The evaluation of an instructional model for developing the reasoning capabilities of students with mathematical learning difficulties in the context of fraction comparisons

This study presents an instructional model that integrates research-based practices from the fields of mathematics education and special education to support the development of students' reasoning and examines how the reasoning of the participants, 30 students with mathematical learning difficulties (ages 10 to 12 years), evolves over time. Nineteen of the students were from urban public schools and 11 were from a private school for students with learning differences in the Southwest USA; eight of the students had a special education diagnosis, and the other 22 students had no diagnosis. The model, which emphasises shared student thinking in a small-group setting and instructional decisions in response to that thinking, was implemented in the context of fraction comparisons. Descriptive and inferential analyses of correctness and completeness of student reasoning on a pre- and post-test measure as well as formative measures incorporated throughout instruction indicated significant findings with respect to growth in student reasoning. The study has implications for future research when considering how to support the development of mathematical reasoning within the population of students who struggle in mathematics.