Research
Geoffrey Saxe is currently involved in two strands of research. One strand is concerned with children’s developing representational practices involving fractions in the upper elementary grades. The second strand focuses on the interplay between culture and cognition.
| Fractions are a continuing challenge for many children through middle school and often high school, and the work is an effort to explore in some analytic depth the interplay between cultural and developmental processes in children’s developing representational practices related to fractions in classrooms. | |
| Children’s developing understanding of fractions is a remarkable process. Children develop rich whole number understandings in the preschool and primary grades. With whole numbers children discover a system of intelligibility involving operations of counting, addition, subtraction, multiplication, and division. With the transition to fractions, apparent paradoxes emerge for children. Though 8 is greater than 7 in whole number terms, eighths are less than sevenths in the logic of fractions. Though multiplication necessarily leads to greater values with whole numbers, multiplication results in lesser values with fractions. What are the cultural and developmental processes that support children’s engagement in new practices involving quantification with fractions? How do children manage them? How can we support children and teachers in this transition? These are some of the broad questions with which we are concerned. | |
Culture
and Cognition Research
| The second strand of work follows up my early work in Papua New Guinea in 1978 and 1980. In 2001, I had the very good fortune of returning to the Oksapmin area in the Sandaun province of Papua New Guinea with two of my graduate students and my 19-year-old son. |  |
| The result was a series of studies that document the interplay between historical changes in practices of economic exchange and schooling and concomitant shifts in individuals’ mathematical practices. | |
| This is a fascinating world in which we learn about the dynamics of social change and changing patterns of thinking occurring in a group, a process that provides insight into the dynamics of harder to reveal processes occurring in our own communities. |  |
In 1978 and then again in 1980, I had the very good fortune of completing a series of studies in a remote part of Papua New Guinea. The research documented the Oksapmin’s number system, and its use in daily activities.
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| OKSAPMIN COUNTING | |
| In pre-contact times (prior to 1940), Oksapmin used a 27-body part count system. To count as Oksapmin do, one begins with the thumb on one hand and enumerates 27 places around the upper periphery of the body, ending on the little finger of the opposite hand. To indicate a particular number, one points to the appropriate body part (for example, the ear) and says the body-part name out loud. Traditionally, each number is labeled by both a word and a gesture (pointing to the body part in question). To continue past the 27th body part (the ‘other little finger’), continue up to the wrist, forearm, and on up and around the body. There is no distinction between the name (including word and gesture) for the 21st body part (tan-besa, meaning ‘other forearm’) and the 29th body part (also tan-besa, or ‘other forearm’). Thus, context is crucial for an understanding of the numerical referent for any number in the Oksapmin counting system. | |
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We
recommend the following paper related to fractions research:
Saxe, Gearhart, & Seltzer,
(1999) PDF
We recommend the following paper related to research on culture and cognition: