Content Standards in an International Context William H. Schmidt Michigan State University
17
© 2006 Michigan State University, Center for Research in Mathematics and Science Education Content Standards in an International Context William H. Schmidt Michigan State University
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Content Standards in an International Context William H. Schmidt Michigan State University. The Economy Has Changed…Have Our Schools?. Non-routine. Analytic. Skills Demanded by the U.S. Economy. 65. Non-routine Interactive. 60. 55. - PowerPoint PPT Presentation
Transcript of Content Standards in an International Context William H. Schmidt Michigan State University
© 2006 Michigan State University, Center for Research in Mathematics and Science Education
Content Standards in an International Context
William H. SchmidtMichigan State University
© 2006 Michigan State University, Center for Research in Mathematics and Science Education
The Economy Has Changed…Have Our Schools?
40
45
50
55
60
65
1960 1970 1980 1990 2002
Mean t
ask
inp
ut
as
perc
en
tile
s of
the 1
96
0 t
ask
dis
trib
uti
on
Non-routine InteractiveNon-routineAnalytic
Routine Cognitive
Routine Manual
Non-routineManual
Sources: Levy and Murnane; Schleicher, 2007
Skills Demanded by the U.S. Economy
© 2006 Michigan State University, Center for Research in Mathematics and Science Education
What Americans Value
Rowing1 Korea 550
2 Finland 548
3 Japan 547
4 New Zealand 533
5 Australia 530
6 Canada 529
7 Belgium 525
8 Switzerland 521
9 Netherlands 520
10 France 519
11 Denmark 517
12 Czech Republic 516
13 Germany 514
14 Sweden 509
15 Austria 506
16 Iceland 505
17 Hungary 501
18 Ireland 499
19 Luxembourg 494
20 Slovak Republic 492
21 Norway 490
22 Poland 487
23 Spain 482
24 United States 477
25 Portugal 470
26 Italy 470
27 Greece 449
Basketball1 Finland 546
2 Canada 534
3 New Zealand 529
4 Australia 528
5 Ireland 527
6 Korea 525
7United
Kingdom 523
8 Japan 522
9 Sweden 516
10 Austria 507
11 Belgium 507
12 Iceland 507
13 Norway 505
14 France 505
15 United States 504
16 Denmark 497
17 Switzerland 494
18 Spain 493
19 Czech Republic 492
20 Italy 487
21 Germany 484
22 Hungary 480
23 Poland 479
24 Portugal 479
25 Greece 474
26 Luxembourg 441
27 Mexico 422
Swimming 1 Finland 563
2 Canada 534
3 Japan 531
4 New Zealand 530
5 Australia 527
6 Netherlands 525
7 Korea 522
8 Germany 516
9 United Kingdom 515
10 Czech Republic 513
11 Switzerland 512
12 Austria 511
13 Belgium 510
14 Ireland 508
15 Hungary 504
16 Sweden 503
17 Poland 498
18 Denmark 496
19 France 495
20 Iceland 491
21 United States 489
22 Slovak Republic 488
23 Spain 488
24 Norway 487
25 Luxembourg 486
26 Italy 475
27 Portugal 474
Triathlon1 Finland 548
2 Korea 547
3 Netherlands 531
4 Switzerland 530
5 Canada 527
6 Japan 523
7 New Zealand 522
8 Belgium 520
9 Australia 520
10 Denmark 513
11 Czech Republic 510
12 Iceland 506
13 Austria 505
14 Germany 504
15 Sweden 502
16 Ireland 501
17 France 496
18 United Kingdom 495
19 Poland 495
20 Slovak Republic 492
21 Hungary 491
22 Luxembourg 490
23 Norway 490
24 Spain 480
25 United States 474
26 Portugal 466
27 Italy 462
Sources: PISA 2004, 2007
U.S. Rankings on Olympics
U.S. Ranks 15th
U.S. Ranks 21st
U.S. Ranks 24thU.S. Ranks 25th
Reading Science Problem Solving
Math
U.S. Rankings on PISA
© 2006 Michigan State University, Center for Research in Mathematics and Science Education
Elementary Students’ Performance on a Fractions Problem
4. Which fraction is located between 8
3 and
8
7 on the number line?
A. 4
1
B. 2
1
C. 8
8
D. 8
10
Grade 3 Grade 4 Grade 5
Mi PROM/SE 19.1 39.8 50.8
© 2006 Michigan State University, Center for Research in Mathematics and Science Education
Elementary & Middle School Students’ Performance on a Fractions Problem
20. What is the value of 15
1
3
1
5
4 ?
