1. From Culture to place Learning & researching in informal and environments

2. Challenges to School learning Western hegemony is replaced by global diversity Educational economists point to the importance of investing in Early childhood education Computational media reshape the frontiers of individual and social action Continuous problems of educational achievement The knowledge society requires innovation and creativity ( schools are hardly the place !)

3. Schooling and inequality ( James Heckman – economist)

4. LIFE ( Learning in Informal and Formal Environments),U.W.,Seattle PRINCIPLES 1. Learning is situated in broad socio-economic and historical contexts and is mediated by local cultural practices and perspectives. 2. Learning takes place not only in school but also in the multiple contexts and valued practices of everyday lives across the life span. 3. All learners need multiple sources of support from a variety of institutions to promote their personal and intellectual development. 4. Learning is facilitated when learners are encouraged to use their home and community language resources as a basis for expanding their linguistic repertoires.

5. Preschool Math the Institute of Education Sciences, U.S. Department of Education, through Grant R305H050035 to Carnegie Mellon University. Encouraging results have been obtained for a variety of instructional programs developed to improve the mathematical knowledge of preschoolers and kindergartners, especially those from low-income backgrounds. There are effective techniques – derived from scientific research on learning – that could be put to work in the classroom today to improve children’s mathematical knowledge.” “Children’s goals and beliefs about learning are related to their mathematics performance... When children believe that their efforts to learn make them ‘smarter,’ they show greater persistence in mathematics learning.”

6. Issue in Mathematics Education: Low-Income Children Lag Behind in Mathematical Proficiency Even Before They Enter School Children vary greatly in mathematical knowledge when they enter school Numerical knowledge of kindergartners from low-income families trails far behind that of peers from higher-income families

7. Applying Theory to Educational Problem Might inadequate representations of numerical magnitudes underlie low-income children’s poor numerical performance?

8. Applied Goal Raised New Theoretical Question: What Leads Anyone to Form Initial Linear Representation? Counting experience is likely helpful and necessary, but insufficient Children can count in a numerical range more than a year before they can generate a linear representation of numerical magnitudes in that range (Condry & Spelke, 2008; LeCorre & Carey, 2007; Schaffer et al., 1974)

9. Playing Board Games Board games might play a crucial role in forming linear representations of numerical magnitudes Designed to promote interactions between parents and peers Also provides rich experiences with numbers

10. Chutes and Ladders

11. Key Properties of Board Games Like Chutes and Ladders The greater the number a token reaches, the greater the Distance that the child has moved the token Number of discrete hand movements the child has made Number of number names the child has spoken Time spent by the child playing the game Thus, playing number board games provides visuo-spatial, kinesthetic, auditory, and temporal cues to links between number symbols and their magnitudes

12. Number Board Game

13. Effects of Playing the Number Board Game Goal was to investigate whether playing the number board game: Improves a broad range of numerical skills and concepts Produces gains that remain stable over time