Mathematics and Virtual Culture: an Evolutionary Perspective on Technology and Mathematics Education

This paper suggests that from a cognitive-evolutionary perspective, computational media are qualitatively different from many of the technologies that have promised educational change in the past and failed to deliver. Recent theories of human cognitive evolution suggest that human cognition has evolved through four distinct stages: episodic, mimetic, mythic, and theoretical. This progression was driven by three cognitive advances: the ability to ‘represent’ events, the development of symbolic reference, and the creation of external symbolic representations. In this paper, we suggest that we are developing a new cognitive culture: a ‘virtual’ culture dependent on the externalization of symbolic processing. We suggest here that the ability to externalize the manipulation of formal systems changes the very nature of cognitive activity. These changes will have important consequences for mathematics education in coming decades. In particular, we argue that mathematics education in a virtual culture should strive to give students generative fluency to learn varieties of representational systems, provide opportunities to create and modify representational forms, develop skill in making and exploring virtual environments, and emphasize mathematics as a fundamental way of making sense of the world, reserving most exact computation and formal proof for those who will need those specialized skills. This revised version was published online in July 2006 with corrections to the Cover Date.     

Characterizing disability in Head Start programs: Not so clearcut

Head Start programs are required to set aside at least 10% of program slots for children with disabilities, but the percentage of children with disabilities served varies depending on the criteria used and source of the information. This study used the Head Start Family and Child Experiences Survey (FACES) 2000 data for a nationally representative sample to identify subgroups of children meeting three different criteria for having a disability or developmental delay. Results indicated that about one-third of children in Head Start (33%) met one or more of the criteria for a disability or delay, about one-third of those children (33%) met criteria for two or for all three of the subgroups. However, only 8% of children in Head Start had an Individualized Education Program (IEP). Children with disabilities or delays, regardless of the subgroup criteria used, had higher levels of many other risk factors associated with poor developmental and school readiness outcomes. They also exhibited poorer performance on early literacy, social, and behavioral measures both at entry into Head Start and at the end of kindergarten compared with children not in each of those subgroups. Implications of the findings for screening and assessment, serving children in Head Start programs, and the need for linkages between Head Start programs and the preschool special education system are discussed.     

A Framework for Evaluation and Use of Automated Scoring

A framework for evaluation and use of automated scoring of constructed‐response tasks is provided that entails both evaluation of automated scoring as well as guidelines for implementation and maintenance in the context of constantly evolving technologies. Consideration of validity issues and challenges associated with automated scoring are discussed within the framework. The fit between the scoring capability and the assessment purpose, the agreement between human and automated scores, the consideration of associations with independent measures, the generalizability of automated scores as implemented in operational practice across different tasks and test forms, and the impact and consequences for the population and subgroups are proffered as integral evidence supporting use of automated scoring. Specific evaluation guidelines are provided for using automated scoring to complement human scoring for tests used for high‐stakes purposes. These guidelines are intended to be generalizable to new automated scoring systems and as existing systems change over time.     

Learning Disabilities and the LRE Mandate: An Examination of National and State Trends

This study was conducted to examine changes in the identification rates and national and state placement practices for school age students with learning disabilities (LD) between 1990–1991 and 2008–2009. Findings revealed that while identification rates of students with LD declined by about 4 percent during this time, general education placements increased over 166 percent, pullout placements declined by more than 50 percent, while students educated in highly restrictive separate class and separate school settings declined by approximately 60 percent. Unlike earlier studies, most states made at least some progress toward educating students with LD in less restrictive settings. Much of the change in placement practices for students with LD occurred since 2000.     

An Alternative Route to Higher Education: An Evaluation of the Senior Colleges in Western Australia

The establishment of two Senior Colleges in Western Australia in 1983 provided adult students with an alternative route to conventional schooling for completing matriculation requirements for entry to higher education. An evaluation of the Colleges involved large samples of students and staff and the triangulation of information obtained by different researchers working independently and using a variety of methods (interview, questionnaires, nominal groups, classroom and school climate assessments). The study attested to the success of the Senior Colleges in creating a positive ethos suited to its adult students and in allowing previously unqualified people to enter higher education and succeed.