Analyses of West Virginia Mathematics and Science Curricular Objectives in effect July 2008 William...

Analyses of West Virginia Mathematics and Science

Curricular Objectives in effect

July 2008

William H. SchmidtUniversity Distinguished Professor

Michigan State University

© 2007 Michigan State University, Center for Research in Mathematics and Science Education

Curricular Content Principles

Curricular CoherenceCurricular Structure

Curricular FocusExposure Time (OTL)

Curricular RigorLevel of Cognitive Complexity


Number of Mathematics Topics Intended in Grades 1-8

l =U.S. Composite

M = Michigan

W = West Virginia, J uly 2008

n = Top Achieving

Countries' Composite

Grade 1 n l

Grade 2 n l

Grade 3 n l

Grade 4 n l

Grade 5 n l

Grade 6 n l

Grade 7 n l

Grade 8 n l

1 9 11 # # # # # # # # # # # # # # # # # # #

W

WM

M

M

M

M

W

25 30 35

W

W

W

W

M

M

W

5

● Gray bars show how many mathematics topics were intended

to be covered at each grade in the 1995 TI MSS countries.

●The bars extend f rom 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.

10 15

M

20


Mathematics Topics Intended in Grades 1-8 by Top Achieving Countries

Grade

Topic 1 2 3 4 5 6 7 8

Whole Number: Meaning l l l l lWhole Number: Operations l l l l lMeasurement Units l l l l l l lCommon Fractions l l l lEquations & Formulas l l l l l lData Representation & Analysis l l l l l2-D Geometry: Basics l l l l l l2-D Geometry: Polygons & Circles l l l l lMeasurement: Perimeter, Area & Volume l l l l lRounding & Significant Figures l lEstimating Computations l l lWhole Numbers: Properties of Operations l lEstimating Quantity & Size l lDecimal Fractions l l lRelation of Common & Decimal Fractions l l lProperties of Common & Decimal Fractions l lPercentages l lProportionality Concepts l l l lProportionality Problems l l l l2-D Geometry: Coordinate Geometry l l l lGeometry: Transformations l l lNegative Numbers, I ntegers, & Their Properties l lNumber Theory l lExponents, Roots & Radicals l lExponents & Orders of Magnitude l lMeasurement: Estimation & Errors lConstructions Using Straightedge & Compass l l3-D Geometry l lGeometry: Congruence & Similarity lRational Numbers & Their Properties lPatterns, Relations & Functions lProportionality: Slope & Trigonometry l I ntended by more than half of the top- achieving countries l


Mathematics Topics Intended at Grades 1-8 by West Virginia

Mathematics Topics G1 G2 G3 G4 G5 G6 G7 G8

Whole Number: Meaning l l l l l

Whole Number: Operations l l l l l

Measurement: Units l l l l l l l

Common Fractions l l l l l l l

Equations & Formulas l l l l l l l l

Data Representation & Analysis l l l l l l l l

2-D Geometry: Basics l l l l l l l

2-D Geometry: Polygons & Circles l l l l l l l l

Measurement: Length, Perimeter, Area, & Volume l l l l l l l

Rounding & Significant Figures l l l l

Estimating Computations 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

Proportionality Problems l l l l

1-D & 2-D Geometry: Coordinate Systems l l l l l l l l

Geometry: Transformations: includ'g Patterns, Symmetry l l l l l l l l

Negative Numbers, Integers & Their Properties l l l

Number Theory: Primes & Factorization; Even/Odd l l l l

Exponents, Roots, & Radicals l l l

Orders of Magnitude & Scientific Notation l l l

Measurement: Estimation & Errors l l l l l

Constructions w/Straightedge & Compass

3-D Geometry l l l l l l l l

Congruence & Similarity l l l l l

Rational Numbers & Their Properties l l

Patterns, Relations & Functions l l l l l l l l

Slope & Right Triangle Trigonometry l l

Grades

West Virginia Standards Objective lMore than Half of Top Achieving Countries


Mathematics Topics Intended at Each Grade by West Virginia


Mathematics Topic G1 G2 G3 G4 G5 G6 G7 G8Whole Number: Meaning l l l l lWhole Number: Operations l l l l lMeasurement: Units l l l l l l lCommon Fractions l l l l l l l

