NUMERACY IN SPAIN A GENERAL OVERVIEW
|
|
- Kristina Hines
- 7 years ago
- Views:
Transcription
1 NUMERACY IN SPAIN A GENERAL OVERVIEW CREA Centre of Research in Theories and Practices that Overcome Inequalities Universitat de Barcelona - SPAIN crea@ub.edu Contents Introduction General framework of the adult educational system in Spain Level 1: State Level 2: Regions (Comunidades Autónomas) - Specific case: Catalonia Numeracy in Spain Numeracy and the Adult Education System in Catalonia 1. Introduction The adult educational system in Spain is decentralized. It means that central Government establishes the general criteria by law, but each region develops their own adult educational system. So, actually there are several systems at the same time. In this report we are going to give a general overview of this system. Firstly some issues related to the general educational system in Spain will be presented. Secondly the main general programs will be highlighted. Thirdly, the Catalonian educational system will be focused on and an explanation will be provided on how the adult educational system is organized in Catalonia. Finally numeracy will be discussed, and the main elements in the adult education curriculum will be expounded, with regards to Mathematics. 2. General framework of the adult educational system in Spain Level 1: State Adult education in Spain offers different kinds of activities. There are both regular and non-regular courses. Also there are courses oriented towards training adults in order to pass specific exams, in order to obtain professional or academic qualifications. Adult education is geared towards people over 16 years old. The Organic Quality of Education Law (Ley Orgánica de Calidad de la Educación) regulates adult education in Spain. This law is based on a lifelong learning concept. Article III is entirely dedicated to adult education. The main objective is to provide adults with basic training in order to open up new possibilities such as promoting adults access to other educational levels, such as access to University courses, 1
2 achieving qualifications and developing their capacity to get involved in social, cultural and political events. The specific objectives of adult education in Spain are the following: - To update the educational background and to facilitate access to different educational levels to each person who may require it. - To develop programs and courses related to specific educational needs from excluded groups. - To improve professional qualifications and/or to acquire training in order to develop other professions. - To develop people s capacity to participate in social, cultural and political events. These are the main objectives for adult education in Spain. People can find both standard and on-line courses. So, there is standard education and distance learning also. Article 52. Objective. Permanent education offers lifelong learning to all members of the public in order to acquire, update, complete and extend their abilities and skills for their professional and personal development. To do this, the administration of education will collaborate with the civil service departments with competencies in terms of adult education, and especially in employment management. (...) Public administrations prioritises all these people who have not completed their basic education, for various reasons. Also people over the age of 16 would be able to participate in adult education if they cannot attend a standard educational centre because of their job or other circumstances. (...) The administration of education will promote specific programs for the Spanish language, culture and other co-official languages in order to integrate the immigrant population. (Source: LOGSE General Arrangement of the Educational System Law). The provision of Adult Education in Spain includes the following options: - Basic Adult Education. - Professional training. - Mentored lessons. - Courses to prepare for exams in order to access other levels of education. - Spanish classes for the immigrant population. - Non-formal educational courses. 2
3 Table 1. The Adult Education system in Spain: a brief overview. ACCESS V.I.A. People over 18 years old. LEVEL 1 LEVEL 2 LITERACY CONSOLIDATION OF KNOWLEDGE AND ACQUISITION OF INSTRUMENTAL TECHNIQUES LITERACY AND NEO-READERS GLOBAL MODULE I GLOBAL MODULE II GLOBAL MODULE III Topics LANGUAGE AND LITERATURE MATHEMATICS SOCIO-NATURAL SCIENCES There is no temporary Deadline: 1 scholar year (It is possible to do it over 2 years with limit to do it justification) Regular attendance Regular attendance or distance courses Duration: 12 weeks Duration: 16 weeks Tutoring: once a week Teachers Students file (contents): V.I.A., assessment report, grades Level 2: Regions (Comunidades autónomas) specific case: Catalonia In Catalonia adult education is defined as lifelong learning. Adult learning refers to all kinds of training activities which allow people to develop their abilities and skills. These courses also allow adults to obtain the Secondary Education Graduate certificate (Graduado en Educación Secundaria GES ). Academic centres (schools for adults but also local centres, etc.) have open and flexible courses on offer. Therefore it is possible to create tailored courses in accordance with individual needs. It is also possible to obtain certificates through distance learning, with a program called Graduï s. Ara en secundària! (You have graduated! Now for the next stage!). Everyone over the age of 18 is able to participate in the adult education system, except people who have already completed standard education courses. It is also possible to enrol people over the age of 16, in order for them to prepare for standard exams for entry into vocational courses. An interdepartmental program in Catalonia manages Adult Education. This means that different departments from the Catalonian government are involved in Adult Education. There are over 5,000 actions taking place, divided into the following fields: - Initial education (ensenyaments inicials) - Basic Adult Education - Vocational training - Education for leisure and culture - Training courses 3
