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Quantitative Measures of Mathematical Knowledge by Jonathan Bostic,Erin Krupa,Jeffrey Shih Pdf
The aim of this book is to explore measures of mathematics knowledge, spanning K-16 grade levels. By focusing solely on mathematics content, such as knowledge of mathematical practices, knowledge of ratio and proportions, and knowledge of abstract algebra, this volume offers detailed discussions of specific instruments and tools meant for measuring student learning. Written for assessment scholars and students both in mathematics education and across educational contexts, this book presents innovative research and perspectives on quantitative measures, including their associated purpose statements and validity arguments.
Quantitative Measures of Mathematical Knowledge by Jonathan Bostic,Erin Krupa,Jeffrey Shih Pdf
The aim of this book is to explore measures of mathematics knowledge, spanning K-16 grade levels. By focusing solely on mathematics content, such as knowledge of mathematical practices, knowledge of ratio and proportions, and knowledge of abstract algebra, this volume offers detailed discussions of specific instruments and tools meant for measuring student learning. Written for assessment scholars and students both in mathematics education and across educational contexts, this book presents innovative research and perspectives on quantitative measures, including their associated purpose statements and validity arguments.
Assessing Children'S Mathematical Knowledge by Cooper, Barry,Dunne, Mairead Pdf
'this work is highly relevant to the proliferation of accountability measures worldwide' James Scheurich and Douglas Foley In many countries, the lives of teachers and children are increasingly dominated by programmes of national testing of mathematics and other subjects. In England, the majority of the items in such tests have set mathematical tasks in every day situations such as 'shopping'. This requires children to make decisions about whether to use or not their own every day knowledge and experience in their problem-solving. Some children are likely to have a better 'feel for this game' than others. Assessing Children's Mathematical Knowledge draws on the analysis of national curriculum test data from more than 600 children of 10-11 and 13-14 years of age, as well as in-depth interviews with 250 of these as they attempt to solve test problems, in order to explore the nature of the difficulties children experience with 'realistic' items. The book shows, by comparing test and interview data, that many children, as a consequence of their confusion over the requirements of 'realistic' test items, fail in tests to demonstrate mathematical knowledge and understanding that they actually possess. The book also explores whether this problem of invalid measurement is equally spread across children from different social backgrounds, and across the sexes. The book will be of interest to academics and teachers studying for advanced degrees in mathematics education, sociology of education and educational assessment.
The Origins of Mathematical Knowledge in Childhood by Catherine Sophian Pdf
This book examines the origins and development of children's mathematical knowledge. It contrasts the widely held view that counting is the starting point for mathematical development with an alternative comparison-of-quantities position. According to the comparison-of-quantities position, the concept of number builds upon more basic concepts of equality, inequality, and less-than and greater-than relations, which derive from comparisons between unenumerated quantities such as lengths. The concept of number combines these basic comparative concepts with the concept of a unit of measure, which allows one quantity to be described as a multiple of another. Sophian examines these alternative accounts of children's developing mathematical knowledge in the light of research: on children's counting; on their reasoning about continuous quantities such as length and area; on the development of the concept of unit; on additive and multiplicative reasoning; and on knowledge about fractions. In the closing chapters, Sophian draws out the developmental and the educational implications of the research and theory presented. Developmentally, the comparison-of-quantities position undermines the idea that numerical knowledge develops through domain-specific learning mechanisms in that it links numerical development both to physical knowledge about objects, which is the starting point for the concept of unit, and to the acquisition of linguistic number terms. Instructionally, the comparison-of-quantities perspective diverges from the counting-first perspective in that it underscores the continuity between whole-number arithmetic and fraction learning that stems from the importance of the concept of unit for both. Building on this idea, Sophian advances three instructional recommendations: First, instruction about numbers should always be grounded in thinking about quantities and how numbers represent the relations between them; second, instruction in the early years should always be guided by a long-term perspective in which current objectives are shaped by an understanding of their role in the overall course of mathematics learning; and third, instruction should be directly toward promoting the acquisition of the most general mathematical knowledge possible. The Origins of Mathematical Knowledge in Childhood is intended for researchers, professionals, and graduate students in developmental psychology, educational psychology, and mathematics education, and as a supplementary text for advanced undergraduate courses in cognitive development, educational psychology, and mathematics education.
