Empowering Mathematical Minds: Educational Technology in Special Education Mathematics

Introduction

Students with disabilities often face significant challenges in mathematics education, leading to decreased confidence and motivation. Educational information technology (IT) offers powerful tools to create inclusive, collaborative, and personalized learning experiences. This article explores how technology can be leveraged to enhance mathematical understanding and skills for students with special needs, addressing declarative, procedural, and conceptual knowledge.

Understanding the Landscape of Math Difficulties

Many students with disabilities struggle to achieve math proficiency, hindering their transition to adulthood and limiting future opportunities. National assessments reveal persistent gaps in math achievement, with students with disabilities often falling behind their peers. To address this, schools must strive for academic proficiency for all students, as emphasized by the No Child Left Behind (NCLB) Act.

The term "math difficulty" encompasses various challenges faced by students at risk, disadvantaged students, and those with dyscalculia or learning disabilities. Understanding the nature of mathematical knowledge is crucial for enhancing learning. Mathematicians and cognitive scientists identify three essential types of mathematical knowledge: declarative, procedural, and conceptual.

Declarative Knowledge: This encompasses factual knowledge about mathematics, such as basic math facts (e.g., 4 + 7 = 11) or definitions (e.g., a square is a four-sided polygon with equal sides and right angles). It serves as the foundation for procedural knowledge.
Procedural Knowledge: This refers to the rules, algorithms, or procedures used to solve mathematical tasks, such as the order of operations.
Conceptual Knowledge: This goes beyond discrete facts and procedures to a deeper understanding of interrelated information. It involves understanding the relationships between different mathematical concepts.

Mathematical competency requires an interactive relationship between these three knowledge types. Technology can play a vital role in building each type of knowledge and fostering the connections between them.

Technology as an Empowerment Tool

In special education, technology can transform the classroom into a space where students feel empowered and engaged. G Suite for Education, including tools like Google Classroom, Drive, Docs, Slides, and Forms, offers a versatile platform for personalized learning.

Personalized Learning with Google Classroom and Choice Boards

Special education students often miss out on elective courses due to the need for supplemental math or reading classes. Integrating student interests into resource rooms can increase engagement and motivation. Choice boards, graphic organizers offering task options, and HyperDocs, digital lesson plans incorporating choice, allow students to personalize their learning experience.

Providing students with required tasks alongside a variety of optional tasks that they can complete at their own pace increases ownership and accountability. Students can choose what they would like to read and view. They can also choose to use Google Slides, their own YouTube video creation, a Google Form to survey others, or other technology tools to show what they’ve learned before sharing with their peers via Google Classroom. This freedom to demonstrate knowledge in their own way fosters investment in learning.

Passion Projects and "20 Percent Time"

Inspired by Google's philosophy, educators can encourage students to dedicate time to passion projects outside the curriculum. Students develop a step-by-step plan to achieve their goals and set timeframes to measure progress. This fosters organizational skills and problem-solving abilities.

For example, a student might draft a graphic novel on paper, scan it to Google Drive, and use annotation tools to add text. Technology enables students to create professional-looking projects that showcase their talents. Sharing these projects with peers through Google Slides or video recordings further enhances the learning experience.

The concept of problem solving is tough for special education students to grasp, but having them work on their own choice of project helps unlock their ability to work through challenges.

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Fostering Discussion and Collaboration

Students with disabilities may struggle with communication and group work. Technology can provide tools to aid discussion and collaboration, ensuring that all students have a voice.

Google Slides Q&A: This feature allows students to post questions anonymously during presentations, empowering quieter students to participate and encouraging presenters to address their concerns.
Verso: This Chrome app allows students to respond to questions without seeing each other's answers until they have posted their own, reducing anxiety and encouraging thoughtful contributions.

By providing alternative avenues for communication, technology can help students overcome communication barriers and engage more effectively in class discussions.

Technology-Based Innovations for Mathematical Competency

Technology-based innovations can form the basis of effective approaches to help students who have difficulty with math strive to achieve parity with their peers. A variety of technologies are available to enhance students’ mathematical competency by building their declarative, procedural, and conceptual knowledge.

Building Computational Fluency

Research suggests that fluent recall of basic math facts is crucial for developing higher-order math skills. Cognitive psychologists have discovered that humans have fixed limits on the attention and memory that can be used to solve problems. One way around these limits is to have certain components of a task become so routine and over-learned that they become automatic. Lack of math fact retrieval can impede participation in math class discussions, successful mathematics problem-solving, and even the development of everyday life skills. Rapid math-fact retrieval has been shown to be a strong predictor of performance on mathematics achievement tests.

The acquisition of math facts in most normally developing children generally progresses from a deliberate, procedural, and error-prone calculation to one that is fast, efficient, and accurate. In contrast, most students with math difficulty, along with those lacking consistent math fact instruction, show a serious problem with respect to the retrieval of elementary number facts.

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To address this, educators have turned to technology to help students achieve fluency in math facts. However, early studies found that computerized drill and practice was ineffective because students were practicing procedural counting strategies instead of developing the ability to recall facts from memory.

