`Mikyung Shin`

(Assistant Professor, West Texas A&M University)
`Jiyeon Park`

(Assistant Professor, Eastern Kentucky University)
`Kimberly Seale`

(Special Education Teacher, Model Lab School)
`Contact`

: mikyung.shin@wtamu.edu

`Slides`

: https://mshin77.github.io/CEC-2024

Council for Exceptional Children 2024 Annual Convention - March 14, 2024

`Agenda`

“Technology” for Teaching Mathematics

Interactive Technology in Math

Types of Interactive Visual Models

Examples and Benefits of Interactive Visual Models

Evaluating Accessible Designs

Case Study on Synchronous Online Instruction

Three-Level Multilevel Modeling for Single-Case Data

`"Technology" for Teaching Mathematics`

**Associated words**with “learning disability,” “mathematics learning disability,” and “dyscalculia”- 488 studies published from 1980 to 2021.
- correlation > .10, 102 nodes and 120 edges.

Dataset: https://github.com/mshin77)

CAI = computer-assisted instruction; EAI = enhanced anchored instruction.

`Interactive Technology in Math`

A dynamic visual model operational in environments like the web.

Initially developed through Flash or Java Applet programs in 1990s.

Adaptable in various forms for extension, transformation, and selection.

Can be employed for conceptual understanding in teaching and learning mathematics.

Offers interactive opportunities for diverse mathematical learning.

HTML5 was released in its public version in January 2008.

With the introduction of HTML5 web standards, became available on mobile devices.

`Types of Interactive Visual Models`

`Examples of Interactive Visual Models`

Source: Shin et al. (2023, p. 201)

`Benefits of Interactive Visual Models`

- Content-specific visual models for targeted mathematics concepts and skills
- Feedback for students to facilitate memory retention
- Free and ready-to-use online materials
- Multiple opportunities for practice
- Integration with other online tools (e.g., digital games, augmented reality, virtual reality)

Augmented Reality - Overlay on the physical learning environment

Source: GeoGebra

`Evaluating Accessible Designs`

Evaluate instructional design features through Mathematics Application Usability Scale (MA-US)

Universal Design for Learning (UDL)

Information, Interface, and Interaction (3Is) design features

`Case Study on Synchronous Online Instruction`

Three fifth-grade students with learning disabilities

Employing a multiple probe across participants single-case design

15 fraction lessons via video conferencing programs

`Adaptation from MSTAR to Online Interventions`

`Key Lesson Features and Results`

- Lessons on Equivalent Fractions, Adapted from MSTAR Interventions (The University of Texas at Austin, 2011)
- Use of digital materials (i.e., virtual manipulatives, interactive whiteboard, and online assessments)
- Explicit instructions (i.e., lesson sequence of Introduction, Demonstration, Guided Practice, Independent Practice, and Closure)
- Students’ performance improved as the intervention was introduced.
- However, the extent and maintenance of improvement varied.

`Visual Analysis Results`

Source: Park et al., (2023)

`Three-Level Multilevel Modeling for Single-Case Data`

35 studies published since 2000 on the effects of using virtual manipulatives for students with disabilities

Case-level variables: grade and disability

Study-level variables: pre-training purpose, Instructional method, type of virtual manipulative, Visual model

Source: Shin et al. (2021)

`Multilevel Data Structure`

Single-case design data are hierarchically structured and can be displayed using three-level multilevel modeling (Baek et al., 2022; Moeyaert et al., 2021; Pustejovsky & Ferron, 2017).

The levels examine repeated measurement occasions (Level 1) nested within cases (Level 2) and cases nested within studies (Level 3).

Applied a piecewise linear regression approach by separately modeling time trends in the baseline and intervention phases (Singer & Willett, 2003).

`Level 1 equation`

\[ \begin{aligned} Y_{i j k}=& \beta_{0 j k}+\beta_{1 j k} \text { Intervention }_{i j k} \\ &+\beta_{2 j k} \text { Time }_{i j k}^{\prime} \times \text { Intervention }_{i j k}+e_{i j k}\\ & \text { with } e_{i j k} \sim N\left(0, \Sigma_e\right) \end{aligned} \]

\(y_{i j k}\) = mathematical accuracy at the measurement occasion, \(i\) th \((I=0,1, \ldots I)\), for the \(j\)th case\((j=1,2, \ldots J)\) in study \(k\); \(\beta_{0 j k}\) = baseline level; \(\beta_{1 j k}\) = change in level when the intervention phase starts (immediate effect); \(\beta_{2 j k}\) = change in slope between the baseline and the intervention phase; and \(e_{i j k}\) is an error term that is assumed to be independent and is normally distributed with a mean of 0 and variance of \(\sigma^2\).

Random effects of immediate outcomes and trends during the use of virtual manipulatives were examined across various cases and studies.

The interactions between each intervention effect and its moderating variables were investigated.

`Key Findings`

- Both the average immediate effect and trend during the intervention were statistically significant.
- The average immediate effect varied significantly by student grade, disability type, developer, device, type of virtual manipulative, and visual model embedded in virtual manipulatives.
- Neither student characteristics nor intervention feature–related moderators significantly influenced the average trend during the use of virtual manipulatives.
`Deviations in the moderation effects corroborate the need to examine trends during the use of virtual manipulatives, even after the immediate effects have been observed (Shin et al., 2021, p. 431)`

`Conclusion and Future Directions`

- The methodology for identifying evidence of interventions can vary based on research design and purpose.
- Visual analysis of graphical data is necessary to validate the functional relationship and intervention effects in the case study.
- Moderation effects can be further examined through single-case and meta-analysis of individual participant data.