Longitudinal Results of Number Name Project

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.


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.


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)


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%


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


Reading two digit numbers


CrosstabCount


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


Modeling two digit numbers with straws


CrosstabCount


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


Thinks about tens place to add and subtract


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


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).


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


.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


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


1year < 2 years .12921 p=.009


1year < 0 years1year < 2 years

.18404

.15628p=.007p=.005

Computation w/Whole numbers


.17535

.09137p=.001p=.049


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).


Factorial ANOVA Fixed factor=test year Random factor = number of years in

study Covariate = LPRS (local percentile)

Available for 2005, 2008, 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


24


21


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)




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


.032 3 .011 1.314 .281 .076

Error .385 48 .008

Total 50.250 57

Corrected Total .659 56





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






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


.015 3 .005 .770 .516 .046

Error .314 48 .007

Total 26.153 57





One way ANOVAs Factorial ANOVAs


1year < 2 years



Computation w/Whole numbers



1year < 0 years2 years < 0 years

Number sense & Operations

0 years < 1 year < 2 years

Mathematical Connections

0 years < 1 year < 2 years


2 years = 1 year < 0 years


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


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


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]


Documents

Longitudinal Results of Number Name Project