Terezinha Nunes, in Ethnomathematics and Everyday Cognition, from the Handbook of Research on Mathematics Teaching and Learning (1992), cites studies showing that people acquire significant amounts of mathematical knowledge outside of school - in the everyday activities of cultures. For example, counting and measuring, problem solving and calculating, and modeling and completing inverse operations - concepts that are central to elementary mathematics in the classroom - are used as tools in everyday activities, such as building, exchanging money, weighing, and cooking.
Teachers can use real-life problem solving concepts in the classroom by finding out if and how students have used those concepts in everyday life, recognizing that use varies across and within cultures. For example, the teacher could give students several problem situations involving fractions without teaching the students how to represent fractions. The students' discussion using their natural language and their attempts to solve the problems would reveal their prior knowledge and use of the concept as a tool and set the stage for mathematical representation of the concept. Such an approach has similarities with learning-to-learn and cognitive apprenticeship models.
This instructional approach involving "mathematizing objects and situations in everyday activity" enables students to construct mathematical knowledge and to link background knowledge, values, and practices in their culture and community with new learning. Not only do such classroom experiences affirm mathematical learning outside of school, but they also help students generalize from the concepts they use as tools.
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