Analyses of West Virginia Mathematics and Science Curricular Objectives in effect
Analyses of West Virginia
Mathematics and Science
Curricular Objectives
in effect
July 2008
William H. Schmidt
University Distinguished Professor
Michigan State University
Curricular Content Principles
Curricular Coherence
Curricular Structure
Curricular Focus
Exposure Time (OTL)
Curricular Rigor
Level of Cognitive Complexity
© 2007 Michigan State University, Center for Research in Mathematics and Science Education
Number of Mathematics Topics Intended in Grades 1-8
● Gray bars show how many mathematics topics were intended
to be covered at each grade in the 1995 TIMSS countries.
●The bars extend from the 25th percentile to the 75th percentile.
●The black line indicates the median number of topics at each grade.
●Michigan Standards were included since they were developed to reflect international benchmarks.
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8 n M n M l n M
W l n M
M
M
W
W l n n
W l
W
M W n W
M W n l l
=
M = Michigan
W = West Virginia, July 2008 n = Top Achieving
Countries' Composite l l l
1 5 9 10 11 # # # 15 # # # # 20 # # # # 25 # # # # 30 # # # # 35
© 2007 Michigan State University, Center for Research in Mathematics and Science Education
Mathematics Topics Intended in Grades 1-8
Topic
Whole Number: Meaning
Whole Number: Operations
Measurement Units
Common Fractions
Equations & Formulas
Data Representation & Analysis
2-D Geometry: Basics
2-D Geometry: Polygons & Circles
Measurement: Perimeter, Area & Volume
Rounding & Significant Figures
Estimating Computations
Whole Numbers: Properties of Operations
Estimating Quantity & Size
Decimal Fractions
Relation of Common & Decimal Fractions
Properties of Common & Decimal Fractions
Percentages
Proportionality Concepts
Proportionality Problems
2-D Geometry: Coordinate Geometry
Geometry: Transformations
Negative Numbers, Integers, & Their Properties
Number Theory
Exponents, Roots & Radicals
Exponents & Orders of Magnitude
Measurement: Estimation & Errors
Constructions Using Straightedge & Compass
3-D Geometry
Geometry: Congruence & Similarity
Rational Numbers & Their Properties
Patterns, Relations & Functions
Proportionality: Slope & Trigonometry
by Top Achieving Countries
1 2 3
Grade
4 5 l l l l l
6 7 l l l l l l l l l l l l
8 l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
Intended by more than half of the top-achieving countries l
© 2007 Michigan State University, Center for Research in Mathematics and Science Education
Mathematics Topics Intended at Grades 1-8 by West Virginia
Mathematics Topics
Whole Number: Meaning
Whole Number: Operations
Measurement: Units
Common Fractions
Equations & Formulas
Data Representation & Analysis
2-D Geometry: Basics
2-D Geometry: Polygons & Circles
Measurement: Length, Perimeter, Area, & Volume
Rounding & Significant Figures
Estimating Computations
Whole Number: Properties of Operations
Estimating Quantity & Size
Decimal Fractions
Relationships of Common & Decimal Fractions
Properties of Common & Decimal Fractions
Percentages
Proportionality Concepts
Proportionality Problems
1-D & 2-D Geometry: Coordinate Systems
Geometry: Transformations: includ'g Patterns, Symmetry
Negative Numbers, Integers & Their Properties
Number Theory: Primes & Factorization; Even/Odd
Exponents, Roots, & Radicals
Orders of Magnitude & Scientific Notation
Measurement: Estimation & Errors
Constructions w/Straightedge & Compass
3-D Geometry
Congruence & Similarity
Rational Numbers & Their Properties
Patterns, Relations & Functions
Slope & Right Triangle Trigonometry
Grades
G1 G2 G3 G4 G5 G6 G7 G8 l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
West Virginia Standards Objective
More than Half of Top Achieving Countries
© 2007 Michigan State University, Center for Research in Mathematics and Science Education l