A. 5
1
B. 5
2
C. 15
7
D. 4
3
E. 5
4
Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8
Mi PROM/SE 14.1 21.2 16.7 28.4 37.7 51.2
© 2006 Michigan State University, Center for Research in Mathematics and Science Education
High School Students’ Performance on a Mathematics Literacy Problem
29. Stu wants to wrap some ribbon around a box as shown below and have 25 centimeters left to tie a bow.
12 cm
8 cm
3 cm
How long a piece of ribbon does he need?
A. 46 cm
B. 77 cm
C. 65 cm
D. 71 cm
Grade 9 Grade 10 Grade 11 Grade 12
Mi PROM/ SE 38.0 41.0 43.3 50.2
© 2006 Michigan State University, Center for Research in Mathematics and Science Education
Average performanceof 15-year-olds in science – extrapolate and apply
High science performance
Low science performance
… 18 countries perform below this line
I srael
I talyPortugal Greece
Russian Federation
LuxembourgSlovak Republic,Spain,I celand
LatviaCroatia
Sweden
DenmarkFrancePoland
Hungary
AustriaBelgiumIreland
Czech Republic SwitzerlandMacao- China
GermanyUnited Kingdom
Korea
J apanAustralia
Slovenia
NetherlandsLiechtenstein
New ZealandChinese Taipei
Hong Kong- China
Finland
CanadaEstonia
United States LithuaniaNorway
445
465
485
505
525
545
565
616
Instructional Content Constructs
Curricular CoherenceCurricular Structure
Curricular FocusExposure Time (OTL)
Curricular RigorLevel of Cognitive Complexity
© 2006 Michigan State University, Center for Research in Mathematics and Science Education
Top Achieving Countries’ Mathematics Curriculum
s I ntended by 4 out of the 6
top- achieving countries
l I ntended by all but one of the
top- achieving countries (5 out of 6).
n I ntended by all of the top- achieving countries.
Grade
Topic 1 2 3 4 5 6 7 8 9 10 11 12
Whole Number: Meaning n n n l lWhole Number: Operations n n n n lMeasurement Units s n n n n n lCommon Fractions s n n lEquations & Formulas s l l l n n n n n nData Representation & Analysis s s l l s s s s s2-D Geometry: Basics s l l l n n l2-D Geometry: Polygons & Circles s l l n n n lMeasurement: Perimeter, Area & Volume l l l l s sRounding & Significant Figures l lEstimating Computations l l lWhole Numbers: Properties of Operations l lEstimating Quantity & Size s sDecimal Fractions l n lRelation of Common & Decimal Fractions s n lProperties of Common & Decimal Fractions l lPercentages l lProportionality Concepts l l l sProportionality Problems l l n n s s2-D Geometry: Coordinate Geometry s s l l n l lGeometry: Transformations l l l s s sNegative Numbers, I ntegers, & Their Properties s lNumber Theory l s sExponents, Roots & Radicals l l n lExponents & Orders of Magnitude s s sMeasurement: Estimation & Errors sConstructions Using Straightedge & Compass n s3-D Geometry l n n l n sGeometry: Congruence & Similarity n lRational Numbers & Their Properties s sPatterns, Relations & Functions s n n n nProportionality: Slope & Trigonometry s l lReal Numbers, Their Subsets & Properties lValidation & J ustification l n l lStructuring & Abstracting sUncertainty & Probability s n lComplex Numbers & Their Properties s sI nfinite Processes n nChange n nVectors n sSystematic Counting s s
© 2006 Michigan State University, Center for Research in Mathematics and Science Education
State K State PTopics G1 G2 G3 G4 G5 G6 G7 G8 Topics G1 G2 G3 G4 G5 G6 G7 G8
Whole Number Meaning Whole Number Meaning Whole Number Operations Whole Number Operations Measurement Units Measurement Units Common Fractions Common Fractions Equations & Formulas Equations & Formulas Data Representation & Analysis Data Representation & Analysis 2-D Geometry: Basics 2-D Geometry: Basics Polygons & Circles Polygons & Circles Perimeter, Area & Volume Perimeter, Area & Volume Rounding & Significant Figures Rounding & Significant Figures
Estimating Computations Estimating Computations Properties of Whole Number Operations Properties of Whole Number Operations Estimating Quantity & Size Estimating Quantity & Size Decimal Fractions Decimal Fractions Relationship of Common & Decimal Fractions Relationship of Common & Decimal Fractions Properties of Common & Decimal Fractions Properties of Common & Decimal Fractions
