Desmo’s main function as a graphics calculator and digital geometry software allows for multiple representation, which positively impacts learning.
Early research on the ability of graphic calculators to impact mathematics education within literature of the early 90’s by Penglase & Arnold (1996) showed common perception that graphics calculators would be revolutionary for both curriculum and instructional methods.
Drijvers & Doorman (1996) and Schwarz & Hershkowitz’s (1999) projected that graphical calculators and similar technologies based on their early investigations learning (functions and transformations) would be greatly enhanced due to the expedient multiple representations they offer. Vaiyavutjamai & Clements (2006) supported this proposing that digital technology use within a functions based pedagogical framework will improve student academic out comes and importantly multi relational understanding.
DGS are most impactful when used in either as an inquiry-based approach or teacher-centric format. Chan & Leung’s (2014) meta-analysis of nine quasi-experimental studies demonstrate teachers using post 2010 DGS with said approach are most effective in increasing student’s mathematical achievement.
Desmos is the preferred suite compared to other apps, programs and calculators for project based learning of graphing equations and inequalities due to its easy-to-use, powerful and intuitive interface (Ebert, 2015)
Liang (2015) found Desmos provides an interactive, dynamic and persuasive approach of teaching limits when utilising a conceptual conflict approach.
Montigo’s (2018) well designed 12 week study on the effect of Desmos versus Ti-83 graphics calculators on mathematical achievement and student confidence in problem solving showed there was a significant statistical difference in favour of Desmos for both middle and high school students.
Chan & Leung’s (2014) showed DGS interventions less than 2 weeks in duration were least effective and may be the result of novelty effects of DGS rather than appropriate instructional design. Koklu & Topcu’s (2012) quasi experimental supported this conclusion studying on effects of DGS assisted instruction on student’s academic scores and commons misconception of quadratics.
Gray & Thomas (2001) investigated the value of conceptual use of graphical calculators by students in a multiple representational environment. They found that student academic outcomes were no greater than that of students receiving only traditional instruction (pen & paper). There are significant factors associated with the outcomes though considering Chan & Leung’s (2014) duration findings; students had never used the graphics calculators before in the Gray & Thomas (2001) investigation. Furthermore, DGS use only consisted of one period of device familiarisation and three periods of instruction with the system.
Pierce, Stacey, Wander, & Ball (2011) explored how to best teach with multiple representations and identify teacher pedagogical choices that might be responsible for the discouraging results of the above studies. Through an adaptive design cycle, they identified several items of consideration that all teachers should be cognisant of when utilising digital technologies to generate multi-representations; primarily negative results were likely due to the Intrinsic cognitive load imposed on students as a result of distributed formats and hence increases with every representation added (Pierce et al., 2011).
Cognitive load theory can be surmised as the brain only being able to process a small amount of new information (working memory) at once but a large amount of stored information (long term memory) (Centre for Education Statistics and Evaluation, 2017).
Pierce et al. (2011) found four areas teacher can easily reduce cognitive load when implementing DGS: Variable naming – software is unable to provide seamless link between representations due the fundamental difference between mathematical variables and computer variables. Clutter – using prepared simple display screens saves times and ensures the focus is on mathematics rather than technology use. Motivation – when implementing multiple representations all representations used must have purpose and bring new learning rather than repetition. Clear lesson focus – with short lesson sequences and time constraints careful choices must be made to select the most purposeful representations for the topic.
Mathematical high school education studies such as O’Connor & Norton (2016) that did not incorporate digital technologies generally drew on the literature above recommending the incorporation of multiple representations as a solution to student’s difficulties without considering cognitive load.
When utilising graphics calculators and DGS to generate multiple representations consideration must be given to the number and purpose of representations used. To help alleviate cognitive load issues following Pierce et al. (2011) four guidelines is recommneded:
- be cognisint of the the possible conflict between mathimatic variables and computer variables.
- prepared screens increase effeciency but students need longer time to familirise themselves with rather than screens they created themselves.
- each representation must be adding new information rather than just a repition for the sake of it.
- any representation used must be the most appropriate to learning goal.
Furthermore, any implementation of the use of graphical digital technologies must be accompanied by a significant investment in student familiarisation as shown by Gray & Thomas (2001) with the overall tool before focusing on individual mathematical learning outcomes.
Centre for Education Statistics and Evaluation. (2017). Cognitive load theory: Research that teachers really need to understand. Retrieved from www.cese.nsw.gov.au
Chan, K. K., & Leung, S. W. (2014). Dynamic geometry software improves mathematical achievement: Systematic review and meta-analysis. Journal of Educational Computing Research, 51(3), 311–325.
Drijvers, P., & Doorman, M. (1996). The graphics calculator in mathematics education. The Journal of Mathematical Behavior, 15(4), 425–440.
Ebert, D. (2015). Graphing Projects with Desmos. The Mathematics Teacher, 108(5), 388. https://doi.org/10.5951/mathteacher.108.5.0388
Gray, R., & Thomas, M. O. J. (2001). Quadratic equation representations and graphic calculators: Procedural and conceptual interactions. In Proceedings of the 24th Mathematics Education Research Group of Australasia Conference (pp. 257–264).
Koklu, O., & Topcu, A. (2012). Effect of Cabri-assisted instruction on secondary school students’ misconceptions about graphs of quadratic functions. International Journal of Mathematical Education in Science and Technology, 43(8), 999–1011.
Liang, S. (2015). Teaching the Concept of Limit by Using Conceptual Conflict Strategy and Desmos Graphing Calculator. International Journal of Research in Education and Science, 2(1), 35. https://doi.org/10.21890/ijres.62743
Montijo, E. (2018). The effects of Desmos and TI-83 Plus graphing calculators on the problem-solving confidence of middle and high school mathematics students. Dissertation Abstracts International Section A: Humanities and Social Sciences. ProQuest Information & Learning. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&db=psyh&AN=2017-29361-010&site=ehost-live
O’Connor, B. R., & Norton, S. (2016). Investigating Students’ Mathematical Difficulties with Quadratic Equations. Mathematics Education Research Group of Australasia.
Penglase, M., & Arnold, S. (1996). The graphics calculator in mathematics education: A critical review of recent research. Mathematics Education Research Journal, 8(1), 58–90.
Pierce, R., Stacey, K., Wander, R., & Ball, L. (2011). The design of lessons using mathematics analysis software to support multiple representations in secondary school mathematics. Technology, Pedagogy and Education, 20(1), 95–112.
Schwarz, B. B., & Hershkowitz, R. (1999). Prototypes: Brakes or levers in learning the function concept? The role of computer tools. Journal for Research in Mathematics Education, 30, 362–389.
Vaiyavutjamai, P., & Ken Clements, M. A. (2006). Effects of classroom instruction on students’ understanding of quadratic equations. Mathematics Education Research Journal. https://doi.org/10.1007/BF03217429