The purposes of this study were to assess the effects of schema-based instruction (SBI) in promoting mathematical problem solving and to investigate schema induction as a mechanism in the development of mathematical problem solving. Twenty-four 3rd-grade teachers, with 366 students, were assigned randomly to conditions that provided instruction on 4 types of word problems. The 3 16-week conditions were contrast, SBI, and SBI with practice in sorting word problems into schemas. Students were pre-and posttested on mathematical problem-solving tests and were posttested on schema development. Students receiving SBI, with and without sorting practice, improved more than the contrast group on problemsolving measures. Concurrently, the SBI groups' schema development exceeded that of the contrast group, and schema development explained a substantial portion of unique variance in students' posttreatment problem-solving performance. Results also suggested the need for additional research testing the contribution of practice in sorting word problems.

Mathematical problem solving is a transfer challenge requiring children to develop schemas for recognizing novel problems as belonging to familiar problem types for which they know solutions. Schema-based transfer instruction (SBTI) explicitly teaches transfer features that change problems in superficial ways to make them appear novel even though they still require known solution strategies. This study assessed the effects of an expanded version of SBTI incorporating more challenging transfer features for broadening schemas and helping children recognize real-life math problems as solvable. Teachers were assigned randomly to 16-week control, SBTI, or expanded SBTI conditions. Students completed pretests and posttests focusing on increasing transfer distances. On a measure approximating real-life problem solving, the expanded SBTI group outperformed the SBTI group, which in turn outperformed the control group.

Efficient lesson planning with universal design for learning (UDL) enables teachers to more effectively meet students’ individual needs. In this study, a comparison of lesson plans by teacher candidates in a teacher preparation program before and after UDL training is presented. After training, teachers ( n = 45) incorporated more differentiated options and varied teacher strategies based on UDL principles into their lesson plans, so that the content was more accessible to all students. A variety of changes and options was examined, and examples of commonly occurring choices selected by the teacher candidates were provided. The improved multiplicity of options in lesson planning demonstrates a better understanding of UDL principles; however, teachers need more experience in actually implementing the UDL principles in their classrooms.

The amendments to the Individuals with Disabilities Education Improvement Act (IDEIA) in 2004 reiterate the significance of producing real postsecondary education, employment, and independent living outcomes. However, current employment data continue to show widespread unemployment and very limited access to inclusive community environments and services for adults with severe intellectual disabilities. On the contrary, data from the Transition Service Integration Model (N. J. Certo et al., 2003) demonstrate that these recalcitrant problems could be attenuated if two changes are implemented: The transition from school to adulthood components of IDEIA be strengthened to explicitly authorize school districts to subcontract with appropriate private agencies at the point of transition to produce direct-hire, individualized employment and adult living outcomes and that the federal government amend the Developmental Disabilities Assistance and Bill of Rights Act to provide an entitlement to long-term support, creating a service system which parallels the functions of IDEIA after school exit.