4 - Courses for people with special needs - Courses for in-service adult teachers In Catalonia there are 5 main domains in adult education: introductory courses, an instrumental training level, secondary education, and teaching geared towards preparing for exams in order to access other educational levels ( such as university, for example) and courses on information society competences. The introductory course includes: the Catalan language, the Spanish language, IT and foreign languages. The Instrumental training level includes reading skills, writing skills, mathematics and general culture. The Secondary education level also includes all these topics, but they are dealt with more in-depth. The third option, preparing for exams in order to access other educational levels, includes: a) access to secondary level vocational training levels (proves d accès a cicles formatius de grau mitjà); b) access to higher vocational training levels (proves d accès a cicles formatius de grau superior); and c) access to Universities. Lastly, courses to learn about information society competences mostly include IT skills and foreign languages. Table 2: Adult Education in Catalonia Introductory courses Instrumental training level Secondary Education Training to prepare exams in order to access other educational levels Courses on Information society competences 3. Numeracy in Spain in relation to the education system Numeracy is an important part of the Spanish curricula. Mathematics is one of the few topics which is present at almost every educational level. The main mathematical objectives within the Spanish curricula are the following (Alsina, 2001): - To incorporate the language and arguments typical of mathematical reasoning (numerical, graphical, geometrical, logical, algebraic, probabilistic) in order to be able to communicate in a precise and rigorous way. - To use logical ways of thinking, to formulate and verify conjectures, to make inferences and deductions, and to 4
5 organize and link information related to daily life and problem solving. - To quantify real situations by virtue of data, measures and numbers while making the appropriate computations. - To elaborate personal strategies for analyzing concrete situations and for problem solving using various resources and instruments, analyzing the final results obtained. - To use elementary techniques for collecting data to obtain information about phenomena and situations and to represent this information by means of numerical or graphical forms in order to evaluate it. - To recognize the diversity of different situations and to see how different points of view can be used to explain it (deterministic / random, finite / infinite, exact / approximate). - To identify shapes and spatial relations present in reality, analyzing geometrical properties and relationships. - To identify the mathematical elements (statistical data, graphics, maps, computations, etc.), which are present in news, pools, commercials, etc., critically analyzing their functions and possibilities for a better understanding of messages. - To approach day-to-day situations and problem solving in a mathematical way (exploring alternatives, using a precise language, etc.). - To know and value personal mathematical skills in order to deal with situations that require their use or in which one can enjoy the creative, manipulative, aesthetic or useful aspects of mathematics (Alsina, 2001: 3-4). As Alsina (2001) claims, the main mathematical concepts in Spanish curricula are: numbers and operations, measures, estimation, calculus of magnitudes, representation and organization of space, interpretation, representation, analysis of information and treatment of the element of chance. Students should be aware of all these ideas, because they are present in the compulsory education system. In Spain children learn to solve equations (at compulsory levels just up until quadratic equations, then teachers introduce linear algebra systems and calculus), problems based on the Pythagorean theorem, situations about similarity (through proportions and applications of Tales theorem), different kinds of word problems, percentages, and so forth. In the last few years the curricula has been more focused on problem solving and a conception of contextualized mathematics, in terms of realistic mathematics and everyday mathematics. 4. Numeracy and the adult education system in Catalonia In Catalonia adult numeracy is focused on the practical application of Mathematics. Mathematical concepts, relations and basic operations are used as tools, in order to interpret and to solve problems in everyday life. So the kinds of activities mainly include practical situations and problems within a context, in the sense of realistic mathematics. Mathematics also has a social component. Because 5
6 of its nature, Mathematics forces people to go backwards and forwards between concrete to abstract ideas. This dynamic encourages the development of logical reasoning and cognitive schemata. So, Mathematics in Catalonia is focused on situations analysis, problem solving, discussions about different resolutions, etc. The starting point is always everyday situations, so that adults people have the opportunity to make connections with their own life experience. There are several adult education centres where the curricula is based on dialogical mathematics or multicultural considerations. Here is an overview of both adult basic education and secondary education Mathematics curricula.. Adult basic education (ABE) curricula in Mathematics The general objectives of the ABE curricula in Mathematics in Catalonia are the following: - To value and use Mathematics as a tool to interpret information from the real world in a critical way. - To search for and to select information in order to share it, to discuss different interpretations of it and to build different strategies to solve problems. - To value Mathematics as a way to collaborate with partners, and to encourage self-confidence. - To carry out the whole process involved in solve a problem, from understanding the problem to checking the answer. - To identify, interpret and use different languages and mathematical codes. - To use mental calculus as well as computer calculus (with a calculator or with a computer). - To interpret numbers as quantitative characters, by using the correct scale from an estimation of the magnitude order. - To identify, represent and classify geometrical shapes, by using t knowledge about the properties and relationships of these shapes, in order to improve spatial understanding. - To identify graphs and tables by using basic techniques to collect data, and by using them to represent and analyse real phenomena. The contents of the ABE curricula in Mathematics in Catalonia are the following: -Procedures- 1. Mathematical procedures: a. To observe, to experiment and to collect data. b. To classify, to compare, to arrange and to measure data. c. To estimate and to check data. 2. Mathematical languages: a. To understand mathematical vocabulary and to use the most regular codes (numbers, units of measurement, etc.). 3. Techniques for calculations: a. Exact calculus and approximations. 6