Equations & Formulas l l l l l l l l l l l l l l l

Data Representation & Analysis l l l l l l l l l l l l l l

2-D Geometry: Basics l l l l l l l l l

2-D Geometry: Polygons & Circles l l l l l l l l l l l

Measurement: Length, Perim, Area, & Vol 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 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 l

Proportionality Concepts l l l l l

Proportionality Problems l l l l l l

1-D & 2-D Geometry: Coordinate Systems l l l l l 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

Negative Numbers, Integers & Their Properties l l l

Number Theory: Primes & Factoriz'n; Even/Odd l l l l

Exponents, Roots, & Radicals l l l l l l l

Orders of Magnitude & Scientific Notation l l l

Measurement: Estimation & Errors l l l l l l

Constructions w/Straightedge & Compass l

3-D Geometry l l l l l l l l l l

Congruence & Similarity l l l l l l

Rational Numbers & Their Properties l l l

Patterns, Relations & Functions l l l l l l l l l l l l l

Slope & Right Triangle Trigonometry l l l l l l

Real Numbers & Their Properties l l l l

Validation & Justification l l l

Structuring & Abstracting l l

Complex Numbers l l

Uncertainty & Probability l l l l l l l l l l l l

Infinite Processes l l l

Change l

Vectors l l

Systematic Counting l l l l l lBinary Arithmetic & / or Other Number BasesLinear Interpolation & Extrapolation lMatrices lTrigonometry & Analytic Geometry l lOther Content l l l l l

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Mathematics Topics Linked to Advanced Cognitive Demand Skills in West Virginia Objectives

WV Standards Objective w/Low Cognitive Demand m

WV Standards Objective w/Advanced Cognitive Demand lMore than Half of Top Achieving Countries

Mathematics Topic G1 G2 G3 G4 G5 G6 G7 G8Whole Number: Meaning m m m m mWhole Number: Operations m l l l lMeasurement: Units m l m l l l lCommon Fractions m m m m l m mEquations & Formulas m m m m l l l l l l l l l l lData Representation & Analysis l l m m l m l l l l l l l l2-D Geometry: Basics m m m m l m l l m2-D Geometry: Polygons & Circles l m m m l l l l l m mMeasurement: Length, Perim, Area, & Vol m l m l l l l l m lRounding & Significant Figures m m m lEstimating Computations m m l l l l l m lWhole Number: Properties of Operations m m m m lEstimating Quantity & Size m m mDecimal Fractions m m l m mRelationships of Common & Decimal Fractions m m m mProperties of Common & Decimal Fractions mPercentages m l l l lProportionality Concepts l m m l lProportionality Problems l l l l l m1-D & 2-D Geometry: Coordinate Systems m m m m l m l m l l l l lGeo:Transform'ns includ'g Patterns, Symmetry m l l l m l l l l m m mNegative Numbers, Integers & Their Properties l m lNumber Theory: Primes & Factoriz'n; Even/Odd m m m lExponents, Roots, & Radicals m l l l m l lOrders of Magnitude & Scientific Notation m l lMeasurement: Estimation & Errors m l m l l lConstructions w/Straightedge & Compass l3-D Geometry l m m m l l l l l mCongruence & Similarity m m l m l lRational Numbers & Their Properties l m mPatterns, Relations & Functions l l l m l l l l l l l l lSlope & Right Triangle Trigonometry m m l l m lReal Numbers & Their Properties l m l lValidation & Justification l l lStructuring & Abstracting m lComplex Numbers l lUncertainty & Probability l l m m l l l l l l l lInfinite Processes m l m l m lChange l lVectors l m lSystematic Counting mBinary Arithmetic & / or Other Number BasesLinear Interpolation & Extrapolation lMatrices l mTrigonometry & Analytic Geometry l l l l lOther Content l

