We present a case study of teaching and learning fraction addition on number lines in one 6th-grade classroom that used the Connected Mathematics Project Bits and Pieces II materials. Our main research questions were (1) What were the primary cognitive structures through which the teacher and students interpreted the lessons? and (2) Were the teacher's and her students' interpretations similar or different, and why? The data afforded particularly detailed analyses of cognitive structures used by the teacher and one student to interpret fractions and their representation on number lines. Our results demonstrate that subtle differences in methods for partitioning unit intervals did not seem important to the teacher but had significant consequences for this student's opportunities to learn. Our closing discussion addresses knowledge for teaching with drawn representations and methods for examining interactions between teachers' and students' interpretations of lessons in which they participate together.
Andrew Izsák, The University of Georgia, Department of Mathematics and Science Education, 105 Aderhold Hall, Athens, GA 30602-7124; firstname.lastname@example.org
Erik Tillema, Indiana University Purdue University Indianapolis, School of Education, 902 West New York Street, ES 3154, Indianapolis, IN 46202-5155; email@example.com
Zelha Tunç-Pekkan, The University of Georgia, Department of Mathematics and Science Education, 105 Aderhold Hall, Athens, GA 30602-7124; firstname.lastname@example.org