number of participants per group.
Each one of these courses is treated as a case.

Method
Sources of data and sample
The data used in this study consisted of two elements.
The first was the set of artifacts (mind maps) created by the students as a final product, which included the students’ texts, images, videos and layouts they used to represent knowledge.
The second source of data was the online records of students’ interaction during collaborative mind mapping, obtained through Mindomo’s, Mindmeister’s and Popplet’s history feature, which allowed researchers to look at the whole process of mind-map construction.
Additionally, a visual version of the interaction was obtained by recording the process of mind map construction in the history feature.
Of the total number of mind maps constructed in each case, for this study the authors selected only those for which students had given consent to participate.
As a result, they used only the mind maps for which all students gave consent to participate, a total of 47 mind maps (out of 93).

Findings and discussion

Stages of knowledge building through mind mapping
Participants in this multiple case study engaged in a process of knowledge building in accordance with the ideas of Bereiter (2002), who, as a part of his connectionist model of the mind, defined knowledge as connections made through common goals, group discussion, and synthesis of ideas.
The visual affordances of mind maps allowed for viewing, linking, and manipulating ideas, which are functions that contribute to collaborative knowledge building, in a way that threaded discussions cannot support (Scardamalia and Bereiter 2003).
Mind maps were an agent that reorganized the ways in which students thought about mathematics, computational thinking, and mathematics pedagogy.
Instead of describing or commenting on different aspects of readings and class activities, as is usually done in threaded forums, mind maps made students abstract the main topic or idea they wanted to communicate and build around that topic.
While comments and descriptions were still part of mind maps, participants changed the ways they started discussions, and how they looked at concepts and the relationships among them.
The different technical characteristics of the three tools (Popplet, Mindmeister and Mindomo) also had an impact in the reorganization of knowledge.
The authors found that the emerging three stages of knowledge building through mind mapping—introducing a topic, building a concept, and making sense of the whole picture—can be compared with the Online Asynchronous Collaboration (OAC) model to support the development of mathematical knowledge for teaching (MKT) proposed by Clay et al. (2012).
In the second stage of knowledge building, when the teacher candidates built a concept, they engaged in activities that included viewing, reviewing and commenting on others’ responses (Stages 3 and 4 in OAC). However, in their grounded theory, they found that in the final stage (making sense of the whole picture) participants did not engage in discussing and revising initial responses (Stages 5 and 6 in OAC).
Instead, the affordances of the tools prompted them to connect ideas and relate concepts.
These kinds of connections, which were not explicitly made in the readings and materials, were a great indicator of teacher candidates’ learning.
However, in their multiple case study, there was still much space for improving collaboration throughout the whole process of mind map construction.
While the final products (mind maps) were presented as collaborative work, the construction process in its two early stages—introducing a topic and building concepts—shows mainly signs of cooperation, understood as a process “in which each member contributes an independent piece to the whole in a form of a division of labour” (Harasim 2017, p. 121).
This result could be due to an issue of authorship, where participants did not feel comfortable adding to or editing work authored by another person.
The authors believe that when a mind map is co-created by students, they feel the need to set boundaries to their own work and that of others, so that they can fulfill the purpose of demonstrating their knowledge and original ideas to the instructor.

Results of knowledge building through mind mapping
The constructs the authors called results of knowledge building through mind mapping—developing discourse and developing leadership—contain elements of the three roles that Borba and Llinares (2012) identified in mathematics education online learning environments.
The first role refers to providing asynchronous collaborative communication interfaces that allow participants to spend more time building their arguments.
While participants in mind maps relied heavily on language to describe concepts and express thoughts, the interface allowed them also to use connectors, shapes, and colours to relate and highlight ideas as part of their discourse development, hence spending more time building arguments than verbally explaining ideas.
The second role refers to providing sharing and co-creating tools that allow teachers to compare and share their ideas.
The mind maps showed that participants engaged in this comparison and sharing as they decided the topics to add, and which colours to use, taking into consideration the topics others had added.
The role of the leader was also important in determining what topics were included and the general structure of the mind map.
The third role refers to the fact that the visual representation serves as a group memory of the work, where participants are reminded of previous ideas and their implications.
In mind maps, the topics introduced by others are visually available at all points of the interaction, so participants did not include those topics again and instead added comments if they agreed or had something to say about a previously included topic.
While the affordances of the mind maps allowed for more direct ways of communicating relationships, highlighting central ideas, and illustrating mathematical concepts through images and videos, and the participants used these features conveniently, they still relied on the power of written speech to articulate and represent most of their thoughts.
Since the mind maps in the study’s context were a case of self-directed learning environments—with minimal to no participation from the instructors—there were many opportunities for participants to develop leadership.
In Garrison’s (2017) model of online interaction, instead of referring to a teacher presence, he refers to a teaching presence, since he observed that when the teacher withdraws from the discussion, participants develop the role of directing the cognitive and social processes.
In the case study, the assumption of this role by some students was a natural response to the task, since the activity prompts did not include any role designations or instructions on how to start and organize the collaborative work.

Concluding remarks
The authors set out to find how preservice mathematics teachers interact and construct knowledge through collaborative mind mapping, which may resemble online discussions carried out through forums, but which have little in common with these forms of linear text.
In the case study, mind maps enabled distinct semiotic possibilities that written conversations do not.
These possibilities included more options in arranging items, sizing, highlighting, linking or separating ideas.
They observed that teacher candidates followed a straight sequence when constructing knowledge through collaborative mind mapping.
There are two byproducts of this process: participants develop a discourse on mathematics and mathematics pedagogy and leadership, while using varied forms of expression according to their preference or the nature of the content.
Finally, the theory generated in this study is valuable for expanding existing literature, especially concerning the use of visual tools for mathematics teacher education, and for informing practice and generating suggestions for teachers and developers to implement this type of learning experience in other courses and/or other education levels, as well as to set the stage for further research.

References
Bereiter, C. (2002). Education and mind in the knowledge age. London: L. Erlbaum Associates.
Borba, M., & Llinares, S. (2012). Online mathematics teacher education: Overview of an emergent field of research. ZDM Mathematics Education, 44, 697–704.
Clay, E., Silverman, J., & Fischer, D. J. (2012). Unpacking online asynchronous collaboration in mathematics teacher education. ZDM, 44(6), 761–773. 
Garrison, D. R. (2017). E-learning in the 21st century: A community of inquiry framework for research and practice. Taylor & Francis Group: Routledge.
Harasim, L. (2017). Learning theory and online technologies (2nd ed.). New York: Routledge.
Scardamalia, M., & Bereiter, C. (2003). Knowledge building. In J. W. Guthrie (Ed.), Encyclopedia of education (2nd ed., pp. 1370–1373). New York: MacMillan Reference.
Stake, R. E. (2005). Qualitative case studies. In N. K. Denzin & Y. S. Lincoln (Eds.), The SAGE handbook of qualitative research (3rd ed., pp. 443–466). Thousand Oaks: SAGE.