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