Математика в МА и NC
В МА школьная математика в конце средней и старшей школе базирована на следующих курсах - Pre-Algebra (8 класс), Algebra I (9 класс), Geometry (10 класс), Algebra II (Trigonometry) - 11 класс , Pre-Calculus (12 класс) and Calculus, Статистика, Дискретная математика для тех, кто прошел стандартные курсы раньше, а школа еще не закончилась. Порядок и приблизительный класс, в котором проходят предмет, я написала по примеру школ, в которых у меня учились дети. Но штат МА большой и школы дают эти предметы кто во что горазд - могут поменять местами Геометрию и Алгебра 2, могут в один год впихнуть два курса, могут начать давать Pre-Algebra до 8 класса, но в общем и целом это дает представление как идет обучении математикой
Algebra 1: Real numbers; solving, writing, and graphing linear equations; quadratic equations and functions; polynomials
Geometry: Plane and solid geometry including constructions, formulas for measurement, and formal proofs
Algebra 2: Continuation of the concepts taught in algebra 1, including a more in-depth study of graphing and solving equations, inequalities, and functions
Trigonometry: Applies algebra and geometry skills to circular and periodic functions. NOTE: Trigonometry is usually not its own class, but is often taught during algebra 2, geometry, or pre-calculus
Pre-Calculus: Series and sequences, probability, statistics, limits, and derivatives
Calculus: Continuation of the concepts taught in pre-calculus, with an emphasis on integration and differentiation
В NC эти курсы распределены по другому. Главное отличие - геометрия теперь не выделена в отдельный годовой курс, а дается внутри общей математики (мне такой подход больше нравится). Math 1 (9 класс), Math 2 (10 класс), Math 3 (11 класс), а в 12 кто что хочет - выбор между Math 4, Сложные функиции (наверное типа Функционального Анализа в нашем прошлом?), Дискретная математика, Статистика, Pre-Calculus and Calculus. Опять-таки, пишу для нашего округа, в других местах набор предложенных курсов может незначительно отличаться. Интересно, что классы еще даются в разном уровне - Foundation (кому математика ну очень тяжело дается, обычный уровень, Honors (продвинутый) и для классов посерьезней можно взять AP (могут засчитаться универом, куда школьник придет после школы).
MATH I The purpose of this course is to formalize and extend the mathematics that students learned in the middle grades. This course deepens and extends understanding of linear relationships, in part by contrasting them with exponential and quadratic phenomena, and in part by applying linear models to data that exhibit a linear trend. In addition to studying bivariate data, students also summarize, represent, and interpret data on a single count or measurement variable. The Geometry standards that appear in this course formalize and extend students’ geometric experiences to explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. The Standards for Mathematical Practice apply throughout each course and, together with the content standards, require that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. This course fulfills the North Carolina high school graduation requirement for Common Core Math I. The final exam is the North Carolina End-of-Course Test based on the Common Core Math 1 Standards.
MATH II In Math II, students continue to deepen their study of quadratic expressions, equations, and functions; comparing their characteristics and behavior to those of linear and exponential relationships from Math I. The concept of quadratics is generalized with the introduction of higher degree polynomials. New methods for solving quadratic and exponential equations are developed. The characteristics of advanced types of functions are investigated (including power, inverse variation, radical, absolute value, piecewise-defined, and simple trigonometric functions). The link between probability and data is explored through conditional probability and counting methods. Students explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. Important differences exist between Math II and the historical approach taken in Geometry classes. For example, transformations are explored early in the course and provide the framework for studying geometric concepts such as similarity and congruence. The study of similarity leads to an understanding of right triangle trigonometry and connects to quadratics through Pythagorean relationships. The Standards for Mathematical Practice apply throughout each course and, together with the content standards, require that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. This course fulfills the North Carolina high school graduation requirement for Math II. The final exam is the North Carolina Final Exam for Math II.
MATH III This course is designed so that students have the opportunity to pull together and apply the accumulation of mathematics concepts learned previously. They apply methods from probability and statistics to draw inferences and conclusions from data. Students expand their repertoire of functions to include polynomial, rational, and radical functions, including an intense study of families of functions and the relationships therein. They expand their study of right triangle trigonometry to include general triangles and in the study of trigonometric functions to model simple periodic phenomena. Finally, students bring together all of their experience with functions and geometry to create models and solve contextual problems. Appropriate technology and tools, including manipulatives and calculators, will be used regularly for instruction and assessment. The Standard for Mathematical Practice apply throughout each course and, together with the content standards, require that students experience mathematics as a coherent, useful, and logical subject that means use of their ability to make sense of problems situations. This course fulfills the North Carolina high school graduation requirement for Math III. The final exam is the North Carolina Final Exam for Math III.
Так вот Соня по окончанию 7 класса в МА сдала на пятерки классы Pre-Algebra, Algebra I и Geometry. Т.е. по логике должна была изучать математику 11 класса будучи в 8 классе. Но приехав в NC мы выяснили, что т.к. геометрия тут не является отдельным предметом и хотя они ее зачли и она пойдет как сданный математический предмет в high school табель, но училась Соня весь прошлый год в Math 2 (т.е. 10 класс, который она проходила в 8-м). На следующий год (9 класс) Соня записалась на Math 3 и Pre-Calculus (не знаю, дадут ли, расписние в старшей школе зависит от кучи факторов).
