Mathematical Flexibility: Aspects of a Continuum and the Role of Prior Knowledge

Abstract

Psychologists and mathematics educators have long viewed flexibility as critical to students’ mathematical development. In this paper, we focused on the multidimensional nature of flexibility to better understand how preference, knowledge, and use of effective methods for solving algebra problems are related. In Study 1, we identified research-based aspects of flexibility with algebra and assessed students on them following a two-step equations unit. Results indicated that certain aspects of flexibility develop prior to others and that prior knowledge of algebra plays a significant role in that development. Study 2 confirmed and elaborated on these results using a larger sample size. Implications for theory and for supporting flexibility in classrooms are discussed.     

Factors in life science textbooks that may deter girls' interest in science

In order to examine factors that may deter girls' interest in science, five seventh-grade life science textbooks were analyzed for sexism in language, images, and curricular content, and for features of activities that have been found to be useful for motivating girls. Although overt sexism was not apparent, subtle forms of sexism in the selection of language, images, and curricular content were found. Activities had some features useful to girls, but other features were seldom included. Teachers may wish to use differences that were found among texts as one basis for text selection.     

Orthographic knowledge: clarifications,challenges, and future directions

Orthographic knowledge is the understanding of how spoken language is represented in print. However, the terms used to describe the two levels of orthographic knowledge, lexical and sublexical orthographic knowledge, have been variably defined and inconsistently measured, potentially contributing to discrepancies in research findings. Dissimilarities in how orthographic knowledge has been operationally defined and measured and the associated differences in tasks used to assess that construct are discussed. As part of that discussion, we relate how some measures assess either implicit or more explicit levels of orthographic knowledge. Using current theories and the existing research, we next provide an argument for how initial development of sublexical orthographic knowledge occurs before lexical orthographic knowledge. Suggestions are provided for what researchers might do in the future to help move the field toward a better understanding of orthographic knowledge. Strategies for assessing orthographic knowledge in literacy research are offered.

     

Parent Surveys for Teacher Evaluation

Parent or guardian perceptions play a specialized role in the evaluation of school teachers. Parents are important stakeholders in teacher success, they are in some instances partners in the teachers' work, parents have unique personal information about student learning, and they can report on the teacher duties to inform parents about the classroom and child progress. This study analyzed the responses of parents to 12 survey items concerning teacher performance in 201 classrooms. The surveys were used as part of an innovative teacher evaluation program in which teachers elected to include parent feedback as one objective data source for annual review. In this study three factors emerged as important concerns for parents: humane treatment of students, support for pupil learning, and effective communication and collaboration with parents. Recommendations for use of specific survey items can be based on the empirical results of this sampling. The data gathered by parent surveys define one dimension of quality which may vary in importance from one teacher to another.     

Distributed leadership for personalized learning

Abstract

Personalized learning refers to a collection of practices designed to place student interests and needs at the heart of schooling. Schools that implement personalized learning need leaders that support educators and students in redesigning the core practices of teaching and learning in K-12 schools. To answer the question of how leaders support this redesign, we use distributed leadership theory to focus on the macrotasks and microtasks that leaders enact to create the conditions for personalized learning practices. Drawing on a five-year, qualitative study of 11 personalized learning programs in the Midwest, we identify three macrotasks supporting personalized learning: reorganizing learning environments to support student voice and choice, assembling idiosyncratic technology ecosystems to distribute teaching and learning tasks, and redesigning instructional time to prioritize student’s interests, agency, and learning relationships. After we describe a number of microtasks associated with each macrotask, we discuss how a consideration of these kinds of leadership tasks can open the contemporary discussion of personalized learning from a narrow focus on learning technologies to an expansive vision of student-centered school reform.     

What good is a scientist in the classroom? Participant outcomes and program design features for a short-duration science outreach intervention in K-12 classrooms

Many short-duration science outreach interventions have important societal goals of raising science literacy and increasing the size and diversity of the science workforce. Yet, these long-term outcomes are inherently challenging to evaluate. We present findings from a qualitative research study of an inquiry-based, life science outreach program to K-12 classrooms that is typical in design and excellent in execution. By considering this program as a best case of a common outreach model, the "scientist in the classroom," the study examines what benefits may be realized for each participant group and how they are achieved. We find that K-12 students are engaged in authentic, hands-on activities that generate interest in science and new views of science and scientists. Teachers learn new science content and new ways to teach it, and value collegial support of their professional work. Graduate student scientists, who are the program presenters, gain teaching and other skills, greater understanding of education and diversity issues, confidence and intrinsic satisfaction, and career benefits. A few negative outcomes also are described. Program elements that lead to these benefits are identified both from the research findings and from insights of the program developer on program design and implementation choices.     

Teachers' education, classroom quality, and young children's academic skills: results from seven studies of preschool programs

In an effort to provide high-quality preschool education, policymakers are increasingly requiring public preschool teachers to have at least a Bachelor's degree, preferably in early childhood education. Seven major studies of early care and education were used to predict classroom quality and children's academic outcomes from the educational attainment and major of teachers of 4-year-olds. The findings indicate largely null or contradictory associations, indicating that policies focused solely on increasing teachers' education will not suffice for improving classroom quality or maximizing children's academic gains. Instead, raising the effectiveness of early childhood education likely will require a broad range of professional development activities and supports targeted toward teachers' interactions with children.     

Resilience to adult psychopathology following childhood maltreatment: evidence from a community sample

OBJECTIVE: Child abuse is an important risk for adult psychiatric morbidity. However, not all maltreated children experience mental health problems as adults. The aims of the present study were to address the extent of resilience to adult psychopathology in a representative community sample, and to explore predictors of a good prognosis. METHODS: Data are drawn from a follow-up of the Isle of Wight study, an epidemiological sample assessed in adolescence and at midlife. Ratings of psychiatric disorder, peer relationships and family functioning were made in adolescence; adult assessments included a lifetime psychiatric history, personality and social functioning assessments, and retrospective reports of childhood sexual and physical abuse. RESULTS: Ten percent of individuals reported repeated or severe physical or sexual abuse in childhood. Prospective measures revealed increased rates of adolescent psychiatric disorders in this group. Rates of adult psychopathology were also high. A substantial minority of abused individuals reported no mental health problems in adult life. Resilience of this kind was related to perceived parental care, adolescent peer relationships, the quality of adult love relationships, and personality style. CONCLUSION: Good quality relationships across childhood, adolescence and adulthood appear especially important for adult psychological well being in the context of childhood abuse.