Conceptual Model Based Problem Solving

Are you having trouble in finding Tier II intervention materials for elementary students who are struggling in math? Are you hungry for effective instructional strategies that will address students’ conceptual gap in additive and multiplicative math problem solving? Are you searching for a powerful and generalizable problem solving approach that will help those who are left behind in meeting the Common Core State Standards for Mathematics (CCSSM)? If so, this book is the answer for you. • The conceptual model-based problem solving (COMPS) program emphasizes mathematical modeling and algebraic representation of mathematical relations in equations, which are in line with the new Common Core. • “Through building most fundamental concepts pertinent to additive and multiplicative reasoning and making the connection between concrete and abstract modeling, students were prepared to go above and beyond concrete level of operation and be able to use mathematical models to solve more complex real-world problems. As the connection is made between the concrete model (or students’ existing knowledge scheme) and the symbolic mathematical algorithm, the abstract mathematical models are no longer “alien” to the students.” As Ms. Karen Combs, Director of Elementary Education of Lafayette School Corporation in Indiana, testified: “It really worked with our kids!” • “One hallmark of mathematical understanding is the ability to justify,... why a particular mathematical statement is true or where a mathematical rule comes from” (http://illustrativemathematics.org/standards). Through making connections between mathematical ideas, the COMPS program makes explicit the reasoning behind math, which has the potential to promote a powerful transfer of knowledge by applying the learned conception to solve other problems in new contexts. • Dr. Yan Ping Xin’s book contains essential tools for teachers to help students with learning disabilities or difficulties close the gap in mathematics word problem solving. I have witnessed many struggling students use these strategies to solve word problems and gain confidence as learners of mathematics. This book is a valuable resource for general and special education teachers of mathematics. - Casey Hord, PhD, University of Cincinnati

Although two federal panels have concluded that all students can learn mathematics and most can succeed through Algebra 2, the abstractness of algebra and missing precursor understandings may be overwhelming to many students … and their teachers. Bridging the Gap Between Arithmetic & Algebra responds to this need for instruction and interventions that go beyond typical math lesson plans. Providing a review of evidence-based practices, the book is an essential reference for mathematics teachers and special education teachers when teaching mathematics to students who struggle with the critical concepts and skills necessary for success in algebra. Audiences: General education (mathematics) teachers, special education teachers, administrators, teacher educators.

This book collects recent research on posing and solving mathematical problems. Rather than treating these two crucial aspects of school mathematics as separate areas of study, the authors approach them as a unit where both areas are measured on equal grounds in relation to each other. The contributors are from a vast variety of countries and with a wide range of experience; it includes the work from many of the leading researchers in the area and an important number of young researchers. The book is divided in three parts, one directed to new research perspectives and the other two directed to teachers and students, respectively.

This book provides prospective and practicing teachers with research insights into the mathematical difficulties of students with learning disabilities and classroom practices that address these difficulties. This linkage between research and practice celebrates teachers as learners of their own students’ mathematical thinking, thus contributing an alternative view of mathematical progression in which students are taught conceptually. The research-based volume presents a unique collaboration among researchers in special education, psychology, and mathematics education from around the world. It reflects an ongoing work by members of the International Group for the Psychology of Mathematics Education (PME) and the North American Chapter of the PME Working Groups. The authors of chapters in this book, who have been collaborating extensively over the past 7 years, are from Australia, Canada, the United Kingdom, and the United States.

th This publication comprises the proceedings of the 29 International Conference on Conceptual Modeling (ER 2010), which was held this year in Vancouver, British Columbia, Canada. Conceptual modeling can be considered as lying at the confluence of the three main aspects of information technology applications –– the world of the stakeholders and users, the world of the developers, and the technologies available to them. C- ceptual models provide abstractions of various aspects related to the development of systems, such as the application domain, user needs, database design, and software specifications. These models are used to analyze and define user needs and system requirements, to support communications between stakeholders and developers, to provide the basis for systems design, and to document the requirements for and the design rationale of developed systems. Because of their role at the junction of usage, development, and technology, c- ceptual models can be very important to the successful development and deployment of IT applications. Therefore, the research and development of methods, techniques, tools and languages that can be used in the process of creating, maintaining, and using conceptual models is of great practical and theoretical importance. Such work is c- ducted in academia, research institutions, and industry. Conceptual modeling is now applied in virtually all areas of IT applications, and spans varied domains such as organizational information systems, systems that include specialized data for spatial, temporal, and multimedia applications, and biomedical applications.

Mathematics plays an important part in every person’s life, so why isn’t everyone good at it? The Routledge International Handbook of Dyscalculia and Mathematical Learning Difficulties brings together commissioned pieces by a range of hand-picked influential, international authors from a variety of disciplines, all of whom share a high public profile. More than fifty experts write about mathematics learning difficulties and disabilities from a range of perspectives and answer questions such as: What are mathematics learning difficulties and disabilities? What are the key skills and concepts for learning mathematics? How will IT help, now and in the future? What is the role of language and vocabulary? How should we teach mathematics? By posing notoriously difficult questions such as these and studying the answers The Routledge International Handbook of Dyscalculia and Mathematical Learning Difficulties is the authoritative volume and is essential reading for academics in the field of mathematics. It is an incredibly important contribution to the study of dyscalculia and mathematical difficulties in children and young adults.

Second Generation Expert Systems have been a very active field of research during the last years. Much work has been carried out to overcome drawbacks of first generation expert systems. This book presents an overview and new contributions from people who have played a major role in this evolution. It is divided in several sections that cover the main topics of the subject: - Combining Multiple Reasoning Paradigms - Knowledge Level Modelling - Knowledge Acquisition in Second Generation Expert Systems - Explanation of Reasoning - Architectures for Second Generation Expert Systems. This book can serve as a reference book for researchers and students and will also be an invaluable help for practitioners involved in KBS developments.

The National Science Foundation funded a synthesis study on the status, contributions, and future direction of discipline-based education research (DBER) in physics, biological sciences, geosciences, and chemistry. DBER combines knowledge of teaching and learning with deep knowledge of discipline-specific science content. It describes the discipline-specific difficulties learners face and the specialized intellectual and instructional resources that can facilitate student understanding. Discipline-Based Education Research is based on a 30-month study built on two workshops held in 2008 to explore evidence on promising practices in undergraduate science, technology, engineering, and mathematics (STEM) education. This book asks questions that are essential to advancing DBER and broadening its impact on undergraduate science teaching and learning. The book provides empirical research on undergraduate teaching and learning in the sciences, explores the extent to which this research currently influences undergraduate instruction, and identifies the intellectual and material resources required to further develop DBER. Discipline-Based Education Research provides guidance for future DBER research. In addition, the findings and recommendations of this report may invite, if not assist, post-secondary institutions to increase interest and research activity in DBER and improve its quality and usefulness across all natural science disciples, as well as guide instruction and assessment across natural science courses to improve student learning. The book brings greater focus to issues of student attrition in the natural sciences that are related to the quality of instruction. Discipline-Based Education Research will be of interest to educators, policy makers, researchers, scholars, decision makers in universities, government agencies, curriculum developers, research sponsors, and education advocacy groups.