Importance of differentiation
The literature on the importance and effect of differentiation on student learning outcomes is strong.
Vygotsky’s (1978) definition of zone of proximal development laid the foundation for modern theories on differentiated learning; the ZPD is where the skills are too difficult to master on their own but can be achieved with the guidance of a more knowledgeable person.
Hattie (2012) details that differentiation is more about addressing students’ different phases of learning rather than just providing different activities for different students. A teacher must cater to the needs and phases of learning as a student progresses from novice to capable to proficient.
Tomlinson (Tomlinson, 2001) key elements of effective differentiation outline how teachers can differentiate through content, process, product and environment.
Figure 1. Key Elements of Effective Differentiation (from Tomlinson & Moon, 2013)
Differentiating with Desmos
Tomlinson’s (2001) categorisations of teacher’s ability to differentiate:
Learning should result in student understanding of important content rather than largely rote memory of learning.
Desmos facilitates differentiation in multitude of ways. When used in a free form manner students are able to utilise tools, skills and knowledge at a level wholly suited to their ability. The classroom activities are produced by both practicing teachers and expert staff, all curated to ensure they are curriculum applicable yet accessible to all learners (Banting, McCormick, Twitchell, & Harvey, 2017).
Students will be able to access different ‘paths’ to master and ‘own’ their knowledge, ideas and skills.
Desmos extensive array of learning activities allow the teacher and students choice in how and when they learn, based on interest and ability. Students are able to see recommended activities based on progress, skip ahead or repeat tasks as necessary. Furthermore, the multiple representations inherent to Desmos support students differing learning profiles.
Students ability to show learning should not be constrained to one product or restrictive final piece of work.
‘Desmos art’ as described by Banting et al. (2017) allows students to demonstrate understanding and skill with a variety of functions. The task is specifically designed so that no one solution or method is correct, allows a multitude of approaches and students can produce work related to personal interests. Desmos learning activities include live tracking enabling constant formative assessment by the teacher of student progress rather than relying on a single summative piece at the end of the unit. The learning activities are also specifically designed to allow for a variety of approaches/solutions.
Students should be able to operate in climate appropriate for learning that also encourages interactions among students and teachers.
Desmos learning activities are explicitly designed with real-time collaboration in mind, be it requiring students to work in assigned or random pairs/groups to complete tasks, sharing of solutions peer examplars and feedback components. The teachers, using the class management component can pause selective all students as required and highlight common misconceptions or correct process as needed (all while maintaining anonymity if so desired). Finally, students can access the material at any time and place of their choosing ensuring the are learning in an environment they feel comfortable.
Untapped potential of Desmos to differentiate
While I am comfortable with the standard Desmos graphing suite and using premade activities I have no familiarity with the activity builder itself. As such there are two powerful options for improved differentiation that have not been described above:
Personally designed learning activities curated by myself taking into consideration my cohorts distinct contextual factors, learning needs and interests. This would allow for more precise and active differentiation (Orr, 2017) rather relying on pre made activities that might not best suite my students needs
Ability to scaffold students to create their own activities do demonstrate understanding (different product, process and content) (Gulati, 2017).
Negative affordances of Desmos in relation to student needs
As mentioned above, the planned usage of Desmos is dependant on a reliance on premade learning activities. The primary userbase of Desmos resides in North America and as such, language, conventions and material have strong North American themes. An example would be a linear relations activity that while extremely well designed for differentiation in content and process, utilising imperial measurement unit. While this might offer an alternative learning opportunity, it would increase cognitive load substantially and impede on the desired learning outcomes related to the structure of linear relationships.
Furthermore, teachers need to be aware of the disparity between notation and input students are familiar with and that require by Desmos. As Pierce, Stacey, Wander, & Ball (2011) explained, difference in notation and input can significantly impact students ability to demonstrate content and product understanding due to a restriction in available processes (single use software). As such, teachers need to be cognisant of these possible issues and misconceptions, proactively addressing them and monitoring to ensure they are not responsible for a reduction in the efficacy of using Desmos.
Banting, N., McCormick, K. K., Twitchell, G., & Harvey, S. (2017). Desmos Art. The Variable, 2(4), 25–28.
Gulati, S. (2017). Create your own interactive activity. At Right Angles, 6(3), 81–88.
Hattie, J. (2012). Visible learning for teachers: Maximizing impact on learning. Routledge.
Orr, J. (2017). Function Transformations and the Desmos Activity Builder. Mathematics Teacher, 110(7), 549–551.
Tomlinson, C. A. (2001). How to Differentiate Instruction in Mixed-Ability Classrooms. Alexandria: Pearson.
Tomlinson, C. A., & Moon, T. R. (2013). Assessment and Student Success in a Differentiated Classroom. ASCD.
Vygotsky, L. S. (1978). Mind in society: the development of higher psychological processes. (M. Cole, V. John-Steiner, S. Scribner, & E. Souberman, Eds.). Harvard University Press.