Search for: All records

An algebraic model uses a set of algebraic equations to describe a situation. Constructing such models is a fundamental skill, but many students still lack the skill, even after taking several algebra courses in high school and college. For such students, we developed instruction that taught students to decompose the to-be-modelled situation into schema applications, where a schema represents a simple relationship such as distance-rate-time or part-whole. However, when a model consists of multiple schema applications, it needs some connection among them, usually representedby letting the same variable appear in the slots of two or more schemas. Students in our studies seemed to have more trouble identifying connections among schema applications than identifying the schema applications themselves. We developed several tutoring systems and evaluated them in university classes. One of them, a step-based tutoring system called OMRaaT (One Mathematical Relationship at a Time), was both reliably superior (p = 0.02, d = 0.67) to baseline and markedly superior (p < 0.001, d = 0.84) to an answer-based tutoring system using only commercially available software (MATLAB Grader). 

An algebraic model uses a set of algebraic equations to describe a situation. Constructing such models is a fundamental skill, but many students still lack the skill, even after taking several algebra courses in high school and college. For underachieving college students, we developed a tutoring system that taught students to decompose the to-be-modelled situation into schema applications, where a schema represents a simple relationship such as distance-rate-time or part-whole. However, when a model consists of multiple schema applications, it needs some connection among them, usually represented by letting the same variable appear in the slots of two or more schemas. Students in our studies seemed to have more trouble identifying connections among schemas than identifying the schema applications themselves. This paper describes a newly designed tutoring system that emphasizes such connections. An evaluation was conducted using a regression discontinuity design. It produced a marginally reliable positive effect of moderate size (d = 0.4). 

Our system classifies audio from microphones worn by the teacher in order to determine (1) whether the teacher is addressing the whole class or talking to individuals or groups of students. In the latter case, it determines (2) whether the teacher is giving formative feedback, giving corrective feedback, chatting socially, or addressing administrative or workflow concerns. This paper reports the initial accuracy of this system against human coding of middle school math classroom behavior. We also compared audio collected through professional hardware versus more accessible alternatives. 

FACT (Formative Assessment with Computational Technology) is an intelligent orchestration system. That is, because it helps the teacher manage the workflow of a complicated set of activities in the classroom, it is an orchestration system. Because it conducts tasks-specific and domain-specific analyses of the students’ mathematical products and their group interactions, it is more intelligent than other orchestration systems. From analyzing videos of our iterative development trials, we realized that too many students needed help simultaneously, but the teacher could only visit one group at a time. Thus, we modified FACT to send a few messages to the students directly instead of sending all its advice to the teacher. This paper reports a successful pilot test of auto-sending. 

Research in the field of collaboration shows that students do not spontaneously collaborate with each other. A system that can measure collaboration in real time could be useful by, for example, helping the teacher locate a group requiring guidance. To address this challenge, my research focuses on building and comparing collaboration detectors for different types of classroom problem solving activities, such as card sorting and hand writing. I am also studying transfer: how collaboration detectors for one task can be used with a new task. Finally, we attempt to build a teachers dashboard that can describe reasoning behind the triggered alerts thereby helping the teachers with insights to aid the collaborative activity. Data for building such detectors were collected in the form of verbal interaction and user action logs from students’ tablets. Three qualitative levels of interactivity was distinguished: Collaboration, Cooperation and Asymmetric Contribution. Machine learning was used to induce a classifier that can assign a code for every episode based on the set of features. Our preliminary results indicate that machine learned classifiers were reliable. 

Collaboration is a 21st Century skill as well as an effective method for learning, so detection of collaboration is important for both assessment and instruction. Speech-based collaboration detection can be quite accurate but collecting the speech of students in classrooms can raise privacy issues. An alternative is to send only whether or not the student is speaking. That is, the speech signal is processed at the microphone by a voice activity detector before being transmitted to the collaboration detector. Because the transmitted signal is binary (1 = speaking, 0 = silence), this method mitigates privacy issues. However, it may harm the accuracy of collaboration detection. To find out how much harm is done, this study compared the relative effectiveness of collaboration detectors based either on the binary signal or high-quality audio. Pairs of students were asked to work together on solving complex math problems. Three qualitative levels of interactivity was distinguished: Interaction, Cooperation and Other. Human coders used richer data (several audio and video streams) to choose the code for each episode. Machine learning was used to induce a detector to assign a code for every episode based on the features. The binary-based collaboration detectors delivered only slightly less accuracy than collaboration detectors based on the high quality audio signal.