Percentages Percentages Proportionality Concepts Proportionality Concepts Proportionality Problems Proportionality Problems 2-D Coordinate Geometry 2-D Coordinate Geometry Geometry: Transformations Geometry: Transformations Negative Numbers, Integers & Their Properties Negative Numbers, Integers & Their Properties Number Theory Number Theory Exponents, Roots & Radicals Exponents, Roots & Radicals Exponents & Orders of Magnitude Exponents & Orders of Magnitude Measurement Estimation & Errors Measurement Estimation & Errors Constructions w/ Straightedge & Compass Constructions w/ Straightedge & Compass 3-D Geometry 3-D Geometry Congruence & Similarity Congruence & Similarity Rational Numbers & Their Properties Rational Numbers & Their Properties Patterns, Relations & Functions Patterns, Relations & Functions Slope & Trigonometry Slope & Trigonometry
State L State QTopics G1 G2 G3 G4 G5 G6 G7 G8 Topics G1 G2 G3 G4 G5 G6 G7 G8
Whole Number Meaning Whole Number Meaning 1111
Whole Number Operations Whole Number Operations 1112
Measurement Units Measurement Units 121
Common Fractions Common Fractions 1121
Equations & Formulas Equations & Formulas 162
Data Representation & Analysis Data Representation & Analysis 171
2-D Geometry: Basics 2-D Geometry: Basics 132
Polygons & Circles Polygons & Circles 133
Perimeter, Area & Volume Perimeter, Area & Volume 122
Rounding & Significant Figures Rounding & Significant Figures 1152
Estimating Computations Estimating Computations 1153
Properties of Whole Number Operations Properties of Whole Number Operations 1113
Estimating Quantity & Size Estimating Quantity & Size 1151
Decimal Fractions Decimal Fractions 1122
Relationship of Common & Decimal Fractions Relationship of Common & Decimal Fractions 1123
Properties of Common & Decimal Fractions Properties of Common & Decimal Fractions 1125
Percentages Percentages 1124
Proportionality Concepts Proportionality Concepts 151
Proportionality Problems Proportionality Problems 152
2-D Coordinate Geometry 2-D Coordinate Geometry 131
Geometry: Transformations Geometry: Transformations 141
Negative Numbers, Integers & Their Properties Negative Numbers, Integers & Their Properties 1131
Number Theory Number Theory 1144
Exponents, Roots & Radicals Exponents, Roots & Radicals 1142
Exponents & Orders of Magnitude Exponents & Orders of Magnitude 1154
Measurement Estimation & Errors Measurement Estimation & Errors 123
Constructions w/ Straightedge & Compass Constructions w/ Straightedge & Compass 143
3-D Geometry 3-D Geometry 134
Congruence & Similarity Congruence & Similarity 142
Rational Numbers & Their Properties Rational Numbers & Their Properties 1132
Patterns, Relations & Functions Patterns, Relations & Functions 161
Slope & Trigonometry Slope & Trigonometry 153
State A State FTopics G1 G2 G3 G4 G5 G6 G7 G8 Topics G1 G2 G3 G4 G5 G6 G7 G8
Whole Number Meaning Whole Number Meaning Whole Number Operations Whole Number Operations Measurement Units Measurement Units Common Fractions Common Fractions Equations & Formulas Equations & Formulas Data Representation & Analysis Data Representation & Analysis 2-D Geometry: Basics 2-D Geometry: Basics Polygons & Circles Polygons & Circles Perimeter, Area & Volume Perimeter, Area & Volume Rounding & Significant Figures Rounding & Significant Figures
Estimating Computations Estimating Computations Properties of Whole Number Operations Properties of Whole Number Operations
Estimating Quantity & Size Estimating Quantity & Size Decimal Fractions Decimal Fractions Relationship of Common & Decimal Fractions Relationship of Common & Decimal Fractions Properties of Common & Decimal Fractions Properties of Common & Decimal Fractions
Percentages Percentages Proportionality Concepts Proportionality Concepts Proportionality Problems Proportionality Problems 2-D Coordinate Geometry 2-D Coordinate Geometry Geometry: Transformations Geometry: Transformations Negative Numbers, Integers & Their Properties Negative Numbers, Integers & Their Properties Number Theory Number Theory Exponents, Roots & Radicals Exponents, Roots & Radicals Exponents & Orders of Magnitude Exponents & Orders of Magnitude
