Judith E. Beauford, Ph.D. University of the Incarnate Word San 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 ValidMissingTotal NPercentNPercentNPercent Was in the experiment %0.0% % Was not in the experiment9100.0%0.0%9100.0% (c) Judith E. Beauford, 2009

Crosstab Count Total Was in the experimentWas not in the experiment readtraditional number names Total Reading two digit numbers Pearson Chi-Square(2) = a p=.008 (c) Judith E. Beauford, 2009

Reading two digit numbers (c) Judith E. Beauford, 2009

Crosstab Count Total Was in the experimentWas not in the experiment modelincorrect066 units011 canonical with unit straws10313 canonical with bundles combination of bundles and straws011 Total Pearson Chi-Square(4) = °, p=.017 Modeling two digit numbers with straws (c) Judith E. Beauford, 2009

Modeling two digit numbers with straws (c) Judith E. Beauford, 2009

Crosstab Count Total Was in the experimentWas not in the experiment thinks10no02020 yes Total Pearson Chi-Square(1) = a 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  Stanford results analysis  Test of difference in mean percent correct among students in the study for  0 years (n 1 = 24),  1 year (n 2 = 29),  2 years (n 3 = 55). (c) Judith E. Beauford, 2009

Levenes df=(2,105)ANOVA statisticsignificance F df significance Number Sense & Operations , Patterns, Relationships, Algebra , Data, Statistics, & Probability , Geometry & Measurement , Communication & Representation , Estimation , Mathematical Connections , Reasoning & Problem Solving , Number Facts , Computation w/Whole numbers , Computation in Context , Computation, Symbolic Notation , Local PRS , (c) Judith E. Beauford, 2009

Group differencesMean differencesSignificance Number Sense & Operations 1year < 2 years.12921p=.009 Reasoning & Problem Solving 1year < 0 years 1year < 2 years p=.007 p=.005 Computation w/Whole numbers 1year < 0 years 1year < 2 years p=.001 p=.049 Computation, Symbolic Notation 1year < 0 years 2 years < 0 years p=.001 p=.033 among students in the study for 0 years (n 1 = 18), 1 year (n 2 = 15), and 2 years (n 3 =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 LabelN Number of years in base10study 0new to STM15 1Kinder only15 2 preK and kinder 27 Stanford Achievement Test year st grade Spring st grade Spring st grade Spring (c) Judith E. Beauford, 2009

Tests of Between-Subjects Effects Dependent Variable: Number Sense & Operations percent correct Source Type III Sum of Squaresdf Mean SquareFSig. Partial Eta Squared Corrected Model1.306 a Intercept LPRS base10study Year of test base10study * Year of test Error Total Corrected Total a. R Squared =.608 (Adjusted R Squared =.543) (c) Judith E. Beauford, 2009

Tests of Between-Subjects Effects Dependent Variable: Communication & Representation percent correct Source Type III Sum of Squaresdf Mean SquareFSig. Partial Eta Squared Corrected Model.274 a Intercept LPRS base10study Year of test base10study * Year of test Error Total Corrected Total a. R Squared =.416 (Adjusted R Squared =.318) (c) Judith E. Beauford, 2009

Tests of Between-Subjects Effects Dependent Variable: Mathematical Connections percent correct Source Type III Sum of Squaresdf Mean SquareFSig. Partial Eta Squared Corrected Model.926 a Intercept LPRS base10study Grade base10study * Grade Error Total Corrected Total a. R Squared =.725 (Adjusted R Squared =.680) (c) Judith E. Beauford, 2009

Tests of Between-Subjects Effects Dependent Variable : Computation/Symbolic Notation percent correct Source Type III Sum of Squaresdf Mean SquareFSig. Partial Eta Squared Corrected Model1.227 a Intercept LPRS base10study Year of test base10study * Year of test Error Total Corrected Total a. R Squared =.796 (Adjusted R Squared =.762) (c) Judith E. Beauford, 2009

 One way ANOVAs  Factorial ANOVAs Number Sense & Operations 1year < 2 years Reasoning & Problem Solving 1year < 0 years 1year < 2 years Computation w/Whole numbers 1year < 0 years 1year < 2 years Computation, Symbolic Notation 1year < 0 years 2 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 Test date 2005K PKK PKK PKK PKK1 (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 Mathematics University of the Incarnate Word    Absael Antelo, Ph.D. Professor of Education University of the Incarnate Word   (c) Judith E. Beauford, 2009