When technology is introduced into the math classroom, one potential pitfall that can impede its integration and the impact it has on student learning is the degree of flexibility it provides in how problems can be solved. With all of the technology possibilities that can be found online, drill and practice activities and games continue to be teachers’ most popular choices. Why? Historically, instructional design in math has been promoted through a linear and cumulative progression whether it’s in the classroom, face to face, or online. It’s familiar. It’s easy. It appears that students are improving their skills when they use it. So what’s the problem?
The problem is that math reasoning and the development of process skills that foster conceptulaization are not best served by linear pathways. Looking back on one of the interviews I conducted earlier in this course, the same dillema presented itself to Teacher B that had integrated technology in her math classroom for her master’s thesis. In her research on teaching mathematics using technology for the purpose of motivation and engagement in 2005, she found the options available online, even with a paid subscription, offered limited potential for flexible thinking. Although teachers might relish the idea that they can track student progress as they work through linear modules relying on algorithmic knowledge are they really promoting knowledge for understanding? Does success in a linear math program transfer to success with math outside that particular context? Why have we become so habituated to students learning math through memorization of symbols and steps?
This perpetuated belief that math is best taught along a direct pathway from A to B bypasses the importance of understanding math processes and developing adaptive expertise that moves beyond the inert knowledge we have previously celebrated. Assessments need to change to reflect what needs to be valued in terms of success with math concepts as well. Technology could be a catalyst for reform if it’s chosen for its ability to challenge ingrained assumptions about how best to teach mathematics. How math is traditionally taught and predominantly supported through technology conflicts with how I believe it needs to be taught and how technology could be used to support it. This is why the Jasper Series caught my attention.
Jasper designers have organized instruction around meaningful problems and have chosen technology that promotes inquiry and reasoning well beyond memorization. Scaffolding necessary skills and developing mathematical schema supports students to learn with understanding, and opportuntities to practice after receiving feedback, make revisions, as well as reflect on their perspective in relation to others, all while promoting “collaboration and distributed expertise, as well as independent learning” (Pellegrino, 2001).
The most impressive component of the Jasper Series, especially considering it’s development and application spanned the late 1980s up until early years of 2000s, is the potential it offers students in developing transfer skills due to its commitment towards encouraging multiple feasible solutions to authentic problems. The motivation and engagement to learn and think critically is nurtured in their efforts to unveil “the relevance of math and science to the world outside the classroom” (Pellegrino, 2001). The instructional designers have debunked the myth that math needs to be taught in a linear manner. It’s just too bad more people weren’t listening 30 years ago because they were really on to something great. Mathematics clasasrooms need to be learning communities that foster inquiry. More efffort needs to be placed on incorporating cognitive theory into instructional design to create experiences that develop a “disposition to skilled learning and thinking … to overcome [the] phenomenon of inert knowledge” (Corte, 2007).
image: Connection to Nowhere by Tom Haymes released under a CC Attribution – Noncommercial – Share Alike license
References
Cognition and Technology Group at Vanderbilt (1992a). The Jasper experiment: An exploration of issues in learning and instructional design. Educational Technology, Research and Development, 40(1), 65-80.
Cognition and Technology Group at Vanderbilt (1992b). The Jasper series as an example of anchored instruction: Theory, program, description, and assessment data. Educational Psychologist, 27(3), 291-315.
Corte, E. (2007). Learning from instruction: The case of mathematics. Learning Inquiry, 1, 119–30. doi: 10.1007/s11519-007-0002-4.
Pellegrino, J.W. & Brophy, S. (2008). From cognitive theory to instructional practice: Technology and the evolution of anchored instruction. In Ifenthaler, Pirney-Dunner, & J.M. Spector (Eds.) Understanding models for learning and instruction, New York: Springer Science + Business Media, pp. 277-303.