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Ratio of Grade 1-8 Mathematics Topics Associated with Advanced Cognitive Demand Skills to Total Topics Intended for Coverage in

West Virginia Objectives

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

Grades


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 14 7 11 10 5 8

Topics Intended 13 14 14 13 13 5 10

Advanced CD Ratio 0.77 1.00 0.50 0.85 0.77 1.00 0.80

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Intended Topic Coverage in West Virginia Mathematics High School Courses (Slide 1)

Code_DescriptionVarious types of percent problems lDirect and inverse proportion lScales: maps and plans lProportions based on similarities l lOperations with rational numbers lOperations with real numbers and absolute value l lPowers (exponents) l lInteger exponents and their properties l lRational exponents and their properties lRoots and radicals and their relation to rational exponents l lReal exponents and logarithm l l lConcepts of complex numbers lAlgebra form of complex numbers and their properties lTrigonometric form of complex numbers and their properties lTree diagrams and other forms of systematic counting l lPermutations, combinations, etc. l lOperations with matrices lEstimating computations lReasonableness lComputations of length, perimeter, area, and volume lLength l lArea l l lSurface Area & Volume lEstimation and errors l

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Code_DescriptionOne & Two Dimension geometry: Coordinate geometry lLine and coordinate graphs l l l lEquation of a line in the plane l lConic sections and their equations l l lPoints, lines, segments, rays, angles, and planes lAngles lParallelism and perpendicularity l lTwo dimension geometry: Polygons and circles lTriangles, quadrilaterals: classification and properties lPythagorean Theorem and applications l l lOther polygons and their properties lCircles and their properties lThree dimensional geometry l3-Dimensional shapes and surfaces and their properties lSpatial perception and visualization lVectors l lPatterns, tessellations, friezes, stencils, etc. l lSymmetry lTransformations l l lIsometries and congruence lSimilarities, similar triangles, and their properties lConstructions using ruler and compasses lValidation and Justification lConditional statements and equivalence of statements lDirect deductive proofs lIndirect proofs and proof by contradiction lProof by induction l lSets, set notation, and set combinations l

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Code_DescriptionSlope and gradient in straight line graphs l lTrigonometry of right-angled triangles l l lLinear interpolation and extrapolation lNumber Patterns l l lRecursion lLinear functions l lQuadratic functions l lLogarithmic and exponential functions l l lTrigonometric functions lFunctions and their properties l l lRepresentation of relations and functions l lFamilies of functions: graphs and properties lOperations on functions lRelated functions (inverse, derivatives, etc.) l l lInterpretation of function graphs lRepresentation of numerical situations l l l l lSolution of equations reducing to quadratics l l lInequalities and their graphical representation l lSystems of equations l lSystems of inequalities lSubstituting into or rearranging formulas l l l lThe general equation of the second degree: conics l lOperations with expressions l lEquivalent expressions (factorization and simplification) l lLinear equations and their formal (closed) solutions l lQuadratic equations and their formal (closed) solutions l lPolynomial equations and their solutions l l lTrigonometrical equations and identities lLogarithmic and exponential equations and their solutions l

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Code_DescriptionTrigonometry & Analytic Geometry lAngle measures: radians & degrees lLaw of sines and cosines lUnit circle and trigonometric functions lParametric equations lPolar coordinates lPolar equations & their graphs lArithmetic and geometric sequences l lArithmetic and geometric series lBinomial Theorem lLimits and convergence of series lLimits and convergence of functions lGrowth and Decay lData Representation and Analysis lCollecting data from experiments and simple surveys l l lCorrelations and other measures of relations lUse and misuse of statisticsRepresenting data l l l lInterpret tables, charts, plots and graphs l l l lMeasures of central tendency l l lMeasures of dispersion l l lSampling, randomness and bias lPrediction and inferences from data l l l lFitting lines and curves to data l l l lInformal likelihoods and the vocabulary of likelihoods lSampling l lHypothesis testing l lBivariate distributions lNumerical probability and probability models l l lCounting principles l lProbability distributions for discrete random variables lProbability distributions for continuous random variables l l l

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Number of Science Topics Intended in Grades 1-8

l = U.S. Composite 25

W= West Virginia, J uly 2008

●The bars represent the middle 50 percent of 1995 TI MSS countries. n = Top Achieving

Countries' Composite

Grade 1 n l W

Grade 2 n W l

Grade 3 n l W

Grade 4 n l W

Grade 5 n W l

Grade 6 W n l

Grade 7 W n l

Grade 8 W n l

2 3 4 6 7 8 36 37 385 40 45 5035 55

Number of Topics

●Gray bars show how many science topics were intended

to be covered at each grade in the 1995 TI MSS countries.

●The black line indicates the median number of topics at each grade.

10 15 20 25 30


Science Topics Intended at Each Grade by Top Achieving Countries

Grade

Topics 1 2 3 4 5 6 7 8

Organs, Tissues l l l l l lPhysical Properties of Matter l l l l l lPlants, Fungi l l l l l lAnimals l l l l l lClassification of Matter l l l l l lRocks, Soil l l l l l lLight l l lElectricity l l l lLife Cycles l l l l lPhysical Changes of Matter l l l l lHeat & Temperature l l l l lBodies of Water l l l l lI nterdependence of Lif e l l l lHabitats & Niches l l l lBiomes & Ecosystems l l l lReproduction l lTime, Space, Motion l l l lTypes of Forces l l l lWeather & Climate l l l lPlanets in the Solar System l l l lMagnetism l l lEarth's Composition l l lOrganism Energy Handling l l lLand, Water, Sea Resource Conservation l l lEarth in the Solar System l l lAtoms, I ons, Molecules l lChemical Properties of Matter l lChemical Changes of Matter l lPhysical Cycles l lLand Forms l lMaterial & Energy Resource Conservation l lExplanations of Physical Changes l lPollution l lAtmosphere l lSound & Vibration l lCells l lHuman Nutrition l lBuilding & Breaking lEnergy Types, Sources, Conversions lDynamics of Motion lOrganism Sensing & Responding l

I ntended by more than half of the top achieving countries l


Science Topics Intended at Grades 1-8 by West Virginia

Topic 1 2 3 4 5 6 7 8

Organs, tissues l l l l l l l lPhysical properties of matter l l l l l lPlants, f ungi l l l l l lAnimal types l l l lClassification of matter l l l l lRocks, soil l l l l l lLight l l l lElectricity l l l lLif e cycles l l l l l l l lPhysical changes of matter l l l l l lHeat & temperature l l l lBodies of water l l l l lI nterdependence of lif e l l l l l l lHabitats & niches l lBiomes & ecosystems

Reproduction l l lTime, space, motion l l l l l lTypes of f orces l l lWeather & climate l l l l l l lPlanets in the solar system l l l lMagnetism l l l lEarth's Composition l lOrganism energy handling l lLand, water, sea resource conservation l l lEarth in the solar system l l l l l l lAtoms, ions, molecules l l l lChemical properties of matter l l l l l lChemical changes of matter l l l lPhysical cycles l l l lLand f orms l l l lMaterial & energy resource conservation l l lExplanations of physical changes lPollution lAtmosphere l lSound & vibration l l l l l l lCells l l l lHuman nutrition

Building & breaking l l l l l lEnergy types, sources, conversions l l l lDynamics of motion l l l l l lOrganism sensing & responding l

Grades



Science Topics Linked to Advanced Cognitive Demand Skills in West Virginia Objectives

