How+Technology+Develops+Students'+Understanding+of+Geometry

Teachers can use technology to boost and support students in their journey learning geometry. Adolescents these days have the world at their fingertips with access to cell phones, computers, and the internet; connecting them not only to teachers and peers anywhere at anytime but also to virtually unlimited mathematical websites for learning and tutoring (Fey & Hollenbeck, 2009 p. 430). Many schools have access to all sorts of technological tools—the real challenge comes when teachers have to know how to use such technology to its full potential in a way that maximizes student learning (Fey & Hollenbeck, 2009, p.431). Taking just a little time to become acquainted with the technological tools available will go a long way in building the conceptual understanding of students.

Technology’s use is particularly beneficial when teaching geometry, a very visual subject where students usually excel when exposed to hands on learning. The National Council of Teachers of Mathematics explains that “spatial visualization—building and manipulating mental representations of two- and three-dimensional objects and perceiving an object from different perspectives—is an important aspect of geometric thinking” (2000, p. 41). Technology allows for students to really experience and live geometry in multiple ways. Virtual simulations make geometric situations reality where students can see for themselves the benefits of understanding geometric concepts.

Technology accomplishes the challenging task of engaging “diverse learners in critical thinking and problem solving”(Suh, 2010, p.441). Classrooms today are made up of students at all different places on the spectrum of learning. Visual representations have proved to be particularly successful for English Language Learners and students with learning disabilities. Many interactive programs provide students access to “mathematical language and academic vocabulary” (Suh, 2010, p.446). This exposes students who are still learning English to the terminology they need to know to be successful at a task. Many manipulatives that proved successful in the past can now be found virtually, such as geo-boards (Fey & Hollenbeck, 2009, p.431). Using technology rather than physical manipulatives also relieves students of the amount of stimuli they are trying to mange while still maintaining the benefits of visualization. This keeps cognitive processes on the task rather than trying to manage physical representations, class discussion, and the task at hand at the same time.

Technology can amplify concepts in math allowing students to manipulate problems and experience ideas rather than sit at a desk with paper and pencil applying algorithms day after day (Suh, 2010, p.441). Student’s visual/physical representations of problems can be displayed using something such as a document camera and archived using snapshots, simultaneously class discussion can occur then be followed by and interactive web activity. Teachers can organize lessons using multiple technologies, combining many ways of learning develop solid understanding in students (Fey & Hollenbeck, 2009, p.431-432). Technology provides many opportunities to tap in on multiple intelligences and take different learning styles into consideration (Dunnerstick, Lindemanm, Wolf & Wolf, 2011, p. 557). Presenting the same idea in various medias accesses different learning styles students may benefit from.

Technology supports a learning environment that focuses on the students (rather than the teacher) (Dunnerstick, Lindemanm, Wolf & Wolf, 2011, p. 557). Classroom discussions are enhanced by technology. Having a student act as the class facilitator and scribe for the day (where one student takes notes/solves tasks on a tablet and the tablet projects what the student writes so the class can follow along—this process is called scribing) allows students to feel as if they are playing an active role in their education. By having a student lead the class in note-taking, students feel more invited to ask questions and for clarification about the content. This is because students feel like they are asking a peer for assistance rather than “challenging” the teacher (Harless, 2011, p.420). Making students feel like they are in charge of their own learning develops a sense of responsibility for their own education.

By creating interactive lessons, students will play a more active role in the learning process and “when a student feels that he or she is more vested in actual learning, retention of the material tends to rise significantly” (Dunnerstick, Lindemanm, Wolf & Wolf, 2011, p. 557). Geometric content seems more applicable to real life when presented via technology rather than in a word problem on paper.

Using interactive whiteboards rather than blackboards allows class to be facilitated from the front of the class or from any computer, by the teacher or by a student (Fey & Hollenbeck, 2009, p.432). This allows the teacher to walk around the room and watch students work as discussion occurs rather than being confined to the front of the classroom.

Using tasks on computer programs and interactive applets helps the teacher make sure students are on the right track. Many programs provide immediate feedback to students on attempted answers, research shows that “they quickly develop their understandings and strategic skills that are the desirable goals of instruction” (Fey & Hollenbeck, 2009, p.433). Providing immediate feedback helps prevent misconceptions from developing as students learn (Suh, 2010, p. 442). Many applets keep track of all the student’s processes and work, allowing both the student and teacher to review and critique procedures (Suh, 2010, p.446). Using technological tasks rather than paper-and-pencil ones will make it easier for the teacher to efficiently know where all students are in their understanding, making the teaching received more individualized for each student’s personal needs.

Teachers can use clickers (or another response system) as a quick and accurate formative assessment to make sure students are following along as the lesson progresses. If many students get the same question incorrect, it is an indicator that there is common obstacle in the students’ understanding and the teacher may need to spend more time here before moving on (Fey & Hollenbeck, 2009, p.433). This is a quick and easy type of formative assessment that gives the teacher an accurate picture of where students are so that instruction can meet students changing needs instantly.

Technology such as scanners, document cameras, and tablets can be used to display students’ solutions to a posed problem, allowing students to critique methods together (Fey & Hollenbeck, 2009, p.433) Technology used as a group “add a social dimension to learning because students share knowledge publicly and learn by making mistakes together” (Dunnerstick, Lindemanm, Wolf & Wolf, 2011, p. 558). Students often feel more comfortable around one another which results in more class discussion.

Some programs construct and transform geometric figures given certain conditions or properties (Fey & Hollenbeck, 2009, p.434). This allows students to construct figures themselves and gain an understanding of different properties of shapes and results in an accurate image.

Technology can “offload some routine task[s]….which provide[s] learning efficiency in terms of compacting and enriching experiences” (Suh, 2010, p. 445). It is imperative that students learn these routine procedures, but once they have been mastered technology can speed up the prep work to allow students more time thinking critically about the task at hand. “When technological tools are available, students can focus on decision making, reflection, reasoning and problem solving” (NCTM, 2000, p.24). When students spend less time performing routine algorithms by using technology as an amplifier, more time is opened up for deeper thinking about the mathematics at hand. It is important for students to have a solid understanding of these routine procedures; however once they are mastered attention can be shifted elsewhere.

Students get bored when they come to class everyday and do the same thing. Every person has been in a math class at some time where everyday class consisted of the teacher lecturing from the board and student taking notes from their desk, with tasks from the book dispersed in. Technology helps keep student interest by presenting content in new ways (Dunnerstick, Lindemanm, Wolf & Wolf, 2011, p. 557). Students learn something new everyday and work in a different way than they did the day before. By keeping students engaged in the class structure, they are being kept engaged in mathematics.

Below is a chart that Suh provides which outlines advantageous elements of technology and how these aspects benefit students with specific learning needs: Dunnerstick, R., Lindeman, P., Wolf, P. & Wolf, T. (2011). Technology with student success. //Mathematics Teaching in the Middle School, 16//(9), 557-560.

Fey, J. & Hollenbeck, R. (2009). Technology and mathematics in the middle grades. //Mathematics Teaching in the Middle School, 14//(7), 430-435.

Harless, P. (2011). Scribing: A technology-based instructional strategy. //Mathematics Teacher, 104//(6), 420-425.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Virginia: NCTM. Suh, J. (2010). Tech-knowledgy & diverse learners//. Mathematics Teaching in the Middle School, 15//(8), 440-447.