7 b. The use of calculus tools. c. Introduction to new technologies as tools for solving problems. 4. Problem solving: a. To build strategies for problem solving. b. To use arithmetic, geometry and measurements for problem solving. -Concepts, ideas- 1. Natural numbers and operations. a. Cardinals & ordinals. b. Position value. c. Addition, subtraction, multiplication and division. 2. Fractions and decimal numbers. a. Fractions as part of a unit or a quantity, as an expression of measurement and as a division. b. Decimal numbers as fractions. c. Percentages. 3. Magnitudes and measurements. a. Magnitudes: length, surface, volume, time, temperature and money value. b. Measurement units. 4. Geometrical shapes: a. Shapes on the plane and in space. Elements of shapes. b. Geometrical relations. c. Location and direction. 5. Introduction to statistics. a. Statistical data. b. Elementary parameters: mean, mode, median. c. Graphics: data representation. -Values, norms, attitudes- 1. To value individual and collective efforts. 2. To value work in small groups as a way to enrichment. 3. Scientific attitude. 4. To consider Mathematics as a tool to represent the real world. 5. To value Mathematics as a tool to plan and to organize concrete situations in the real world. 6. To use estimation, rounding-up, and mental calculus. 7. The value of error and its usefulness within the learning process. 8. To consider the usefulness of technological tools as calculators, computers, etc., as tools to facilitate mathematical routines. Secondary curricula in Mathematics The curricular design at this level begins with the knowledge acquired in the previous steps (adult basic education). The main goal is to promote the development of a scientific attitude. The curriculum combines both theoretical and 7
8 practical components. It is focused on values such as the promotion of the pleasure of observing, understanding, and discovering. This approach promotes people s real world understanding. The curriculum expects to offer a scientific-technologic view of society and also to promote a scientific way of reasoning and understanding. Mathematics is presented along with science and technology. The general objectives at this level are the following: - To understand Mathematics as an open and dynamic science which addresses problem solving, with its own history. - To value the instrumental character of Mathematics for other fields of knowledge. More specifically, to underline the capacity of mathematical models to describe, to interpret and to understand the physical and natural world and also society. - To acquire the skills needed to compare, to use, and to evaluate different mathematical models. To apply mathematical methods in a creative way when facing new situations. - To recognize the role of the current technological media in Mathematics, such as tools to carry out mechanical procedures. - To understand and to value one s own mathematical skills and to use them in a flexible way. To have enough resources to use to solve problematic situations (either in everyday situations or mathematical situations). - To observe both quantitative and geometric aspects from the real world and also from society in a systematic way. To organize data in a clear way that makes their analysis and understanding easier. - To express and to interpret the data collected correctly, as well as graphs, tables, and so forth. - To use different mathematical languages (algebra, statistics, geometry, etc.) when it is useful in order to represent and describe questions and their answers. - To understand and to use terminology, symbolism, and scientific tools correctly in order to understand scientific compositions. - To observe, describe and classify objects, organisms, phenomena and processes related to the physical environment. - To value scientific attitudes like curiosity, objectivity, observation and the different processes of scientific investigation. The main contents of secondary curricula in Mathematics in Catalonia are the following: -Procedures- 1. Languages and processes a. The use of different mathematical languages: numerical expressions, algebraic expressions, functional language, graphic language, and geometrical language. b. Translation. c. Classification. Arrangement. d. Application of deductive and/or inductive methods. 8
9 e. Problem solving. 2. Techniques to take measurements and to calculate them a. Techniques for symbolic and graphical number representation. b. Techniques to take direct measurements (with the use of tools) and indirect measurements (through algorithms, and scalar representations). c. Exact calculus and approximations. The use of a scientific calculator. d. Elementary ways to solve equations. e. Permutations. f. Techniques to calculate statistical parameters. 3. The use of geometrical models. a. The application of geometrical models to interpret real situations. b. Scalar representation in the plane of geometrical shapes. c. Break plane shapes into more elemental shapes. d. Plane representation of spatial shapes. 4. Collecting data. a. Techniques to collect data. b. Direct observation of objects, phenomena and procedures. c. Observation of figures, models and scale models. d. The use of technological media. 5. Data processing. a. Building tables (of items and frequencies). b. Graphic representation of phenomena in the X-Y axis. c. Specific techniques for graphic representation of statistical data. d. Graphic and symbolic representation of technical data. e. Creation and use of formula to make links between variables. f. Analysis of functional dependences. g. Analysis of statistical variables. h. Interpretation of schema, symbols and symbol sequences. i. Random phenomena processing. Calculus of probabilities. j. Interpretation of data collected. -Concepts, ideas- 1. Numbers. a. Natural numbers. Divisibility. b. Whole numbers. c. Rational numbers and decimal numbers. d. Numbers and the use of the scientific calculator. e. Magnitudes. f. Equations. 2. Plane and space. a. Elements and organization in the plain. b. Elements and organization in the space. c. Metric relations and trigonometric. 3. Dependence between variables. a. X-Y axis. General characteristics of graphs. b. Functions: dependence and associated ideas. c. Lineal function. 9
