MC-Lesson 1: Info-Vis – GSP Math Lesson
Technology Explored: Geometer’s Sketchpad
Group: Marc Aubanel (Administrator & Technology Teacher) & Evonne Tutkaluk (High School Math Teacher)
MCL1-GSP Teacher lesson-Evonne & Marc
MCL1-GSP Student Wkst-Evonne & Marc
Learning is being transformed with technology which includes experiencing authentic learning situations using technology. Geometric reasoning problems in high school mathematics such as the concept of angles formed by parallel lines and transversals continue to be problematic for high school students to visualize. Technology programs such as Geometer’s Sketchpad (GSP), version 5.04, are designed to incorporate cognitive information-processing views of learning with a constructivist approach (Knuth & Hartmann, 2005).
With GSP, students learn within an interface that supports a variety of potential interactions, manipulations and tools. One of the affordances of the technology is to quickly perform basic geometry in a very neat and effective manner. The user-friendly nature of GSP as positioned by Knuth and Hartmann (2005) guides, supports, and augments students’ internal mental processes where students can create their own understanding of the mathematical concepts through ‘conceptual conversations’. Knuth and Hartmann (2005) further that GSP enables teachers to complement their teaching strategies by engaging students in meaningful and purposeful activities where students learn by doing where learning is situated and interlinked with being social, collaborative and interactive through ‘conceptual conversations’. Knuth and Hartmann (2005) agree with Marrades and Gutierrez (2000) that related technological and mathematical learning outcomes can be achieved while providing authentic learning experiences to students via accessing programs like GSP. Student learning of mathematics and geometry can then take place, anytime, anywhere. Knuth and Hartmann (2005) describe GSP as an interactive geometry technology that affords teachers the opportunity to focus students’ attention on specific mathematical relationships in a dynamically visual way (enhancing objects, manipulating and visualizing objects changing in slow motion simulation) that may not be otherwise possible.
Jones & Mooney (2003) discuss the contradiction with the rise of sophisticated algebraic techniques with the “renaissance in geometry” that is seen in computer animation, medical imaging, GPS, architecture and robotics to name a few (Jones & Mooney, 2003, p. 4). The authors see a disparity in the necessity of expanding needs of algebra and geometry with little time spent on geometry in primary education. Do visualization tools allow younger students to explore more advanced concepts with straight forward software tools? Do visualization tools make geometry more accessible to younger students? Marrades and Gutierrez (2000) and Knuth and Hartman (2005) would say yes! Visualizations and simulations via technology provide students with information needed to acquire and assess specified knowledge and skills and afford a “powerful means of fostering students’ understandings and intuitions of mathematics” (Knuth & Hartmann, 2005, p.151).
How do visualization tools affect students ability to comprehend geometrical proofs? Hadas, Hershkowitz and Schwarz (2000) were looking for ways of promoting proofs by having students confront uncertainty and contradiction in Geometry. The authors raise the concerns that dynamic Geometry environments can prevent students from needing to require proofs in understanding geometric concepts. The author’s use of uncertainty is similar to the T-GEM process of Generate, Evaluate and Modify (Khan, 2010). Our proposed GSP lesson (angles of parallel lines & transversals) has an open investigatory approach to a topic in geometry.
Considering what we (Marc and Evonne) have read and our own personal experiences, we agree with many of the authors that students can explore mathematical, geometric and spacial connections in a more dynamic and more powerful way using technology such as GSP. In our opinions, technologies such as GSP can be used to enhance students’ skills while they are actively engaged in constructive, collaborative, contextual, conversational, intentional and reflective activities.
References
Geometer’s Sketchpad Download http://www.keypress.com/x24795.xml
Geometer’s Sketchpad Resource Center http://www.dynamicgeometry.com/JavaSketchpad.html
Hadas, N., Schwarz, B., & Hershkowitz, R. (2000). The role of contradiction and uncertainty in promoting the need to prove in dynamic geometry environments. Educational Studies in Mathematics,44 (1-2), 127-150.
Khan, S. (2010). New pedagogies for teaching with computer simulations. Journal of Science Education and Technology, 20(3), 215-232.
Knuth, E. J. & Hartmann, C.E. (2005). Using technology to foster students’ mathematical understandings and intuitions. In Masalaski, W.J, & Elliott, P.C. (Eds.). (2005). Technology-supported mathematics learning environments, (pp. 151-165). Reston, VA: National Council of Teachers of Mathematics.
Jones, K. and Mooney, C. (2003), Making Space for Geometry in Primary Mathematics. In: I. Thompson (ed), Enhancing Primary Mathematics Teaching. London: Open University Press. pp 3-15.
Jones, K. (2000), The Student Experience of Mathematical Proof at University Level. International Journal of Mathematical Education, 31(1), 53-60.
Marrades, R. & Gutierrez, A. (2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics,44(1-2), 87-125.