Date of Award:


Document Type:


Degree Name:

Doctor of Philosophy (PhD)


School of Teacher Education and Leadership

Department name when degree awarded

Mathematics Education and Leadership

Committee Chair(s)

Patricia S. Moyer-Packenham


Patricia S. Moyer-Packenham


Beth MacDonald


Jessica F. Shumway


Kerry Jordan


Colby Tofel-Grehl


High cognitive demand (HCD) tasks can help students develop a deeper understanding of mathematics. Teachers need interventions that encourage students to engage in HCD activities. Small-group discourse provides HCD opportunities for students while solving mathematics problems. Discourse can take place after students solve problems individually (reflective) or in groups as students solve problems (exploratory). This study looks at the relationship between these two types of small-group discourse and student-enacted cognitive demand.

This study looks at how students engage with tasks that were designed at four different cognitive demand levels using Webb’s depth of knowledge (DOK) framework. Ninety-seven grade 5 students from four different classrooms were grouped in small groups of two or three students to solve two sets of mathematics problems on operations with fractions and decimals. Each class engaged in Reflective Discourse after solving one set and engage in Exploratory Discourse while solving the other set. To help understand any order effects, half the classes used Reflective Discourse with Set 1 while the other half used Exploratory Discourse with Set 1. Then, they switched for Set 2, so that whoever used Reflective Discourse with Set 1 used Exploratory Discourse with Set 2 and vice versa.

The researcher analyzed whether there were patterns in levels of cognitive demand and quality of the discussion when students engaged in each type of discourse for math problems at four different levels. First, the researcher looked at any numerical differences between the intended cognitive demand of the problems and how students engaged with the problems using frequency tables, heat maps, and statistical analyses. Next, the researcher looked at differences in student actions and the way they talked about the math problems.

Findings showed that both Reflective and Exploratory Discourse can be used by teachers to promote high student-enacted levels of cognitive demand. Results also showed that a supportive environment, such as the environment created by Reflective Discourse, can help support typically struggling students. Finally, this research reinforced the importance of dissonance in prompting students to engage with the tasks at higher levels of cognitive demand.



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