10 d. Quadratic function. e. Increase and decrease of different kind of functions. 4. Elemental statistics and chance. a. Basic concepts in statistics. b. Parameters of centrality / dispersion c. Random phenomena. d. Probability: concept and main principia. -Values, norms, attitudes- 1. To make questions and research problems receptive to mathematical understanding. 2. Systematization of work with mathematics. 3. To value mathematical tools. 4. To use technological media with wisdom. 5. Confidence in one s own ability to solve real problems in a mathematical way. 6. Interest in self-study and lifelong learning. At the end of the secondary level, adults should be able to understand different types of numbers and their properties, as well as different ways to represent numbers (whole numbers, fractions, percentages, scientific notations, etc.). Adults should be able to use algorithms, solve equations, recognize different kind of problems, make connections between Mathematics and the real world and use Mathematics to represent real situations and try to find answers to real problems. Therefore, and to conclude, in Catalonia numeracy means to have a mathematical understanding of the real world, as well as having mathematical skills to solve problems in everyday life. References Alsina, C. (2001). Reference levels in School Mathematics Education in Europe. National presentation: Spain. EMS. European Mathematical Society. Committee on Mathematics Education. BOP. (2002) Decret d 1 d agost pel qual s estableix l ordenació curricular de la formació bàsica de les persones adultes. Ministerio de Educación. (2006). 10
Big Ideas in Mathematics
Big Ideas in Mathematics which are important to all mathematics learning. (Adapted from the NCTM Curriculum Focal Points, 2006) The Mathematics Big Ideas are organized using the PA Mathematics Standards
More informationMathematics Georgia Performance Standards
Mathematics Georgia Performance Standards K-12 Mathematics Introduction The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by
More informationCurrent Standard: Mathematical Concepts and Applications Shape, Space, and Measurement- Primary
Shape, Space, and Measurement- Primary A student shall apply concepts of shape, space, and measurement to solve problems involving two- and three-dimensional shapes by demonstrating an understanding of:
More informationGeorgia Department of Education Kathy Cox, State Superintendent of Schools 7/19/2005 All Rights Reserved 1
Accelerated Mathematics 3 This is a course in precalculus and statistics, designed to prepare students to take AB or BC Advanced Placement Calculus. It includes rational, circular trigonometric, and inverse
More informationPrentice Hall: Middle School Math, Course 1 2002 Correlated to: New York Mathematics Learning Standards (Intermediate)
New York Mathematics Learning Standards (Intermediate) Mathematical Reasoning Key Idea: Students use MATHEMATICAL REASONING to analyze mathematical situations, make conjectures, gather evidence, and construct
More informationGlencoe. correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 3-3, 5-8 8-4, 8-7 1-6, 4-9
Glencoe correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 STANDARDS 6-8 Number and Operations (NO) Standard I. Understand numbers, ways of representing numbers, relationships among numbers,
More informationDELAWARE MATHEMATICS CONTENT STANDARDS GRADES 9-10. PAGE(S) WHERE TAUGHT (If submission is not a book, cite appropriate location(s))
Prentice Hall University of Chicago School Mathematics Project: Advanced Algebra 2002 Delaware Mathematics Content Standards (Grades 9-10) STANDARD #1 Students will develop their ability to SOLVE PROBLEMS
More informationPrentice Hall Algebra 2 2011 Correlated to: Colorado P-12 Academic Standards for High School Mathematics, Adopted 12/2009
Content Area: Mathematics Grade Level Expectations: High School Standard: Number Sense, Properties, and Operations Understand the structure and properties of our number system. At their most basic level
More informationIn mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.
MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target
More informationCHICAGO PUBLIC SCHOOLS (ILLINOIS) MATH & SCIENCE INITIATIVE COURSE FRAMEWORK FOR ALGEBRA Course Framework: Algebra
Chicago Public Schools (Illinois) Math & Science Initiative Course Framework for Algebra Course Framework: Algebra Central Concepts and Habits of Mind The following concepts represent the big ideas or
More informationNEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS
NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS TEST DESIGN AND FRAMEWORK September 2014 Authorized for Distribution by the New York State Education Department This test design and framework document
More informationNEW MEXICO Grade 6 MATHEMATICS STANDARDS
PROCESS STANDARDS To help New Mexico students achieve the Content Standards enumerated below, teachers are encouraged to base instruction on the following Process Standards: Problem Solving Build new mathematical
More informationPrentice Hall Connected Mathematics 2, 7th Grade Units 2009
Prentice Hall Connected Mathematics 2, 7th Grade Units 2009 Grade 7 C O R R E L A T E D T O from March 2009 Grade 7 Problem Solving Build new mathematical knowledge through problem solving. Solve problems
More informationInteger Operations. Overview. Grade 7 Mathematics, Quarter 1, Unit 1.1. Number of Instructional Days: 15 (1 day = 45 minutes) Essential Questions
Grade 7 Mathematics, Quarter 1, Unit 1.1 Integer Operations Overview Number of Instructional Days: 15 (1 day = 45 minutes) Content to Be Learned Describe situations in which opposites combine to make zero.
More informationOverview. Essential Questions. Precalculus, Quarter 4, Unit 4.5 Build Arithmetic and Geometric Sequences and Series
Sequences and Series Overview Number of instruction days: 4 6 (1 day = 53 minutes) Content to Be Learned Write arithmetic and geometric sequences both recursively and with an explicit formula, use them
More informationAcademic Standards for Mathematics
Academic Standards for Grades Pre K High School Pennsylvania Department of Education INTRODUCTION The Pennsylvania Core Standards in in grades PreK 5 lay a solid foundation in whole numbers, addition,
More informationTennessee Mathematics Standards 2009-2010 Implementation. Grade Six Mathematics. Standard 1 Mathematical Processes
Tennessee Mathematics Standards 2009-2010 Implementation Grade Six Mathematics Standard 1 Mathematical Processes GLE 0606.1.1 Use mathematical language, symbols, and definitions while developing mathematical
More informationCURRICULUM FOR THE COMMON CORE SUBJECT OF MATHEMATICS
CURRICULUM FOR THE COMMON CORE SUBJECT OF Dette er ei omsetjing av den fastsette læreplanteksten. Læreplanen er fastsett på Nynorsk Established as a Regulation by the Ministry of Education and Research
More informationCORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREER-READY FOUNDATIONS IN ALGEBRA
We Can Early Learning Curriculum PreK Grades 8 12 INSIDE ALGEBRA, GRADES 8 12 CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREER-READY FOUNDATIONS IN ALGEBRA April 2016 www.voyagersopris.com Mathematical
More informationCreating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities
Algebra 1, Quarter 2, Unit 2.1 Creating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned
More informationAMSCO S Ann Xavier Gantert
AMSCO S Integrated ALGEBRA 1 Ann Xavier Gantert AMSCO SCHOOL PUBLICATIONS, INC. 315 HUDSON STREET, NEW YORK, N.Y. 10013 Dedication This book is dedicated to Edward Keenan who left a profound influence
More informationGrade 6 Mathematics Assessment. Eligible Texas Essential Knowledge and Skills
Grade 6 Mathematics Assessment Eligible Texas Essential Knowledge and Skills STAAR Grade 6 Mathematics Assessment Mathematical Process Standards These student expectations will not be listed under a separate
More informationCurriculum Map by Block Geometry Mapping for Math Block Testing 2007-2008. August 20 to August 24 Review concepts from previous grades.
Curriculum Map by Geometry Mapping for Math Testing 2007-2008 Pre- s 1 August 20 to August 24 Review concepts from previous grades. August 27 to September 28 (Assessment to be completed by September 28)
More informationWhitnall School District Report Card Content Area Domains
Whitnall School District Report Card Content Area Domains In order to align curricula kindergarten through twelfth grade, Whitnall teachers have designed a system of reporting to reflect a seamless K 12
More informationAlgebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard
Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express
More informationMeasurement with Ratios
Grade 6 Mathematics, Quarter 2, Unit 2.1 Measurement with Ratios Overview Number of instructional days: 15 (1 day = 45 minutes) Content to be learned Use ratio reasoning to solve real-world and mathematical
More informationGRADES 7, 8, AND 9 BIG IDEAS
Table 1: Strand A: BIG IDEAS: MATH: NUMBER Introduce perfect squares, square roots, and all applications Introduce rational numbers (positive and negative) Introduce the meaning of negative exponents for
More informationStandards for Mathematical Practice: Commentary and Elaborations for 6 8
Standards for Mathematical Practice: Commentary and Elaborations for 6 8 c Illustrative Mathematics 6 May 2014 Suggested citation: Illustrative Mathematics. (2014, May 6). Standards for Mathematical Practice:
More informationMathematics. What to expect Resources Study Strategies Helpful Preparation Tips Problem Solving Strategies and Hints Test taking strategies
Mathematics Before reading this section, make sure you have read the appropriate description of the mathematics section test (computerized or paper) to understand what is expected of you in the mathematics
More informationMath at a Glance for April
Audience: School Leaders, Regional Teams Math at a Glance for April The Math at a Glance tool has been developed to support school leaders and region teams as they look for evidence of alignment to Common
More informationThe program also provides supplemental modules on topics in geometry and probability and statistics.
Algebra 1 Course Overview Students develop algebraic fluency by learning the skills needed to solve equations and perform important manipulations with numbers, variables, equations, and inequalities. Students
More informationAlgebra I Credit Recovery
Algebra I Credit Recovery COURSE DESCRIPTION: The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics,
More informationPCHS ALGEBRA PLACEMENT TEST
MATHEMATICS Students must pass all math courses with a C or better to advance to the next math level. Only classes passed with a C or better will count towards meeting college entrance requirements. If
More informationEMS. National Presentation Grand-Duchy of L U X E M B 0 U R G
Niveaux de référence pour l'enseignement des mathématiques en Europe Reference levels in School Mathematics Education in Europe EMS European Mathematical Society http://www.emis.de/ Committee on Mathematics
More informationDiablo Valley College Catalog 2014-2015
Mathematics MATH Michael Norris, Interim Dean Math and Computer Science Division Math Building, Room 267 Possible career opportunities Mathematicians work in a variety of fields, among them statistics,
More informationMathematics. Programme of study for key stage 3 and attainment targets (This is an extract from The National Curriculum 2007)
Mathematics Programme of study for key stage 3 and attainment targets (This is an extract from The National Curriculum 2007) Crown copyright 2007 Qualifications and Curriculum Authority 2007 Curriculum
More informationMathematics Policy. Michael Sobell Sinai School
Mathematics Policy 2014 Mathematics Policy Section 1: Introduction Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some
More informationHow To Teach Math
Mathematics K-12 Mathematics Introduction The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by using manipulatives and a variety
More informationMATH. ALGEBRA I HONORS 9 th Grade 12003200 ALGEBRA I HONORS
* Students who scored a Level 3 or above on the Florida Assessment Test Math Florida Standards (FSA-MAFS) are strongly encouraged to make Advanced Placement and/or dual enrollment courses their first choices
