Explicit formal expression
“the very need for remote communication of mathematical ideas – either synchronous or asynchronous – provides a motivation to produce explicit formal expression of mathematical ideas” (Hoyles & Noss, 2019, p. 141)
Communication
The affordances of new media help preservice teachers to communicate mathematics in multimodal ways and to see mathematics as a collaborative enterprise.(Gadanidis & Namukasa, 2013)
Multimodal
Collaboration
But in online learning...
For Cognition
Highlighted students’ contradictions (Johnson, 2016), misconceptions, and knowledge gaps (Wilson et al., 2016).Improved self-evaluations (Balım, 2013).Increased comprehension and ability to recall information. This led to more active learning (Balım, 2013).Positive impact in knowledge visualization and establishing relationships between science concepts and inter-disciplinary content (Himangshu-Pennybacker, 2016).Students could extrapolate knowledge of a given case study to a local and global context (Himangshu-Pennybacker, 2016).Both collaboratively generating and critiquing visual representations can enhance concept understanding (Schwendimann, 2016).
For Collaboration
Group cognitive processing was enhanced (Wu et al., 2016).Learners returned more easily to the main discussion from off-topic discussions (Wu et al., 2016).It works better to pair the use of visual representations with appropriate digital and scaffolding tools (Iaosanurak et al., 2016).In conceptual tasks, the visual representations allowed more discussion on disputation rather than on information exchange (Wang et al., 2017).In design tasks, visual representations allowed for less discussion on task planning and fewer questions asked (Wang et al., 2017).In project-based learning, visual representations allowed more comparison, testing and analyzing (Wu & Hou, 2014).
For Attitude
Increased motivation and interest towards learning (Balım, 2013; Lin et al., 2016; Ahmed & Abdelraheem, 2016; Wilson et al., 2016).More creative and fertile learning environment, accommodating different learning preferences (Wilson et al., 2016).Students would continue to use visual representations in the future (Draper, 2015).Students felt insecure when trying the visual representation for the first time, but they found the outcomes to be encouraging (Tobaja Márquez et al., 2017).On conceptual tasks, students enjoyed doing a collaborative visual representation, they showed less anxiety and improved their relationships with other students from the group (Wang et al., 2017).
UDL Guidelines
Vary demands and resources to optimize challenge (checkpoint 8.2). Foster collaboration and community (checkpoint 8.3). Optimize relevance, value, and authenticity (checkpoint 7.2). Offer ways of customizing the display of information (checkpoint 1.1).Illustrate through multiple media (checkpoint 2.5). Provide options for expression and communication (guideline 5).
Allow choice on how to contribute
Inform about display options
Emphasize on collaboration
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)?
Case Studies
The activity
Group Size: 4-8 participantsInstructor moderation: low to noneIntroductory activity:Case 1: a video on how to use the tool and in-class discussion about connecting ideas in Popplet.Case 2: videos about the use of Mindmeister + an instructor-led live presentation with Q&A.Case 3: the instructor only provided a video about the tool.Access:Cases 1 & 2: Prior to each online week, TCs received a link with access to their group’s mind map.Case 3: TCs to created their own mind maps and invited the instructor to view them (rather than instructors creating blank canvases and sending the links to the TCs).
Sample mind maps
Case 1
Case 2
Case 3
What we found
Stages
Introducing topics
Building Concepts
Making Sense
Products
Developing Leadership
Developing Discourse
Expression Variations
Collaborating in real time
Using descriptions
Using images
Using Videos
Using the chat
Ahmed, A., & Abdelraheem, A. (2016). Investigating the Effectiveness of Digital - Based Concept Mapping on Teaching Educational Technology for Undergraduate Students. Journal Of Educational & Psychological Studies / Magallat Al-Dirasat Al-Tarbawiyyat Wa-Al-Bafsiyyat, 10(4), 737-747.Balım, A. G. (2013). Use of technology-assisted techniques of mind mapping and concept mapping in science education: a constructivist study. Irish Educational Studies, 32(4), 437-456. doi:10.1080/03323315.2013.862907Draper, D. C. (2015). Collaborative instructional strategies to enhance knowledge convergence. American Journal of Distance Education, 29(2), 109-125. doi:10.1080/08923647.2015.1023610Gadanidis, G., & Namukasa, I. (2013). New Media and Online Mathematics Learning for Teachers. In D. Martinovic, V. Freiman, & Z. Karadag (Eds.), Visual Mathematics and Cyberlearning, Mathematics Education in the Digital Era 1 (pp. 163–186). Dordrecht: Springer. doi:10.1007/978-94-007-2321-4 7Himangshu-Pennybacker S. (2016) Transforming Science Pedagogy: Using Concept Mapping to Design an Interdisciplinary Approach to Teaching Middle School Science. In: Cañas A., Reiska P., Novak J. (eds) Innovating with Concept Mapping. CMC 2016. Communications in Computer and Information Science, vol 635. (pp 265-274) Springer, Cham.Hoyles, C., & Noss, R. (2009). The Technological Mediation of Mathematics and Its Learning. Human Development, 52, 129–147. doi:10.1159/000202730Iaosanurak, C., Chanchalor, S., & Murphy, E. (2016). Social and emotional learning around technology in a cross-cultural, elementary classroom. Education & Information Technologies, 21(6), 1639-1662. doi:10.1007/s10639-015-9406-4Johnson, L. L. (2016). Writing 2.0: How English teachers conceptualize writing with digital technologies. English Education, 49(1), 28-62.Lin, Y., Chang, C., Hou, H., & Wu, K. (2016). Exploring the effects of employing google docs in collaborative concept mapping on achievement, concept representation, and attitudes. Interactive Learning Environments, 24(7), 1552-1573. doi:10.1080/10494820.2015.1041398Schwendimann, B.A. (2016) Critiquing as an Alternative to Generating Concept Maps to Support Knowledge Integration Processes. In: Cañas A., Reiska P., Novak J. (eds) Innovating with Concept Mapping. CMC 2016. Communications in Computer and Information Science, vol 635. (pp 40-53) Springer, Cham.Tobaja Márquez, L., Llinás, J. G., & Macías, F. S. (2017). Collaborative learning: use of the jigsaw technique in mapping concepts of physics. Problems of Education In The 21St Century, 75(1), 92-101.Wang, M., Cheng, B., Chen, J. Mercer, N., Kirschner, P. (2017) The use of web-based collaborative concept mapping to support group learning and interaction in an online environment. The Internet and Higher Education, 34, 28-40. doi: 10.1016/j.iheduc.2017.04.003.Wilson, K., Copeland-Solas, E., & Guthrie-Dixon, N. (2016). A Preliminary Study on the use of Mind Mapping as a Visual-Learning Strategy in General Education Science classes for Arabic speakers in the United Arab Emirates. Journal of The Scholarship of Teaching & Learning, 16(1), 31-52. doi:10.14434/josotl.v16i1.19181Wu, S., & Hou, H. (2014). Exploring the Process of Planning and Implementation Phases in an Online Project-Based Discussion Activity Integrating a Collaborative Concept-Mapping Tool. The Asia-Pacific Education Researcher, 23(1), 135-141. doi:10.1007/s40299-013-0089-6Wu, S., Chen, S. Y., & Hou, H. (2016). Exploring the interactive patterns of concept map-based online discussion: a sequential analysis of users’ operations, cognitive processing, and knowledge construction. Interactive Learning Environments, 24(8), 1778-1794. doi:10.1080/10494820.2015.1057740