A Teacher's Guide to Using the Common Core State Standards with Mathematically Gifted and Advanced Learners

By Susan Assouline, Susan Johnsen and Gail Ryser

A Teacher's Guide to Using the Common Core State Standards With Mathematically Gifted and Advanced Learners provides teachers and administrators with practical examples of ways to build a comprehensive, coherent, and continuous set of learning experiences for gifted and advanced students. It describes informal, traditional, off-level, and 21st century math assessments that are useful in making educational decisions about placement and programming. Featuring learning experiences for each grade within one math progression, the book offers insight into useful ways of both accelerating and enriching the CCSS mathematics standards. Each of the learning experiences includes a sequence of activities, implementation examples, and formative assessments. Specific instructional and management strategies for implementing the standards within the classroom, school, and school district will be helpful for both K-12 teachers and administrators.

• Language: English
• Publisher: Sourcebooks
• Release date: Nov 15, 2013
• ISBN: 9781618211743

Susan Assouline

Susan Assouline, Ph.D., has an appointment as a Clinical Associate Professor in the School of Psychology at the University of Iowa and is the Associate Director and Clinical Supervisor at the University's Belin-Blank Center. She serves as the center's primary consultant regarding whole-grade acceleration, mathematically talented students, and students who are gifted and also have an exceptionality that may interfere with the manifestation of their gift.

Book preview

Director

Preface

Over the past three decades, national and state standards have been established for preparing teachers, developing programs and services, and designing curriculum for specific subject domains. Within gifted education, the National Association for Gifted Children (NAGC) in collaboration with the Council for Exceptional Children, The Association for the Gifted (CEC-TAG), has developed standards that provide guidelines for universities and school districts in designing coursework and/or professional development for teachers and developing services for gifted education programming (NAGC, 2010; NAGC & CEC-TAG, 2006).

More recently, teachers, researchers, leading experts, and professional associations have made recommendations for the design of the Common Core State Standards (CCSS). Built on state and international standards, these standards are aligned with college and career readiness expectations. Authors of the CCSS suggest that these standards are rigorous, evidence-based, and informed by other top performing countries (National Governors Assocation [NGA] Center for Best Practices & Council of Chief State School Officers [CCSSO], 2010c). Because most states have adopted these standards, they will replace former state standards and provide the foundation for the future design of comprehensive assessment systems to measure student progress. They will therefore have a tremendous impact on the education of all children, including those with gifts and talents.

In November 2012, NAGC copublished Using the Common Core State Standards for Mathematics (CCSSM) With Gifted and Advanced Learners (Johnsen & Sheffield, 2013) to examine how the CCSSM were adapted and differentiated for gifted and advanced learners. It was clear to these authors that although the CCSSM were strong, they were not sufficiently advanced for gifted and advanced learners. This initial book provided an overview of a variety of topics, including standards, assessment, research support, talent trajectories, collaboration, a timeline for implementation, and differentiated LEs. Given practitioners’ strong interest in this first book and their desire for more differentiated LEs, the Professional Standards Committee within the NAGC initiated the development of this new book. Similar to the first book, work teams of professionals who have expertise in gifted education and math (or in English language arts or science) and were interested in developing the new books in each of these domains worked together in identifying topics that needed more in-depth discussions. They decided to include assessment, scope and sequence, managing differentiated curriculum, additional resources, and new LEs that were not included in the first book. This book is the culmination of the team’s work.

Our hope is that this book provides classroom teachers and administrators with an understanding of expectations within a learning progression and practical examples of assessments, learning experiences, and methods for implementing differentiated curriculum in mathematics. We decided to develop a set of K–12 LEs within a single domain so that practitioners might use these as a prototype for planning LEs in other mathematical domains. We also included examples of assessments that would be helpful in assessing more complex, creative performances and in recognizing students who might have a particular aptitude for mathematics. Concrete methods for implementing differentiated LEs, along with the expanded set of resources, might also be used as a springboard for innovating more enriched and accelerated practices with gifted and advanced students.