Mathematics Topics Intended at Each Grade by West Virginia
Grades
Mathematics Topic
Whole Number: Meaning
Whole Number: Operations
Measurement: Units
Common Fractions
Equations & Formulas
Data Representation & Analysis
G1 G2 G3 G4 G5 G6 G7 G8 l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
2-D Geometry: Basics
2-D Geometry: Polygons & Circles
Measurement: Length, Perim, Area, & Vol l l l l l l l l l l l l l l l l l l l
Rounding & Significant Figures l l l l
Estimating Computations l l l l l l l l
Whole Number: Properties of Operations l l l l l
Estimating Quantity & Size l l l
Decimal Fractions l l l l l
Relationships of Common & Decimal Fractions l l l l
Properties of Common & Decimal Fractions l
Percentages l l l l
Proportionality Concepts l l l l l
Proportionality Problems
Negative Numbers, Integers & Their Properties l l l l l
1-D & 2-D Geometry: Coordinate Systems l l l l l l l l
Geo:Transform'ns includ'g Patterns, Symmetry l l l l l l l l l l l l l l l l l l l
Number Theory: Primes & Factoriz'n; Even/Odd l l
Exponents, Roots, & Radicals
Orders of Magnitude & Scientific Notation l l l l l l l l l l l l l l l l l l
Measurement: Estimation & Errors
Constructions w/Straightedge & Compass
3-D Geometry
Congruence & Similarity
Rational Numbers & Their Properties
Patterns, Relations & Functions
Slope & Right Triangle Trigonometry
Real Numbers & Their Properties
Validation & Justification
Structuring & Abstracting
Complex Numbers
Uncertainty & Probability l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
Infinite Processes l l l
Change l
Vectors l l l l l l l l
Systematic Counting
Binary Arithmetic & / or Other Number Bases
Linear Interpolation & Extrapolation
Matrices
Trigonometry & Analytic Geometry
Other Content l l l l l l l l l
West Virginia Standards Objective
More than Half of Top Achieving Countries
© 2007 Michigan State University, Center for Research in Mathematics and Science Education l
Mathematics Topics Linked to Advanced Cognitive Demand Skills in
West Virginia Objectives
Grades
Mathematics Topic
Whole Number: Meaning
Whole Number: Operations
Measurement: Units
Common Fractions
Equations & Formulas
Data Representation & Analysis
2-D Geometry: Basics
2-D Geometry: Polygons & Circles
Measurement: Length, Perim, Area, & Vol
G1 G2 G3 G4 G5 G6 G7 G8 m m m m m m l l l l m l m l l l l m m m m l m m m m m m l l l l l l l l l l l l l m m l m l l l l l l l l m m m m l m l l m m m l l l l m l m l l l l l l l m m m l m
Rounding & Significant Figures
Estimating Computations
Whole Number: Properties of Operations
Estimating Quantity & Size
Decimal Fractions m m m l m m l l l l l m m m m m m m m l m m l m m l
Relationships of Common & Decimal Fractions
Properties of Common & Decimal Fractions
Percentages
Proportionality Concepts
Proportionality Problems
1-D & 2-D Geometry: Coordinate Systems
Geo:Transform'ns includ'g Patterns, Symmetry
Negative Numbers, Integers & Their Properties m l
Number Theory: Primes & Factoriz'n; Even/Odd m m m m m m m l l m m l l l l l m l m l l l l l m m l l l l l l m m m m m l m l m l l l m
Exponents, Roots, & Radicals
Orders of Magnitude & Scientific Notation m l l l m l l
Measurement: Estimation & Errors m l m l l l l m l l m l l m l
Constructions w/Straightedge & Compass
3-D Geometry
Congruence & Similarity
Rational Numbers & Their Properties
Patterns, Relations & Functions
Slope & Right Triangle Trigonometry
Real Numbers & Their Properties
Validation & Justification
Structuring & Abstracting
Complex Numbers
Uncertainty & Probability
Infinite Processes
Change
Vectors
Systematic Counting l m m m l l l l m m l m l m l m l l l l l l l m l l l m l l l m m l l l l l l m m l l m l l l l m m m l l l l m l l l l l l l l m l m m l l l l l l
Binary Arithmetic & / or Other Number Bases
Linear Interpolation & Extrapolation
Matrices
Trigonometry & Analytic Geometry l l l l l l l m
