Browsing by Author "Willoughby, Laura"
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Item Backward transfer, the relationship between new learning and prior ways of reasoning, and action versus process views of linear functions(Mathematical Thinking and Learning, 2022-02-16) Hohensee, Charles; Willoughby, Laura; Gartland, SaraBackward transfer is defined as the influence that new learning has on individuals’ prior ways of reasoning. In this article, we report on an exploratory study that examined the influences that quadratic functions instruction in real classrooms had on students’ prior ways of reasoning about linear functions. Two algebra classes and their teachers at two comprehensive high schools served as the participants. Both schools drew from low-socioeconomic urban populations. The study involved paper-and-pencil assessments about linear functions that were administered before and after a four- to five-week instructional unit on quadratic functions. The teachers were instructed to teach the quadratic functions unit using their regular approach. Qualitative analysis revealed three kinds of backward transfer influences and each influence was related to a shift in how the students reasoned about functions in terms of an action or process view of functions. Additionally, features of the instruction in each class provided plausible explanations for the similarities and differences in backward transfer effects across the two classrooms. These results offer insights into backward transfer, the relationship between prior knowledge and new learning, aspects of reasoning about linear functions, and instructional approaches to teaching functions.Item How do students with low interest in mathematics react to tasks?: an investigation of triggering interest(University of Delaware, 2023) Willoughby, LauraThe purpose of this study is to investigate the reactions students with low interest in mathematics have to multiple mathematics tasks. Interest has been shown to influence students’ engagement, motivation, and achievement (Renninger & Bachrach, 2015; Hidi & Harackiewicz, 2000; Kang & Keinonen, 2018). Therefore, understanding what triggers the interest of students with low interest in a particular subject has been, and remains to be, an important goal for educators so students’ experiences and achievement are improved. ☐ My study focused on triggered situational interest, which is the first of the four phases of Hidi and Renninger’s (2006) four-phase model of interest. One of the ways that may be used to initiate or trigger student interest in math is through the tasks students encounter in the classroom. To this end, I elicited students’ in-the-moment reactions to math tasks that included three task features: realistic context, the opportunity to justify an answer, and a visual representation of data. Their responses informed my answers to the following research questions: ☐ Research Question 1: Among high school students who reported having low situational interest in mathematics, to which aspects of mathematical tasks did these students react? In what ways did the students react to the aspects and what explanations did they provide for their reactions? Which, if any, of the aspects were intended features of the focus tasks? ☐ Research Question 2: What are the different cases that emerge when considering students who reported having low situational interest in mathematics that frequently and consistently reacted to a particular task aspect across most, or all, of the five different mathematical tasks? Within each case, how were the students’ explanations for their reactions to that particular task aspect similar and different across the mathematical tasks? How do their explanations for their reactions support the concluding stances for that particular task aspect? ☐ I used a Two Cycle coding process (Miles et al., 2018) to analyze the transcript data. Through this process, I developed codes to capture students’ reactions to each of the three task features as well as their reactions to two task aspects that emerged from the data: mathematical topic, and perceived difficulty. I used the frequency of the assigned codes to answer research question one. I then used the assigned codes along with analytic memos (Miles et al., 2018) to select three student cases to answer my second research question. ☐ Students generally reacted in ways that aligned with previous research for the task features, but their explanations were not always the same as those found in the research. For the emergent task aspects, students generally reacted positively to topics they had previous success with and reported having a general preference for ease. However, there were exceptions to these trends. ☐ This study highlights the benefit of eliciting the students’ voices to learn about their experiences. My results illustrate a range of ways that interest can be triggered by concurrent aspects of mathematics tasks among students who report having low interest in mathematics. My results suggest the importance of task selection and task launching in a classroom setting. I suggest future research that expands on the current study to include students with higher levels of interest in mathematics, or by using tasks that are included in current classroom curricula.