Ch. 5Geometry and Algebra Redefined!<br />By: Duy Nguyen<br />
Why Redefine?<br />Technological Advances:- Graphing Software- Geometer’s Sketchpad (GSP)<br />Future Workforce Skills<br />Multiple Means of Representation<br />Deeper Understanding of Mathematics<br />
Contemporary Geometry<br />Secondary students need more hands-on experiences with 3-D shapes.<br />Interdisciplinary by NatureEx. Biology and Art<br />Develop an appreciation in building and exploring models.<br />Technology is a must!<br />
Prove It<br />Redefine the formal proofs of Euclidean geometry in the perspectives of synthetic, analytical, and transformational.<br />Synthetic Geometry: prove geometric relationships based on the use of a rational sequence of definitions, postulates and theorems.<br />Analytic Geometry: given a fundamental problem, one can find an equation to solve it (usually done through graphing technologies and computer software).<br />Transformational Geometry: explore geometric concepts through the use of transformational techniques (i.e. altering the parent graphs of y = x2 to be reflected and shifted).<br />
Inductive and Deductive Reasoning<br />Inductive Reasoning: based on observations and collected data, generalizations are made.<br />Deductive Reasoning: based on accepted statements and a logical structure to reach a conclusion.<br />Contemporary Geometry can help introduce visuals for inductive and deductive reasoning and prepare students for formal proofs, with techniques such as mathematical induction.Ex. Linear Programming<br />
Contemporary Algebra<br />Emphasizes relationships among quantities, including functions, ways of representing mathematics relationships, and the analysis of change.<br />Technological Representations:- Numeric- Symbolic- Tabular- Graphical<br />3 types of Algebra today:- Generative Activities (solving equations)- Transformational (finding equivalent expressions)- Problem Solving, Modeling, Proving Theorems, and Predicting New Relationships<br />Multiple Representations other than symbols to generalize quantitative relationships (graphical, tabular, etc.) <br />
21st Century Skills<br />The integration of a non-discrete algebra and geometry.<br />Technology can greatly assist students in a contemporary algebra where it is used today.<br />Technology can be: computers, software, probeware, graphing calculators, scientific calculators, or manipulatives.<br />
Technology and Algebra<br />Solve systems of equations and inequalities, along with different types of equations such as linear, quadratic, etc.<br />Describe behaviors of multiple functions at once.<br />A need to model problems and demonstrate problem-solving skills through the use of technology for the current workforce, either after high school or college.<br />The goal is to present algebra to more students and can be approached in many different ways.<br />
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