Mathematics for Sustainability by John Roe,Russ deForest,Sara Jamshidi Pdf
Designed for the 21st century classroom, this textbook poses, refines, and analyzes questions of sustainability in a quantitative environment. Building mathematical knowledge in the context of issues relevant to every global citizen today, this text takes an approach that empowers students of all disciplines to understand and reason with quantitative information. Whatever conclusions may be reached on a given topic, this book will prepare the reader to think critically about their own and other people’s arguments and to support them with careful, mathematical reasoning. Topics are grouped in themes of measurement, flow, connectivity, change, risk, and decision-making. Mathematical thinking is at the fore throughout, as students learn to model sustainability on local, regional, and global scales. Exercises emphasize concepts, while projects build and challenge communication skills. With no prerequisites beyond high school algebra, instructors will find this book a rich resource for engaging all majors in the mathematics classroom. From the Foreword No longer will you be just a spectator when people give you quantitative information—you will become an active participant who can engage and contribute new insights to any discussion.[...] There are many math books that will feed you knowledge, but it is rare to see a book like this one that will help you cultivate wisdom.[...] As the authors illustrate, mathematics that pays attention to human considerations can help you look at the world with a new lens, help you frame important questions, and help you make wise decisions. Francis Edward Su, Harvey Mudd College
Assessment in Mathematics Education Contexts by Jonathan D. Bostic,Erin E. Krupa,Jeffrey C. Shih Pdf
This book aims to provide theoretical discussions of assessment development and implementation in mathematics education contexts, as well as to offer readers discussions of assessment related to instruction and affective areas, such as attitudes and beliefs. By providing readers with theoretical implications of assessment creation and implementation, this volume demonstrates how validation studies have the potential to advance the field of mathematics education. Including chapters addressing a variety of established and budding areas within assessment and evaluation in mathematics education contexts, this book brings fundamental issues together with new areas of application.
Approaches to Qualitative Research in Mathematics Education by Angelika Bikner-Ahsbahs,Christine Knipping,Norma Presmeg Pdf
This volume documents a range of qualitative research approaches emerged within mathematics education over the last three decades, whilst at the same time revealing their underlying methodologies. Continuing the discussion as begun in the two 2003 ZDM issues dedicated to qualitative empirical methods, this book presents astate of the art overview on qualitative research in mathematics education and beyond. The structure of the book allows the reader to use it as an actual guide for the selection of an appropriate methodology, on a basis of both theoretical depth and practical implications. The methods and examples illustrate how different methodologies come to life when applied to a specific question in a specific context. Many of the methodologies described are also applicable outside mathematics education, but the examples provided are chosen so as to situate the approach in a mathematical context.
The AMTE Handbook of Mathematics Teacher Education by Babette M. Benken Pdf
This new volume of The Association of Mathematics Teacher Educators (AMTE) Professional Book Series is a critical and timely resource that paves the way and guides the future of mathematics teacher education. The collection of work in this AMTE Handbook of Mathematics Teacher Education reflects on research and what we know about how best to prepare and support both mathematics teachers and mathematics teacher educators and presents what is happening in the field. Examples included in the 22 chapters highlight how we are preparing teachers across multiple contexts (e.g., within district, in content courses for the major) and grade ranges (K-20+) and all chapters highlight relevant connections to the AMTE Standards for Preparing Teachers of Mathematics. Most importantly, this volume explores what we do not yet fully understand and where we are going. In essence, it considers how we can move the field forward. The 95 contributing authors range from graduate students to those who have served as leaders in the field in multiple ways for many years. Authors include K-12 teachers, school administrators, district leaders, graduate students, higher education faculty, and professional development facilitators.
Essentials of WISC-IV Assessment by Dawn P. Flanagan,Alan S. Kaufman Pdf
A successor to the extremely popular Essentials of WISC-III/WPPSI-R Assessment(0-471-34501-6), Essentials of WISC-IV Assessment provides beginning and seasoned clinicians comprehensive guidelines to administering, scoring, and interpreting the latest revision of the Wechsler Intelligence Scales for Children. Featuring the popular Essentials format of call-out boxes, Test Yourself questions and step-by-step instructions, this handy resource also includes strengths and weaknesses of the instrument, practical clinical applications, and illustrative case reports. This detailed guide to using this immensely popular measure of intelligence is a must-have for anyone involved in the psychological testing of children.
Large-Scale Studies in Mathematics Education by James A. Middleton,Jinfa Cai,Stephen Hwang Pdf
In recent years, funding agencies like the Institute of Educational Sciences and the National Science Foundation have increasingly emphasized large-scale studies with experimental and quasi-experimental designs looking for 'objective truths'. Educational researchers have recently begun to use large-scale studies to understand what really works, from developing interventions, to validation studies of the intervention, and then to efficacy studies and the final "scale-up" for large implementation of an intervention. Moreover, modeling student learning developmentally, taking into account cohort factors, issues of socioeconomics, local political context and the presence or absence of interventions requires the use of large data sets, wherein these variables can be sampled adequately and inferences made. Inroads in quantitative methods have been made in the psychometric and sociometric literatures, but these methods are not yet common knowledge in the mathematics education community. In fact, currently there is no volume devoted to discussion of issues related to large-scale studies and to report findings from them. This volume is unique as it directly discusses methodological issue in large-scale studies and reports empirical data from large-scale studies.
