1. Judith E. Beauford, Ph.D. University of the Incarnate Word San Antonio, Texas (c) Judith E. Beauford, 2009

2.  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

3.  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

4.  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

5.  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

6. Case Processing Summary ValidMissingTotal NPercentNPercentNPercent Was in the experiment10100.0%0.0%10100.0% Was not in the experiment9100.0%0.0%9100.0% (c) Judith E. Beauford, 2009

7. Crosstab Count Total Was in the experimentWas not in the experiment readtraditional102030 number names352560 Total504595 Reading two digit numbers Pearson Chi-Square(2) = 9.764 a p=.008 (c) Judith E. Beauford, 2009

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

9. Crosstab Count Total Was in the experimentWas not in the experiment modelincorrect066 units011 canonical with unit straws10313 canonical with bundles403474 combination of bundles and straws011 Total504595 Pearson Chi-Square(4) =12.026 °, p=.017 Modeling two digit numbers with straws (c) Judith E. Beauford, 2009

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

11. Crosstab Count Total Was in the experimentWas not in the experiment thinks10no02020 yes502575 Total504595 Pearson Chi-Square(1) = 28.148 a p=.000 Thinks about tens place to add and subtract (c) Judith E. Beauford, 2009

12. Thinks about tens place to add and subtract (c) Judith E. Beauford, 2009

13.  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

14.  Grade 1 2005-2009  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

15. Levenes df=(2,105)ANOVA statisticsignificance F df significance Number Sense & Operations 1.810.1694.626 2, 105.012 Patterns, Relationships, Algebra.004.996.767 2, 105.467 Data, Statistics, & Probability.267.766 2.010 2, 105.139 Geometry & Measurement.776.463.661 2, 105.519 Communication & Representation.306.737.249 2, 105.780 Estimation 2.880.061.450 2, 105.639 Mathematical Connections.639.530 2.501 2, 105.087 Reasoning & Problem Solving.074.929 6.410 2, 105.002 Number Facts.898.411.700 2, 105.499 Computation w/Whole numbers 2.920.058 7.333 2, 105.001 Computation in Context 3.328.0401.943 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

16. Group differencesMean differencesSignificance Number Sense & Operations 1year < 2 years.12921p=.009 Reasoning & Problem Solving 1year < 0 years 1year < 2 years.18404.15628 p=.007 p=.005 Computation w/Whole numbers 1year < 0 years 1year < 2 years.17535.09137 p=.001 p=.049 Computation, Symbolic Notation 1year < 0 years 2 years < 0 years.17241.10083 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

17.  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

18. Between-Subjects Factors Value LabelN Number of years in base10study 0new to STM15 1Kinder only15 2 preK and kinder 27 Stanford Achievement Test year 2005 1st grade Spring 05 12 2008 1st grade Spring 08 24 20091st grade Spring 09 21 (c) Judith E. Beauford, 2009

19. 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 8.1639.324.000.608 Intercept2.3811 136.016.000.739 LPRS.5951 33.994.000.415 base10study.1352.0683.870.028.139 Year of test.0092.004.252.778.010 base10study * Year of test.0493.016.931.433.055 Error.84048.018 Total35.79057 Corrected Total2.14656 a. R Squared =.608 (Adjusted R Squared =.543) (c) Judith E. Beauford, 2009

21. 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 8.0344.270.001.416 Intercept6.0311 752.122.000.940 LPRS.1471 18.347.000.277 base10study.0192.0101.204.309.048 Year of test.0112.006.699.502.028 base10study * Year of test.0323.0111.314.281.076 Error.38548.008 Total50.25057 Corrected Total.65956 a. R Squared =.416 (Adjusted R Squared =.318) (c) Judith E. Beauford, 2009

23. 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 8.11615.842.000.725 Intercept2.9101 398.164.000.892 LPRS.6041 82.592.000.632 base10study.1042.0527.112.002.229 Grade.0572.0293.902.027.140 base10study * Grade.0603.0202.715.055.145 Error.35148.007 Total37.52557 Corrected Total1.27756 a. R Squared =.725 (Adjusted R Squared =.680) (c) Judith E. Beauford, 2009

25. 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 8.15323.435.000.796 Intercept1.3291 203.019.000.809 LPRS.7831 119.566.000.714 base10study.0622.0314.703.014.164 Year of test.0082.004.641.531.026 base10study * Year of test.0153.005.770.516.046 Error.31448.007 Total26.15357 Corrected Total1.54256 a. R Squared =.796 (Adjusted R Squared =.762) (c) Judith E. Beauford, 2009

27.  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

28. Grade level School year200420052006200720082009 Test date 2005K12345 2006PKK1234 2007PKK123 2008PKK12 2009PKK1 (c) Judith E. Beauford, 2009

29.  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

30.  Judith E. Beauford, Ph.D. Professor of Mathematics University of the Incarnate Word  210-829-3171  beauford@uiwtx.edu beauford@uiwtx.edu  Absael Antelo, Ph.D. Professor of Education University of the Incarnate Word  210-832-3215  antelo@uiwtx.edu antelo@uiwtx.edu (c) Judith E. Beauford, 2009