Measurement Estimation & Errors Measurement Estimation & Errors Constructions w/ Straightedge & Compass Constructions w/ Straightedge & Compass
3-D Geometry 3-D Geometry Congruence & Similarity Congruence & Similarity Rational Numbers & Their Properties Rational Numbers & Their Properties Patterns, Relations & Functions Patterns, Relations & Functions Slope & Trigonometry Slope & Trigonometry
State B State GTopics G1 G2 G3 G4 G5 G6 G7 G8 Topics G1 G2 G3 G4 G5 G6 G7 G8
Whole Number Meaning Whole Number Meaning Whole Number Operations Whole Number Operations Measurement Units Measurement Units Common Fractions Common Fractions Equations & Formulas Equations & Formulas Data Representation & Analysis Data Representation & Analysis 2-D Geometry: Basics 2-D Geometry: Basics Polygons & Circles Polygons & Circles Perimeter, Area & Volume Perimeter, Area & Volume Rounding & Significant Figures Rounding & Significant Figures Estimating Computations Estimating Computations Properties of Whole Number Operations Properties of Whole Number Operations Estimating Quantity & Size Estimating Quantity & Size Decimal Fractions Decimal Fractions Relationship of Common & Decimal Fractions Relationship of Common & Decimal Fractions Properties of Common & Decimal Fractions Properties of Common & Decimal Fractions Percentages Percentages Proportionality Concepts Proportionality Concepts Proportionality Problems Proportionality Problems 2-D Coordinate Geometry 2-D Coordinate Geometry Geometry: Transformations Geometry: Transformations Negative Numbers, Integers & Their Properties Negative Numbers, Integers & Their Properties Number Theory Number Theory Exponents, Roots & Radicals Exponents, Roots & Radicals Exponents & Orders of Magnitude Exponents & Orders of Magnitude Measurement Estimation & Errors Measurement Estimation & Errors Constructions w/ Straightedge & Compass Constructions w/ Straightedge & Compass 3-D Geometry 3-D Geometry Congruence & Similarity Congruence & Similarity Rational Numbers & Their Properties Rational Numbers & Their Properties Patterns, Relations & Functions Patterns, Relations & Functions Slope & Trigonometry Slope & Trigonometry
State U State DTopics G1 G2 G3 G4 G5 G6 G7 G8 Topics G1 G2 G3 G4 G5 G6 G7 G8
Whole Number Meaning Whole Number Meaning Whole Number Operations Whole Number Operations Measurement Units Measurement Units Common Fractions Common Fractions Equations & Formulas Equations & Formulas Data Representation & Analysis Data Representation & Analysis 2-D Geometry: Basics 2-D Geometry: Basics Polygons & Circles Polygons & Circles Perimeter, Area & Volume Perimeter, Area & Volume Rounding & Significant Figures Rounding & Significant Figures Estimating Computations Estimating Computations Properties of Whole Number Operations Properties of Whole Number Operations Estimating Quantity & Size Estimating Quantity & Size Decimal Fractions Decimal Fractions Relationship of Common & Decimal Fractions Relationship of Common & Decimal Fractions Properties of Common & Decimal Fractions Properties of Common & Decimal Fractions
Percentages Percentages Proportionality Concepts Proportionality Concepts Proportionality Problems Proportionality Problems 2-D Coordinate Geometry 2-D Coordinate Geometry Geometry: Transformations Geometry: Transformations Negative Numbers, Integers & Their Properties Negative Numbers, Integers & Their Properties Number Theory Number Theory Exponents, Roots & Radicals Exponents, Roots & Radicals Exponents & Orders of Magnitude Exponents & Orders of Magnitude Measurement Estimation & Errors Measurement Estimation & Errors Constructions w/ Straightedge & Compass Constructions w/ Straightedge & Compass 3-D Geometry 3-D Geometry Congruence & Similarity Congruence & Similarity Rational Numbers & Their Properties Rational Numbers & Their Properties Patterns, Relations & Functions Patterns, Relations & Functions Slope & Trigonometry Slope & Trigonometry
State E State ITopics G1 G2 G3 G4 G5 G6 G7 G8 Topics G1 G2 G3 G4 G5 G6 G7 G8
Whole Number Meaning 1111 Whole Number Meaning 1111
