Date of Award


Degree Name

Doctor of Education


Special Education and Literacy Studies

First Advisor

Dr. Shaila Rao

Second Advisor

Dr. Luchara Wallace

Third Advisor

Dr. Kate Kline


Elementary education, fractions, formative assessment, math disability


In an attempt to close the mathematic achievement gap between students from the United States and students from other countries, a new national set of standards, the Common Core State Standards for Mathematics, was developed and adopted by the state of Michigan in 2010. These standards emphasize mathematical reasoning and application, rather than the previous emphasis on performing calculations. Unfortunately, teachers generally have had little training in how to assess students’ mathematical reasoning, how to teach mathematical reasoning, or how to provide remediation to those students who show need. The purpose of this study was to see if use of the new online Math Reasoning Inventory (MRI) developed by Marilyn Burns assisted four volunteer fourth and fifth grade teachers from a local public school in assessing students’ conceptual knowledge of fractions and in targeting instruction about fractions. This study employed a mixed-design using both qualitative and quantitative measures. The four teachers were observed at the beginning of the unit on fractions in order to determine which reasoning strategies they modeled for their students to use in solving fraction problems. These teachers were observed a second time after they had been trained to administer the MRI near the beginning of the unit on fractions and again after the teachers had administered the MRI midway through the fraction unit in order to see if teachers’ strategy modeling increased. Teachers administered the MRI again at the end of the fraction unit and students’ pre- and posttest data were compared in order to assess whether or not there was an increase in students’ use of reasoning strategies. Finally, the teachers completed a survey in which they evaluated the usefulness of the inventory. Results showed few significant differences in student achievement or in teachers’ use of mental reasoning strategies in instruction as a result of using the Math Reasoning Inventory.

Access Setting

Dissertation-Open Access