More informationMathematics (MAT) MAT 061 Basic Euclidean Geometry 3 Hours. MAT 051 Pre-Algebra 4 Hours
MAT 051 Pre-Algebra Mathematics (MAT) MAT 051 is designed as a review of the basic operations of arithmetic and an introduction to algebra. The student must earn a grade of C or in order to enroll in MAT
More informationLAKE ELSINORE UNIFIED SCHOOL DISTRICT
LAKE ELSINORE UNIFIED SCHOOL DISTRICT Title: PLATO Algebra 1-Semester 2 Grade Level: 10-12 Department: Mathematics Credit: 5 Prerequisite: Letter grade of F and/or N/C in Algebra 1, Semester 2 Course Description:
More informationPerformance Level Descriptors Grade 6 Mathematics
Performance Level Descriptors Grade 6 Mathematics Multiplying and Dividing with Fractions 6.NS.1-2 Grade 6 Math : Sub-Claim A The student solves problems involving the Major Content for grade/course with
More information096 Professional Readiness Examination (Mathematics)
096 Professional Readiness Examination (Mathematics) Effective after October 1, 2013 MI-SG-FLD096M-02 TABLE OF CONTENTS PART 1: General Information About the MTTC Program and Test Preparation OVERVIEW
More informationProblem of the Month: Perfect Pair
Problem of the Month: The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards:
More informationMATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab
MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab MATH 0110 is established to accommodate students desiring non-course based remediation in developmental mathematics. This structure will
More informationPre-Algebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems
Academic Content Standards Grade Eight Ohio Pre-Algebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small
More informationChapter 111. Texas Essential Knowledge and Skills for Mathematics. Subchapter B. Middle School
Middle School 111.B. Chapter 111. Texas Essential Knowledge and Skills for Mathematics Subchapter B. Middle School Statutory Authority: The provisions of this Subchapter B issued under the Texas Education
More informationPolynomial Operations and Factoring
Algebra 1, Quarter 4, Unit 4.1 Polynomial Operations and Factoring Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned Identify terms, coefficients, and degree of polynomials.
More informationSequence of Mathematics Courses
Sequence of ematics Courses Where do I begin? Associates Degree and Non-transferable Courses (For math course below pre-algebra, see the Learning Skills section of the catalog) MATH M09 PRE-ALGEBRA 3 UNITS
More informationNumeracy and mathematics Experiences and outcomes
Numeracy and mathematics Experiences and outcomes My learning in mathematics enables me to: develop a secure understanding of the concepts, principles and processes of mathematics and apply these in different
More informationFor example, estimate the population of the United States as 3 times 10⁸ and the
CCSS: Mathematics The Number System CCSS: Grade 8 8.NS.A. Know that there are numbers that are not rational, and approximate them by rational numbers. 8.NS.A.1. Understand informally that every number
More informationCrosswalk Directions:
Crosswalk Directions: UMS Standards for College Readiness to 2007 MLR 1. Use a (yes), an (no), or a (partially) to indicate the extent to which the standard, performance indicator, or descriptor of the
More informationGrade Level Year Total Points Core Points % At Standard 9 2003 10 5 7 %
Performance Assessment Task Number Towers Grade 9 The task challenges a student to demonstrate understanding of the concepts of algebraic properties and representations. A student must make sense of the
More informationLAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE
LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE MAT 119 STATISTICS AND ELEMENTARY ALGEBRA 5 Lecture Hours, 2 Lab Hours, 3 Credits Pre-
More informationA Correlation of Pearson Texas Geometry Digital, 2015
A Correlation of Pearson Texas Geometry Digital, 2015 To the Texas Essential Knowledge and Skills (TEKS) for Geometry, High School, and the Texas English Language Proficiency Standards (ELPS) Correlations
More informationMathematics Cognitive Domains Framework: TIMSS 2003 Developmental Project Fourth and Eighth Grades
Appendix A Mathematics Cognitive Domains Framework: TIMSS 2003 Developmental Project Fourth and Eighth Grades To respond correctly to TIMSS test items, students need to be familiar with the mathematics
More informationNCTM Curriculum Focal Points for Grade 5. Everyday Mathematics, Grade 5
NCTM Curriculum Focal Points and, Grade 5 NCTM Curriculum Focal Points for Grade 5 Number and Operations and Algebra: Developing an understanding of and fluency with division of whole numbers Students
More informationKEANSBURG SCHOOL DISTRICT KEANSBURG HIGH SCHOOL Mathematics Department. HSPA 10 Curriculum. September 2007
KEANSBURG HIGH SCHOOL Mathematics Department HSPA 10 Curriculum September 2007 Written by: Karen Egan Mathematics Supervisor: Ann Gagliardi 7 days Sample and Display Data (Chapter 1 pp. 4-47) Surveys and
More informationTExMaT I Texas Examinations for Master Teachers. Preparation Manual. 087 Master Mathematics Teacher EC 4
TExMaT I Texas Examinations for Master Teachers Preparation Manual 087 Master Mathematics Teacher EC 4 Copyright 2006 by the Texas Education Agency (TEA). All rights reserved. The Texas Education Agency
More informationPrentice Hall MyMathLab Algebra 1, 2011
Prentice Hall MyMathLab Algebra 1, 2011 C O R R E L A T E D T O Tennessee Mathematics Standards, 2009-2010 Implementation, Algebra I Tennessee Mathematics Standards 2009-2010 Implementation Algebra I 3102
More informationCabrillo College Catalog 2015-2016
MATHEMATICS Natural and Applied Sciences Division Wanda Garner, Division Dean Division Office, Room 701 Jennifer Cass, Department Chair, (831) 479-6363 Aptos Counselor: (831) 479-6274 for appointment Watsonville
More informationCORE Assessment Module Module Overview
CORE Assessment Module Module Overview Content Area Mathematics Title Speedy Texting Grade Level Grade 7 Problem Type Performance Task Learning Goal Students will solve real-life and mathematical problems
More informationIV. ALGEBRAIC CONCEPTS
IV. ALGEBRAIC CONCEPTS Algebra is the language of mathematics. Much of the observable world can be characterized as having patterned regularity where a change in one quantity results in changes in other
More informationCourse Syllabus. MATH 1350-Mathematics for Teachers I. Revision Date: 8/15/2016
Course Syllabus MATH 1350-Mathematics for Teachers I Revision Date: 8/15/2016 Catalog Description: This course is intended to build or reinforce a foundation in fundamental mathematics concepts and skills.
