From Culture to place

1. From Culture to place Learning& researching in informaland environments

2. Challenges to Schoollearning • Western hegemony is replaced by global diversity • Educationaleconomists point to the importance of investing in Earlychildhoodeducation • Computational mediareshape the frontiers of individual and social action • Continuousproblems of educationalachievement • The knowledge society requiresinnovation and creativity ( schoolsarehardly 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 • culturalpractices 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 personaland intellectualdevelopment. • 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. PreschoolMath 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