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)

Beth L. MacDonald


Beth L. MacDonald


Marla Robertson


Patricia S. Moyer-Packenham


Kady Schneiter


Jessica F. Shumway


Adaptive reasoning is one of five components students use to develop mathematical expertise and become mathematically proficient. When students adapt their reasoning they are logically thinking about the mathematical relationships between concepts and adapting their thinking to solve problems. Three Act Math Tasks are popular math problems used in schools in which students engage in adaptive reasoning. These types of problems are beneficial to students because they engage students in inquiry-based learning, a kind of learning where students work to pose questions, interpret data, design ways to solve the problem and present their solutions. Little is known about how students adapt their reasoning as they partake in these types of tasks. The objective of this study is to better understand what adaptive reasoning strategies seventh graders used and how they used these strategies when engaged in inquiry-based mathematical tasks.

To accomplish this, the study observed 18 seventh grade students as they worked through three mathematical tasks. The researcher observed student discussions and their drawings to see what adaptive reasoning strategies were being used by students and how the strategies were used throughout different stages of the tasks. In this way a more complete picture of how students adapted their reasoning was obtained. The researcher analyzed student use of six different adaptive reasoning indicators, including: 1) relationships and connections, 2) justifications, 3) alternates pursued, 4) prior knowledge, 5) legitimacy determined, and 6) pattern recognition.

Results indicate that students used all six adaptive reasoning strategies. Students primarily adapted their reasoning by finding relationships and connections and making justifications. Additionally, each student demonstrated a unique pattern of adaptive reasoning strategies which was mediated by their partner. Use of the other four indicators, alternates pursued, prior knowledge, legitimacy determined and pattern recognition were used in conjunction with the two primary indicators. Additionally, different patterns of use were identified within the separate modalities of student drawings and discussions.

This study is beneficial because it helps teachers and researchers better understand what adaptive reasoning strategies students are utilizing and the relationship between these strategies in a classroom setting. This affords teachers and researchers opportunities to develop better learning experiences and understand how students reason in light of mathematical proficiency.



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