Math
In order for students to become proficient in mathematics, instruction must include content standards, process standards and areas of mathematical proficiency.According to NCTM's Guiding Principles for Mathematics Curriculum and Assessment, students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.
Mathematics education is a balance of both content and process. The content standards represent what is to be learned. The process standards represent ways of doing mathematics, that is, ways of acquiring and using content knowledge.
Content standards include: Numbers and Operations, Measurement, Geometry, Algebraic Concepts and Data Analysis and Probability. A definition and additional information about each of the content standards can be found at www.nctm.org.
The process standards include: Problem Solving, Reasoning and Proof, Communication, Connections and Representations. A definition and additional information about each of the process standards can be found at www.nctm.org. In addition, one can see what the process standards look like at various grade level strands by visiting the Standards Aligned System-Mathematics website at www.pde.state.pa.us/sas. The Standards Aligned System-Mathematics website also delineates the big ideas, concepts, competencies, vocabulary, exemplars and essential questions related to each grade level's standards aligned content.
As part of instruction that encompasses both content and process should be the intertwined areas of mathematical proficiency. The areas of mathematical proficiency include: Conceptual Understanding, Procedural Fluency, Strategic Competence, Adaptive Reasoning, and Productive Disposition. One can read more about the areas of mathematical proficiency in the book, Adding It Up: Helping Children Learn Mathematics, which was published by the National Research Council. This book can be read for free online at www.nap.edu/catalog.php?record_id=9822.
Another resource that everyone teaching mathematics should be familiar with is the final report of the National Math Panel. The National Math Panel was assembled by President George Bush and consisted of a 22 member panel of experts in the field. This panel included mathematicians, math educators, psychologists and representatives of U.S. government agencies/initiatives. The National Math Panel's final report can be found at www.ed.gov/about/bdscomm/list/mathpanel/index.html.
Working toward and beyond Pennsylvania's Mathematics Standards requires students to apply their knowledge of mathematical concepts in a variety of problem solving situations. Therefore, the focus of instruction for students with disabilities, as for all students, must go beyond computation and memorization.
One way to ensure that mathematics instruction includes content, process and areas of mathematical proficiency is through the implementation of Pennsylvania's Response to Instruction and Intervention (RtII) framework. For more information on RtII please visit www.pattan.net/teachlead/ResponsetoIntervention.aspx.
For those teaching mathematics to students receiving special education services, PaTTAN's training opportunities provide participants with effective instructional interventions. The goals of PaTTAN's staff development opportunities are to help participants: