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

Taking a future-oriented approach, this book addresses students’ ways of thinking in STEM-based problem solving. It provides a rich set of chapters that explore how we can advance important thinking skills in STEM education for K-12 students. STEM education is essential to understanding and solving many of the world’s major challenges. However, the kind of interdisciplinary modes of thinking required to tackle such unforeseen problems is lacking in most STEM education delivery. This book examines the various ways of thinking that can be applied to effective STEM-based problem solving across K-12 education. These include design and design-based thinking, systems thinking and modeling, critical thinking, innovative and adaptive thinking, intuition in problem solving, and computational and algorithmic thinking. Across the chapters, the authors’ interdisciplinary perspectives give further depth to understanding how students learn and apply their thinking to solve STEM-based problems. The book also provides guidance on how to assess ways of thinking in STEM education, to ensure educators can recognize students’ progress and development. Bringing together a team of international experts, this book is essential reading for pre-service teachers, teacher educators, and researchers in STEM education.

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.

Conceptual model building is accepted as a key phase in Soft Systems Methodology. Despite the recognition of the importance of the SSM, students are still experiencing difficulty with the basic process of conceptual model building. This book addresses that issue.

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.

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.