Similar to the previous book, the authors firmly believe that giftedness in any domain is developed over time through interaction with nurturing environmental conditions within and outside the classroom setting. Students need learning experiences to develop their talents in mathematics. These experiences are particularly important for students in poverty, who might not have access to opportunities in extracurricular contexts. Students who participate in stimulating and challenging learning experiences may accelerate their trajectory, making it possible for them to achieve success with even more challenging mathematics. Practitioners should note that the recommendations in this book also might be used with learners who have potential to develop their motivation and interest in mathematics. Moreover, administrators and those involved with the implementation of the CCSSM may use this book as a guide for differentiating state and local school district curricula and assessments so that students who are advanced and gifted in mathematics have the same opportunities to show progress as typical students.

Susan K. Johnsen

Gail R. Ryser

Susan G. Assouline

Chapter 1

Overview

In this chapter, we provide an overview of this book and how the Common Core State Standards might be implemented with learners who are gifted and advanced in mathematics. Specifically, we address standards, differentiation, scope and sequence, assessments, differentiated learning experiences, and management strategies within the classroom, school, and district.

Standards

Within the past 30 years, standards have assumed an important role in schools. They define the important knowledge and skills within a specific subject area and provide guidelines for the development of curriculum, assessments, and critical benchmarks for students. Understanding the domain along with evidence-based instructional practices can help individual teachers establish a set of clear expectations and ultimately improve student outcomes. Common standards also provide consistency so that no matter where [students] live, [they] are well-prepared with the skills and knowledge necessary to collaborate and compete with their peers in the United States and abroad (NGA & CCSSO, 2010c). In this section, we will discuss the Common Core State Standards for Mathematics and their alignment to 21st century skills (Partnership for 21st Century Skills, n.d.) and the NAGC Gifted Education Programming Standards (NAGC, 2010).

Common Core State Standards for Mathematics

Adopted by 45 states, the District of Columbia, and four territories to this date, the Common Core State Standards for Mathematics (CCSSM; NGA & CCSSO, 2010a, 2010b) have quickly become the foundation for developing learning activities in mathematics. Designed by teams of math specialists across states, the new standards are intended to prepare K–12 students for college and the workplace. They emphasize thinking, problem solving, collaboration, and communication and are informed by research and reports from national and international studies such as the National Assessment of Educational Progress (NAEP, 2011) Mathematics Framework and the Trends in International Mathematics and Science Study (TIMSS) report in mathematics (National Center for Education Statistics [NCES], 2007).

In mathematics, two sets of standards are described: Standards for Mathematical Content (CCSSM-C) and Standards for Mathematical Practice (CCSSM-P). The CCSSM-C are organized by grade and secondary levels, standards, clusters, and domains. Standards define what students should understand and be able to do, clusters summarize groups of related standards, and domains are larger groups of related standards. For example, at the fifth-grade level, within the domain of Operations and Algebraic Thinking (5.OA), the student is expected to write and interpret numerical expressions (cluster heading) by using parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols and by writing simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them (standards; NGA & CCSSO, 2010a, p. 35).

It is important to notice that the standards and clusters may be related to other domains at the same grade level or across domains at different levels, forming a learning progression. For example, in measurement, students use measurable attributes to describe and compare objects, situations, or events at the elementary level; use measurable attributes in models and formulas at the middle school level; and explore measurement systems and measurement of more complex or abstract quantities at the high school level. Similarly, graphing is used to represent data in the Measurement and Data domain, to solve problems in the Geometry domain by graphing points on the coordinate plane, and to analyze patterns and relationships in the Operations and Algebraic Thinking domain by graphing ordered pairs on a coordinate plane.

Therefore, when educators are teaching the Common Core, they need to be cognizant of vertical and lateral alignments within the standards. Domains included within the CCSSM-C and the grade levels in which they are addressed are:

•  Counting and Cardinality (K),

•  Operations and Algebraic Thinking (K–5),

•  Number and Operations in Base Ten (K–5),

•  Measurement and Data (K–5),

•  Geometry (K–HS),

•  Number and Operations: Fractions (3–5),

•  Ratios and Proportional Relationships (6–7),

•  The Number System (6–8),

•  Expressions and Equations (6–8),

•  Statistics and Probability (6–HS),

•  Functions (8–HS),

•  Number and Quantity (HS),

•  Algebra (HS), and

•  Modeling (HS).

The CCSSM-P define the process skills that educators need to develop in their students (NGA & CCSSO, 2010a). The following practice standards are for all students in grades kindergarten through college and careers.