Other Content l
WV Standards Objective w/Low Cognitive Demand m
WV Standards Objective w/Advanced Cognitive Demand l
More than Half of Top Achieving Countries
© 2007 Michigan State University, Center for Research in Mathematics and Science Education
Ratio of Grade 1-8 Mathematics Topics Associated with Advanced
Cognitive Demand Skills to Total Topics Intended for Coverage in
West Virginia Objectives
Grades
G1 G2 G3 G4 G5 G6 G7 G8
Advanced CD Links 5 7 4 8 15 16 20 17
Topics Intended 19 20 20 23 26 24 26 21
Advanced CD Ratio 0.26
0.35
0.20
0.35
0.58
0.67
0.77
0.81
© 2007 Michigan State University, Center for Research in Mathematics and Science Education
Ratio of High School Course Mathematics Topics Associated with
Advanced Cognitive Demand Skills to Total Topics Intended for
Coverage in West Virginia Objectives
Advanced CD Links 10
Topics Intended 13
14
14
7
14
11
13
10
13
5
5
8
10
Advanced CD Ratio 0.77
1.00
0.50
0.85
0.77
1.00
0.80
© 2007 Michigan State University, Center for Research in Mathematics and Science Education
Intended Topic Coverage in West Virginia
Mathematics High School Courses (Slide 1)
Code_Description
Various types of percent problems
Direct and inverse proportion
Scales: maps and plans
Proportions based on similarities
Operations with rational numbers
Operations with real numbers and absolute value
Powers (exponents)
Integer exponents and their properties
Rational exponents and their properties
Roots and radicals and their relation to rational exponents
Real exponents and logarithm
Concepts of complex numbers
Algebra form of complex numbers and their properties
Trigonometric form of complex numbers and their properties
Tree diagrams and other forms of systematic counting
Permutations, combinations, etc.
Operations with matrices
Estimating computations
Reasonableness
Computations of length, perimeter, area, and volume
Length
Area
Surface Area & Volume
Estimation and errors l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
© 2007 Michigan State University, Center for Research in Mathematics and Science Education
Intended Topic Coverage in West Virginia
Mathematics High School Courses (Slide 2)
Code_Description
One & Two Dimension geometry: Coordinate geometry
Line and coordinate graphs
Equation of a line in the plane
Conic sections and their equations
Points, lines, segments, rays, angles, and planes
Angles
Parallelism and perpendicularity
Two dimension geometry: Polygons and circles
Triangles, quadrilaterals: classification and properties
Pythagorean Theorem and applications
Other polygons and their properties
Circles and their properties
Three dimensional geometry
3-Dimensional shapes and surfaces and their properties
Spatial perception and visualization
Vectors
Patterns, tessellations, friezes, stencils, etc.
Symmetry
Transformations
Isometries and congruence
Similarities, similar triangles, and their properties
Constructions using ruler and compasses
Validation and Justification
Conditional statements and equivalence of statements
Direct deductive proofs
Indirect proofs and proof by contradiction
Proof by induction
Sets, set notation, and set combinations l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
© 2007 Michigan State University, Center for Research in Mathematics and Science Education l l l l
Intended Topic Coverage in West Virginia
Mathematics High School Courses (Slide 3)
Code_Description
Slope and gradient in straight line graphs
Trigonometry of right-angled triangles
Linear interpolation and extrapolation
Number Patterns
Recursion
Linear functions
Quadratic functions
Logarithmic and exponential functions
Trigonometric functions
Functions and their properties
Representation of relations and functions
Families of functions: graphs and properties
Operations on functions
Related functions (inverse, derivatives, etc.)
Interpretation of function graphs
Representation of numerical situations
Solution of equations reducing to quadratics
Inequalities and their graphical representation
Systems of equations
Systems of inequalities
Substituting into or rearranging formulas
The general equation of the second degree: conics
Operations with expressions
Equivalent expressions (factorization and simplification)
Linear equations and their formal (closed) solutions
Quadratic equations and their formal (closed) solutions
Polynomial equations and their solutions
Trigonometrical equations and identities
Logarithmic and exponential equations and their solutions l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
© 2007 Michigan State University, Center for Research in Mathematics and Science Education
Intended Topic Coverage in West Virginia
Mathematics High School Courses (Slide 4)
Code_Description
Trigonometry & Analytic Geometry
Angle measures: radians & degrees
Law of sines and cosines
Unit circle and trigonometric functions
Parametric equations
Polar coordinates
Polar equations & their graphs
Arithmetic and geometric sequences
Arithmetic and geometric series
Binomial Theorem
Limits and convergence of series
Limits and convergence of functions
Growth and Decay
Data Representation and Analysis
Collecting data from experiments and simple surveys
Correlations and other measures of relations
Use and misuse of statistics
Representing data
Interpret tables, charts, plots and graphs
Measures of central tendency
Measures of dispersion
Sampling, randomness and bias
Prediction and inferences from data
Fitting lines and curves to data
Informal likelihoods and the vocabulary of likelihoods
Sampling
Hypothesis testing
Bivariate distributions
Numerical probability and probability models
Counting principles
Probability distributions for discrete random variables
Probability distributions for continuous random variables l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
© 2007 Michigan State University, Center for Research in Mathematics and Science Education
Number of Science Topics Intended in Grades 1-8
●Gray bars show how many science topics were intended
to be covered at each grade in the 1995 TIMSS countries.
●The bars represent the middle 50 percent of 1995 TIMSS countries.
●The black line indicates the median number of topics at each grade.
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8 n n n l W
W l l W n l n W
W l
W n
W
W l = U.S. Composite
W = West Virginia, July 2008 n = Top Achieving
Countries' Composite
25 n l n l l
2 3 4 5 6 7 8 10 15 20 25 30
Number of Topics
35 36 37 38 40 45 50 55
© 2007 Michigan State University, Center for Research in Mathematics and Science Education
Organs, Tissues
Topics
Physical Properties of Matter
Plants, Fungi
Animals
Classification of Matter
Rocks, Soil
Light
Electricity
Life Cycles
Physical Changes of Matter
Heat & Temperature
Bodies of Water
Interdependence of Life
Habitats & Niches
Biomes & Ecosystems
Reproduction
Time, Space, Motion
Types of Forces
Weather & Climate
Planets in the Solar System
Magnetism
Earth's Composition
Organism Energy Handling
Land, Water, Sea Resource Conservation
Earth in the Solar System
Atoms, Ions, Molecules
Chemical Properties of Matter
Chemical Changes of Matter
Physical Cycles
Land Forms
Material & Energy Resource Conservation
Explanations of Physical Changes
Pollution
Atmosphere
Sound & Vibration
Cells
Human Nutrition
Building & Breaking
Energy Types, Sources, Conversions
Dynamics of Motion
Organism Sensing & Responding
Science Topics Intended at Each Grade by Top Achieving Countries
1 2 l l l l l l l l l l l l l l l l l l l l l l l l l
8 l l l l l l l l l l l l l l l l
3 l l
4
Grade
5 l
6 l
7 l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
Intended by more than half of the top achieving countries l
© 2007 Michigan State University, Center for Research in Mathematics and Science Education
Science Topics Intended at Grades 1-8 by West Virginia
Topic
Organs, tissues
Physical properties of matter
Plants, fungi
Animal types
Classification of matter
Rocks, soil
Light
Electricity
Life cycles
Physical changes of matter
Heat & temperature
Bodies of water
Interdependence of life
Habitats & niches
Biomes & ecosystems
Reproduction
Time, space, motion
Types of forces
Weather & climate
Planets in the solar system
Magnetism
Earth's Composition
Organism energy handling
Land, water, sea resource conservation
Earth in the solar system
Atoms, ions, molecules
Chemical properties of matter
Chemical changes of matter
Physical cycles
Land forms
Material & energy resource conservation
Explanations of physical changes
Pollution
Atmosphere
Sound & vibration
Cells
Human nutrition
Building & breaking
Energy types, sources, conversions
Dynamics of motion
Organism sensing & responding
Grades
1 2 3 4 5 6 7 8 l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
West Virginia Standards Objective l
More than Half of Top Achieving Countries
© 2007 Michigan State University, Center for Research in Mathematics and Science Education
Science Topics Linked to Advanced Cognitive Demand Skills in West Virginia Objectives
Topic
Organs, tissues
Physical properties of matter
Plants, fungi
Animal types
Classification of matter
Rocks, soil
Light
Electricity
Life cycles
Physical changes of matter
Heat & temperature
Bodies of water
Interdependence of life
Habitats & niches
Biomes & ecosystems
Reproduction
Time, space, motion
Types of forces
Weather & climate
Planets in the solar system
Magnetism
Earth's Composition
Organism energy handling
Land, water, sea resource conservation
Earth in the solar system
Atoms, ions, molecules
Chemical properties of matter
Chemical changes of matter
Physical cycles
Land forms
Material & energy resource conservation
Explanations of physical changes
Pollution
Atmosphere
Sound & vibration
Cells
Human nutrition
Building & breaking
Energy types, sources, conversions
Dynamics of motion
Organism sensing & responding
Grades
1 2 3 4 5 6 7 8 m m m m m m l l m m m m m m m m m m m m m l m l l l m m m m m m m m m l l m m l l l m m m m m m m m l m m l l m m l m l m m l l m m m l m l m m m m l m m m m m m m m m m m m l l m m m l m m m m m m m m m m m m m m m l m m m m m l l m m m l m m m m m m l m l m m m m m m m m l m m l l l m m m m l m m m m m l m m m m m m m m m m m m m m m m l l m
WV Standards Objective w/ Low Cognitive Demand
WV Standards Objective w/ Advanced Cognitive Demand
More than Half of Top Achieving Countries m l
© 2007 Michigan State University, Center for Research in Mathematics and Science Education
Intended Topic Coverage in West Virginia
Science High School Courses (Slide 1)
Topics
Earth Features
Earth's composition
Landforms
Bodies of water
Atmosphere
Rocks, soil
Earth Processes
Weather & climate
Physical cycles
Building & breaking
Earth's history
Earth and the Universe
Earth, sun, moon in the solar system
Planets in the solar system
Beyond the solar system
Evolution of the universe
Motion and location of celestial bodies
Environmental and Resource Issues
Pollution - Causes and Treatment
Land, Water, Sea Resource Conservation
Material & Energy Resource Conservation
Effects of Natural Disasters l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
© 2007 Michigan State University, Center for Research in Mathematics and Science Education l l l l
Intended Topic Coverage in West Virginia
Science High School Courses (Slide 2)
Topics
Diversity, Organization, Structure of Living Things
Plants, fungi (types)
Green plants, nonvascular and vascular
Animals (types)
Other organisms (types of microorganisms)
Systems, organs, tissues
The complementarity of structure and function
Systems (circulatory, respiratory, movement)
Organs (plant leaves, roots, eyes, ears), tissues
Cells
Cell structure and basic function
Types of cells, diversity of cells
Chemistry of cells (enzymes); reproduction;communication
Life Processes & Systems Enabling Life Functions
Energy handling, biochemistry of systems
Energy handling
Biochemistry of systems (e.g., digestive, excretive, nervous)
Biofeedback in systems, homeostasis, sensory systems
Biochemical processes in cells
Human Biology & Health
Prevention of disease, maintaining good health
Types and causes of disease, remedies l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
© 2007 Michigan State University, Center for Research in Mathematics and Science Education l l l l l l l l l l l l l
Intended Topic Coverage in West Virginia
Science High School Courses (Slide 3)
Topics
Life Spirals, Genetic Continuity, Diversity
Life cycles of plants, insects, etc.; reproduction, dispersal
Cell division, cell differentiation
Reproduction (plant/animal reproduction, asexual/sexual)
Variation and inheritance
Meiosis, Mendelian/non-Mendelian genetics
Population genetics, biotechnology and application
Evolution, speciation, diversity
Variation as a natural phenomenon, importance of diversity
Evidence for evolution, effects of evolution, processes
Nature of species, domestication
DNA, the hereditary substance; structure; replication; RNA