Digital Games and Mathematics Learning by Tom Lowrie,Robyn Jorgensen (Zevenbergen) Pdf
Digital games offer enormous potential for learning and engagement in mathematics ideas and processes. This volume offers multidisciplinary perspectives—of educators, cognitive scientists, psychologists and sociologists—on how digital games influence the social activities and mathematical ideas of learners/gamers. Contributing authors identify opportunities for broadening current understandings of how mathematical ideas are fostered (and embedded) within digital game environments. In particular, the volume advocates for new and different ways of thinking about mathematics in our digital age—proposing that these mathematical ideas and numeracy practices are distinct from new literacies or multiliteracies. The authors acknowledge that the promise of digital games has not always been realised/fulfilled. There is emerging, and considerable, evidence to suggest that traditional discipline boundaries restrict opportunities for mathematical learning. Throughout the book, what constitutes mathematics learnings and pedagogy is contested. Multidisciplinary viewpoints are used to describe and understand the potential of digital games for learning mathematics and identify current tensions within the field. Mathematics learning is defined as being about problem solving; engagement in mathematical ideas and processes; and social engagement. The artefact, which is the game, shapes the ways in which the gamers engage with the social activity of gaming. In parallel, the book (as a te xtual artefact) will be supported by Springer’s online platform—allowing for video and digital communication (including links to relevant websites) to be used as supplementary material and establish a dynamic communication space.
Contemporary Intellectual Assessment by Dawn P. Flanagan,Erin M. McDonough Pdf
This leading practitioner reference and text--now in a revised and expanded fourth edition--provides the knowledge needed to use state-of-the-art cognitive tests with individuals of all ages, from preschoolers to adults. The volume examines major theories and tests of intelligence (in chapters written by the theorists and test developers themselves) and presents research-based approaches to test interpretation. Contributors address critical issues in evaluating culturally and linguistically diverse students, gifted students, and those with intellectual disability, sensory–motor impairments, traumatic brain injuries, and learning difficulties and disabilities. The fourth edition highlights the use of cognitive test results in planning school-based interventions. New to This Edition *Complete coverage of new or updated tests: WPPSI-IV, WISC-V, WISC-V Integrated, WJ IV, ECAD, CAS2, RIAS-2, KABC-II Normative Update, and UNIT2. *Chapters on cutting-edge approaches to identifying specific learning disabilities and reading disorders. *Chapters on brain imaging, neuropsychological intervention in schools, adult intellectual development, and DSM-5 criteria for learning disorders. *Updated chapters on theories of intelligence, their research base, and their clinical utility in guiding cognitive and neuropsychological assessment practice.
Essentials of KTEA-3 and WIAT-III Assessment by Kristina C. Breaux,Elizabeth O. Lichtenberger Pdf
Written by expert authors Kristina Breaux and Elizabeth Lichtenberger, Essentials of KTEA-3 and WIAT-III Assessment offers up-to-date, comprehensive, step-by-step instruction in the accurate and effective use of the newest editions of the Kaufman Test of Educational Achievement (KTEA-3) Comprehensive Form, KTEA-3 Brief Form, and the Wechsler Individual Achievement Test (WIAT-III). Designed to provide in-depth information in an easy to use reference format, the book provides guidelines and tips for administration, scoring, and interpretation that go beyond the information provided in the test manuals. A complete guide is included for digital administration and scoring using Q-interactive, automated scoring using Q-global, and hand scoring. Essentials of KTEA-3 and WIAT-III Assessment makes score interpretation easier by explaining what each score measures and the implications of a high or low score. Learn how to increase the diagnostic utility of the KTEA-3 and WIAT-III by taking full advantage of their capabilities for error analysis, qualitative observations, and progress monitoring, and by pairing the results with measures of cognitive ability such as the WISC-V and KABC-II. Clinicians will find a helpful discussion of how these tests may be interpreted using either a CHC or neuropsychological approach to assessment. Case studies illustrate the use of these tests to respond to various referral concerns. Annotations within each case report provide a window into the mind of the examiner throughout the assessment process. This book provides a depth and breadth of understanding that is appropriate for all assessment professionals, regardless of their level of training or experience. Extensive illustrations, call-out boxes, and "Test Yourself" questions help students and clinicians quickly absorb the information they need. Essentials of KTEA-3 and WIAT-III Assessment is the clear, focused guide to using these tests to their fullest potential.
Epistemological Beliefs and Critical Thinking in Mathematics by Benjamin Rott Pdf
Epistemological beliefs—i.e. beliefs on the nature of knowledge, its limits, sources, and justification—play an important role both in everyday life and in learning processes. This book comprises several studies dealing with such beliefs in the domain of mathematics; amongst others a qualitative interview study, and quantitative studies for which a new questionnaire has been developed. In this new instrument, belief position (e.g. “mathematical knowledge is certain” vs. “uncertain”) and belief argumentation (the way those positions are justified) are differentiated. Additionally, a test for mathematical critical thinking has been designed.The results show significant correlations between sophisticated belief argumentations and high scores in the critical thinking test, but no correlations regarding belief positions.