1.  Make sense of problems and persevere in solving them.

2.  Reason abstractly and quantitatively.

3.  Construct viable arguments and critique the reasoning of others.

4.  Model with mathematics.

5.  Use appropriate tools strategically.

6.  Attend to precision.

7.  Look for and make use of structure.

8.  Look for and express regularity in repeated reasoning.

To develop innovative and creative mathematicians, Sheffield (2006; Johnsen & Sheffield, 2013) proposed a ninth standard: Solve problems in novel ways and pose new mathematical questions of interest to investigate. In addition to the practice standards, educators should encourage their students to develop a deep understanding of mathematics and aspire to become creative and investigative mathematicians (Johnsen & Sheffield, 2013; Sheffield, 2000, 2003). This outcome can be achieved by (a) having students pose new mathematical questions, add new ideas for solving problems, and create innovative solutions; and (b) having teachers ask questions that encourage mathematical creativity and use assessment criteria that focuses on fluency, flexibility, originality, elaboration or elegance, generalizations, and extensions (Chapin, O’Connor, & Anderson, 2009; Sheffield, 2000).

21st Century Skills

The Mathematical Practice Standards are closely aligned with key 21st century student outcomes (Partnership for 21st Century Skills, n.d.; see Table 1.1). Some of these standards include creativity and innovation, critical thinking and problem solving, and communication and collaboration.

Table 1.1

Comparison Across Standards

Creativity and innovation. Students are encouraged to think creatively using a wide range of ideas, creating new and worthwhile ideas, and elaborating and refining their own ideas. They are also expected to work creatively with others by communicating new ideas effectively, being responsive to diverse perspectives, and viewing failure as an opportunity to learn. Moreover, in implementing innovations, students need to learn how to act on creative ideas and make a useful contribution to their field (Partnership for 21st Century Skills, n.d.).

Critical thinking and problem solving. In using these two processes, students need to learn how to reason effectively, use systems thinking to analyze how parts of a whole interact with one another, make judgments and decisions, and solve problems by identifying and asking significant questions that lead to better solutions (Partnership for 21st Century Skills, n.d.).

Communication and collaboration. Students are expected to communicate clearly by articulating their thoughts, listening effectively, using communication for a range of purposes, using and evaluating multiple media and technologies, and communicating effectively in diverse environments. Moreover, they need to learn how to collaborate with others by demonstrating their ability to work effectively and respectfully with diverse teams, exercising flexibility and willingness to be helpful to accomplish a common goal, assuming shared responsibility for collaborative work, and valuing individual contributions (Partnership for 21st Century Skills, n.d.).

Gifted Education Programming Standards

The NAGC Gifted Education Programming Standards (NAGC, 2010) are aligned to the standards of mathematical practice and the 21st century skills (see Table 1.1). For example, gifted and talented students are expected to develop competence in interpersonal and technical communication skills (NAGC, 2010) similar to the 21st century skill of communicating with others and evaluating multiple media. Moreover, teachers of gifted

Reviews for A Teacher's Guide to Using the Common Core State Standards with Mathematically Gifted and Advanced Learners

[miss_melissa-1 · Rating: 3 out of 5 stars]

This book does a wonderful job showing that differentiating instruction is what makes successful learners; Each student learns in different ways. This book is geared towards the Common Core Standards and greatly shows ways to get your classroom to fit the new standards. Would recommend to anyone looking for new ideas to meet the changing standards in their classroom.

[marieange-7 · Rating: 4 out of 5 stars]

A thorough and succinct guide to using the CC method for the mathematically gifted.This book is an excellent resource for teachers, covering everything they will need to know regarding CC standards for mathematics. Topics covered include CC standards, Adapting learning progressions for gifted and advanced learners, with descriptions of learning progressions, assessment, different learning experiences, sample activities, and management strategies. Contains several charts and tables to aid the teacher. Highly recommended.

[mrbove · Rating: 4 out of 5 stars]

This book is designed for the educational professional who works with gifted students, one their own or in a general education classroom. It is well-written and nicely organized, though there is not as much "original" material (read, "stuff we haven't already heard in classes on teaching the gifted") as I might have liked. The chapter on differentiated instruction was especially well done, and fortunately comprises a huge percentage of the book, since this is what most teachers working with gifted students consistently struggle with. All told, a good resource to have on hand if this is the population you are going to be teaching.