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Through an inquiry lesson, students work through the lesson to gain understanding about the concept of infinite geometric series. The students are taught by providing an activity that allows them to explore a problem and gain a conceptual understanding geared towards longer results in terms latency of the knowledge rather than through direct teacher instruction.======

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Constructive theory believes that knowledge cannot be passively transmitted from other person to another, and that knowledge is passed on from experiences. The lesson intends to create a memorable learning experience revolving around the concepts of divergence and convergence of series, sequences, infinite geometric series.======

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By discussing understanding of the concepts, students are encouraged to create knowledge. The current lesson can be classified as inherently constructivist, because it is accompanied by significant mental processes along the way.======

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A Constructivist classroom can include some individual work, pencil and paper tests and even lectures. This theory is why this lesson incorporates additional inquiries of practical applications of infinite series which exist today in the everyday world. Students are encouraged to share their findings through peer to peer discussions.======

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Often, In giving students instruction about why the noted infinite series converges to the number 1, teachers fail to help students understand. This is an example where students are told something is true without an explanation (Brahier, p. 56). In this lesson we move away from that approach of teaching students rules to be memorized, to guiding students in the discovery of relationships (Brahier, p. 57). Particularly, students work through the activity and verify/reinvent the mathematical rule (p. 58)======

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Remember, Piaget, the constructivism theorist related that "knowledge is not passive, but built and constructed through experience (Brahier, p. 57). This construction occurs not only by doing but by reflecting and discussing. In this discussion students are led in comparing and contrasting ideas about patterns and belief about concepts (p. 59). Throughout the activity, students not only get hands on experience working with the infinite series; following the constructivist theory, we also guide students in sharing and justifying their point of view and giving meaningful feedback to their peers.======


 * 1) ======We selected an appropriate activity from among the 12 activities on pages 211-216 of Brahier's text. We decided on the infinite series (#8) activity because it was similar to Brahier's "Paper Folding Activity" on page 57, and sufficiently "hands on" for us to implement the theory effectively.======
 * 2) ======We sought to guide the students in the exploration of the infinite series concept. We decided to integrate a few PowerPoint slides into the presentation to guide students into the activity.======

Ultimately, we modeled the lesson so that students thinking would be the focal point of the discussion, and we strove to emphasize a shift from a content centered to student centered approach. From Table 3.4 "Comparison of Traditional and Constructivist Classrooms (Brahier, p. 60), we drew on various elements of Constructivist Classrooms to guide us in the formation of the lesson:

-Curriculum is presented whole to part, with emphasis on big concepts. -Pursuit of student questions is highly valued. - Curricular activities rely heavily on primary sources of data and manipulative materials. -Students are viewed as thinkers with emerging theories about the world. -Teachers generally behave in an interactive manner, mediating the environment for students. -Teachers seek the students' point of view in order to understand students' present conceptions for use in subsequent lessons. -Assessment of student learning is interwoven with teaching and occurs through teacher observations of students at work and through student exhibitions and portfolios