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While deficits for students with learning disabilities (LD) are prevalent in almost all aspects of mathematics, difficulty in the application and understanding of problem-solving tasks are much more challenging to remediate than computational and procedural skills. Given the complexities involved in authentic problem-solving activities emphasized in current mathematics standards and the inherent challenges presented to students with LD, the importance of using strategies and techniques guided by evidence-based practices is paramount. Yet, ineffective instructional strategies for problem solving are still widespread in both mathematics curricula and available teacher resources. In this chapter, we provide a description of a commonly used ineffective problem-solving strategy (i.e., the keyword strategy), an overview of the keyword research, and an explanation for its ineffectiveness. We conclude with a description of three evidenced-based problem-solving approaches and practices that significantly improve the mathematical performance of students with LD.

The conceptual framework of mathematical modeling (e.g., Lesh & Doerr, 2003) is a vital area in mathematics education research, and its implementation has potential for deeply involving children in integrated and meaningful learning. In mathematical modeling learners are active agents in content-integrated, real-world problem solving. This emphasis on integrating multiple content areas to answer big questions, the pursuit of mathematical modeling, descends from Dewey’s work. We present the definition, principles, and design of modeling practices for readers who may be familiar with early childhood curriculum but less so with using modeling for learning. We explore the application of mathematical modeling to early childhood classrooms and its compatibility with early childhood pedagogies and philosophies. Young children may often be underestimated, assumed to be unable to pose big questions that can be answered through activity, experience, and data; but we discuss how young children can be engaged in problems through mathematical modeling. Finally, as preservice teacher educators, we discuss preparing preservice and in-service teachers for modeling in their classrooms. We offer examples and guidance for early childhood teachers to engage in authentic practice – meeting children where their interests are and creating integrated problem-solving experiences.

We conducted a comprehensive review of the literature on mathematical interventions for secondary students with learning disabilities (LD) and the identified studies were analyzed in light of the mathematical practices as outlined by the Common Core State Standards Initiative (CCSSI, 2010). Results indicated that Standard 2, reason abstractly and quantitatively, was the most common practice addressed. Furthermore, the studies that examined the effects of Enhanced Anchored Instruction (EAI) contained the most practice standards of the studies reviewed. However, the majority of studies provided evidence of addressing only one practice standard. It is recommended that future studies need to address these standards and/or be more explicit in the inclusion of the standards.

Problems with learning disabilities are life affecting (Murray, C., Goldstein, D. E., & Nourse, S. (2000). The postsecondary school attendance and completion rates of high school graduates with learning disabilities. Learning Disabilities Research and Practice, 15, 182–186; Westby, 2000; Rojewski, 1999a; Hall et al., 2002). The impact of poor mathematical skills on employment prospects is even bigger than the influence of poor reading skills (Dowker, 2005). After an introduction on the definition, prevalence and impact, gender and birth order, subtypes, comorbidity and assessment of cognition and metacognition in mathematical learning disabilities, we will focus on the features of mathematical learning disabilities in adolescence and adulthood and on the STI(mulation), CO(mpensation), R(emediation) and DI(spensation) (STICORDI) devices to help students with mathematical learning disabilities. With such devices “reasonable” adjustments are provided to ensure that disabled students are not placed at a substantial disadvantage compared to non-disabled students.

This chapter reviews research on math disabilities (MD) from two different points of view: Italian and American. Our goal is to gain consensus on identifying the cognitive deficits that underlie problems associated with MD as well as to provide an overview of some of the instructional approaches to remediate these deficits. The review outlines similarities and differences in the research perspectives between the two countries. Although the results show some consensus on the identification of MD and the cognitive mechanisms associated with this deficit (e.g., working memory), some differences remain between the two research perspectives (e.g., incidence of MD).

Mathematics can be a challenging content area for all students and especially for students with disabilities. Assistive technology can support the access, participation and achievement of students with disabilities in mathematics in general and in inclusive mathematics settings in particular. In this chapter, assistive technology to academic and functional mathematics will be discussed; particularly, manipulatives, calculators and other technology-mediated mathematics interventions (e.g., apps or computer programs) will be highlighted.

Students with mathematics-related learning difficulties (MLD) experience difficulties in many areas of mathematics achievement; without intervention, these difficulties will persist. In this chapter, I first review research examined cognitive processes deficits of MLD. Because difficulties in learning mathematics are presumably due to these cognitive deficits, findings of these studies can shed light on developing effective intervention programs. Second, using Response to Intervention (RTI) as a framework to distinguish the intensity level of intervention, I review findings from existing Tier 2 and Tier 3 intervention studies and synthesize the instructional approaches used in these studies as well as the factors researchers used to intensify the intervention. Finally, Data-Based Individualization (DBI), a systematic approach to intensify intervention, commonly used at the Tier 3 level, is review. Suggestions for future research directions for intensive mathematics intervention are also provided.

This chapter synthesized some of the published literature comparing the cognitive functioning of children with math disabilities (MD) with (1) average achieving children, (2) children with reading disabilities (RD), and (3) children with comorbid disabilities (RD+MD). Twenty-one studies, which yielded 194 effect sizes (ESs), indicated that average achievers outperformed children with MD on measures of verbal problem solving (M=−0.58), naming speed (M=−0.70), verbal (M=−0.70) and visual-spatial working memory (WM, M=−0.63), and long-term memory (LTM, M=−0.72). The results further indicated that children with MD outperformed children with combined disabilities on measures of literacy (M=0.75), visual-spatial problem solving (M=0.51), LTM (M=0.44), short-term memory (STM) for words (M=0.71), and verbal WM (M=0.30). Children with MD could only be clearly differentiated from children with RD on measures of naming speed (−0.23) and visual-spatial WM (−0.30). The magnitude of ESs was persistent across age and severity of math disability. Hierarchical linear modeling (HLM) indicated that the magnitude of ES in overall cognitive functioning between MD and average achievers was due to verbal WM deficits when the effect of all other variables (e.g., age, IQ, reading level, other domain categories) were partialed out. The results are discussed within the context of defining MD by level of severity of WM abilities.