Response to Intervention in Math


Book Description

Provides educators with instructions on applying response-to-intervention (RTI) while teaching and planning curriculum for students with learning disabilities.




Schemas in Problem Solving


Book Description

Schemas in Problem Solving introduces a new approach to the study of learning, instruction, and assessment. Focusing on the area of arithmetic story problems, Marshall shows how instruction can lead to more meaningful learning by emphasizing the ways students acquire and store knowledge in memory. She identifies major knowledge structures called schemas, describes instruction designed around theses structures, and assesses the strengths and weaknesses in the knowledge that the students demonstrate following instruction. To evaluate the success of her approach, Marshall describes traditional experiments and computer simulations of student performance.




Conceptual Model-Based Problem Solving


Book Description

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




Elementary and Middle School Mathematics


Book Description

Elementary and Middle School Mathematics: Teaching Developmentally provides an unparalleled depth of ideas and discussion to help teachers develop a real understanding of the mathematics they will teach and the most effective methods of teaching the various mathematics topics. This text reflects the NCTM and Common Core State Standards and the benefits of problem-based mathematics instruction. It is structured for maximum flexibility, offering 23 chapters that may be mixed and matched to fit any course or teaching approach. This comprehensive, practical text offers readers a strong theoretical perspective reflecting the most current research on how students learn mathematics, ways to best teach it, and many problem-based activities to engage students. An important reference to consult throughout a teaching career, Van de Walle, Karp and Bay-William's book helps teachers and their preK-8 students find the excitement that happens when mathematics makes sense.




Implementing Schema-Based Instruction in the Elementary Classroom


Book Description

Solving mathematical word problems is an ongoing problem for students with both reading and math learning disabilities (Powell, 2011). As more and more students with learning disabilities are included in the general education classroom, teachers must differentiate instruction to benefit all learners. The current strategies emphasized in textbooks are misleading and too general for students who struggle (Jitendra, 2008). Schema-based instruction is an alternative problem solving strategy, which requires students to identify the underlying structure (schema) which each word problem belongs, to translate important information to a diagram, and then to solve the problem. This project uses cognitive theory as a theoretical framework and analyzes the effects of schema-based instruction on students with learning disabilities and their general education peers. Enhancement materials for implementing schema-based instruction were created so that teachers in a small, urban, parochial school could meet the mathematical needs of a diverse population of students. The key features of the enhancement materials include descriptions of each schema, directions for delivering explicit instruction, example and practice word problems, and student reference materials/manipulatives.




Cognitive Foundations for Improving Mathematical Learning


Book Description

The fifth volume in the Mathematical Cognition and Learning series focuses on informal learning environments and other parental influences on numerical cognitive development and formal instructional interventions for improving mathematics learning and performance. The chapters cover the use of numerical play and games for improving foundational number knowledge as well as school math performance, the link between early math abilities and the approximate number system, and how families can help improve the early development of math skills. The book goes on to examine learning trajectories in early mathematics, the role of mathematical language in acquiring numeracy skills, evidence-based assessments of early math skills, approaches for intensifying early mathematics interventions, the use of analogies in mathematics instruction, schema-based diagrams for teaching ratios and proportions, the role of cognitive processes in treating mathematical learning difficulties, and addresses issues associated with intervention fadeout. Identifies the relative influence of school and family on math learning Discusses the efficacy of numerical play for improvement in math Features learning trajectories in math Examines the role of math language in numeracy skills Includes assessments of math skills Explores the role of cognition in treating math-based learning difficulties




Solving Math Word Problems


Book Description

This is a detailed-scripted program using Schema-Based Instruction (SBI), designed as a framework for instructional implementation. It is primarily for school practitioners (e.g., special and general education teachers, school psychologists, etc.) teaching critical word problem solving skills to students with disabilities, grades 1-8.




Mathematics Word Problem Solving: An Investigation Into Schema-Based Instruction in a Computer-Mediated Setting and a Teacher-Mediated Setting with Mathematically Low-Performing Students


Book Description

Substantial evidence indicates that teacher-delivered schema-based instruction (SBI) facilitates significant increases in mathematics word problem solving (WPS) skills for diverse students; however research is unclear whether technology affordances facilitate superior gains in computer-mediated (CM) instruction in mathematics WPS when compared to teacher-mediated (TM) instruction particularly for low-performing students. This study investigated the differential effects of CM-SBI compared to TMSBI on mathematics WPS performance of mathematically low-achieving third-grade students using two commercially available packages (i.e., GO Solve Word Problems computer software [Tom Snyder Productions, 2005] and Solving Math Word Problems: Teaching Students with Learning Disabilities Using Schema-Based Instruction [Pro-Ed, 2007]). In addition, teacher and student satisfaction with strategy instruction and program materials were examined. Twenty-five students from one school district were randomly assigned to either a CM condition or a TM condition. Both conditions employed SBI that guided students to identify the problem type, and map the problem features using diagrams. Further, both conditions employed key instructional design principles and mathematics problem solving instructional features identified in the literature as effective for teaching students with disabilities (e.g., schematic diagrams, worked examples, visual representations, modeling). Intervention in both conditions consisted of 15 instructional sessions spanning six school weeks and session times remained constant between conditions. A pretest-posttest-delayed posttest repeated measures design (2 Group x 3 Times) with random assignment evaluates WPS gains of the two conditions using criterion-referenced WPS pretest, posttest and maintenance tests. Overall, results indicated that students in both conditions made significant gains in WPS performance and maintained gains after four weeks with no significant differences between conditions. Results suggest that SBI was effective at increasing and maintaining student skills in WPS performance regardless of instructional mode. Results also revealed no significant difference between conditions on student satisfaction or motivation and the teachers' preference for the TM curriculum over the computer software was indicated. Results suggest that the most important variable in terms of student gains in WPS acquisition and maintenance for mathematically low-performing students in CM settings is the strategy implemented (e.g., SBI that employs key instructional design features). Implications, limitations and recommendations for future research are discussed.




HOW TO SOLVE WORD PROBLEMS IN MATHEMATICS (EBOOK)


Book Description

Presents tools for mastering math word problems, including step-by-step guidance, examples, and problems with explained answers.