Wolfram+Demonstrations

=Wolfram Demonstrations=

The Wolfram Demonstrations Project was developed by Stephen Wolfram, the creator of the interactive computer software, //Mathematica// (“High School,” 2011)//.// At this website, users have access to a myriad of interactive illustrations and visualizations that pertain to a wide variety of mathematical topics. Many of these illustrations allow users to manipulate equations, figures, and graphs in order to learn and ultimately gain a better understanding of certain concepts. Even more, through altering these demonstrations, users are able to better comprehend how these changes affect a final solution or result and how these concepts may be applied in a real-world setting.

Strategy 1: "Provide...technology that makes some aspects of the task easier" (Ormrod, 2011, 46)

According to sociocultural learning theory, physical and cognitive tools that are passed down from generation to generation help make life more productive and efficient (Ormrod, 2011). A cognitive tool can be defined as a “concept, symbol, strategy, procedure, or other culturally constructed mechanism that helps people think about and respond to situations more effectively” (Ormrod, 2011, p. 40). By allowing students to utilize an interactive computer software program, both a cognitive and physical tool, I would aim to help enhance their understanding of abstract mathematical concepts. Thus, my strategy would consist of providing this physical and cognitive tool to make their task easier, which Ormrod suggests is an effective method to facilitate student learning (2011). I would first present a topic or problem and then allow the students to explore their understanding of this topic with a related Wolfram demonstration. As suggested by Vacca, Vacca, and Mraz (2011), after their initial explorations, I would then “bring the students together intermittently…to share their work or to build strategic knowledge and skills related to the effective use of the Internet as a tool for learning” (p. 44). Hence, I would engage my students by first allowing them to explore these concepts through Wolfram demonstrations. Then, I would scaffold their behavior by providing them with hints, tips, and questions to further enhance their understanding and hopefully allow them to arrive at certain realizations that they would have not been able to make on their own. Through scaffolding, I would aim to move the students into their zone of proximal development, where learning would be able to occur, according to sociocultural learning theory (Ormrod, 2011).

Strategy 2: "Incorporating classroom subject matter into real-world tasks" (Ormrod, 2011, p. 231)

Another strategy that I could use to engage my students would be to supplement real-world problems with Wolfram demonstrations. Since many of the demonstrations allow users to manipulate real-world figures and plug in their own data into equations and graphs, I would be able to incorporate this text into mathematical projects that relate to the real world. According to constructivism, students are motivated to learn when presented with problems that require their active involvement and when they are able to see their applications to real life (Ormrod, 2011). Thus, I would aim for these real-life demonstrations combined with my scaffolds to aid the students in arriving at solutions that they would then be able to present in the form of a project or presentation. This would serve as an effective means to engage the students and help them visualize the applications of their data to ultimately enhance their learning, which ties in to constructivist and sociocultural learning theories (Ormrod, 2011).

Strategy 3: Internet Workshops (Vacca, Vacca, & Mraz, 2011, p. 44)

A final strategy that I could utilize to engage my students would be to guide them to access certain Wolfram Demonstrations in the form of an internet workshop. Vacca, Vacca and Mraz (2011) present that, in these workshops, "students are directed to the website(s) to engage in a content literacy in much the same way as they would in a textbook or other print resources" (p. 44). This use of interactive demonstrations relates to Gardener’s Theory of Multiple Intelligences. This theory holds that traditional activities and assessments often do not take into account the various learning styles and strengths of students. Interactive and visual demonstrations highly “appeal to students’ spatial intelligence” (Brahier, 2008, p. 50), in addition to their logical-mathematical intelligence. Thus, guiding the students to engage in activities with this text is much more likely to engage students by appealing to their multiple intelligences, rather than solely one, as would be the case with traditional forms of instruction.

These are two Wolfram Demonstrations that could be used to engage students in solving equations and inequalities with absolute value:

[|Number Line Solutions to Absolute Value Equations and Inequalities]

[|Graphing Systems of Inequalities]