A review of Windows of Opportunity: Mathematics for Students With Special Needs
M. Katherine Gavin
University of Connecticut
In Windows of Opportunity: Mathematics for Students with Special Needs, the National Council of Teachers of Mathematics (NCTM) has furnished a professional resource for both regular classroom teachers and teachers of students with special needs, including students who are gifted and talented in mathematics. The educators who collaborated in writing the chapters impart the philosophy of the NCTM Standards (National Council of Teachers of Mathematics, 1989) and share practical, effective instructional strategies for implementation. A particular focus that binds the chapters together is a nurturing of mathematical thinking through relevant, problem-centered instruction. This focus is important to note since teachers, in interpreting the Standards, often zero in on the need for students to “do” mathematics, but are less aware of the Standards’ emphasis on the mathematical reflection required for true discovery and understanding. All the authors in the text agree that a classroom environment based on the Standards is one that creates opportunities to discover mathematically talented students. They recognize the importance of a constructivist approach to mathematical investigations and offer many practical examples with extensions focusing on differentiation. The text is divided into three major sections: current issues relating to equitable programs for students with special needs, major curriculum thrusts in mathematics, and promising practices of several existing programs that include, or are designed for, students with special needs.
Focusing specifically on the attention and information given to students who are mathematically talented, let us begin by looking at the chapter “Issues of Identification” by Downs, Matthew, and McKinney. Writing for the regular classroom teacher, these authors present a concise and accurate overview of the major issues in the definition and identification of talented students. Concerns centering around the disparity in defining giftedness by leading theorists in the field and varying interpretations of the federal definition at the state and local levels are discussed. The practical tips offered to teachers to help them recognize talent in their students, especially students who do not fit the stereotype, including economically disadvantaged and underachieving gifted students, are a breath of fresh air. The authors caution against the sole use of standardized tests in identification, stressing the cultural and gender bias that may be inherent in these tests. Although they list other good alternatives for identification, I found peer, self, and parent nominations unfortunate omissions. Overall, this section is well done and, in summary, the authors offer some excellent advice: “Schools should be oriented toward collecting and analyzing data that will be used for instructional planning as opposed to simply collecting data to justify a label” (p. 69).
Another chapter on planning for instruction introduces the idea of developing a Mathematics Individualized Learning Plan (MILP) for all talented math students. Similar to an Individualized Education Plan (IEP) for special education students, this plan would be a year-long program with individualized goals, objectives, instructional materials, and assessment techniques designed by a team including the classroom teacher, the math specialist, the enrichment specialist, and the parent. A detailed MILP for a second-grade girl is included in the appendix with a list of 25 objectives including materials and activities. The numerous resources stress differentiation and high-end learning. The links to other subject areas are interesting and encourage independent projects. However, there should be a greater focus in this chapter, as well as the entire book, on assessing the interests of students and using these interests in program planning. I also think there should be more emphasis on real-world applications, i.e. creating useful products for a specific audience.
Perhaps the chapter that best illustrates what the authors in this text believe and promote as appropriate math instruction for talented students is “Flexible Pathways: Guiding the Development of Talented Students.” In this chapter, Eddins and House state “…our responsibility as educators is to offer flexible pathways along which gifted students can encounter rich ideas through challenging, nonstandard learning experiences” (p. 313). They recognize that there are different types of mathematically talented students and they make the important distinction between students who are experts at arithmetic and algorithmic applications and those who are creative problem solvers. They also emphasize that “although…much of what is good for gifted students also is good for their less-talented peers, the fact remains that gifted students have special needs that require both an enriched curriculum and a challenging delivery system” (p. 312). The chapter outlines an excellent unit for a secondary math gifted program which relates geometry transformations to matrices. It is filled with challenging activities and extensions in a variety of directions to stimulate mathematical thinking and creativity.
I recommend this text as a good resource for teachers seeking to understand how to meet the needs of gifted and talented math students within the context of the Standards. However, I offer a word of caution. Although there is a focus in many of the chapters on meeting the needs of talented math students in the regular classroom through extension activities, the actual unit of instruction presented as appropriate curriculum for gifted students is designed for an entire class of students in a special school or summer program. The reader must determine how to adapt this instruction to mathematically talented students in a heterogeneous classroom. This is not an easy task. In conclusion, since the heterogeneous classroom is becoming increasingly common at all grade levels, I would like to see a chapter added that would specifically deal with instructional strategies beyond extension activities for talented math students in the regular classroom at the elementary, middle school, and secondary levels. The MILP could be included as part of this curriculum. Key features that regular classroom educators should be made aware of include curriculum compacting, cluster grouping, interest centers, independent research projects based on student interest, mentoring, alternative assessment, and classroom management techniques.