Introduction
Educational and career opportunities today demand high levels of mathematics proficiency, including algebra proficiency (Mathematics Learning Study Committee 2001). State standards and high-stakes assessments reflect these demands. However, evidence suggests that the current pedagogical and curricular approaches students receive in U.S. schools fall short of helping all students think mathematically. Fortunately, empirical and logical analyses of the changes necessary to progress to universal mathematical proficiency have been detailed (MLSC 2001; Schmidt, Houang, and Cogan 2002). Developing more effective curriculum and pedagogical approaches, while a complex process requiring diligence, is critical and possible. One element that is lacking in many contemporary curricular programs is an attention to the needs of low-performing students, including students with disabilities. In particular, secondary mathematics is often considered to be unattainable for students with learning disabilities. Making mathematics more accessible must be a goal in new program and pedagogical development.

Students who struggle with mathematics, including students with disabilities, often experience developmental differences that result in barriers to achievement in the mathematics classroom (Chard and Kame'enui 1995). There is reason to believe, however, that many—if not all—learners with disabilities can meet high achievement standards if our curricula, curricular programs, and pedagogies provide differentiated instruction to meet individual needs.

Teachers are often convinced that students with disabilities possess individual differences that require them to make special accommodations in the classroom. Special education, as defined by the Individuals with Disabilities Education Act, includes "specially designed instruction to meet the unique needs" of the learner. Frequently, however, it is assumed that all instruction for students with disabilities must be specially designed and, therefore, is impossible to provide in the general education classroom. On the contrary, specially designed instruction is special education. Rather than redesigning the content of general education, the focus of instruction provided to students in the general education classroom should be on accessibility. To make mathematics instruction accessible for the widest range of learners, we must consider learner characteristics that represent some of the primary barriers to learning. Students who experience learning difficulties are often challenged by memory and conceptual difficulties, background-knowledge deficits, linguistic and vocabulary difficulties, and strategy knowledge and use. The following discussion addresses these four barriers and offers teaching strategies to address their needs.

Memory and Conceptual Difficulties
Students with memory and conceptual difficulties experience problems remembering key principles or understanding the critical features of a particular concept. For example, while they may be able to solve an equation when given the value of a particular variable, they may not understand the concept of a linear function. Simultaneously, they often attend to irrelevant features of a concept or problem, paying attention to information that is interesting but designed to be distracting. Students with memory or conceptual problems benefit from instruction that initially introduces mathematical concepts and principles explicitly with a high degree of clarity and continues to reinforce the most significant topics (Gersten, Chard, Baker, Lee, and Fuchs 2002). By optimizing the clarity of initial instruction, students with disabilities focus on the critical conceptual features rather than irrelevant features. Explicit instruction also includes making the content relevant. Mathematics becomes relevant, and thus accessible for learning, when descriptions and examples go beyond procedures to include not only how we solve problems but "why" we do what we do mathematically. The following guidelines should be considered in designing instruction to address the needs of students who experience memory and conceptual difficulties in mathematics:

• Thoroughly develop examples of concepts, principles, and strategies.
• Gradually develop knowledge and skills that move from simple to complex.
• Provide counter-examples of concepts, principles, and strategies to illustrate the relevant mathematical features.
• Include a planful system of review.

Background-Knowledge Deficits
Students with deficits in background knowledge experience a wide range of problems in learning complex mathematical content. These deficits might stem from a lack of number sense or from inadequate teaching and learning of skills and strategies that are fundamental to later mathematics learning. Students experiencing deficits in background knowledge benefit from instruction that includes pre-teaching opportunities to ensure that students will be successful with new content; assessment of background knowledge; and differentiated instruction and practice to scaffold learning.

Linguistic and Vocabulary Difficulties
Students with linguistic and vocabulary difficulties may be challenged at two levels. First they may be unable to distinguish among the important symbols in mathematics that represent key concepts and principles. Additionally, many students struggle with mathematical vocabulary. This is, in large part, because of an underdeveloped knowledge of morphemes and/or word-recognition skills. Students with linguistic and vocabulary challenges benefit from instruction that includes attention to defining and using mathematical symbols in a wide variety of contexts and with a high degree of precision. Instruction should include careful attention to the description and development of vocabulary knowledge, and encourage the use of mathematical vocabulary in classroom discourse. Finally, students should have plenty of opportunities to talk mathematically and receive feedback regarding their use of terminology.

Strategy Knowledge and Use
Many students, even typically developing learners, experience difficulties with strategic learning. Consequently, problem solving poses inordinate challenges. Not only do they experience difficulties working through the steps of a strategy, but they often do not understand which strategy to apply and when. Students experiencing difficulties with strategy knowledge and use benefit from teaching that includes modeled instruction of important problem-solving strategies followed by verbal rehearsal of the strategy steps. They should also receive deliberate attention to the "how" as well as the "why" and "when" of strategy application. Additionally, instructors should use mid-level strategies that work rather than generic problem-solving approaches.

Conclusion
The need to develop a high level of mathematical proficiency for the broadest range of learners dictates that curricular materials be designed that support teachers' efforts to teach complex mathematical knowledge. These materials must reflect our knowledge of the characteristics shared by many struggling learners.

References
Chard, D. J., and E. J. Kame'enui. 1995. Mathematics instruction for students with diverse learning needs: Heeding the message of the Cheshire Cat. Focus on Learning Problems in Mathematics 17, no. 2: 24–38.

Gersten, R., D. J. Chard, S. Baker, D. S. Lee, and L. S. Fuchs. 2002. Experimental and quasiexperimental research on instructional approaches for teaching mathematics to students with learning disabilities. Technical Report #2002–01. Washington, DC: Office of Special Education Programs.

Mathematics Learning Study Committee. 2001. Adding it up. Washington, DC: National Academy Press.