The FASTT (Fluency and Automaticity through Systematic Teaching with Technology) approach, developed by Hasselbring and Goin, assists students in developing declarative fact knowledge through these design features:

Systematic teaching of strategies: Teaches strategies that enable students to quickly associate a problem with its answer.
Metacognitive strategies: Teaches students to monitor their own learning and understanding to create a mental link between facts and answers.
Motivation: Uses motivational techniques to encourage students to focus on learning the facts.
Appropriate pacing: Paces instruction to ensure that students are challenged but not overwhelmed.
Ongoing assessment: Provides ongoing assessment to track student progress and adjust instruction accordingly.
Computer monitoring of student performance: Monitors student performance to identify areas where they need additional support.

FASTT Math, a software program incorporating these principles, has been shown to be effective in developing mathematical fluency when used consistently. The key to success appears to lie in the consistent use of the program. As expected, students who use the program regularly do much better than students who are irregular users.

Addressing Procedural Knowledge

Technology can assist with converting mathematical symbols and notations, calculating mathematical operations, and inputting/organizing data.

Enhancing Conceptual Knowledge

Technology can be used to build conceptual understanding, problem-solving, and reasoning skills.

Overcoming Barriers to Technology Integration

While technology offers numerous benefits, several barriers can hinder its effective integration into special education mathematics:

Lack of Time: Teachers often cite a lack of time for training and implementation.
Cost: The cost of software and hardware can be a significant barrier.
Lack of Technology: Insufficient access to technology in the classroom can limit its use.

To overcome these barriers, administrators should provide ongoing training and support for technology integration.

Collaboration and Professional Development

NCTM and CEC believe that for students with disabilities, mathematical learning is a shared responsibility between mathematics educators, special educators, administrators, related service providers, families, and other interested partners who must work within the limits of their professional knowledge and skills. It is critical to align what mathematics students learn, how they will learn it, and how they will be assessed.

Core or Tier 1 instruction should reflect the principles of Universal Design for Learning (UDL) by proactively considering barriers to engagement, representation, and expression to facilitate student access to grade level or course content. Collaboration and co-teaching are important responses to address these different teacher knowledge bases.

Teacher content knowledge and pedagogical content knowledge are important to facilitate successful learning. Student learning is improved when general and special education teachers engage in collaboration and co-planning that draws from, coordinates, and extends teachers’ areas of expertise.

Using multiple representations is essential for making sense of mathematics across all domains. For example, including Concrete-Semiconcrete-Abstract (CSA) simultaneously focuses instruction on the fluent movement among concrete representations/models (e.g., manipulative materials) and semi-concrete (e.g., drawings, sketches, graphs) and abstract incorporating symbols, numerals, equations, mentally solving problems, or using stories with mathematical ideas.

True collaboration for effective intervention in a preventative model (e.g., Response to Intervention, Multi-Tiered System of Supports) requires advanced planning between the special and mathematics educators. Before a new lesson, the two experts come together to determine the foundational knowledge needed to effectively access the more sophisticated ideas ahead.

Fostering Asset-Based Learning Environments

Students with disabilities benefit from asset-based learning environments where they are recognized and positioned as capable and competent mathematics learners. Educators’ beliefs and expectations about students influence their instructional decisions and student learning outcomes. Asset-based environments must leverage the knowledge students bring from family and community spaces. Students must have a sense of belonging with adults, peers, and parents. Students with disabilities benefit from opportunities to develop a positive math identity that connects to their perspectives and experiences. Mathematics learning is mediated through students’ opportunities to participate in, perform, and use mathematics in meaningful ways.

Recommendations for Educators and Researchers

Require special education majors to take a minimum of one mathematics methods course with field-based learning opportunities and mathematics content courses directed specifically to PK-12 mathematics.
Provide co-teaching learning opportunities and field-based experiences in which mathematics educators and special educators collaborate.
Plan proactively using a preventative model for instruction.
Position students with disabilities as valuable owners of and contributors to the mathematics being learned.
Provide paired time for students to share and rehearse their thinking and ideas in multimodal ways before moving to a whole group discussion.
Provide a variety of interactive learning experiences.
Use flexible grouping structures to cultivate a community of learning.
Ensure the delivery of ongoing professional learning on evidence-based mathematics practices, including practical, hands-on experiences.
Encourage collaborative research with specific cross-disciplinary language in requests for proposals.
Engage in cross-disciplinary research (e.g., build relationships with cross-disciplinary colleagues, read literature across fields).
Design and implement a conference for mathematics education and special education researchers to identify an agenda for action for future collaborative research.
Support the publication in professional journals of co-authored articles through active recruitment of cross-disciplinary teams.
Create cross-disciplinary teams to design and deliver webinars and other professional learning experiences.
Build the resources for classroom teachers to support this cross-disciplinary work.
Identify shared language to support better communication and an understanding of significant dimensions of teaching, learning, and research in both mathematics education and special education.

The Role of Teacher Knowledge and Beliefs

Teachers’ knowledge, beliefs, and self-efficacy play a critical role in technology integration. Technology-related knowledge, encompassing knowledge of content and pedagogical affordances of technology, appropriate uses of technology with respect to learners, and existing technological tools, is essential.

Beliefs about technology integration, including pedagogical orientation, self-efficacy beliefs, and valuative beliefs, also influence technology use. Positive beliefs about the value of technology in the classroom are associated with increased adoption of technology integration.

Self-efficacy beliefs, reflecting teachers’ confidence in their ability to learn and use technology for educational purposes, are strong predictors of technology use and integration.

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