数学教学中的开放式教学——创造一种课堂数学文化

数学教学中需要对开放式教学进行合作研究。在日本的开放式教学中，数学问题被选择是用来说明一个问题的多种解法或多个正确答案。数学教学要实现一种全新的课堂数学文化，这种数学形式的特点是：问题开放、解决问题的过程开放、构建问题开放、评价开放，使学生能自由地思考，发展学生的思维能力。     

Young children teach themselves to read and write

Too often young children are hurried into formal academic tasks before they are ready. This push for abstract reading and writing skills in early childhood settings can actually inhibit young children's language development. However, teachers who allow children to naturally acquire reading and writing provide a print-rich environment that encourages experimentation with language.     

Mathematical thinking in second-grade children with different forms of LD

Based on their performance on a standardized achievement test, second-grade children (N = 49) were classified as having mathematics difficulties with normal reading achievement (MD only), both mathematics and reading difficulties (MD/RD), reading difficulties with normal mathematics achievement (RD only) and normal mathematics and reading achievement (NA). Each child was given a series of tasks so that we might assess their thinking across four areas of mathematics: number facts, story problems, place value, and written calculation. Children with MD/RD performed significantly worse than NA children in most areas of mathematical thinking, whereas children with MD only performed worse than NA children only on complex story problems. The MD-only group outperformed the MD/RD group on story problems and written calculation. No significant differences were found between the RD-only and NA groups on any of the tasks. The results suggested that among children with mathematics difficulties, the MD/RD subgroup is distinct from the MD-only subgroup, with the former being characterized by pervasive deficiencies in mathematical thinking and the latter by more specific deficits in problem solving.     

Structural and conceptual interweaving of mathematics methods coursework and field practica

This paper describes a study of observed relationships between the design of a preservice elementary mathematics methods course with accompanying field practicum and changes in the extent to which participating prospective teachers identified themselves with the mathematics reform movement after becoming practicing teachers. The curriculum of the course with its embedded field practicum experiences was designed to support prospective teachers in interweaving methods coursework and pedagogical instruction with classroom practice. University and elementary school structures were interwoven by conducting weekly mathematics methods course sessions at a school site followed immediately by related practicum experiences in classrooms in the school. The interweaving of conceptualizations about mathematics teaching and learning was facilitated as the methods instructor provided professional development for classroom teachers simultaneously with the methods course, encouraging the teachers to create “reform-friendly” classroom environments. Survey data from 68 prospective teachers involved in the project were analyzed to identify and describe relationships between course/practicum experiences and the degree to which they as practicing teachers, 1–3 years following the course/practicum, identified with a reform mathematics perspective, as well as to examine factors influencing those relationships.