#### Date of Award

August 2020

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Teaching and Leadership

#### Advisor(s)

Joanna Masingila

#### Keywords

Creative mathematical reasoning, Imitative reasoning, Mathematical Reasoning, Mathematical task solving, Mathematics problem solving, Out-of-school mathematics

#### Subject Categories

Education

#### Abstract

The purpose of this study was to investigate the various aspects of middle school students’ mathematics task solving in a context that connects the students’ experiences in out-of-school and in within-school contexts. Specifically, the study explores the forms of mathematical reasoning that the students used while engaged in such contexts and also the influence of collaboration on the forms of mathematical reasoning used. Since the term mathematical reasoning is often used in mathematics education research and practice without clear definition, a considerable part of the literature review is dedicated towards identifying a reasonable conceptualization and framework for mathematical reasoning. In order to meet the goals identified above, the study analyzed a small section of existing data from a broader NSF-funded study known as Connecting In-school and Out-of-school Mathematics Practice whose main aim was to have mathematics learning and practice in and out of school integrated and be complementary. For the purposes of this study, the focus was on the work of four pairs of students. To develop the findings, the study analyzed both the students’ written work and audio transcripts from their small group and whole-class discussion sessions during task solving.

Findings indicate that when students are engaged in task solving in a context that connects their relevant out-of-school and within-school experiences, they use creative mathematical reasoning more often than imitative reasoning. Furthermore, working collaboratively in terms of setting common goals and exploring various strategies to meet such goals in a joint problem space has significant impacts on the forms of mathematical reasoning used. Specifically, collaboration tended to encourage production of more nuanced argumentation and hence conceptual mathematical understandings. Although relatively fewer, there were also instances where collaboration tended to lead to imitative reasoning. Implications on how these findings could be useful for mathematics teacher education programs, textbook authors, and mathematics teachers are discussed.

#### Access

Open Access

#### Recommended Citation

Geteregechi, Joash M., "Investigating Middle School Students’ Mathematical Reasoning in a Connected In-school and Out-of-School Context" (2020). *Dissertations - ALL*. 1213.

https://surface.syr.edu/etd/1213