Topic 1 2 3 4 5 6 7 8

Organs, tissues m m m m m m l lPhysical properties of matter m m m m m mPlants, f ungi m m m l m lAnimal types m m l mClassification of matter m m l m mRocks, soil m m m m l lLight m m m mElectricity l l l mLif e cycles m m m m m m m lPhysical changes of matter m m l m m lHeat & temperature m m m lBodies of water l l m m mI nterdependence of lif e m m l m m m lHabitats & niches l lBiomes & ecosystems

Reproduction m m mTime, space, motion m m m l m lTypes of f orces m m mWeather & climate m m m m m m mPlanets in the solar system m m m mMagnetism m m m lEarth's Composition m mOrganism energy handling m mLand, water, sea resource conservation m m lEarth in the solar system m m m m l m mAtoms, ions, molecules m l m lChemical properties of matter m m m m m mChemical changes of matter m m m mPhysical cycles m m m mLand f orms l l l lMaterial & energy resource conservation m m mExplanations of physical changes lPollution lAtmosphere m mSound & vibration m m l m m m mCells m l m mHuman nutrition

Building & breaking m m m m m mEnergy types, sources, conversions m m m lDynamics of motion m m m m m lOrganism sensing & responding m

Grades

WV Standards Objective w/ Low Cognitive Demand mWV Standards Objective w/ Advanced Cognitive Demand l

More than Half of Top Achieving Countries


Intended Topic Coverage in West Virginia Science High School Courses (Slide 1)

Topics Gra

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Earth FeaturesEarth's composition l l l lLandforms l lBodies of water lAtmosphere lRocks, soil l lEarth Processes l lWeather & climate l l l lPhysical cycles l l lBuilding & breaking l l l lEarth's history l l l lEarth and the Universe l l lEarth, sun, moon in the solar system l l l lPlanets in the solar system lBeyond the solar system Evolution of the universe l l l lMotion and location of celestial bodies l l

Environmental and Resource Issues

Pollution - Causes and Treatment l l

Land, Water, Sea Resource Conservation l

Material & Energy Resource Conservation l l l

Effects of Natural Disasters l

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Topics Gra

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Diversity, Organization, Structure of Living Things l lPlants, fungi (types) lGreen plants, nonvascular and vascular lAnimals (types)Other organisms (types of microorganisms) lSystems, organs, tissues lThe complementarity of structure and function l l lSystems (circulatory, respiratory, movement) l l lOrgans (plant leaves, roots, eyes, ears), tissues l l lCellsCell structure and basic function l l l lTypes of cells, diversity of cells l l lChemistry of cells (enzymes); reproduction;communication l l l lLife Processes & Systems Enabling Life FunctionsEnergy handling, biochemistry of systems lEnergy handling l l l lBiochemistry of systems (e.g., digestive, excretive, nervous) lBiofeedback in systems, homeostasis, sensory systems l lBiochemical processes in cells l l lHuman Biology & Health l l lPrevention of disease, maintaining good health lTypes and causes of disease, remedies l

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Topics Gra

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Life Spirals, Genetic Continuity, DiversityLife cycles of plants, insects, etc.; reproduction, dispersal l l lCell division, cell differentiation l lReproduction (plant/animal reproduction, asexual/sexual) l l lVariation and inheritanceMeiosis, Mendelian/non-Mendelian genetics l l l lPopulation genetics, biotechnology and application l lEvolution, speciation, diversity lVariation as a natural phenomenon, importance of diversity lEvidence for evolution, effects of evolution, processes l l lNature of species, domestication lDNA, the hereditary substance; structure; replication; RNA l l l lGene expression, mutation, the Operon model in bacteria l l l lGenetic engineering l l lInteractions of Living ThingsBiomes & ecosystems l l lHabitats & niches lInterdependence of life l l lFood webs/chains, adaptations to various habitat conditions l lCompetition among organisms, mutual interactions l l lAnimal behavior lTerritorialism; social groupings, mating behavior and selection lNeeds of living things (for growth and development) l