More informationPrentice Hall Mathematics: Course 1 2008 Correlated to: Arizona Academic Standards for Mathematics (Grades 6)
PO 1. Express fractions as ratios, comparing two whole numbers (e.g., ¾ is equivalent to 3:4 and 3 to 4). Strand 1: Number Sense and Operations Every student should understand and use all concepts and
More informationThe Most Widely Used. Mathematics Textbook Series in Japan is Now in English! Introducing Tokyo Shoseki s. and
The Most Widely Used Mathematics Textbook Series in Japan is Now in English! Introducing Tokyo Shoseki s Mathematics International (Elementary School, s 1 to 6) and Mathematics International (Lower Secondary
More informationFairfield Public Schools
Mathematics Fairfield Public Schools AP Statistics AP Statistics BOE Approved 04/08/2014 1 AP STATISTICS Critical Areas of Focus AP Statistics is a rigorous course that offers advanced students an opportunity
More informationMath Placement Test Study Guide. 2. The test consists entirely of multiple choice questions, each with five choices.
Math Placement Test Study Guide General Characteristics of the Test 1. All items are to be completed by all students. The items are roughly ordered from elementary to advanced. The expectation is that
More informationIndiana State Core Curriculum Standards updated 2009 Algebra I
Indiana State Core Curriculum Standards updated 2009 Algebra I Strand Description Boardworks High School Algebra presentations Operations With Real Numbers Linear Equations and A1.1 Students simplify and
More informationPearson Algebra 1 Common Core 2015
A Correlation of Pearson Algebra 1 Common Core 2015 To the Common Core State Standards for Mathematics Traditional Pathways, Algebra 1 High School Copyright 2015 Pearson Education, Inc. or its affiliate(s).
More informationPA Academic Standards. 2.4. Mathematical Reasoning and Connections 2.5. Mathematical Problem Solving and Communication
Curriculum Category Shift Standard Areas Grades K-8 and High School PA Academic Standards 2.4. Mathematical Reasoning and Connections 2.5. Mathematical Problem Solving and Communication PA Common Core
More informationPHILOSOPHY OF THE MATHEMATICS DEPARTMENT
PHILOSOPHY OF THE MATHEMATICS DEPARTMENT The Lemont High School Mathematics Department believes that students should develop the following characteristics: Understanding of concepts and procedures Building
More informationGeometry, Technology, and the Reasoning and Proof Standard inthemiddlegradeswiththegeometer ssketchpad R
Geometry, Technology, and the Reasoning and Proof Standard inthemiddlegradeswiththegeometer ssketchpad R Óscar Chávez University of Missouri oc918@mizzou.edu Geometry Standard Instructional programs from
More informationAnchorage School District/Alaska Sr. High Math Performance Standards Algebra
Anchorage School District/Alaska Sr. High Math Performance Standards Algebra Algebra 1 2008 STANDARDS PERFORMANCE STANDARDS A1:1 Number Sense.1 Classify numbers as Real, Irrational, Rational, Integer,
More informationBridging Documents for Mathematics
Bridging Documents for Mathematics 5 th /6 th Class, Primary Junior Cycle, Post-Primary Primary Post-Primary Card # Strand(s): Number, Measure Number (Strand 3) 2-5 Strand: Shape and Space Geometry and
More informationMinnesota Academic Standards
A Correlation of to the Minnesota Academic Standards Grades K-6 G/M-204 Introduction This document demonstrates the high degree of success students will achieve when using Scott Foresman Addison Wesley
More informationSchool of Mathematics, Computer Science and Engineering. Mathematics* Associate in Arts Degree COURSES, PROGRAMS AND MAJORS
Mathematics School of Mathematics, Computer Science and Engineering Dean: Lianna Zhao, MD Academic Chair: Miriam Castroconde Faculty: Miriam Castroconde; Terry Cheng; Howard Dachslager, PhD; Ilknur Erbas
More informationMATHEMATICS GRADES 10 12
MATHEMATICS GRADES 10 12 INTRODUCTION The Mathematics Grades 10 12 Program of Studies has been derived from The Common Curriculum Framework for Grades 10 12 Mathematics: Western and Northern Canadian Protocol,
More informationYOU CAN COUNT ON NUMBER LINES
Key Idea 2 Number and Numeration: Students use number sense and numeration to develop an understanding of multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and
More informationPlease start the slide show from the beginning to use links. Click here for active links to various courses
Please start the slide show from the beginning to use links Click here for active links to various courses CLICK ON ANY COURSE BELOW TO SEE DESCRIPTION AND PREREQUISITES To see the course sequence chart
More informationSouth Carolina College- and Career-Ready (SCCCR) Pre-Calculus
South Carolina College- and Career-Ready (SCCCR) Pre-Calculus Key Concepts Arithmetic with Polynomials and Rational Expressions PC.AAPR.2 PC.AAPR.3 PC.AAPR.4 PC.AAPR.5 PC.AAPR.6 PC.AAPR.7 Standards Know
More informationPROVINCE OF THE EASTERN CAPE EDUCATION
PROVINCE OF THE EASTERN CAPE EDUCATION DIRECTORATE: CURRICULUM FET PROGRAMMES LESSON PLANS TERM 3 MATHEMATICS GRADE 10 FOREWORD The following Grade 10, 11 and 12 Lesson Plans were developed by Subject
More informationPrentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary)
Core Standards of the Course Standard 1 Students will acquire number sense and perform operations with real and complex numbers. Objective 1.1 Compute fluently and make reasonable estimates. 1. Simplify
More informationNorth Carolina Math 2
Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4.
