Conceptual Model-based Problem Solving: A Response to Intervention Program for Students with Learning Difficulties in Mathematics

This project will develop a cross-platform mathematics tutoring program that addresses the problem-solving skill difficulties of second- and third-grade students with learning disabilities in mathematics (LDM). COMPS-A is a computer-generated instructional program focusing on additive word problem solving; it will provide tutoring specifically tailored to each individual student's learning profile in real time. 

Full Description: 

The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools. Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.

The 3-year exploratory project, Conceptual Model-based Problem Solving: A Response to Intervention Program for Students with Learning Difficulties in Mathematics, will develop a cross-platform mathematics tutoring program that addresses the problem-solving skill difficulties of second- and third-grade students with learning disabilities in mathematics (LDM). While mathematics problem-solving skills are critical in all areas of daily life, many students with LDM do not acquire key math concepts such as additive and multiplicative reasoning in a proficient manner during the early school years. In fact, about 5-10% of school-age children are identified as having mathematical disabilities which might cause them to experience considerable difficulties in the upper grades and experience persistent academic, life, and work challenges. Despite the proliferation of web-based mathematical games for early learners, there are very few programs or tools that target growth in the conceptual understanding of fundamental mathematical ideas, which is essential in enabling young students with LDM to perform proficiently in mathematical and everyday contexts. COMPS-A is a computer-generated instructional program focusing on additive word problem solving; it will provide tutoring specifically tailored to each individual student's learning profile in real time. COMPS-A will also make the reasoning and underlying mathematical model more explicit to them, and the tool's flexibility will facilitate group or one-on-one instruction in regular classroom settings, in other sessions during or after the school day, and at home. COMPS-A addresses a significant practical issue in today's classrooms by providing individualized and effective RtI intervention programs for students with LDM.

COMPS-A program represents a mathematical model-based problem-solving approach that emphasizes understanding and representation of mathematical relations in algebraic equations and, thus, will support growth in generalized problem-solving skills.COMPS-A will achieve the following objectives: 1) Create the curriculum content, screen design, and a teacher's manual for all four modules in the area of additive word problem solving; 2) Design and develop the cross-platform computer application that can be ported as a web-based, iPad, Android, or Windows app, and this flexibility will make the program accessible to all students; and 3) Conduct small-scale single subject design and randomized controlled trial studies to evaluate the potential of COMPS-A to enhance students' word problem-solving performance. The following research questions will be resolved: (1) What is the functional relationship between the COMPS-A program and students' performance in additive mathematics problem solving? (2) What is the teacher's role in identifying students' misconceptions, alternative reasoning, and knowledge gaps when students are not responsive to the intervention program? (3) What are the necessary instructional scaffolds that will address students' knowledge gaps and therefore facilitate the connection between students' conceptual schemes and the mathematical models necessary for problem solving in order to promote meaningful understanding and construction of additive reasoning? A functional prototype of the COMPS-A will be developed followed by a single-subject design study with a small group of students with LDM to field-test the initial program. Finally, a pretest-posttest, comparison group design with random assignment of participants to groups will then be used to examine the effects of the two intervention conditions: COMPS-A and business as usual. An extensive dissemination plan will enable the project team to share results to a wider community that is responsible for educating all students and, especially, students with LDM.

 

National/Internationally Refereed Journal Articles

Xin, Y. P., Kim, S. J., Lei, Q., Wei, S., Liu, B., Wang, W., Kastberg, S., Chen, Y., Yang, X., Ma, X., Richardson, S. E. (2020). The impact of a conceptual model-based intervention program on math problem-solving performance of at-risk English learners. Reading and Writing Quarterly, 36(2), 104-123. https://www.tandfonline.com/doi/full/10.1080/10573569.2019.1702909

Xin, Y. P., Park, J., Tzur, R., & Si, L. (2020). The impact of a conceptual model-based mathematics computer tutor on multiplicative reasoning and problem-solving of students with learning disabilities. The Journal of Mathematical Behavior, 58. available online Feb 27, 2020. https://doi.org/10.1016/j.jmathb.2020.100762

Xin, Y. P. (2019). The effect of a conceptual model-based approach on “additive” word problem solving of elementary students who are struggling in mathematics.  ZDM: Mathematics Education, 51(1), 139-150. DOI: 10.1007/s11858-018-1002-9

Xin, Y. P.,Chiu, M. M., Tzur, R.  Ma, X., Park, J., Yang, X. (2019). Discourse-oriented instruction: How does a teacher’s talk affect math problem solving and reasoning of students with Learning disabilities. Learning Disability Quarterly, 43, 43-56 doi.org/10.1177/0731948719858707".

Xin, Y. P., Tzur, Si, L. Hord, C., Liu, J., Park, J. Y. (2017). An intelligent tutor-assisted math problem-solving intervention program for students with learning difficulties. Learning Disability Quarterly, 40(1), 4-16.