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Topics Gra

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MatterHomogeneous/heterogeneous, elements, compounds l lSolutions, suspensions, colloids l lPhysical properties l l lWeight, mass, volume, density, hardness, shape, color l l l l l l lStates of matter -- gases, liquids, solids lChemical properties l l l l l lPeriodic table l l l lAcids, bases, salts; pH scale l lOrganic/inorganic l lStructure of MatterAtoms, ions, molecules (as the basis for different substances) l l lElementary atomic theory (incl'g atomic mass / atomic number), oxidation statel l lPeriodicity, metals and nonmetals l lIonic and covalent compounds l lFormulas, equations, nomenclature; stoichiometry; mole concept l l l lMacromolecules, crystals, amorphous (polymers, shape/function of biological molecules, crystal structure, bonding in crystalline solids, glass)l l lElectrons, protons, neutrons l lIsotopes lProperties of quantum objects; quantum nos. and orbital energies lElectron configuration and periodicity l lPhysical TransformationsChanges in states of matter, gas laws, phase changes & diagrams l l l l lMixing, solutions, colligative properties l lExplanations of physical changes (general explanations) lInter-particle forces, dispersion and flocculation of colloids lKinetic-molecular theory (gases, liquids, solids) l l lChemical Tranformations l lDefinition of chemical change, evidence of chemical change l lTypes of reactions; coordination chemistry l l l lIonization energy, electron affinity, electronegativity l lIonic and covalent bonding l l l lMolecular shape; periodic trends of reactivity, electron configur'ns l lRate of change and equilibria Reaction rates and reaction mechanisms (rate laws, catalysis) lEnergy and chemical change (activation energy) lCalorimetry, exothermic and endothermic reactions l lFirst law of thermodynamics, enthalpy lOrganic & biochemical changes; biochemistry lNuclear chemistry l l l l lElectrochemistry l

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Topics Gra

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Energy and Physical ProcessesWork energy and power, efficiency; simple machines l l lEnergy types, conversions, sources l l l l lHeat and temperature (scales, heat as energy, heat versus temp) l l l l l l lHeat & energy, changes of state; thermal expansion; kin'c-molec'r theory l l l lThermal equilibrium; thermodynamics l lWave phenomena, types, interactions, movement l l l l l lSound & vibration; including standing waves; Doppler effect l l l l lLight l lReflection, refraction, diffraction (electromagnetic spectrum) l lOptics l lNature of light, quantum theory of light, intensity, luminosity l l lElectricity l lElectric charge, Coulomb's law, conductors, insulators, static electricity, electrical fields, alternating/direct currentl l l lAC/DC circuits, capacitors, resistors, electronics, semi-conductors l l l lMagnetism l lMagnetic materials, fields, forces, properties l l lInduction, charges in electric and magnetic flds, electromagnetism lPhysical changes l lTypes of forces lGravitational, electromagnetic, frictional, centripetal, nuclear forces l l l lStatic equilibrium lPressure l l l lTime, space and motionMeasurement of time, space and mass l l lTypes of motion; describing motion l l l l l lDynamics of motionLaws of motion, momentum and collisions l l l lBalanced and unbalanced forces, buoyancy, action/reaction l lRelativity theory l lSpeed of light; relativistic effects at speeds near the speed of light lAir / fluid behavior (density, pressure, Archimedes, Bernoulli) l l l

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Topics Gra

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Nature or Conceptions of Technology l l l l l l l l l l lInteractions of Science, Mathematics, & TechnologyMathematics, technology influence on science l l l l l l l l l l lScience applications in mathematics, technology l l l l l l l l l l lInteractions of Science, Technology and Society l l l l l l l l l l lInfluence of science, technology on society l lInfluence of society on science, technology lHistory of Science & Technology l lNature of Scientific Knowledge l l l l l l l l l l lThe Scientific Enterprise l l l l l l l l l l lScience & Mathematics l l l l l l l l

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Analyses of West Virginia Mathematics and Science Curricular Objectives in effect July 2008 William...

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