First Grade Children's Understanding of Multi-Digit Numbers.

A broad range of research efforts are currently examining the quality and nature of the mathematics instructional program in the early grades. The purpose of this paper was to report on the assessment of a teaching-learning program in grade one classrooms. The major goals of the study were to: (1) identify patterns and change in children's thinking and solution procedures related to pre place value and informal place value tasks; (2) to assess the effects of an enriched number program on children's understanding and competence with multi-digit numbers; (3) to assess the effect of the program on teachers' and preservice teacher mentors' pedagogical beliefs; (4) to study mentor effectiveness in generating "inquiry mathematics" and small-group cooperative learning; and (5) to examine evidence of shared pedagogical beliefs resulting from interactions among researchers, teachers, and mentors. Twelve preservice mathematics teachers served as mentors for 41 first-grade students in 2 first grade classrooms of a University laboratory school for 8 weeks during each of 2 semesters. Children typically worked in pairs with one of the mentors with occasional whole- and small-group lessons. One-to-one assessment data of the children and observational, survey, and interview data of the teacher mentors were collected. Analysis of the data led to the following findings: (1) on common assessment items, average response rates increased from 65% to 78% by mid-year; (2) students adopted more flexible approaches to solving numerical problems; (3) teachers reported student success on some tasks that they would not normally expect them to succeed on at this stage; and (4) mentors revealed a more sophisticated approach to teaching both in their beliefs and in their actual practices. Assessment protocols and the instrument for mentor perceptions and beliefs are appended. (Contains 16 references.) (MDH)