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This open access report explores the nature and extent of students’ misconceptions and misunderstandings related to core concepts in physics and mathematics and physics across grades four, eight and 12. Twenty years of data from the IEA’s Trends in International Mathematics and Science Study (TIMSS) and TIMSS Advanced assessments are analyzed, specifically for five countries (Italy, Norway, Russian Federation, Slovenia, and the United States) who participated in all or almost all TIMSS and TIMSS Advanced assessments between 1995 and 2015. The report focuses on students’ understandings related to gravitational force in physics and linear equations in mathematics. It identifies some specific misconceptions, errors, and misunderstandings demonstrated by the TIMSS Advanced grade 12 students for these core concepts, and shows how these can be traced back to poor foundational development of these concepts in earlier grades. Patterns in misconceptions and misunderstandings are reported by grade, country, and gender. In addition, specific misconceptions and misunderstandings are tracked over time, using trend items administered in multiple assessment cycles. The study and associated methodology may enable education systems to help identify specific needs in the curriculum, improve inform instruction across grades and also raise possibilities for future TIMSS assessment design and reporting that may provide more diagnostic outcomes.
How do we understand numbers? Do animals and babies have numerical abilities? Why do some people fail to grasp numbers, and how we can improve numerical understanding? Numbers are vital to so many areas of life: in science, economics, sports, education, and many aspects of everyday life from infancy onwards. Numerical cognition is a vibrant area that brings together scientists from different and diverse research areas (e.g., neuropsychology, cognitive psychology, developmental psychology, comparative psychology, anthropology, education, and neuroscience) using different methodological approaches (e.g., behavioral studies of healthy children and adults and of patients; electrophysiology and brain imaging studies in humans; single-cell neurophysiology in non-human primates, habituation studies in human infants and animals, and computer modeling). While the study of numerical cognition had been relatively neglected for a long time, during the last decade there has been an explosion of studies and new findings. This has resulted in an enormous advance in our understanding of the neural and cognitive mechanisms of numerical cognition. In addition, there has recently been increasing interest and concern about pupils' mathematical achievement in many countries, resulting in attempts to use research to guide mathematics instruction in schools, and to develop interventions for children with mathematical difficulties. This handbook brings together the different research areas that make up the field of numerical cognition in one comprehensive and authoritative volume. The chapters provide a broad and extensive review that is written in an accessible form for scholars and students, as well as educationalists, clinicians, and policy makers. The book covers the most important aspects of research on numerical cognition from the areas of development psychology, cognitive psychology, neuropsychology and rehabilitation, learning disabilities, human and animal cognition and neuroscience, computational modeling, education and individual differences, and philosophy. Containing more than 60 chapters by leading specialists in their fields, the Oxford Handbook of Numerical Cognition is a state-of-the-art review of the current literature.
This open access book presents a person-centered exploration of student profiles, using variables related to motivation to do school mathematics derived from the IEA’s Trends in International Mathematics and Science Study (TIMSS) data. Statistical cluster analysis is used to identify groups of students with similar motivational profiles, across grades and over time, for multiple participating countries. While motivational variables systematically relate to school outcomes, linear relationships can obscure the diverse makeup of student subgroups, each with varying combinations of motivation, emotions, and attitudes. In this book, a person-centered analysis of distinct and meaningful motivational profiles and their differences on sociodemographic variables and mathematics performance broadens understanding about the role that motivation characteristics play in learning and achievement in mathematics. Exploiting the richness of IEA’s TIMSS data from many countries, extracted clusters reveal consistent, as well as certain nuanced patterns that are systematically linked to sociodemographic and achievement measures. Student clusters with inconsistent motivational profiles were found in all countries; mathematics self-confidence then emerged as the variable more closely associated with average achievement. The findings demonstrate that teachers, researchers, and policymakers need to take into account differential student profiles, prioritizing techniques that target skill and competence in mathematics, in educational efforts to develop student motivation.
This volume offers insights from modeling relations between teacher quality, instructional quality and student outcomes in mathematics across countries. The relations explored take the educational context, such as school climate, into account. The International Association for the Evaluation of Educational Achievement’s Trends in Mathematics and Science Study (TIMSS) is the only international large-scale study possessing a design framework that enables investigation of relations between teachers, their teaching, and student outcomes in mathematics. TIMSS provides both student achievement data and contextual background data from schools, teachers, students and parents, for over 60 countries. This book makes a major contribution to the field of educational effectiveness, especially teaching effectiveness, where cross-cultural comparisons are scarce. For readers interested in teacher quality, instructional quality, and student achievement and motivation in mathematics, the comparisons across cultures, grades, and time are insightful and thought-provoking. For readers interested in methodology, the advanced analytical methods, combined with application of methods new to educational research, illustrate interesting novel directions in methodology and the secondary analysis of international large-scale assessment (ILSA).
