System for co-clustering of student assessment data
View Patent ↗A system and method for making use of formative assessment data collected is disclosed that identifies clusters of students and concurrently determines the characteristics of the student clusters. A decomposition of the data is performed with spectral theories of graphs and fuzzy logic algorithms to identify the clusters of students, clusters of assessment data and relationships between them. An actionable output is presented to teachers for the evaluation of educational progress.
1. A system for educational assessment of student groups, comprising:
a processor; and
a non-transitory computer readable memory storing instructions that are executable by the processor to include:
a clustering engine that includes a student identification module that identifies student clusters and associated metadata having characteristics of each of the student clusters, and an assessment identification module that concurrently identifies assessment data clusters among assessment data for students belonging to the student clusters;
a transformation engine that compiles the assessment data from formative assessments provided to the plurality of students and creates bipartite graphs of student data for each student and assessment evaluations from the assessment data;
an adjacency mapping engine that maps adjacency relationships between the students and the assessment data by creating at least one adjacency matrix from the bipartite graphs;
a decomposition engine that performs spectral decomposition on the adjacency matrix and establishes weighted distances for each relationship, wherein the decomposition engine is configured to estimate distances between homogenous groups of data and dissimilar groups of data among the student data and the assessment data, wherein homogenous groups include student data and student clusters, and assessment data and assessment clusters, and dissimilar groups include a combination of the homogenous groups; and
a display module that compiles the metadata related to the student clusters and the assessment data clusters, and provides relationships between the student clusters and the assessment data clusters with the metadata in a visible medium.
2. The system of claim 1 , wherein the student clusters are assigned to hard clustering and the assessment data is assigned to soft clustering.
3. The system of claim 1 , wherein the characteristics corresponding to the student clusters include problem subject matter areas for each student cluster.
4. The system of claim 2 , wherein the adjacency mapping engine transforms the bipartite graph into adjacency matrices that identifies the relationships of students to questions, concepts, and error modes related to the assessment data of the formative assessments.
5. A method for co-clustering student data and assessment data from formative assessments on a processor having a non-transitory computer readable memory storing executable instructions for the method, comprising:
transforming student data from formative assessments into one or more bipartite graphs;
mapping adjacency relationships between the students and the assessment data by creating one or more adjacency matrices from the one or more bipartite graphs;
simultaneously clustering the student data into student clusters and the assessment data from the formative assessments into assessment data clusters while extracting metadata pertaining to each student cluster and having characteristics of students belonging to each student cluster;
decomposing each adjacency matrix with a spectral decomposition algorithm and establishing weighted distances for the relationships, wherein one or more of the weighted distances are adjustable by a user and are between homogenous groups of data and dissimilar groups of data among the student data and the assessment data, wherein homogenous groups include student data and student clusters, and assessment data and assessment clusters, and dissimilar groups include a combination of the homogenous groups; and
compiling the metadata related to the student clusters and the assessment data clusters, and providing relationships between the student clusters and the assessment data clusters with the metadata in a visible medium.