Whole Number Operations 1112 Whole Number Operations 1112
Measurement Units 121 Measurement Units 121
Common Fractions 1121 Common Fractions 1121
Equations & Formulas 162 Equations & Formulas 162
Data Representation & Analysis 171 Data Representation & Analysis 171
2-D Geometry: Basics 132 2-D Geometry: Basics 132
Polygons & Circles 133 Polygons & Circles 133
Perimeter, Area & Volume 122 Perimeter, Area & Volume 122
Rounding & Significant Figures 1152 Rounding & Significant Figures 1152
Estimating Computations 1153 Estimating Computations 1153
Properties of Whole Number Operations 1113 Properties of Whole Number Operations 1113
Estimating Quantity & Size 1151 Estimating Quantity & Size 1151
Decimal Fractions 1122 Decimal Fractions 1122
Relationship of Common & Decimal Fractions 1123 Relationship of Common & Decimal Fractions 1123
Properties of Common & Decimal Fractions 1125 Properties of Common & Decimal Fractions 1125
Percentages 1124 Percentages 1124
Proportionality Concepts 151 Proportionality Concepts 151
Proportionality Problems 152 Proportionality Problems 152
2-D Coordinate Geometry 131 2-D Coordinate Geometry 131
Geometry: Transformations 141 Geometry: Transformations 141
Negative Numbers, Integers & Their Properties 1131 Negative Numbers, Integers & Their Properties 1131
Number Theory 1144 Number Theory 1144
Exponents, Roots & Radicals 1142 Exponents, Roots & Radicals 1142
Exponents & Orders of Magnitude 1154 Exponents & Orders of Magnitude 1154
Measurement Estimation & Errors 123 Measurement Estimation & Errors 123
Constructions w/ Straightedge & Compass 143 Constructions w/ Straightedge & Compass 143
3-D Geometry 134 3-D Geometry 134
Congruence & Similarity 142 Congruence & Similarity 142
Rational Numbers & Their Properties 1132 Rational Numbers & Their Properties 1132
Patterns, Relations & Functions 161 Patterns, Relations & Functions 161
Slope & Trigonometry 153 Slope & Trigonometry 153
State STopics G1 G2 G3 G4 G5 G6 G7 G8
Whole Number Meaning Whole Number Operations Measurement Units Common Fractions Equations & Formulas Data Representation & Analysis 2-D Geometry: Basics Polygons & Circles Perimeter, Area & Volume Rounding & Significant Figures Estimating Computations Properties of Whole Number Operations Estimating Quantity & Size Decimal Fractions Relationship of Common & Decimal Fractions Properties of Common & Decimal Fractions Percentages Proportionality Concepts Proportionality Problems 2-D Coordinate Geometry Geometry: Transformations Negative Numbers, Integers & Their Properties Number Theory Exponents, Roots & Radicals Exponents & Orders of Magnitude Measurement Estimation & Errors Constructions w/ Straightedge & Compass 3-D Geometry Congruence & Similarity Rational Numbers & Their Properties Patterns, Relations & Functions Slope & Trigonometry
State OTopics G1 G2 G3 G4 G5 G6 G7 G8
Whole Number Meaning Whole Number Operations Measurement Units Common Fractions Equations & Formulas Data Representation & Analysis 2-D Geometry: Basics Polygons & Circles Perimeter, Area & Volume Rounding & Significant Figures
Estimating Computations
Properties of Whole Number Operations Estimating Quantity & Size
Decimal Fractions Relationship of Common & Decimal Fractions Properties of Common & Decimal Fractions Percentages Proportionality Concepts Proportionality Problems 2-D Coordinate Geometry Geometry: Transformations Negative Numbers, Integers & Their Properties Number Theory Exponents, Roots & Radicals Exponents & Orders of Magnitude
Measurement Estimation & Errors Constructions w/ Straightedge & Compass 3-D Geometry Congruence & Similarity Rational Numbers & Their Properties Patterns, Relations & Functions Slope & Trigonometry
State C State H State MTopics G1 G2 G3 G4 G5 G6 G7 G8 Topics G1 G2 G3 G4 G5 G6 G7 G8 Topics G1 G2 G3 G4 G5 G6 G7 G8
Whole Number Meaning Whole Number Meaning Whole Number Meaning
