Learning Outcomes In The Diverse Classroom Education Essay

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The inclusion of technology in the mathematics curriculum is an important component that does enhance the learning outcomes. Heutinch and Munshin (2000) stated that "technology makes an additional topic in mathematics less important, others more important, and new topics possible." According to the National Council of Teacher of Mathematic's (2000), "Technology is essential in teaching and learning of mathematics; it influences the mathematics that is taught and enhances student's learning". In response to need to craft appropriate roles for technology in school mathematics, new technological approaches have been applied to the teaching and learning of mathematics, and the effects of these technological approaches have been examined by researchers worldwide.

Van de Walle (1998) outlines three ways technology is changing the nature of mathematics education. The first is that some mathematics skills have decreased in importance. Time taken to perform tedious written computations, such as long division or constructions such as graphical representations, can be put to better use in more reasoning and interpretation oriented endeavors. This approach according to Van de Walle (1998) mirrors ways technology is used in everyday life and is the pedagogical idea that mathematics can be taught more effectively using technology. For example, visual and contextual representations that might not otherwise be available can be included. And teachers can use computer-based simulations to provide students with opportunities to work on problem situations that are difficult to experience without technology. National Council of Teacher of Mathematic's (2000) states "Students can learn more mathematics more deeply with appropriate use of technology". Some mathematics topics an skills are more accessible or can receive greater emphasis. Data analysis is an example; The internet provides access to an abundance of information that combined with data analysis tools and computer generated graphs and tables allows children to gather, represent, analyze and interpret data at earlier ages and in expanded ways. Teachers also have the opportunities to gain insight into new mathematical methods; these changes impact mathematics content and curriculum, instrumental methodologies, learning styles, and the nature of mathematical thinking and understandings (Cho and Abramovich, 2009). National Council of Teacher of Mathematic's (2000) notes, "When a curriculum is implemented, time and emphasis must be given to the use of technology to teach mathematics concepts, skills and applications in the ways they are encounted in an age of ever increasing access to more powerful technology." Changes in favor of greater use of computers in mathematics education align nicely with other methodological emphases presently espoused by experts in the field, most notable, student responsibility for their own learning (Heid, 1997). Students become more autonomous, teachers more facilitative and learning more authentic during carefully designed, computer based projects according to Van de Walle (1998) and this student centered environment also lends itself to collaborative group work, students can also pursue mathematics oriented goals in dyads at the computer, or they can work independently and then share the results of their work with other students. Coyne, Kame'enui and Carnine (2007) believes that technology can naturally support interdisciplinary learning by situating mathematics concepts in contexts and providing access to global data and communications.

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The clearest message from research is that technology alone is not what makes the different in mathematics teaching and learning according to Van de Walle (1998), it is the confluence of technological environment, teachers, learners, curriculum and mathematical activity that sets the stage for chances in the teaching and learning of mathematics in the context of technology. The way in which technology is used in the mathematics classroom is determined by choices the teacher makes in engaging students in technology-supported mathematics. Choices teachers make include emphasizing procedures or concepts (Zbick and Hollebrands, 2008) and electing to use one representation over another. This privileging of representation type affects what representations students choose to use, and privileging of subject matter affects what students learn (Zbick and Hollebrands). Although a variety of external factors (eg. time, support staff, external assessments, logistics) impact the ways in which teachers use technology in their teaching (Zbick and Hollebrands), the choices teachers make are also related to internal factors such as how the teacher and the students relate to the technology. Those relationships change as a function of the technology-related experiences of teachers and students. The development of this relationship has even been named; instructional genesis (Guin and Trouche, 1998). In the process of their individual instrumental geneses, the teacher and students shape the tool for their own purposes and the tool shapes the way the teacher and students think about mathematics. The development of instrumentation processes with one tool affects the instrumentation processes developed with subsequent tools (Zbiek and Hollebrands, 2008).

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Zbieck and Hollebrands (2008) propose a four-stage process in which teachers experience growth in their use of technology in the mathematics classroom; first teachers learn technology, then learn to do mathematics with technology, then use technology with students, and finally attend to student learning in the context of technology. These experiences mold teachers' understandings, conceptions and perceptions; the key to what happens as technology enters their classrooms. As they use technology in their teaching, teachers may improve their own knowledge of the mathematics (Zbieck and Hollebrands, 2008) and as they use technology with their students, their conception of mathematics changes. National Council of Teacher of Mathematic's (2000) states that "The effective use of technology in the mathematics classroom depends on the teacher. Technology is not a panacea and as with any teaching tool, it can be used well or poorly. Teachers should use technology to enhance their students' learning opportunities by selecting or creating mathematical tasks that take advantage of what technology can do efficiently and well graphing, visualizing and computing."

