Integrating Computer Science Techniques into Differentiated Instruction of Mathematical Word Problem Solving
Luo Si and Yan Ping Xin, Purdue University
Mathematics is integral to all areas of daily life. However, assessments conducted at state, national, and international levels over the past 30 years indicate that U.S. students are “notably deficient” in their ability to solve mathematical problems [National Research Council, 2001]. Students with learning disabilities [LD] manifest even more severe problems [Cawley et al., 2001]. Contemporary research has identified effective conceptual model-based problem solving strategies for students to recognize word problem structures that underlie problems with various surface features and complexity levels and formulate model-based representation for solution.
Differentiated instruction plays a critical role in today’s inclusive classrooms to meet the diverse needs of individual students for allowing all students to access the same classroom curriculum by providing different entry points and learning tasks that are tailored to students’ needs.
The proposed research is to construct an exploratory but fully functioning differentiated instructional system of mathematical word problem solving with the following functionalities.
- First, the system maintains a pool of instructional materials generated by pre-defined templates or shared from students/teachers; features such as readability and the noise level of irrelevant information will be automatically extracted from instructional materials by proposed statistical natural language processing techniques.
- Second, the system provides computer-assisted instruction to train students’ abilities for analyzing and solving mathematical word problems.
- Third, it enables formative evaluation to monitor students’ progress.
- Fourth, the system provides the recommendation of differentiated instructional materials for a specific student by utilizing a student performance-driven recommendation algorithm.
The proposed work includes cutting-edge research for computer science techniques. A joint statistical learning algorithm will be designed for identifying levels of readability, word difficulty, and syntactic complexity of available instructional materials in a unified framework. A relational learning algorithm will be designed for identifying sentences with relevant information from sentences with irrelevant information in a mathematical word problem.