Whole Number Operations Whole Number Operations Whole Number Operations Measurement Units Measurement Units Measurement Units Common Fractions Common Fractions Common Fractions Equations & Formulas Equations & Formulas Equations & Formulas Data Representation & Analysis Data Representation & Analysis Data Representation & Analysis 2-D Geometry: Basics 2-D Geometry: Basics 2-D Geometry: Basics Polygons & Circles Polygons & Circles Polygons & Circles Perimeter, Area & Volume Perimeter, Area & Volume Perimeter, Area & Volume Rounding & Significant Figures Rounding & Significant Figures Rounding & Significant Figures Estimating Computations Estimating Computations Estimating Computations Properties of Whole Number Operations Properties of Whole Number Operations Properties of Whole Number Operations Estimating Quantity & Size Estimating Quantity & Size Estimating Quantity & Size Decimal Fractions Decimal Fractions Decimal Fractions Relationship of Common & Decimal Fractions Relationship of Common & Decimal Fractions Relationship of Common & Decimal Fractions Properties of Common & Decimal Fractions Properties of Common & Decimal Fractions Properties of Common & Decimal Fractions
Percentages Percentages Percentages Proportionality Concepts Proportionality Concepts Proportionality Concepts Proportionality Problems Proportionality Problems Proportionality Problems 2-D Coordinate Geometry 2-D Coordinate Geometry 2-D Coordinate Geometry Geometry: Transformations Geometry: Transformations Geometry: Transformations Negative Numbers, Integers & Their Properties Negative Numbers, Integers & Their Properties Negative Numbers, Integers & Their Properties Number Theory Number Theory Number Theory Exponents, Roots & Radicals Exponents, Roots & Radicals Exponents, Roots & Radicals Exponents & Orders of Magnitude Exponents & Orders of Magnitude Exponents & Orders of Magnitude Measurement Estimation & Errors Measurement Estimation & Errors Measurement Estimation & Errors Constructions w/ Straightedge & Compass Constructions w/ Straightedge & Compass Constructions w/ Straightedge & Compass 3-D Geometry 3-D Geometry 3-D Geometry Congruence & Similarity Congruence & Similarity Congruence & Similarity Rational Numbers & Their Properties Rational Numbers & Their Properties Rational Numbers & Their Properties Patterns, Relations & Functions Patterns, Relations & Functions Patterns, Relations & Functions Slope & Trigonometry Slope & Trigonometry Slope & Trigonometry
State R State JTopics G1 G2 G3 G4 G5 G6 G7 G8 Topics G1 G2 G3 G4 G5 G6 G7 G8
Whole Number Meaning Whole Number Meaning
Whole Number Operations Whole Number Operations Measurement Units Measurement Units Common Fractions Common Fractions Equations & Formulas Equations & Formulas Data Representation & Analysis Data Representation & Analysis 2-D Geometry: Basics 2-D Geometry: Basics Polygons & Circles Polygons & Circles Perimeter, Area & Volume Perimeter, Area & Volume Rounding & Significant Figures Rounding & Significant Figures Estimating Computations Estimating Computations Properties of Whole Number Operations Properties of Whole Number Operations Estimating Quantity & Size Estimating Quantity & Size Decimal Fractions Decimal Fractions Relationship of Common & Decimal Fractions Relationship of Common & Decimal Fractions Properties of Common & Decimal Fractions Properties of Common & Decimal Fractions Percentages Percentages Proportionality Concepts Proportionality Concepts Proportionality Problems Proportionality Problems 2-D Coordinate Geometry 2-D Coordinate Geometry
Geometry: Transformations Geometry: Transformations Negative Numbers, Integers & Their Properties Negative Numbers, Integers & Their Properties Number Theory Number Theory Exponents, Roots & Radicals Exponents, Roots & Radicals Exponents & Orders of Magnitude Exponents & Orders of Magnitude Measurement Estimation & Errors Measurement Estimation & Errors Constructions w/ Straightedge & Compass Constructions w/ Straightedge & Compass 3-D Geometry 3-D Geometry Congruence & Similarity Congruence & Similarity Rational Numbers & Their Properties Rational Numbers & Their Properties Patterns, Relations & Functions Patterns, Relations & Functions Slope & Trigonometry Slope & Trigonometry
State N State TTopics G1 G2 G3 G4 G5 G6 G7 G8 Topics G1 G2 G3 G4 G5 G6 G7 G8
Whole Number Meaning Whole Number Meaning
