The Role of Sequence in the Experience of Mathematical Beauty

Dietiker, Leslie

doi:10.5642/jhummath.201601.10

Cited by 5 publications

(4 citation statements)

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“…Furthermore, this sixth-grade classroom is not the only place where student captivation to unfolding mathematical content can occur. The mathematical stories that have accompanied other such responses have been documented and analyzed using the mathematical story framework in a variety of other contexts such as lower elementary and high school (Dietiker, 2016;Dietiker et al, 2016). However, these analyses constitute merely a start; further studies are needed to discover and document the variety of mathematical sequences that occur in aesthetically rich lessons.…”

Section: Discussionmentioning

confidence: 99%

“…The key elements of literary stories (i.e., characters, action, and setting) can be mapped to their corresponding aspects within an enacted mathematics lesson (Dietiker, 2015(Dietiker, , 2016. The mathematical characters of a mathematical story are the mathematical objects, (e.g.…”

Section: The Mathematical Story Frameworkmentioning

confidence: 99%

“…Just as in literary stories, something must happen; in mathematical stories, the mathematical characters are acted upon (what we refer to as mathematical action) with procedures, such as addition and subtraction. The mathematical characters and the actions on them take place within representations (what we call mathematical settings), such as a number line or the real-world context of a posed problem (Dietiker, 2015(Dietiker, , 2016).…”

Section: The Mathematical Story Frameworkmentioning

confidence: 99%

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The plot thickens: The aesthetic dimensions of a captivating mathematics lesson

Richman

Dietiker

Riling

2019

The Journal of Mathematical Behavior

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Section: Discussionmentioning

confidence: 99%

Section: The Mathematical Story Frameworkmentioning

confidence: 99%

Section: The Mathematical Story Frameworkmentioning

confidence: 99%

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The plot thickens: The aesthetic dimensions of a captivating mathematics lesson

Richman

Dietiker

Riling

2019

The Journal of Mathematical Behavior

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“…Although characteristics of lesson experiences that relate to situated interest are relatively unknown, some evidence has shown that incongruity, surprise, and novelty are particularly influential (Matarazzo, Durik, & Delaney, 2010).Situated interest is only one dimension of the potential emotional effects a particular experience can offer. The way in which a mathematical lesson moves an individual also involves reactions to beauty, exciting action, and suspense--aspects of an experience that we refer to as aesthetic dimensions (Dewey, 1934;Dietiker, 2016;Sinclair, 2001). Researchers are beginning to explore how to design and enact what Sinclair (2001) calls "aesthetically-rich" mathematical experiences, which are those that "enable children to wonder, to notice, to imagine alternatives, to appreciate contingencies and to experience pleasure and pride" (p. 26).…”

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confidence: 99%

How Do Students Experience Mathematics? Designing and Testing a Lesson-Specific Tool to Measure Student Perceptions

Riling¹

2019

Proceedings of the 2019 AERA Annual Meeting

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How can secondary mathematics teachers enact learning experiences that are mathematically captivating (i.e., lessons that draw students in, spur student curiosity, and motivate students to engage and anticipate how the lesson will end)? Unfortunately, evidence suggests that captivating experiences for high school mathematics students are not common. For example, the 2015 National Assessment of Educational Progress (NAEP) survey shows that a majority of 8th graders (55%) describe mathematics learning as typically not engaging or interesting and that this problem is increasingly worsening over time (National Center for Education Statistics, 2015).Fortunately, there are efforts to shift the student experience in secondary mathematical lessons so that students are motivated to ask and answer mathematical questions (e.g., 3-Act Plays). Connecting the designs of lessons that are mathematically captivating with student perceptions of these lessons (i.e., learning why and how they captivate students) could support the development of curriculum and instructional strategies that shift long-term student attitudes. However, existing tools that measure mathematics students' perceptions focus on general dispositions, but not lesson-specific attitudes; even when a mathematical lesson spurs positive student emotions, we do not yet have a tool designed to measure it.This paper describes our efforts to design and test a survey that can enable us to reliably measure students' perceptions (i.e., interesting, boring) of a mathematics lesson. As part of a larger study, this survey was developed to enable researchers to connect how students describe their experiences (i.e., "exciting") with the designs of mathematical lessons. This tool will enable researchers to identify and study lessons that secondary students indicate are mathematically captivating learning experiences (what we will refer to as MCLEs). Theoretical FrameworkTypically, when students report "I like math," they are describing an enduring, long-term interest in mathematics (Hidi & Renninger, 2006). In contrast, we are interested in learning about students' momentary attraction toward the content (e.g., during a lesson), which is more reflective of situated interest (Hidi & Renninger, 2006). Although characteristics of lesson experiences that relate to situated interest are relatively unknown, some evidence has shown that incongruity, surprise, and novelty are particularly influential (Matarazzo, Durik, & Delaney, 2010).Situated interest is only one dimension of the potential emotional effects a particular experience can offer. The way in which a mathematical lesson moves an individual also involves reactions to beauty, exciting action, and suspense--aspects of an experience that we refer to as aesthetic dimensions (Dewey, 1934;Dietiker, 2016;Sinclair, 2001). Researchers are beginning to explore how to design and enact what Sinclair (2001) calls "aesthetically-rich" mathematical experiences, which are those that "enable children to wonder, to notice, to imagine alternati...

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Narrative characteristics of captivating secondary mathematics lessons

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Why do some mathematics lessons captivate high school students and others not? This study explores this question by comparing how the content unfolds in the lessons that students rated highest with respect to their aesthetic affordances (e.g., using terms like “intriguing,” “surprising”) with those the same students rated lowest with respect to their aesthetic affordances (e.g., “just ok,” “dull”). Using a framework that interprets the unfolding content across a lesson as a mathematical story, we examine how some lessons can provoke curiosity or enable surprise. We identify eight characteristics that distinguish captivating lessons and show how some, such as the average number of questions under consideration at any point in the lesson, are strongly related to student aesthetic experiences. In addition, the lessons that students described as more interesting included more instances of misdirection, such as when students’ false assumptions provide opportunities for surprising results. These findings point to the characteristics of future lesson designs that could enable more students to experience curiosity and wonder in secondary mathematics classrooms.

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The Role of Sequence in the Experience of Mathematical Beauty

Cited by 5 publications

References 14 publications

The plot thickens: The aesthetic dimensions of a captivating mathematics lesson

The plot thickens: The aesthetic dimensions of a captivating mathematics lesson

How Do Students Experience Mathematics? Designing and Testing a Lesson-Specific Tool to Measure Student Perceptions

Narrative characteristics of captivating secondary mathematics lessons

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