Distinguishing schemes and tasks in children's development of multiplicative reasoning

We present a synthesis of findings from constructivist teaching experiments regarding six schemes children construct for reasoning multiplicatively and tasks to promote them. We provide a task-generating platform game, depictions of each scheme, and supporting tasks. Tasks must be distinguished from children’s thinking, and learning situations must be organized to (a) build on children’s available schemes, (b) promote the next scheme in the sequence, and (c) link to intended mathematical concepts

Using Visual Modeling Tools to Reach Students with Learning Disabilities

Teachers can use electronic visual modeling tools to help students with learning disabilities visualize and understand mathematical concepts such as proportions, dilations, and scale factors. In this article, the authors describe strategies for using static and dynamic visuals for supporting the memory and processing of students with learning disabilities as they engage in challenging mathematics

Distinción de esquemas y tareas en el desarrollo del razonamiento multiplicativo de los niños

We present a synthesis of findings from constructivist teaching experiments regarding six schemes children construct for reasoning multiplicatively and tasks to promote them. We provide a task-generating platform game, depictions of each scheme, and supporting tasks. Tasks must be distinguished from children’s thinking, and learning situations must be organized to (a) build on children’s available schemes, (b) promote the next scheme in the sequence, and (c) link to intended mathematical concepts.Presentamos una síntesis de hallazgos de experimentos de enseñanza constructivistas en relación con seis esquemas que los niños construyen para razonar multiplicativamente y tareas para promoverlos. Proveemos una plataforma de juego generadora de tareas, descripciones de cada esquema y tareas para apoyarlos. Las tareas deben distinguirse del pensamiento de los niños, y las situaciones de aprendizaje deben organizarse para que (a) se basen en los esquemas que los niños tienen disponibles, (b) promuevan el siguiente esquema en la secuencia y (c) se relacionen con los conceptos matemáticos pretendidos.This research was supported by the US National Science Foundation under grant DRL 0822296, which funded the activities of the Nurturing Multiplicative Reasoning in Students with Learning Disabilities in a Computerized Conceptual-Modeling Environment (NMRSD) project. The opinions expressed in this article do not necessarily reflect the views of the Foundation

Applying the concrete-semiconcrete-abstract instructional sequence in model-based teaching to facilitate the learning of area and volume by students with mild intellectual disability

In the current educational climate of IDEA 2004 and No Child Left Behind, teachers are required to find methods to give all students, including students with mild intellectual disability, access to the general education curriculum. The purpose of this study was to investigate the effects of instruction integrating the concrete-semiconcrete-abstract teaching sequence into model-based problem solving to teach area and volume to sixth grade students with mild intellectual disability. This study employed a multiple baseline design to establish the functional relationship between the intervention and students\u27 performance on area and volume problems. The participants improved at solving area and volume problems and showed some success in making generalizations about area and volume concepts

An Interdisciplinary Learning Community of Education and Psychology Majors

The researchers conducted a qualitative case study to describe the experiences (over the course of a semester) of an interdisciplinary team of three special education and three psychology undergraduates who participated in a relational learning community and a graduate student who designed and facilitated this learning community. An Associate Professor and special education researcher oversaw and co-facilitated the project. The design of the learning community promoted the building of rapport and trust among the group members and the progress of the group toward a common goal of incorporating principles from psychology to develop teaching strategies for students who are struggling in math and experiencing severe math anxiety. Gathering more frequent and individualized feedback would have helped the learning community facilitator make some key adjustments earlier in the project, but the incorporation of rapport building activities that supported trust and collaboration among the group was supportive of group progress toward a common goal. We learned key lessons about how to design and implement a learning community that can be applied to the field of education, interdisciplinary collaboration, and other contexts

A Rationale for the Use of Case Reports in Special Education: The Significance of Detailed Descriptions of Assessment and Intervention Scenarios for Bridging the Research-to-Practice Gap

Case reports make up a significant part of the medical literature by documenting unique clinical scenarios or exemplary treatment practices from which real-life lessons can be learned. But while such studies play an essential role in medical research, they rarely appear in special education journals. Competently assessing and instructing children, adolescents, and adults with special needs is complicated. Case reports that explicitly illustrate how to carry out such challenging tasks could be just as helpful in special education as they are in various medical fields. In this paper, we argue for the importance of such accounts and provide guidelines for how to structure them as a sound scholarly outlet

Interpretations of slope through written and verbal interactions between a student and her tutors in algebra 1

There is an ongoing need to support students’ learning of linear functions, and the study of slope makes up a foundational component of this learning. We applied techniques from systemic functional linguistics to document the meanings that were established through spoken interaction between a student and her tutors during discussions of slope. We found that, while fraction notation gave the student and tutors a common reference point to discuss slope, it also masked important differences in how the student interpreted slope compared to her tutors. The findings of this analysis imply the need not only to attend to how students quantify slope, but also whether students recognize slope as an attribute of a line.Existe una necesidad continua de apoyar el aprendizaje de los estudiantes sobre las funciones lineales y el estudio de la pendiente es un componente fundamental de este aprendizaje. Aplicamos técnicas de lingüística funcional sistémica para documentar los significados que se establecieron a través de la interacción oral entre una alumna y sus tutores discutiendo la pendiente. Descubrimos que, aunque la notación de fracciones le dio a la estudiante y a los tutores un punto de referencia común para discutir la pendiente, también ocultó diferencias importantes en cómo la estudiante interpretó la pendiente en comparación con sus tutores. Los resultados de este análisis implican la necesidad no solo de atender la forma en que los estudiantes cuantifican la pendiente, sino también si los estudiantes reconocen la pendiente como atributo de una línea

Predicting Correctness of Problem Solving in ITS with a Temporal Collaborative Filtering Approach

Collaborative filtering (CF) is a technique that utilizes how users are associated with items in a target application and predicts the utility of items for a particular user. Temporal collaborative filtering (temporal CF) is a time-sensitive CF approach that considers the change in user-item interactions over time. Despite its capability to deal with dynamic educational applications with rapidly changing user-item interactions, there is no prior research of temporal CF on educational tasks. This paper proposes a temporal CF approach to automatically predict the correctness of students’ problem solving in an intelligent math tutoring system. Unlike traditional user-item interactions, a student may work on the same problem multiple times, and there are usually multiple interactions for a student-problem pair. The proposed temporal CF approach effectively utilizes information coming from multiple interactions and is compared to i) a traditional CF approach, ii) a temporal CF approach that uses a sliding-time-window but ignores old data and multiple interactions and iii) a combined temporal CF approach that uses a sliding-time-window together with multiple interactions. An extensive set of experiment results show that using multiple-interactions significantly improves the prediction accuracy while using sliding-time-windows doesn’t make a significant difference

Detecting Students’ Off-Task Behavior in Intelligent Tutoring Systems with Machine Learning Techniques

Identifying off-task behaviors in intelligent tutoring systems is a practical and challenging research topic. This paper proposes a machine learning model that can automatically detect students\u27 off-task behaviors. The proposed model only utilizes the data available from the log files that record students\u27 actions within the system. The model utilizes a set of time features, performance features, and mouse movement features, and is compared to 1) a model that only utilizes time features and 2) a model that uses time and performance features. Different students have different types of behaviors; therefore, personalized version of the proposed model is constructed and compared to the corresponding nonpersonalized version. In order to address data sparseness problem, a robust Ridge Regression algorithm is utilized to estimate model parameters. An extensive set of experiment results demonstrates the power of using multiple types of evidence, the personalized model, and the robust Ridge Regression algorithm