![]() The students are recipients of knowledge who may write down notes but are not otherwise involved in knowledge production. Teacher-Centered Instruction: Instruction that is involves teacher dissemination of material, often in a lecture format. Preservice Teachers: Students in a teacher preparation program who are working towards becoming certified teachers. Student-Centered Instruction: Instruction that involves student engagement and exploration, with the teacher as facilitator. Examples from two specific units of instruction will be highlighted: a unit on trigonometry and a unit on lines and planes in space. The objectives of this chapter are to provide specific and varied examples of how Desmos and GeoGebra can be used to teach mathematics topics at the Algebra 2 and Precalculus levels, with advice on how to create, select, modify, and use these resources with students. As a high school mathematics teacher, the author has used these platforms extensively with his students and can provide numerous detailed examples of how to: a) select, modify, and create applets using these platforms b) use these platforms in a classroom setting to enhance student learning and engagement and c) ensure that students use these resources in ways that develop their conceptual understanding and promote meaning-making. In the context of secondary mathematics courses at the Algebra 2 and Precalculus levels, these goals can be addressed through intentional use of the free online platforms Desmos ( ). One of the Common Core Mathematics Practice standards affirms that mathematically proficient students can use technology to visualize the results of varying assumptions and to explore and deepen their conceptual understanding (National Governors Association, 2010). The PISA 2018 mathematical framework included references to students’ use of technology to portray mathematical relationships and to approximate solutions and called for the use of dynamic geometry software to manipulate and interpret shapes (OECD, 2019). The use of technology in teaching mathematics has been called for by various organizations. These graphical platforms can assist with derivations of mathematical procedures, can help students make sense of what they are doing and the answers they are getting, and can promote student engagement and discovery. Free and interactive technological platforms exist which can empower students to make sense of algebraic work with visual, graphical representations. Mathematics is a difficult subject for many students and is made even more difficult when they are asked to simply memorize definitions and procedures without understanding, or when they are asked to perform algebraic manipulations without any alternative representations which could be used to make sense of their work.
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