Longitudinal Results of Number Name Project

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

2. Names vs. Meanings • 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. (c) Judith E. Beauford, 2009 Names vs. Meanings • 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.

4. Implementation • 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 Experimental design

6. (c) Judith E. Beauford, 2009 Preliminary longitudinal results Case Processing Summary Valid Missing Total N 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% 9 100.0%

7. (c) Judith E. Beauford, 2009 Preliminary longitudinal results Reading two digit numbers Crosstab Count Total Was in the experiment Was not in the experiment read traditional 10 20 30 number names 35 25 60 Total 50 45 95 Pearson Chi-Square (2) = 9.764a p=.008

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

9. (c) Judith E. Beauford, 2009 Preliminary longitudinal results Modeling two digit numbers with straws Crosstab Count Total Was in the experiment Was not in the experiment model incorrect 0 6 6 units 0 1 1 canonical with unit straws 10 3 13 canonical with bundles 40 34 74 combination of bundles and straws 0 1 1 Total 50 45 95 Pearson Chi-Square (4) =12.026°, p=.017

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

11. (c) Judith E. Beauford, 2009 Preliminary longitudinal results Thinks about tens place to add and subtract Crosstab Count Total Was in the experiment Was not in the experiment thinks10 no 0 20 20 yes 50 25 75 Total 50 45 95 Pearson Chi-Square (1) = 28.148a p=.000

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

13. (c) Judith E. Beauford, 2009 stanford Achievement tests • 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

14. 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 One way ANOVAS

15. (c) Judith E. Beauford, 2009

16. (c) Judith E. Beauford, 2009 Tukey’s Post Hoc for difference in mean percent correct among students in the study for 0 years (n1 = 18), 1 year (n2 = 15), and 2 years (n3=55).

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 Controlling for ‘achievement’

18. (c) Judith E. Beauford, 2009 Controlling for ‘achievement’

19. (c) Judith E. Beauford, 2009 Number Sense & Operations

20. (c) Judith E. Beauford, 2009 Number Sense & Operations

21. (c) Judith E. Beauford, 2009 Communication & Representation

22. (c) Judith E. Beauford, 2009 Communication & Representation

23. (c) Judith E. Beauford, 2009 Mathematical Connections

24. (c) Judith E. Beauford, 2009 Mathematical Connections

25. (c) Judith E. Beauford, 2009 Computation/Symbolic

26. (c) Judith E. Beauford, 2009 Computation/Symbolic

27. (c) Judith E. Beauford, 2009 Summary of results • One way ANOVAs • Factorial ANOVAs

28. (c) Judith E. Beauford, 2009 What’s next?

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 Multi-site project

30. Judith E. Beauford, Ph.D. Professor of Mathematics University of the Incarnate Word • 210-829-3171 • beauford@uiwtx.edu • AbsaelAntelo, Ph.D. Professor of Education University of the Incarnate Word • 210-832-3215 • antelo@uiwtx.edu (c) Judith E. Beauford, 2009 Contact information