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Faculty Resources for Online Teaching

Classifications of Online Teaching


The SAMR Hierarchy Bray and Tangney (2017)

Substitution - Online teaching acts as a direct substitution of in-person teaching with no change. Examples: live/videos of lectures going through worked examples, posting of solutions, whole-class discussions online, Powerpoint presentations.

Augmentation -  The role traditionally associated with the teacher to deliver content has been outsourced to the technology (e.g., Khan Academy, YouTube, MyMathLab). The use of online tutorial material reflects a view of learning as a cognitive process (internal mental process including information processing and memory). The technology acts as a substitute for the teacher, with the added potential for learning 24/7 in any location. 

Modification - The online learning environment involves technology that allows for task redesign (e.g., students using GeoGebra to express rotations and translations as a sequence of reflections). Students can work in pairs or small groups in order to solve tasks. In this way, their learning is constructed in a social environment. The technology facilitates new approaches to the solution of the problem, through the dynamic aspects of the software. In addition, the distribution of the process of problem-solving amongst participants through interactions with each other and the technology benefits collaboration. The main aim of tasks is to increase collaboration and mathematical creativity. 

Redefinition - A variety of technologies are used together, in accordance with a pedagogic approach, along with the provision of support for the student and the teacher. In this case, Exploratory Learning Environments are combiner with Computer-Supported Collaborative Tools in one web platform. Students use a computer-supported collaborative learning environment to communicate. Both online communication and the exploratory task would not have been possible without the use of technology. There is a particular focus on the impact that the collaborative technology, in conjunction with the specific tasks, has on the students' meaning-making process.

Discussion (Bray and Tangney, 2017)

There is evidence from literature that substitution and augmentation are widely utilized in classrooms. The majority usage of technology at the lower levels of the SAMR hierarchy shows that the potential of technology to improve the learning experience is not generally being promoted in classrooms. Furthermore, the potential of the technology to "transform" the learning experience of students, is not being harnessed. At the moment, it is more often used to simply enhance traditional lecture practice. Although it provides easy access, it does not require the user being required to understand the intricacies of their calculation.

In order to radically change the dominant pattern of substitution and augmentative technology usage in classrooms, it is likely that a change in focus away from prevalent high-stakes assessment and associated curriculum pressures will be required. 

Traditionally, didactic teaching methods with an emphasis on procedure over understanding, and rote learning of subject content over literacy are adopted in many classrooms. This has a negative impact on students' engagement with, and confidence in, mathematics. Digital technologies that align with a more constructive approach may address these issues. That is the use of technology should be emphasized primarily in situations that could not have been completed without it. Positive effects of technology are strongest when combined with a constructivist, team-based, project-based pedagogical approach, and non-standardized assessment methods. Larger positive effects on learning are identified when the students did not have a one-to-one relationship with the technology. Teachers act as facilitators to the students, providing structure and advice and keeping track of their progress.

Teachers will only expend the effort required to integrate technology into their teaching practice when they can see that there are significant benefits in terms of learning outcomes. For change to be successful, teachers require resources, practical examples, and support from colleagues and management. 



Bray, A., & Tangney, B. (2017). Technology usage in mathematics education research – A systematic review of recent trends. Computers and Education, 114, 255–273.

Teaching Math Online by Matthew Cheung. This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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