In the United States, students with and without disabilities are performing below grade-level standards in math and demonstrate low mathematics literacy. The majority of 4thand 8th-grade students, with and without disabilities, are performing at or below basic levels in math (National Center for Education Statistics [NCES], 2013); approximately 26% of 15-year-old students in the United States failed to demonstrate math reasoning and scored at the lowest level on the Program for International Student Assessment (PISA) 2013. PISA assesses the degree to which 15-year-old students "can understand, use, and reflect on mathematics for a variety of real-life problems and settings that they may not encounter in the classroom" (Kelly et al., 2013, p. 1). Many students in general are not able to engage in math reasoning, and this hinders their ability to elaborate and reconstruct problems, look for inconsistencies in proposed solutions, make modifications to their approach, apply their current understanding in novel contexts, and reflect on their processes (Kelly et al., 2013; Resnick, 1987).
Being literate in mathematics involves more than manipulating mathematical symbols and following mathematical rules to solve equations (Ojose, 2011; Resnick, 1987; Steen, 2009). Mathematics literacy encompasses a range of competencies and functions, from solving problems found in daily life (e.g., paying bills, following a bus schedule, or analyzing election results) to solving trigonometry and calculus problems (e.g., calculating the trajectory of a rocket).
Despite the low performance of students in mathematics, teachers receive little to no professional development on how to provide evidence-based instruction in mathematics instruction and intervention (National Mathematics Advisory Panel [NMAP], 2008). Therefore, it becomes important to apply research-supported instructional approaches that facilitate contextual learning of both mathematical content and math reasoning as states implement new and updated standards, such as the Common Core State Standards for Mathematics (CCSSM, 2010).
Reconciling Rigorous Standards for Students Who Struggle With Math
With the implementation of the CCSSM (2010), a new challenge emerges for teachers of students with disabilities. One of the most marked changes is the emphasis on paired mathematics procedures and reasoning. Not only are students expected to learn the content and the procedures for calculating an answer, they also must explain their mathematical reasoning during problem-solving (CCSSM, 2010). To help guide teachers, the CCSSM provides eight math practice standards for developing students' approach to reasoning through their problem-solving process (CCSSM, p. 8):
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.
These practices build students' mathematics literacy, providing them with a foundational knowledge base from which they can synthesize novel information, use language to articulate their math reasoning processes, and apply these higher-level skills when solving real-world problems (NMAP, 2008). The challenge is how to increase mathematics literacy and reasoning skills for students who struggle to master foundational math concepts, such as numeracy, or who...