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The researchers had good reason to believe that teaching physics to young children would work best if children could rub their ideas against others. However, the ideas they are asked to investigate need to be in carefully designed work.

In the 'salad bowl' of ethnic and cultural diversity of Hawai'i, there are attempts to make school work more relevant to all cultures, including involuntary minorities such as the indigenous Hawaiians. Teaching geometry in new ways is the focus of the research described here.

Many years of patient research have discovered how new ideas get formed, embedded, and remembered at the 8- to 12-year-old level. The conclusions are vital for all teaching.