Gene expression, mutation, the Operon model in bacteria
Genetic engineering
Interactions of Living Things
Biomes & ecosystems
Habitats & niches
Interdependence of life
Food webs/chains, adaptations to various habitat conditions
Competition among organisms, mutual interactions
Animal behavior
Territorialism; social groupings, mating behavior and selection
Needs of living things (for growth and development) l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
© 2007 Michigan State University, Center for Research in Mathematics and Science Education l l l l l l l l l
Intended Topic Coverage in West Virginia
Science High School Courses (Slide 4)
Topics
Matter
Homogeneous/heterogeneous, elements, compounds
Solutions, suspensions, colloids
Physical properties
Weight, mass, volume, density, hardness, shape, color
States of matter -- gases, liquids, solids
Chemical properties
Periodic table
Acids, bases, salts; pH scale
Organic/inorganic
Structure of Matter
Atoms, ions, molecules (as the basis for different substances)
Periodicity, metals and nonmetals
Ionic and covalent compounds
Formulas, equations, nomenclature; stoichiometry; mole concept
Electrons, protons, neutrons
Isotopes
Properties of quantum objects; quantum nos. and orbital energies
Electron configuration and periodicity
Physical Transformations
Changes in states of matter, gas laws, phase changes & diagrams
Mixing, solutions, colligative properties
Explanations of physical changes (general explanations)
Inter-particle forces, dispersion and flocculation of colloids
Kinetic-molecular theory (gases, liquids, solids)
Chemical Tranformations
Definition of chemical change, evidence of chemical change
Types of reactions; coordination chemistry
Ionization energy, electron affinity, electronegativity
Ionic and covalent bonding
Molecular shape; periodic trends of reactivity, electron configur'ns
Rate of change and equilibria
Reaction rates and reaction mechanisms (rate laws, catalysis)
Energy and chemical change (activation energy)
Calorimetry, exothermic and endothermic reactions
First law of thermodynamics, enthalpy
Organic & biochemical changes; biochemistry
Nuclear chemistry
Electrochemistry l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
© 2007 Michigan State University, Center for Research in Mathematics and Science Education l l
Intended Topic Coverage in West Virginia
Science High School Courses (Slide 5)
Topics
Energy and Physical Processes
Work energy and power, efficiency; simple machines
Energy types, conversions, sources
Heat and temperature (scales, heat as energy, heat versus temp)
Heat & energy, changes of state; thermal expansion; kin'c-molec'r theory
Thermal equilibrium; thermodynamics
Wave phenomena, types, interactions, movement
Sound & vibration; including standing waves; Doppler effect
Light
Reflection, refraction, diffraction (electromagnetic spectrum)
Optics
Nature of light, quantum theory of light, intensity, luminosity
Electricity l l l l l l l l l l l l l l l l l l l l l l
AC/DC circuits, capacitors, resistors, electronics, semi-conductors
Magnetism
Magnetic materials, fields, forces, properties
Induction, charges in electric and magnetic flds, electromagnetism
Physical changes
Types of forces
Gravitational, electromagnetic, frictional, centripetal, nuclear forces
Static equilibrium
Pressure
Time, space and motion
Measurement of time, space and mass
Types of motion; describing motion
Dynamics of motion
Laws of motion, momentum and collisions
Balanced and unbalanced forces, buoyancy, action/reaction
Relativity theory
Speed of light; relativistic effects at speeds near the speed of light
Air / fluid behavior (density, pressure, Archimedes, Bernoulli) l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
© 2007 Michigan State University, Center for Research in Mathematics and Science Education l l l l l l l l l l l l l l l l l l l l l
Intended Topic Coverage in West Virginia
Science High School Courses (Slide 6)
Topics
Nature or Conceptions of Technology
Interactions of Science, Mathematics, & Technology
Mathematics, technology influence on science
Science applications in mathematics, technology
Interactions of Science, Technology and Society
Influence of science, technology on society
Influence of society on science, technology
History of Science & Technology
Nature of Scientific Knowledge
The Scientific Enterprise
Science & Mathematics l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
© 2007 Michigan State University, Center for Research in Mathematics and Science Education
