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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.

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.

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).

Before 2011, student performance rates in college algebra and trigonometry at North Carolina A&T State University (NCA&TSU) were consistently below 50%. To remedy this situation, the Mathematics Department implemented the math emporium model (MEM) instructional method. The underlying principle behind MEM is that students learn math by doing math (Twigg, 2011). The MEM requires students to work on math problems and spend more time on material that they do not understand while allowing them to spend less time on material that they do understand. Also, students receive immediate feedback on problems from teaching assistants as they work through their online assignments. After implementing the MEM, student pass rates improved for both the MEM and traditional sections. Data to date also show that female students outperform male students in both instructional models. Further study is needed to determine the factors that have caused improvement in pass rates in addition to the implementation of the MEM. Some important lessons learned by the NCA&TSU math faculty from implementing the MEM into the college algebra and trigonometry courses are that successful implementation requires a long-term commitment, internal and external collaborations, and the collective ability to determine what works for the local setting.

Amidst a worldwide concern with teacher quality, recent teacher reforms often focus on how to certify teachers, how to evaluate teachers, how to recruit the best and brightest people to be teachers, and how to fire bad teachers. The political discourse of these policy reforms oftentimes depicts teachers as largely inactive transmitters of knowledge and does not recognize the agency they have in affecting standards. Yet, such a narrow framework may suppress teacher pedagogy, practices, and also teacher beliefs. In this chapter, we seek to understand the extent that two types of math teacher beliefs – traditional and constructivist orientations – are related to national cultural factors. In doing so, we test both “culturist” and “neo-institutional” hypotheses by observing how those beliefs vary across different nations.

This chapter reviews the intervention research literature – particularly interventions deemed evidence-based – for students with intellectual disability across academic and life-skills instruction. Although the focus of this chapter is the spectrum of students covered under the term “intellectual disability,” the majority of research on evidence-based interventions for students with intellectual disability focus on students with more moderate and severe intellectual disability, rather than students with mild intellectual disability. The majority of the interventions determined to be evidence-based within the literature for students with intellectual disability – across both academic and life skills – tend to be those that fall within the purview of systematic instruction.

This chapter provides a synthesis of the research project which investigated whether or not the most recent mathematics curriculum reform has reached the classroom and influenced classroom practice and student learning in the mainland China. Three types of evidence for change as a result of the curriculum reform were examined. These included the beliefs and perceptions of teachers about learning and teaching mathematics, the cognitive features of learning tasks and of classroom interaction that were implemented in classroom, and student learning outcomes. Two groups of elementary math teachers and their students participated in the study. One group had participated in the reform implementation in classroom for several years, and the other group had used the conventional curriculum when the project was conducted in 2005. About 150 videotaped class sessions were analyzed from 58 classrooms of the two groups. Survey methods were used to probe the changes in the beliefs and perceptions of teachers about teaching and learning mathematics. The student learning outcomes were assessed for three times with multiple measures of mathematics achievement. Findings of the project provide the converging evidence that the curriculum reform has resulted in some of the expected changes. Reform teachers were more likely to hold a dynamic view of mathematics and to indicate the importance to provide students the learning opportunity to hypothesize, to proof, and to communicate in learning mathematics. The reform classrooms used more learning tasks with higher cognitive demands. The teachers in the reform classrooms asked more questions that required students to describe procedures leading to their answers and the students in the reform classrooms raised more questions in learning mathematics. Students of the reform classrooms showed to have achieved a relatively more balanced development in different cognitive areas of mathematics achievement.

As early as 1928, Lewis Meriam’s research report to the Secretary of Interior indicated that American Indian and Alaska Native (AI/AN) schools were understaffed, had irrelevant curricula, and employed under qualified teachers. There continues to be a categorical need for professionally developed curriculum materials that reflect the local culture and language of AI/AN students. There is an equivalent need for instructional strategies that can succeed with AI/AN students. Over the past decade, reports (Deyhle & Swisher, 1997; Pavel, 1999; Swisher & Tippeconnic, 1999) have reinforced the need for educational programs for AI/AN schools and communities that are based on local culture and employ a group’s vernacular language as a part of schooling. This is a reversal from earlier more assimilationist models of education, which have been promulgated by the federal government through its policy on first language (other than English) and cultural exclusion. This call for programs based on culture and vernacular language is due, in part, to the persistent nationwide gap in the academic performance of AI/AN students and their non-native peers (Berlak, 2001).

Being numerate involves the ability to use mathematical knowledge meaningfully across multiple contexts allowing us to order our day, optimise our health and well-being, and function in technology rich environments. Addressing numeracy from the early years of learning, and across all areas of the education curriculum, is key to lifelong learning and quality of life. Being numerate, however, is more than mathematical knowledge; the language that underpins it heavily impacts how we become numerate. This chapter examines numeracy, or mathematical literacy, investigating how literacy can include, and exclude, students from opportunities to learn at school and beyond. This chapter will also examine how numeracy can be used to provide access to educational curricula and personalised goals for students with diverse learning needs in ways that many have ignored.

Over the past 20 years, research on the role of mathematical proficiency in academic and economic success has proliferated. Understanding how mathematical development and learning can be fostered in both in- and out-of-school settings is key to ensuring widespread numerical literacy. Much of what is known about how children develop mathematical knowledge and the educational practices that support such development come out of high-income countries. Widening the lens of research to include children and youth across languages, cultures, and contexts is essential to informing practices and policies across the globe. From pre-primary through primary grades, this chapter examines the increasing emphasis on supporting mathematical development in early childhood, efforts to move away from memorization-based instruction toward support of conceptual understanding, out-of-school influences on mathematical learning, and promising instructional practices.