Plane Geometry - Bruce E. Shapiro
Plane Geometry - Bruce E. Shapiro Plane Geometry - Bruce E. Shapiro
12 SECTION 3. CA STANDARDIn 2005 California also adopted a Mathematics Framework for CaliforniaPublic Schools. The purpose of this framework was to provide for “instructionalprograms and strategies, instructional materials, professionaldevelopment, and assessments that are aligned with the standards” withthe intent of providing a “context for continuing a coordinated effort to enableall California students to achieve rigorous, high levels of mathematicsproficiency.” These are largely derived from the NCTM standards, and aresummarized in the boxes on this and the following pages.An important part of the framework is balance. A balanced program shouldgive the student (a) proficiency in basic skills; (b) conceptual understanding;and (c) problem solving ability.1. Become proficient in basic computational and procedural skills.These are the basic skills that all students should learn to use routinely andautomatically. They should be practiced sufficiently and used frequentlyenough to commit them to memory and ensure that these skills are retainedand maintained over the years.2. Develop conceptual understanding. Students who do not have a deepunderstanding of mathematics suspect that it is just a jumble of unrelatedprocedures and incomprehensible formulas. In seeing the larger pictureand in understanding the underlying concepts, students are in a strongerposition to apply their knowledge to new situations and problems and torecognize when they have made procedural errors.3. Become adept at problem solving. Problem solving in mathematicsis a goal-related activity that involves applying skills, understandings, andexperiences to resolve new, challenging, or perplexing mathematical situations.Problem solving involves a sequence of activities directed toward aspecific mathematical goal, such as solving a word problem, a task that ofteninvolves the use of a series of mathematical procedures and a conceptualrepresentation of the problem to be solved.All three components are important; none is to be neglected or underemphasized.Balance, however, does not imply allocating set amounts oftime for each of the three components.professor Barry Simon, Caltech, in a freshman mathematics class.]« CC BY-NC-ND 3.0. Revised: 18 Nov 2012
SECTION 3. CA STANDARD 13Goals for Teachers (2005 CA. Framework)1. Increase teachers’ knowledge of mathematics content through professional developmentfocusing on standards-based mathematics.2. Provide an instructional program that preserves the balance of computational andprocedural skills, conceptual understanding, and problem solving.3. Assess student progress frequently toward the achievement of the mathematics standardsand adjust instruction accordingly.4. Provide the learning in each instructional year that lays the necessary groundwork forsuccess in subsequent grades or subsequent mathematics courses.5. Create and maintain a classroom environment that fosters a genuine understandingand confidence in all students that through hard work and sustained effort, they canachieve or exceed the mathematics standards.6. Offer all students a challenging learning experience that will help to maximize theirindividual achievement and provide opportunities for students to exceed the standards.7. Offer alternative instructional suggestions and strategies that address the specificneeds of California’s diverse student population.8. Identify the most successful and efficient approaches within a particular classroom sothat learning is maximized.Goals for Students (2005 CA. Framework)1. Develop fluency in basic computational and procedural skills, an understanding ofmathematical concepts, and the ability to use mathematical reasoning to solve mathematicalproblems, including recognizing and solving routine problems readily andfinding ways to reach a solution or goal when no routine path is apparent.2. Communicate precisely about quantities, logical relationships, and unknown valuesthrough the use of signs, symbols, models, graphs, and mathematical terms.3. Develop logical thinking in order to analyze evidence and build arguments to supportor refute hypotheses.4. Make connections among mathematical ideas and between mathematics and otherdisciplines.5. Apply mathematics to everyday life and develop an interest in pursuing advancedstudies in mathematics and in a wide array of mathematically related career choices.6. Develop an appreciation for the beauty and power of mathematics.Revised: 18 Nov 2012 « CC BY-NC-ND 3.0.
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12 SECTION 3. CA STANDARDIn 2005 California also adopted a Mathematics Framework for CaliforniaPublic Schools. The purpose of this framework was to provide for “instructionalprograms and strategies, instructional materials, professionaldevelopment, and assessments that are aligned with the standards” withthe intent of providing a “context for continuing a coordinated effort to enableall California students to achieve rigorous, high levels of mathematicsproficiency.” These are largely derived from the NCTM standards, and aresummarized in the boxes on this and the following pages.An important part of the framework is balance. A balanced program shouldgive the student (a) proficiency in basic skills; (b) conceptual understanding;and (c) problem solving ability.1. Become proficient in basic computational and procedural skills.These are the basic skills that all students should learn to use routinely andautomatically. They should be practiced sufficiently and used frequentlyenough to commit them to memory and ensure that these skills are retainedand maintained over the years.2. Develop conceptual understanding. Students who do not have a deepunderstanding of mathematics suspect that it is just a jumble of unrelatedprocedures and incomprehensible formulas. In seeing the larger pictureand in understanding the underlying concepts, students are in a strongerposition to apply their knowledge to new situations and problems and torecognize when they have made procedural errors.3. Become adept at problem solving. Problem solving in mathematicsis a goal-related activity that involves applying skills, understandings, andexperiences to resolve new, challenging, or perplexing mathematical situations.Problem solving involves a sequence of activities directed toward aspecific mathematical goal, such as solving a word problem, a task that ofteninvolves the use of a series of mathematical procedures and a conceptualrepresentation of the problem to be solved.All three components are important; none is to be neglected or underemphasized.Balance, however, does not imply allocating set amounts oftime for each of the three components.professor Barry Simon, Caltech, in a freshman mathematics class.]« CC BY-NC-ND 3.0. Revised: 18 Nov 2012
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