More informationCommon Core Unit Summary Grades 6 to 8
Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity- 8G1-8G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations
More informationSouth Carolina College- and Career-Ready (SCCCR) Algebra 1
South Carolina College- and Career-Ready (SCCCR) Algebra 1 South Carolina College- and Career-Ready Mathematical Process Standards The South Carolina College- and Career-Ready (SCCCR) Mathematical Process
More information2016 CLS Summer Schedule and Tuition. Academic Program:
Providing direct support to students through tutoring, testing, providing enrichment activities, emphasizing critical thinking activities, mentoring, and supporting our students to increase personal academic
More informationhttp://www.aleks.com Access Code: RVAE4-EGKVN Financial Aid Code: 6A9DB-DEE3B-74F51-57304
MATH 1340.04 College Algebra Location: MAGC 2.202 Meeting day(s): TR 7:45a 9:00a, Instructor Information Name: Virgil Pierce Email: piercevu@utpa.edu Phone: 665.3535 Teaching Assistant Name: Indalecio
More informationMACMILLAN/McGRAW-HILL. MATH CONNECTS and IMPACT MATHEMATICS WASHINGTON STATE MATHEMATICS STANDARDS. ESSENTIAL ACADEMIC LEARNING REQUIREMENTS (EALRs)
MACMILLAN/McGRAW-HILL MATH CONNECTS and IMPACT MATHEMATICS TO WASHINGTON STATE MATHEMATICS STANDARDS ESSENTIAL ACADEMIC LEARNING REQUIREMENTS (EALRs) And GRADE LEVEL EXPECTATIONS (GLEs) / Edition, Copyright
More informationAlgebra 1 Course Information
Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through
More informationMATHS LEVEL DESCRIPTORS
MATHS LEVEL DESCRIPTORS Number Level 3 Understand the place value of numbers up to thousands. Order numbers up to 9999. Round numbers to the nearest 10 or 100. Understand the number line below zero, and
More informationMathematics. Mathematics MATHEMATICS. 298 2015-16 Sacramento City College Catalog. Degree: A.S. Mathematics AS-T Mathematics for Transfer
MATH Degree: A.S. AS-T for Transfer Division of /Statistics & Engineering Anne E. Licciardi, Dean South Gym 220 916-558-2202 Associate in Science Degree Program Information The mathematics program provides
More informationUPPER SCHOOL COURSE CATALOG Grades 6-7
UPPER SCHOOL COURSE CATALOG Grades 6-7 Of Nevada 2015-2016 1 P a g e DORAL ACADEMY of NEVADA MISSION STATEMENT Doral Academy of Nevada is dedicated to providing an enhanced educational experience. We will
More informationPocantico Hills School District Grade 1 Math Curriculum Draft
Pocantico Hills School District Grade 1 Math Curriculum Draft Patterns /Number Sense/Statistics Content Strands: Performance Indicators 1.A.1 Determine and discuss patterns in arithmetic (what comes next
More informationMathematics SL subject outline
Diploma Programme Mathematics SL subject outline First examinations 2014 This document explains the major features of the course, and outlines the syllabus and assessment requirements. More detailed information
More informationHigher Education Math Placement
Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication
More informationExecutive Summary Principles and Standards for School Mathematics
Executive Summary Principles and Standards for School Mathematics Overview We live in a time of extraordinary and accelerating change. New knowledge, tools, and ways of doing and communicating mathematics
More informationMajor Work of the Grade
Counting and Cardinality Know number names and the count sequence. Count to tell the number of objects. Compare numbers. Kindergarten Describe and compare measurable attributes. Classify objects and count
More informationAdvanced Higher Mathematics Course Specification (C747 77)
Advanced Higher Mathematics Course Specification (C747 77) Valid from August 2015 This edition: April 2015, version 1.1 This specification may be reproduced in whole or in part for educational purposes
More informationMATHEMATICS COURSES Grades 8-12 2015-2016
MATHEMATICS COURSES Grades 8-12 2015-2016 Calculus III H Calculus II H A.P. Calculus BC A.P. Statistics A.P. Calculus AB A.P. Calculus BC Algebra II H* Pre-Calculus H Calculus/Stats H A.P. Calculus AB
More information