Computers have many features that can enhance student learning. Guin and Trouche (1998) state their multimedia capabilities lend a sensory component that may help reinforce concepts and appeal to a wider variety of learning styles. Zbieck and Hollebrands (2008) also make note that graphical aspects help students visualize two and three dimensional geometric figures and represent mathematical ideas such as the nature of arithmetic versus exponential growth; students can also make conjectures and experiment with these graphical representations to see the results. In dynamic, interactive geometry programs according to Zbieck and Hollebrands (2008) students may directly manipulate figures that remain intact as they change shape in continuous fashion, allowing students to see intermediate states.

Technology can serve as a cognitive technology, a medium that helps "transcend the limitations of the mind, in thinking, learning and problem solving" (Pea, 1997). A cognitive technology can affect mathematics curricula in two major ways; as an amplifier or as a reorganizer (Pea, 1997). Technology extends the existing mathematics curriculum by increasing the number and nature of examples that students encounter; as a reorganizer, technology changes the nature and arrangement of the curriculum states Zbieck and Hollebrands (2008) and that the metaphor of technology as a reorganizer fits the body of research well since much of the research on the impact of technology on the teaching and learning of mathematics has been situated in curricular settings that are fashioned to be fundamentally different from traditional school mathematics curricula. For example, research has been conducted on the effects of computer algebra systems on the teaching and learning of algebra and calculus (Heid, 2008), systems on the teaching and learning of geometry (Clements, 2008) and on the effects of a range of technological applications on the teaching and learning of rational number (Olive and Lobato, 2008). The inclusion of technology into mathematics classrooms brought with it the opportunity to develop curricula that focused on mathematical objects instead of primarily on the procedures to be performed on those objects. Algebra courses, for example, were afforded the opportunity to focus on the concept and uses of function instead of solely on solving equations and generating equivalent expressions (Heid, 1997) and geometry classes could focus on generating conjectures to prove instead of on providing statements whose logical necessity had long been established (Zbieck and Hollebrands, 2008). These approaches to mathematics substantially change the usual foci of these courses. Technology has the potential for affecting the content of mathematics because of its capacity for changing the mathematical activities in which students engage.

Technology in schools has changed beyond recognition and has taken on board the study of mechanisms. However, Clements (2008) believes technology has only been pursued by a minority of students. When technology is placed alongside mathematics as a core subject to be studied by all has made it opened up exciting possibilities for cross-curricular co-operation, Heid (1997) believes and that traditionally mathematics teachers have approached the teaching of geometry in a very static way, and even the introduction of transformation geometry in the past was largely abstract and seemed to have little relevance to the real world. But while this was happening a development was occurring to enlightened technology mechanisms which could so easily have complemented the new approach to geometry.

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Technology enhances the teaching of mathematics by presenting concepts in exciting new ways. Guin and Trouche (1998) believe that children learn the concept of place value by reading their textbook, then translating the words and numbers to a calculator or mathematic software, they use technology to gain basic skills or to practice instant recall of facts and figures. For higher level thinking, calculators and computers enable students to explore patterns and relations of very large numbers and offer explanations about why certain sequences occur. Clements (2008) states to promote problem solving abilities, technology presents complex scenarios of how numbers are used in real life scenarios that mathematics students have sought for and enabling students to perform routine computations quickly and efficiently, technology allows students to focus on the language, meaning and applications of their answers. Clements (2008) also believes that students gain ownership with abstract mathematics and are enriched by the range, quality and realism of the investigations presented and that technology in mathematics classes enhances teaching for understanding. Students can examine more examples using technology than was ever possible by hand. The power of the graphics calculator addressed the visual learner, while manipulatives connect the symbols and pictorial representations for the tactile student according to Zbieck and Hollebrands (2008) and geometry software allows students to experiment with properties of shapes and draws conclusions about relationships when measurements are adjusted, and furthermore computational capacity extends the range of problems presented to students and provides choices to teachers when presenting abstract mathematical concepts.

The boundaries of mathematics are suddenly transformed with technology, teachers connect with student skills to basic development of mathematical understanding, enabling primary school students to organize and analyze large sets of numbers while high school students use simulations to visualize complex computer algebra systems and random generators enhance probability experiments that approach realistic situations. Sample sizes become huge, and students suggest more realistic predictions about real life situations using technology based tools such as spreadsheets (Zbieck and Hollebrands, 2008). With the use of technology, adoptions are now possible for diverse classrooms, allowing individual instructional needs to be met. Programs individualize specific content area, and their personalized reports give feedback to teachers who are able to modify their presentations accordingly. Students who are visual, pictorial and tactile are stimulated by learning are able to have their greatest success with the fusion of technology and mathematics.