Да, и тем, кто думает, что такие успехи у Сони потому, что у нее мама-учитель математики - я честно скажу, это ее собственная заслуга + все эти годы RSM (школа математики, в которой я преподаю и Соня учится) - там преподают на год-два опережая школьную программу плюс намного глубже и качественнее, чем в школе, что Соне очень помогает в школьной математике.
Algebra 1: Real numbers; solving, writing, and graphing linear equations; quadratic equations and functions; polynomials
Geometry: Plane and solid geometry including constructions, formulas for measurement, and formal proofs
Algebra 2: Continuation of the concepts taught in algebra 1, including a more in-depth study of graphing and solving equations, inequalities, and functions
Trigonometry: Applies algebra and geometry skills to circular and periodic functions. NOTE: Trigonometry is usually not its own class, but is often taught during algebra 2, geometry, or pre-calculus
Pre-Calculus: Series and sequences, probability, statistics, limits, and derivatives
Calculus: Continuation of the concepts taught in pre-calculus, with an emphasis on integration and differentiation
В NC эти курсы распределены по другому. Главное отличие - геометрия теперь не выделена в отдельный годовой курс, а дается внутри общей математики (мне такой подход больше нравится). Math 1 (9 класс), Math 2 (10 класс), Math 3 (11 класс), а в 12 кто что хочет - выбор между Math 4, Сложные функиции (наверное типа Функционального Анализа в нашем прошлом?), Дискретная математика, Статистика, Pre-Calculus and Calculus. Опять-таки, пишу для нашего округа, в других местах набор предложенных курсов может незначительно отличаться. Интересно, что классы еще даются в разном уровне - Foundation (кому математика ну очень тяжело дается, обычный уровень, Honors (продвинутый) и для классов посерьезней можно взять AP (могут засчитаться универом, куда школьник придет после школы).
MATH I The purpose of this course is to formalize and extend the mathematics that students learned in the middle grades. This course deepens and extends understanding of linear relationships, in part by contrasting them with exponential and quadratic phenomena, and in part by applying linear models to data that exhibit a linear trend. In addition to studying bivariate data, students also summarize, represent, and interpret data on a single count or measurement variable. The Geometry standards that appear in this course formalize and extend students’ geometric experiences to explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. The Standards for Mathematical Practice apply throughout each course and, together with the content standards, require that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. This course fulfills the North Carolina high school graduation requirement for Common Core Math I. The final exam is the North Carolina End-of-Course Test based on the Common Core Math 1 Standards.
MATH II In Math II, students continue to deepen their study of quadratic expressions, equations, and functions; comparing their characteristics and behavior to those of linear and exponential relationships from Math I. The concept of quadratics is generalized with the introduction of higher degree polynomials. New methods for solving quadratic and exponential equations are developed. The characteristics of advanced types of functions are investigated (including power, inverse variation, radical, absolute value, piecewise-defined, and simple trigonometric functions). The link between probability and data is explored through conditional probability and counting methods. Students explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. Important differences exist between Math II and the historical approach taken in Geometry classes. For example, transformations are explored early in the course and provide the framework for studying geometric concepts such as similarity and congruence. The study of similarity leads to an understanding of right triangle trigonometry and connects to quadratics through Pythagorean relationships. The Standards for Mathematical Practice apply throughout each course and, together with the content standards, require that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. This course fulfills the North Carolina high school graduation requirement for Math II. The final exam is the North Carolina Final Exam for Math II.
MATH III This course is designed so that students have the opportunity to pull together and apply the accumulation of mathematics concepts learned previously. They apply methods from probability and statistics to draw inferences and conclusions from data. Students expand their repertoire of functions to include polynomial, rational, and radical functions, including an intense study of families of functions and the relationships therein. They expand their study of right triangle trigonometry to include general triangles and in the study of trigonometric functions to model simple periodic phenomena. Finally, students bring together all of their experience with functions and geometry to create models and solve contextual problems. Appropriate technology and tools, including manipulatives and calculators, will be used regularly for instruction and assessment. The Standard for Mathematical Practice apply throughout each course and, together with the content standards, require that students experience mathematics as a coherent, useful, and logical subject that means use of their ability to make sense of problems situations. This course fulfills the North Carolina high school graduation requirement for Math III. The final exam is the North Carolina Final Exam for Math III.
Так вот Соня по окончанию 7 класса в МА сдала на пятерки классы Pre-Algebra, Algebra I и Geometry. Т.е. по логике должна была изучать математику 11 класса будучи в 8 классе. Но приехав в NC мы выяснили, что т.к. геометрия тут не является отдельным предметом и хотя они ее зачли и она пойдет как сданный математический предмет в high school табель, но училась Соня весь прошлый год в Math 2 (т.е. 10 класс, который она проходила в 8-м). На следующий год (9 класс) Соня записалась на Math 3 и Pre-Calculus (не знаю, дадут ли, расписние в старшей школе зависит от кучи факторов).
Да, и тем, кто думает, что такие успехи у Сони потому, что у нее мама-учитель математики - я честно скажу, это ее собственная заслуга + все эти годы RSM (школа математики, в которой я преподаю и Соня учится) - там преподают на год-два опережая школьную программу плюс намного глубже и качественнее, чем в школе, что Соне очень помогает в школьной математике.