# Conceptualizations of Students with and without Disabilities as Mathematical Problem Solvers in Educational Research: A Critical Review

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## Abstract

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## 1. Introduction

## 2. Conceptual Framework

Disability studies has arisen in the past twenty years to focus an organized critique on the constricted, inadequate, and inaccurate conceptualizations of disability that have dominated academic inquiry. Above all, the critique includes a challenge to the notion that disability is primarily a medical category. Consequently, disability studies contests the current academic division of labor in which the study of the phenomenon rests in the specialized applied fields (rehabilitation, special education, health, and so on) and the rest of the academy is largely exempt from meaningful inquiry into the subject of disability.

#### 2.1. Historical Roots of Mathematics Education

#### 2.2. Historical Roots of Special Education

#### 2.3. Research on Problem Solving

#### 2.4. Neuroscience and Education

## 3. Methods

## 4. Findings

#### 4.1. Medical Theoretical Orientation

#### 4.2. Behavioral Theoretical Orientation

#### 4.3. Informational Processing Theoretical Orientation

#### 4.4. Constructivist Theoretical Orientation

#### 4.5. Sociocultural Theoretical Orientation

#### 4.6. Sociopolitical Pedagogical Orientation

#### 4.7. Word Problems and Problem Posing

## 5. Discussion

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Academic field in which the problem solving articles were published, comparing articles with a focus on disability (Disability Set) to those articles without a focus on disability (No-Disability Set).

**Figure 2.**Methodologies of problem solving articles, comparing articles with a focus on disability (Disability Set) to those articles without a focus on disability (No-Disability Set). Percentages do not equal 100% since we were not able to code every article based on methodology.

**Figure 3.**Theoretical orientations of problem solving articles, comparing articles with a focus on disability (Disability Set) to those articles without a focus on disability (No-Disability Set). Percentages do not equal 100% since we were unable to code all articles based on theoretical orientation.

Theoretical Orientation | Definition for Coding and Keywords. |
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Medical | Abstract, title and/or keywords included terms that suggested an emphasis on understanding the biological basis of mathematical learning. Keywords included: cognitive domains, neurology, magnetic resonance imaging, cognitive sub skills, neuroscience, numerical magnitude representation, approximate number system. |

Behavioral | Abstract, title and/or keywords included terms that suggested an emphasis on understanding learning through behavior. Keywords included: behaviors, conditions, rewards, feedback, reinforcements, and training, direct instruction, explicit instruction, and mastery through repetitive practice. |

Information Processing | Abstract, title and/or keywords included terms that suggested an emphasis on understanding individual cognition as a strategic process. Keywords included: self-regulatory strategies, executive functioning, working memory, and metacognition. All generalized strategies (not specific to mathematics) were coded as information processing. We coded studies that mentioned Concrete Representational Abstract under this category. |

Constructivist. | Abstract, title and/or keywords included terms that suggested an emphasis on understanding individual learners’ understanding of mathematical concepts, understanding learning as being actively constructed through new experiences. Keywords include prior knowledge, learner conceptions, assimilation, cognitive disequilibrium, misconceptions, authentic instruction, project based learning, and inquiry-based learning. We classified studies of teachers’ mathematical knowledge for teaching in this orientation. |

Sociocultural | Abstract, title and/or keywords included terms that suggested an emphasis on understanding mathematical learning through social participation. Keywords included: discourse, identity, activity systems, figured worlds, communities of practice, semiotic mediation. |

Sociopolitical | Abstract, title and/or keywords included terms that suggested an emphasis on understanding mathematical learning through understanding of broader sociopolitical contexts, including how those contexts are reflected at the individual and classroom level. Keywords included: sociopolitical, neoliberal, racialized, power, positioning. Attention to identity groups was included in this category, as long as it was not simply a mention of the participant’s race, class, gender or disability status, but an investigation into how these categories mattered in the mathematics classroom. |

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**MDPI and ACS Style**

Lambert, R.; Tan, P. Conceptualizations of Students with and without Disabilities as Mathematical Problem Solvers in Educational Research: A Critical Review. *Educ. Sci.* **2017**, *7*, 51.
https://doi.org/10.3390/educsci7020051

**AMA Style**

Lambert R, Tan P. Conceptualizations of Students with and without Disabilities as Mathematical Problem Solvers in Educational Research: A Critical Review. *Education Sciences*. 2017; 7(2):51.
https://doi.org/10.3390/educsci7020051

**Chicago/Turabian Style**

Lambert, Rachel, and Paulo Tan. 2017. "Conceptualizations of Students with and without Disabilities as Mathematical Problem Solvers in Educational Research: A Critical Review" *Education Sciences* 7, no. 2: 51.
https://doi.org/10.3390/educsci7020051