Xin, Y. P., Liu, J., Jones, S., Tzur, R., SI, L. (2016). A preliminary discourse analysis of constructivist-oriented math instruction for a student with learning disabilities. The Journal of Educational Research, 109(4), 436-447. DOI:10.1080/00220671.2014.979910

Xin, Y. P. & Hord, C. (2013). Conceptual model-based teaching to facilitate geometry learning of students who struggle in mathematics. Journal of Scholastic Inquiry: Education, 1(1), 147-160.

Hord, C. & Xin, Y. P. (2013). Intervention research for helping elementary school students with math learning difficulties understand and solve word problems: 1996-2010.  Learning Disabilities: A Multidisciplinary Journal, 19(1), 3-17.

Zhang, D, Xin, Y. P., & Si, L. (2013). Transition from intuitive to advanced strategies in multiplicative reasoning for students with math difficulties. The Journal of Special Education, 47(1), 50-64.

Xin, Y. P., Si, L., Hord, C., Zhang, D., Cetintas, S., & Park. J. Y. (2012). The effects of computer-assisted instruction in teaching Conceptual Model-Based problem solving. Learning Disabilities: A Multidisciplinary Journal, 18(2), 71-85. 

Xin, Y. P., Zhang, D., Park, J. Y., Tom, K., Whipple, A., & Si, L. (2011). A comparison of two mathematics problem-solving strategies: Facilitate algebra-readiness. The Journal of Educational Research, 104, 381-395.

Cetintas, S, Si,  L., Xin, Y. P., Zhang, D., Park, J. Y. & Tzur, R. (2010). A joint probabilistic classification model of relevant and irrelevant sentences in mathematical word problems. Journal of Educational Data Mining, 2(1), 83-101. 

Cetintas, S., Si, L., Xin, Y. P., and Hord, C. (2010). Automatic detection of off-task behaviors in intelligent tutoring systems with machine learning techniques. IEEE Transactions on Learning Technologies, 3(3), 228-236.

Xin, Y. P. & Zhang, D. (2009). Exploring a conceptual model-based approach to teaching situated word problems.  The Journal of Educational Research, 102(6), 427-441.

Xin, Y. P. (2008). The effect of schema-based instruction in solving word problems: An emphasis on pre-algebraic conceptualization of multiplicative relations. Journal for Research in Mathematics Education, 39, 526-551.

Xin, Y. P., Wiles, B., & Lin, Y. (2008). Teaching conceptual model-based word-problem story grammar to enhance mathematics problem solving. The Journal of Special Education, 42, 163-178.

Peer-Reviewed Proceedings

Kim, S., Kastberg, S. Xin, Y. P. Chen Y. & Wei, S. (2018).  Development of the composite unit in additive problem solving of student with mathematics difficulty in a computer based-learning environment. In Hodges, T.E., Roy, G. J., & Tyminski, A. M. (Eds.). (2018). Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (p.1280). Greenville, SC: University of South Carolina & Clemson University.

Lei, Q., Xin, Y., P., Morita-Mullaney, T., & Tzur, R. (2018). Analyzing a discourse of scaffolds for mathematics instruction for an ELL with learning disabilities. In Hodges, T.E., Roy, G. J., & Tyminski, A. M. (Eds.). (2018). Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 460-467). Greenville, SC: University of South Carolina & Clemson University.

Wei, S., Xin,Y.P., & Chen,Y. (2020). Visualizing Students' Eye Movement to Understand Their Problem-Solving Process". Accepted by the Proceedings of the 22nd International Conference on Human Computer Interaction, Copenhagen, Denmark.

Wei, S., Lei, Q., Chen, Y., Xin, Y. P., Kastberg, S., & Kim, S. (2018). Evaluating the effects of highlighting text animations on the attention distribution of students with math learning difficulties.  Proceedings of the 2018 American Society for Engineering Education (ASEE) Conference.

Wei, S., Chen, Y., Xin, Y. P., Kastberg, S. (2018). An exploratory approach to analyzing students’ eye movements when solving math problems. In Hodges, T.E., Roy, G. J., & Tyminski, A. M. (Eds.). (2018). Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1259-1262). Greenville, SC: University of South Carolina & Clemson University.

Xin, Y. P., Kim; S., Kastberg, S., Chen, Y., Liu, B., Lei, Q., Wang, W., Richardson, S. E., Wei, S. (2018). The effect of a computer-assisted model-based problem-solving program for students with learning difficulties in mathematics. In Hodges, T.E., Roy, G. J., & Tyminski, A. M. (Eds.). (2018). Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp.1267-1270). Greenville, SC: University of South Carolina & Clemson University.

Xin, Y. P., Kastberg, Si., & V. Chen. (2017). Conceptual Model-based Problem Solving: A response to intervention program for students with LDM. In E. Galindo & J. Newton (Eds.) Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators, pp. 326.

Xin, Y. P., Yang, X., Tzur, R. Park J., Ma. X (2016). PGBM-COMPS math problem-solving program: promote independent problem solving of students with LD.  Proceedings of 13th International Congress on Mathematical Education (ICME), Hamburg Germany.

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