| Mathematics
The Tennessee Mathematics Framework for grades 9 through 12 includes skills for many different High School level courses, and contains the following process standards:
MATHEMATICS AS PROBLEM SOLVING
The study of mathematics must emphasize Problem Solving opportunities which require various approaches to investigate, understand, and apply mathematical concepts.
The development of each learner’s ability to solve problems is essential if he or she is to be a productive citizen. We strongly endorse the first recommendation of An Agenda for Action (NCTM, 1980): "Problem solving must be the focus of school mathematics." To develop such abilities, students need to work on problems that may take hours, days, and even weeks to solve. Some may be relatively simple exercises to be accomplished independently; some should involve small groups or an entire class working cooperatively; and some problems should also be open-ended with no single right answer.
"Mathematics as Problem Solving" emphasizes the learners’ use of a broad base of strategies to:
Investigate and understand mathematical content
Recognize and formulate problems from within and outside of mathematics
Use mathematical modeling and appropriate technology to solve a wide variety of problems, including real-world problems.
Generalize solutions and strategies, applying them to new problems
Increase confidence in their ability to use mathematics meaningfully and to become independent problem solvers.
MATHEMATICS AS COMMUNICATION
The study of mathematics must emphasize Communication by requiring opportunities to explain, conjecture, summarize, and defend one’s ideas orally, in writing, and through the use of technology.
The development of a learner’s power to think mathematically involves learning the signs, symbols, and terms of mathematics. This is best accomplished in problem situations in which students have an opportunity to read, write, and discuss ideas in which the use of the language of mathematics becomes natural. As students communicate their ideas, they learn to clarify, refine, and consolidate their answers.
"Mathematics as Communication" focuses on the learners’ development of using language and symbols to:
Reflect and clarify thinking about mathematical ideas and situations
Express mathematical ideas and relationships, orally, in writing, and with physical material, pictures, and diagrams
Understand and value the role of mathematical notation
Realize that representing, discussing, listening, writing, and reading mathematics are vital aspect of mathematics study and use
Use mathematical notation to formulate generalizations.
MATHEMATICS AS REASONING
The study of mathematics must emphasize Reasoning which requires critical thinking, logical argument, and justification of solutions, of thought processes, and of conjectures.
Making conjectures, gathering evidence, and building an argument to support such notions are fundamental to doing mathematics. In fact, a demonstration of good reasoning should be rewarded even more than the learner’s ability to find correct answers.
"Mathematics as Reasoning" concentrates on leading the learners to:
Make and test mathematical conjectures
Make, follow, and judge the value of mathematical arguments
Draw logical conclusions
Justify solution-finding processes and answers.
MATHEMATICAL CONNECTIONS
The study of mathematics must emphasize making Connections among the various topics within mathematics, between mathematics and other disciplines, and between mathematics and "real world" situations.
The mathematics curriculum is often viewed as consisting of several discrete stands; so topics tend to be taught in isolation. Unless the learners connect ideas both among and between areas of mathematics, they learn isolated skills rather than develop the ability to recognize general principles and procedures relevant to several areas. Connecting conceptual understanding to procedures will enable learners to apply, recreate, and invent new procedures when needed. Failure to connect conceptual understanding to procedures results in a view of mathematics as an arbitrary set of rules. Learners should have many opportunities to observe and work with the interaction of mathematics with other subjects and with everyday society. Problems become meaningful when they relate to the learners’ experiences. Mathematics must be integrated into contexts that give its symbols and processes practical meaning. The school environment is rich with opportunities to use mathematics in other subject areas as well as other subject area content in mathematics.
"Mathematical Connections" concentrate on enabling the learners to:
Appreciate mathematics as an integrated whole, linking conceptual and procedural knowledge within the discipline and relating multiple representations of concepts or procedures to one another.
Apply mathematical thinking and modeling to solve substantial problems that arise in other disciplines and curriculum areas, such as art, business, music, psychology, industrial arts, computer technology, social studies, and sciences, such as biology, chemistry, and physics.
Use, recognize, and value the varied roles of mathematics in their lives, cultures, and society.
The Principles and Standards for School Mathematics describe the mathematical understanding, knowledge, and skills that students should acquire from prekindergarten through grade 12.
Algebra I is the Tennessee End-of-course test that must be passed before graduation to earn a high school diploma.
Foundations II
The Tennessee End-of-Course Tests for mathematics include a Foundations II test. Foundations II is a course that uses problem situations, physical models, and appropriate technology to investigate concepts and topics that prepare students for higher level mathematics. Problem solving situations will provide all students an environment that promotes communication and fosters connections within mathematics, to other disciplines, and to the real world. Students will use physical models to represent, explore, and develop abstract concepts. The use of appropriate technology will help students apply mathematics in an increasingly technological world. The concepts emphasized in the course include investigating and analyzing the real number system and its properties, developing and applying skills in measurement and computation, recognizing and applying patterns to solve problems, investigating basic functions and their graphs, evaluating algebraic expressions and solving equations, developing basic concepts of statistics and probability, and investigating geometric properties and relationships.
Algebraic Concepts
The Algebraic Concepts Unit includes Competencies/Objectives which focus on algebraic equations and operations. Students explore the symbolic nature of algebraic concepts by identifying and extending patterns in algebra, by following algebraic procedures, and by proving theorems with properties.
Data Interpretation
The Data Interpretation Unit includes Competencies/Objectives which focus on the study and use of graphical forms. Students collect and classify data, organize and display data, use logical reasoning, and problem solving.
Fractions
The Fractions Unit includes Competencies/Objectives which focus on number sense and operations with fractions. Students compare and order fractions, study fraction parts, estimate with fractions, reason using fractions, and problem solve using fractions.
Functions
The Functions Unit includes Competencies/Objectives which focus on exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions.
Geometry
The Geometry Unit includes Competencies/Objectives which focus on exploring geometric concepts from multiple perspectives. Students study properties and construction of figures, proofs and theorems, history of geometry, transformations, logic, and problem solving.
Integers
The Integers Unit includes Competencies/Objectives which focus on number sense and operations with integers. Students compare integers, perform operations with integers, convert integers to other number forms, use manipulatives to demonstrate integers, and solve problems with integers in real world contexts.
Measurement
The Measurement Unit includes Competencies/Objectives which focus on measurement concepts, applications, and analysis. Students study length, area, circumference, perimeter, volume, weight, formulas, distance, calendar, money, tools, accuracy, units, constructions, patterns, and problem solving.
Number Theory
The Number Theory Unit includes Competencies/Objectives which focus on manipulating number forms and classifications. Students make connections between number forms and their real world applications.
Numeration
The Numeration Unit includes Competencies/Objectives which focus on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships.
Perspective/Role in Society
The Perspective/Role in Society Unit includes Competencies/Objectives which focus on real world mathematics. Students study the mathematics of society and the role of mathematics in personal finance and careers.
Probability/Statistics
The Probability/Statistics Unit includes Competencies/Objectives which focus on data analysis and probability concepts. Students collect, analyze, and make sense of real world data (including overlapping data, inconclusive data, etc.).
Problem Solving
The Problem Solving Unit includes Competencies/Objectives which focus on analyzing problems, evaluating solutions, exploring problems, and developing strategies for solving problems.
Rational and Irrational Numbers
The Rational and Irrational Numbers Unit includes Competencies/Objectives which focus on number concepts. Students manipulate, compare, and perform operations with rational and irrational numbers.
Real Numbers and the Coordinate Plane
The Real Numbers and the Coordinate Plane Unit includes Competencies/Objectives which focus on graphing concepts. Students graph equations and make connections between algebraic concepts and their geometric correspondences.
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