Whole Number Operations Whole Number Operations Measurement Units Measurement Units Common Fractions Common Fractions Equations & Formulas Equations & Formulas Data Representation & Analysis Data Representation & Analysis 2-D Geometry: Basics 2-D Geometry: Basics Polygons & Circles Polygons & Circles Perimeter, Area & Volume Perimeter, Area & Volume Rounding & Significant Figures Rounding & Significant Figures Estimating Computations Estimating Computations Properties of Whole Number Operations Properties of Whole Number Operations Estimating Quantity & Size Estimating Quantity & Size Decimal Fractions Decimal Fractions Relationship of Common & Decimal Fractions Relationship of Common & Decimal Fractions Properties of Common & Decimal Fractions Properties of Common & Decimal Fractions
Percentages Percentages Proportionality Concepts Proportionality Concepts Proportionality Problems Proportionality Problems 2-D Coordinate Geometry 2-D Coordinate Geometry Geometry: Transformations Geometry: Transformations Negative Numbers, Integers & Their Properties Negative Numbers, Integers & Their Properties Number Theory Number Theory Exponents, Roots & Radicals Exponents, Roots & Radicals Exponents & Orders of Magnitude Exponents & Orders of Magnitude Measurement Estimation & Errors Measurement Estimation & Errors Constructions w/ Straightedge & Compass Constructions w/ Straightedge & Compass
3-D Geometry 3-D Geometry Congruence & Similarity Congruence & Similarity Rational Numbers & Their Properties Rational Numbers & Their Properties Patterns, Relations & Functions Patterns, Relations & Functions Slope & Trigonometry Slope & Trigonometry
21 States’ Mathematics Standards
© 2006 Michigan State University, Center for Research in Mathematics and Science Education
Distribution of Mean District IGP for PROM/SE Mathematics Classes by GradeDistribution of Mean District IGP for Mathematics Classes by Grade across PROM/SE
Districts
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
1 2 3 4 5
Mea
n D
istr
ict
IGP
© 2006 Michigan State University, Center for Research in Mathematics and Science Education
Distribution of Mean District IGP for PROM/SE Mathematics Classes by GradeDistribution of Mean District IGP for Mathematics Classes by Grade across PROM/SE
Districts
-4
-3
-2
-1
0
1
2
6 7 8
Mea
n D
istr
ict
IGP
© 2006 Michigan State University, Center for Research in Mathematics and Science Education
Instructional Days Spent on Selected Areas of Mathematics at Elementary and Middle Grades
0
20
40
60
80
100
120
140
160
180
Grade 2: Arithmetic Grade 4: Arithmetic Grade 6: Transition Arithmetic Grade 8: Algebra
Inst
ruct
ion
al D
ays
N=552 N=542 N=268 N=254
© 2006 Michigan State University, Center for Research in Mathematics and Science Education
• Fundamentals of Algebra • Advanced Algebra• Algebra I• Algebra IA • Algebra IB • Algebra IC• Algebra I Hons.• Basic Algebra I• Elementary Algebra• Essentials of Algebra• Introduction to Algebra• Enrich. Algebra
Are All Algebra Courses the Same?
© 2006 Michigan State University, Center for Research in Mathematics and Science Education
• Academic Math I• Accel. Math I• Alt. Math• Basic Math• Consumer Math• Contemporary Math• Corrective Math• Fundamentals of Math• General Math• Math Skills• Life Skills Math
• Math Proficiency• Transitional Math• Unified Math’• Tech. Math• Voc. Math• Senior Math
What Mathematics is Covered in These Courses?
© 2006 Michigan State University, Center for Research in Mathematics and Science Education
Percent of Population with HS Degree or Equivalent
%
Notes: 1) Excluding ISCED 3C short programmes; 2) Year of reference 2004; 3) Including some ISCED 3C short programmes; 4) Year of reference 2003.
Source: Schleicher 2007
As Others Rise to the Challenge, U.S. Advantage Drops
13
127
1
1960s
1970s
1980s
1990s
© 2006 Michigan State University, Center for Research in Mathematics and Science Education
Even in Higher Education, the World is Catching up…
Note: Net graduation rate is calculated by summing the graduation rates by single year of age in 2005. Year of reference 2004.
Source: OECD 2007
15
2
2005
1995
College Graduation Rates
%