The "U.S. TIMSS and PIRLS 2011 Technical Report and User's Guide" provides an overview of the design and implementation of the Trends in International Mathematics and Science Study (TIMSS) 2011 and the Progress in International Reading Literacy Study (PIRLS) 2011 in the United States and the nine participating benchmarking states: Alabama, California, Colorado, Connecticut, Florida, Indiana, Massachusetts, Minnesota, and North Carolina, along with information designed to facilitate access to the U.S. TIMSS and PIRLS 2011 data. The Trends in International Mathematics and Science Study (TIMSS) 2011 is the fifth such study since this international comparison of student achievement was first conducted in 1995. Developed and implemented at the international level by the International Association for the Evaluation of Educational Achievement (IEA), an international organization of national research institutions and governmental research agencies, TIMSS is used to measure trends in the mathematics and science knowledge and skills of fourth- and eighth-graders. TIMSS is designed to align broadly with mathematics and science curricula in the participating countries. The results, therefore, suggest the degree to which students have learned mathematics and science concepts and skills likely to have been taught in school. TIMSS also collects background information on students, teachers, curricula, and schools to allow cross-national comparisons of educational contexts related to student achievement. In 2011, there were 54 countries and 20 other education systems (including all nine benchmarking states) that participated in TIMSS at the fourth- or eighth-grade level, or both. Also referenced here are three additional reports that provide a detailed treatment of TIMSS 2011 from an international perspective. Two of those reports are available in ERIC and are cross referenced at the end of this abstract. The Progress in International Reading Literacy Study (PIRLS) is an international comparative study of student achievement. PIRLS 2011 represents the third such study since PIRLS was first conducted in 2001. Developed and implemented by the International Association for the Evaluation of Educational Achievement (IEA), an international organization of national research institutions and governmental research agencies, PIRLS is used to measure the reading knowledge and skills of fourth-graders over time. PIRLS is designed to align broadly with reading curricula in the participating education systems. The results, therefore, suggest the degree to which students have learned reading concepts and skills likely to have been taught in school. PIRLS also collects background information on students, teachers, schools, curricula, and official education policies to allow cross-national comparison of educational contexts that may be related to student achievement. In 2011, there were 40 countries and 13 other education systems (including Florida) that participated in PIRLS. Titles of two additional companion reports that provide a detailed treatment of PIRLS 2011 from an international perspective published by the IEA are provided here. Those that are available in ERIC are cross referenced at the end of this abstract. Descriptions of data collection activities and their timing within the United States provide a foundation for researchers seeking to understand the detail of the data. These activities are listed in exhibit 1-1 along with the timing of their implementation. The activities are described in detail in chapter 4 of this report. The basic parameters of the design and administration of TIMSS and PIRLS 2011 in the United States are outlined and a more detailed treatment is provided in subsequent chapters of this report. Appended are: (1) State Sampling Tables; (2) State Participation Rates; (3) TIMSS & PIRLS 2011 Recruitment Materials; (4) Informational Materials; (5) Field Staff Training Materials; (6) U.S. Versions of TIMSS and PIRLS 2011 Student, School, Teacher and Curriculum Questionnaires; and (7) TIMSS and PIRLS 2011 Questionnaire Adaptations. [The following companion reports are available in ERIC: (1) "TIMSS 2011 International Results in Mathematics" (Mullis, Martin, Foy, & Arora, 2012) (ED544554); (2) "TIMSS 2011 International Results in Science" (Martin, Michael O.; Mullis, Ina V. S.; Foy, Pierre; Stanco, Gabrielle M.) (ED544560); (3) "Highlights from TIMSS 2011: Mathematics and Science Achievement of U.S. Fourth- and Eighth-Grade Students in an International Context. NCES 2013-009" (ED537756); (4) "PIRLS 2011 International Results in Reading" (Mullis, Martin, Foy, & Drucker, 2012) (ED544362); and (5) "Highlights from PIRLS 2011: Reading Achievement of U.S. Fourth-Grade Students in an International Context. NCES 2013-010" (ED537758).].