The variable i stands for our informal experiences and actually has two parts, i(sub1) and i(sub 2). i(sub1) refers to our informal mathematical experiences. Children have variable informal opportunities to count place settings, divide up Halloween candy, play numerical board games like Candyland, or share continuous quantities like pudding or juice.
Sadly, the variation often falls along socio-economic lines, with kids from poorer homes experiencing fewer early number experiences. It matters, just as it does in reading. Children who grow up in a home full of books, who are read to and enjoy rich language exchanges with family members come to school familiar with the alphabetic principle and the structure of books. They have a growing vocabulary and a head start in learning to read. Similarly, kids who play board games (the research is very strong here), read thermometers, tell time, count anything, share equally, and do all kinds of other informal numerical stuff have a richer number sense when they start school. They are ready to learn math.
In addition, children have all kinds of informal experiences that have nothing directly to do with math but a lot to do with their attitudes and abilities as learners. Chronic stress (like hunger or fear) early in life, for instance, may contribute to a reduced working memory capacity that in turn hinders the acquisition of certain math skills, like math fact automaticity. Early responsibilities, actions, and interactions can influence the development of self-regulation and executive function, the ability to control and manage one’s actions. Children who can monitor their own behavior are highly correlated to academic success. Put simply, students with the skills and attitudes tuned to school culture and formal learning increase their likelihood of classroom success across the content areas.