Autonomous learning helps out adaptive expertise of students and teachers: The division with decimal numbers

Abstract

The present study has the purpose of exploring how the autonomous learning helps out adaptive expertise in elementary school students and teachers. The research involved 30 students of 6th grade and 12 teachers of 1st to 6th degrees, both populations of different schools located in Mexico. Participants solved worksheets designed to promote autonomous learning by creating different unconventional procedures to solve division problems. On these worksheets is requested to estimate the quotient before performing arithmetic operations, in order to start understanding the problem. In various procedures generated by the participants, we find the strategy of placing subtractions in the decimal partial dividends. We think this strategy is a contribution to teaching because it was effective in understanding division with decimal point. The teachers considered important to analyze their teaching practice through videotaping and reflect on solution procedures of their students.