Judith E. Beauford, Ph.D.University of the Incarnate WordSan Antonio, Texas
(c) Judith E. Beauford, 2009
Asian languages uses explicit number names 26 is said “two-ten six” 11 new words needed
to count 1 to 100
Among the many advantages Chinese have for superior performance in mathematics, explicit language may play a role.
(c) Judith E. Beauford, 2009
English speaking children learn 26 new words or word parts to count to 100
Place value is a separate topic of study for many years in the curriculum
Spanish speakers have 28 new words or word parts to learn
Most children from both language heritages score at or below average in international testing.
(c) Judith E. Beauford, 2009
Refer to the meaning of the number rather than the traditional name
Use of straws, linking cubes, other small items that can be bundled or used singly
Every number named by its meaning Calendar work Counting Time Measure (c) Judith E. Beauford, 2009
Pre-experimental design Treatment – post test Treatment – test – treatment – test (pilot study)
Quasi-experimental design Control group Intact groups
(public ISD and Longitudinal study)
(c) Judith E. Beauford, 2009
Case Processing Summary
Valid Missing TotalN Percent N Percent N Percent
Was in the experiment 10 100.0% 0 .0% 10 100.0%Was not in the experiment 9 100.0% 0 .0% 9100.0%
(c) Judith E. Beauford, 2009
CrosstabCount
TotalWas in the experiment Was not in the
experimentread traditional 10 20 30
number names 35 25 60
Total 50 45 95
Reading two digit numbers
Pearson Chi-Square (2) = 9.764a
p=.008
(c) Judith E. Beauford, 2009
Reading two digit numbers
(c) Judith E. Beauford, 2009
CrosstabCount
TotalWas in the experiment Was not in the
experimentmodel incorrect 0 66
units 0 1 1canonical with unit straws 10 3
13canonical with bundles 40 34 74combination of bundles and straws 0 1
1Total 50 45 95Pearson Chi-Square (4) =12.026°, p=.017
Modeling two digit numbers with straws
(c) Judith E. Beauford, 2009
Modeling two digit numbers with straws
(c) Judith E. Beauford, 2009
CrosstabCount
TotalWas in the experiment Was not in the
experimentthinks10 no 0 20 20
yes 50 25 75Total 50 45 95
Pearson Chi-Square (1) = 28.148a p=.000
Thinks about tens place to add and subtract
(c) Judith E. Beauford, 2009
Thinks about tens place to add and subtract
(c) Judith E. Beauford, 2009
Number Sense & Operations
Patterns, Relationships, Algebra
Data, Statistics, & Probability
Geometry & Measurement
Communication & Representation
Estimation
Mathematical Connections
Reasoning & Problem Solving
Number Facts
Computation with Whole Numbers
Computation in Context
Computation, Symbolic Notation
(c) Judith E. Beauford, 2009
Grade 1 2005-2009 Stanford results analysis Test of difference in mean percent
correct among students in the study for
0 years (n1 = 24),
1 year (n2 = 29),
2 years (n3= 55).
(c) Judith E. Beauford, 2009
Levenes df=(2,105) ANOVAstatistic significance F df significance
Number Sense &Operations
1.810 .169 4.626 2, 105 .012
Patterns, Relationships,Algebra
.004 .996 .767 2, 105 .467Data, Statistics, &Probability
.267 .766 2.010 2, 105 .139Geometry & Measurement .776 .463 .661 2, 105 .519
Communication & Representation
.306 .737 .249 2, 105 .780Estimation 2.880 .061 .450 2, 105 .639Mathematical Connections .639 .530 2.501 2, 105 .087
Reasoning & Problem Solving
.074 .929 6.410 2, 105 .002
Number Facts .898 .411 .700 2, 105 .499Computation w/Whole numbers
2.920 .058 7.333 2, 105 .001
Computation in Context 3.328 .040 1.943 2, 46.091 .155
Computation, Symbolic Notation
1.543 .218 7.445 2, 105 .001
Local PRS 3.031 .057 2.644 2, 105 .080(c) Judith E. Beauford, 2009
Group differences Mean differences Significance
Number Sense &Operations
1year < 2 years .12921 p=.009
Reasoning & Problem Solving
1year < 0 years1year < 2 years
.18404
.15628p=.007p=.005
Computation w/Whole numbers
1year < 0 years1year < 2 years
.17535
.09137p=.001p=.049
Computation, Symbolic Notation
1year < 0 years2 years < 0 years
.17241
.10083p=.001p=.033
among students in the study for 0 years (n1 = 18), 1 year (n2 = 15), and 2 years (n3=55).
