John Lannin and Delinda van Garderen, University of Missouri, are conducting a three-year exploratory study that targets 1st and 2nd grade students who struggle in the area of number and operations. The research questions are as follows: (1) What cognitive obstacles exist for 1st and 2nd grade children who struggle with number and operations? (2) What similarities and differences exist in the cogntive obstacles for these groups of children? (3) What impact do the identified cognitive obstacles have on the learning trajectory for these groups of children? Utilizing design research methodology with a longitudinal component, classrooms are set up so that six pairs of students will work in joint activity on tasks that address both routine and transfer. Deliverables include publications in journals and the development of a design-driven model that will help struggling students at the primary grades deal with number and operations. The model includes a conceptual framework and a refined learning trajectory with implications for instruction. The emerging learning trajectory could potentially inform and guide educational researchers, curriculum designers, assessment developers, and teachers as they address the needs of children with learning difficulties in mathematics at the primary school level. Multiple case studies are developed; data from classroom observations during mathematics instruction and interviews with teachers are included in the analysis. Interviews with teachers about student work and their students' thinking are also used to learn more about the interventions used in the teaching experiments. Data analysis involves constructing case studies of struggling students in order to establish learning trajectories in the area of number and operations. The product will be a set of cases that will lend insight into how struggling students might be supported as they learn about number and operations at the primary grades, thus helping link assessment and instructional practice in a grounded way, and contributing to the knowledge base regarding interventions for a range of struggling young students in the area of number and operations.