(c) Judith E. Beauford, 2009
Factorial ANOVA Fixed factor=test year Random factor = number of years in
study Covariate = LPRS (local percentile)
Available for 2005, 2008, 2009
(c) Judith E. Beauford, 2009
Between-Subjects Factors
Value Label NNumber of years in base10study
0 new to STM 15
1 Kinder only 15
2 preK and kinder
27
Stanford Achievement Test year
2005 1st grade Spring 05
12
2008 1st grade Spring 08
24
2009 1st grade Spring 09
21
(c) Judith E. Beauford, 2009
Tests of Between-Subjects Effects
Dependent Variable: Number Sense & Operations percent correct
Source
Type III Sum of Squares df
Mean Square F Sig.
Partial Eta Squared
Corrected Model 1.306a 8 .163 9.324 .000 .608
Intercept 2.381 1 2.381 136.016 .000 .739
LPRS .595 1 .595 33.994 .000 .415
base10study .135 2 .068 3.870 .028 .139
Year of test .009 2 .004 .252 .778 .010
base10study * Year of test
.049 3 .016 .931 .433 .055
Error .840 48 .018
Total 35.790 57
Corrected Total 2.146 56
a. R Squared = .608 (Adjusted R Squared = .543)
(c) Judith E. Beauford, 2009
(c) Judith E. Beauford, 2009
Tests of Between-Subjects Effects
Dependent Variable: Communication & Representation percent correct
SourceType III Sum of Squares df
Mean Square F Sig.
Partial Eta Squared
Corrected Model .274a 8 .034 4.270 .001 .416
Intercept 6.031 1 6.031 752.122 .000 .940
LPRS .147 1 .147 18.347 .000 .277
base10study .019 2 .010 1.204 .309 .048
Year of test .011 2 .006 .699 .502 .028
base10study * Year of test
.032 3 .011 1.314 .281 .076
Error .385 48 .008
Total 50.250 57
Corrected Total .659 56
a. R Squared = .416 (Adjusted R Squared = .318)
(c) Judith E. Beauford, 2009
(c) Judith E. Beauford, 2009
Tests of Between-Subjects Effects
Dependent Variable: Mathematical Connections percent correct
SourceType III Sum of Squares df
Mean Square F Sig.
Partial Eta Squared
Corrected Model .926a 8 .116 15.842 .000 .725
Intercept 2.910 1 2.910 398.164 .000 .892
LPRS .604 1 .604 82.592 .000 .632
base10study .104 2 .052 7.112 .002 .229
Grade .057 2 .029 3.902 .027 .140
base10study * Grade
.060 3 .020 2.715 .055 .145
Error .351 48 .007
Total 37.525 57
Corrected Total 1.277 56
a. R Squared = .725 (Adjusted R Squared = .680)
(c) Judith E. Beauford, 2009
(c) Judith E. Beauford, 2009
Tests of Between-Subjects Effects
Dependent Variable : Computation/Symbolic Notation percent correct
Source
Type III Sum of Squares df
Mean Square F Sig.
Partial Eta Squared
Corrected Model 1.227a 8 .153 23.435 .000 .796
Intercept 1.329 1 1.329 203.019 .000 .809
LPRS .783 1 .783 119.566 .000 .714
base10study .062 2 .031 4.703 .014 .164
Year of test .008 2 .004 .641 .531 .026
base10study * Year of test
.015 3 .005 .770 .516 .046
Error .314 48 .007
Total 26.153 57
Corrected Total 1.542 56
a. R Squared = .796 (Adjusted R Squared = .762)
(c) Judith E. Beauford, 2009
(c) Judith E. Beauford, 2009
One way ANOVAs Factorial ANOVAs
Number Sense &Operations
1year < 2 years
Reasoning & Problem Solving
1year < 0 years1year < 2 years
Computation w/Whole numbers
1year < 0 years1year < 2 years
Computation, Symbolic Notation
1year < 0 years2 years < 0 years
Number sense & Operations
0 years < 1 year < 2 years
Mathematical Connections
0 years < 1 year < 2 years
Computation, Symbolic Notation
2 years = 1 year < 0 years
(c) Judith E. Beauford, 2009
Grade level
School year 2004 2005 2006 2007 2008 2009
Test date
2005 K 1 2 3 4 5
2006 PK K 1 2 3 4
2007 PK K 1 2 3
2008 PK K 1 2
2009 PK K 1
(c) Judith E. Beauford, 2009
Quasi-experimental design For a short term experiment, we need a control
group Longitudinal study uses children who have not
attended the school in the pre-K and K as the control group
St. Thomas More, San Antonio, TX Colegio Americano, Saltillo, MX Tic Tac Toe School, Cochabamba, BO American School, Santa Cruz, BO
(c) Judith E. Beauford, 2009
Judith E. Beauford, Ph.D.Professor of MathematicsUniversity of the Incarnate Word 210-829-3171 [email protected]
Absael Antelo, Ph.D.Professor of EducationUniversity of the Incarnate Word 210-832-3215 [email protected]
(c) Judith E. Beauford, 2009
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